date_created
timestamp[ns] | abstract
string | title
string | categories
string | arxiv_id
string | year
int32 | embedding
list | data_map
list | category_name
string | supercategory_name
string | primary_field
string | secondary_field
string | tertiary_field
string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
2007-04-02T19:18:42
|
A fully differential calculation in perturbative quantum chromodynamics is
presented for the production of massive photon pairs at hadron colliders. All
next-to-leading order perturbative contributions from quark-antiquark,
gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as
all-orders resummation of initial-state gluon radiation valid at
next-to-next-to-leading logarithmic accuracy. The region of phase space is
specified in which the calculation is most reliable. Good agreement is
demonstrated with data from the Fermilab Tevatron, and predictions are made for
more detailed tests with CDF and DO data. Predictions are shown for
distributions of diphoton pairs produced at the energy of the Large Hadron
Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs
boson are contrasted with those produced from QCD processes at the LHC, showing
that enhanced sensitivity to the signal can be obtained with judicious
selection of events.
|
Calculation of prompt diphoton production cross sections at Tevatron and
LHC energies
|
hep-ph
|
0704.0001
| 2,007
|
[
-0.01377881783992052,
-0.003169021802023053,
0.01137604471296072,
-0.05111551284790039,
-0.0023174069356173277,
0.03664056956768036,
0.0282911229878664,
0.04017116129398346,
-0.04735743626952171,
-0.022754916921257973,
-0.04226990416646004,
0.03984418883919716,
0.0076903593726456165,
-0.006648519542068243,
0.008698747493326664,
0.012191514484584332,
0.05076798424124718,
0.02453082799911499,
-0.04904179275035858,
-0.011243856512010098,
-0.04398415610194206,
-0.030839836224913597,
-0.053262095898389816,
-0.047857195138931274,
0.0634845644235611,
-0.024878699332475662,
0.005668438971042633,
0.019262688234448433,
-0.07967349141836166,
0.021629314869642258,
0.05298300087451935,
-0.060485243797302246,
0.03794313967227936,
-0.02370580844581127,
-0.0328725203871727,
-0.03802146017551422,
0.06937763094902039,
-0.017020924016833305,
0.005859333090484142,
0.001664299052208662,
0.06206259876489639,
-0.029318539425730705,
-0.0065029519610106945,
-0.051458269357681274,
-0.00411874009296298,
0.031673457473516464,
0.00279025686904788,
0.001988082192838192,
0.008853215724229813,
0.011557947844266891,
-0.024136319756507874,
0.033181484788656235,
0.01839115098118782,
-0.014151442795991898,
0.015426786616444588,
0.049827806651592255,
-0.006073249038308859,
-0.03576771542429924,
0.046771127730607986,
0.004098605830222368,
0.02043852210044861,
0.03622620180249214,
-0.016901355236768723,
-0.014290071092545986,
0.0125524140894413,
-0.05253894627094269,
-0.010579661466181278,
-0.03135889768600464,
0.019525369629263878,
-0.03139832615852356,
0.010440376587212086,
-0.006161130964756012,
0.035153910517692566,
0.055149201303720474,
0.007497614715248346,
0.01623564399778843,
0.012400238774716854,
0.0009790565818548203,
-0.007351744920015335,
0.005198062863200903,
-0.042440302670001984,
-0.013325583189725876,
0.04893898591399193,
0.000435293884947896,
0.07041779160499573,
0.00484731700271368,
-0.017345184460282326,
0.04543275758624077,
-0.03943309560418129,
0.09118178486824036,
0.05311436578631401,
0.007751823868602514,
0.08643683046102524,
0.053011927753686905,
-0.056458257138729095,
0.038186024874448776,
-0.032253462821245193,
0.04250436648726463,
-0.009267779067158699,
-0.07277897000312805,
0.008038577623665333,
0.07576081156730652,
-0.0011297643650323153,
-0.0001357317523797974,
0.04713098332285881,
0.033195607364177704,
0.03614075109362602,
-0.018363559618592262,
0.006146655883640051,
-0.013373990543186665,
-0.09325097501277924,
0.0002835089107975364,
-0.014323334209620953,
-0.01738208904862404,
-0.01894286833703518,
-0.08271677792072296,
0.05926736816763878,
-0.11154879629611969,
-0.03197012096643448,
0.09237594157457352,
-0.0002798889181576669,
-0.028962045907974243,
-0.04557240754365921,
0.026290414854884148,
0.03287355229258537,
0.036487363278865814,
-0.09696982800960541,
0.02988927625119686,
0.05484921112656593,
0.028245767578482628,
0.033234983682632446,
0.0025717909447848797,
-0.030863776803016663,
0.056478165090084076,
0.05038909614086151,
-0.015214328654110432,
0.047033220529556274,
-0.012254751287400723,
0.03926590457558632,
-0.02640371583402157,
0.04470014199614525,
0.03378523886203766,
0.010161279700696468,
-0.02230256050825119,
0.02210412733256817,
-0.054201073944568634,
0.00039455649675801396,
-0.02903180755674839,
-0.020455513149499893,
0.013597196899354458,
0.05981631949543953,
0.019548378884792328,
0.052313461899757385,
0.007059196010231972,
-0.029579106718301773,
-0.023916535079479218,
-0.01487466599792242,
-0.03511512652039528,
0.024107029661536217,
0.04542440176010132,
-0.03194744884967804,
0.02449754998087883,
-0.07576069980859756,
0.03146757185459137,
0.0063977777026593685,
-0.03879914432764053,
0.042656220495700836,
-0.015390021726489067,
0.003872812492772937,
0.0616387203335762,
-0.02766575664281845,
-0.012782060541212559,
0.009050574153661728,
-0.014396429061889648,
0.017735661938786507,
0.013512305915355682,
0.010267182253301144,
-0.04581127315759659,
-0.023103024810552597,
0.04019076004624367,
0.0959581807255745,
-0.02234405279159546,
0.015347426757216454,
0.07658838480710983,
-0.001031580613926053,
0.00009919534932123497,
-0.02781960740685463,
-0.015327119268476963,
-0.006655754521489143,
0.018611440435051918,
-0.029805487021803856,
0.0540662445127964,
-0.02830149605870247,
-0.053118668496608734,
0.0007991804741322994,
-0.047578953206539154,
0.042736101895570755,
-0.052632950246334076,
0.017693113535642624,
-0.0008334253798238933,
-0.07236102968454361,
-0.0034216975327581167,
-0.03510772064328194,
0.016569575294852257,
-0.01975255087018013,
0.06130635738372803,
0.028362825512886047,
0.0024298056960105896,
0.004243112169206142,
-0.014540465548634529,
0.06215392053127289,
0.007252251263707876,
-0.03903712332248688,
0.010746028274297714,
-0.034836508333683014,
-0.013039568439126015,
-0.014208215288817883,
-0.04241374507546425,
-0.05536186695098877,
0.08123303949832916,
-0.004022623877972364,
0.005255234427750111,
0.014119247905910015,
-0.006315931677818298,
0.0335831455886364,
0.03618984296917915,
-0.025419140234589577,
-0.02227739244699478,
-0.050569694489240646,
-0.009682622738182545,
0.0034595392644405365,
0.003685598960146308,
-0.013758005574345589,
-0.01577768847346306,
-0.001804254949092865,
0.011230124160647392,
-0.022008884698152542,
0.026677504181861877,
0.05517439916729927,
0.08059032261371613,
0.01928211934864521,
-0.015440351329743862,
0.018816586583852768,
-0.0331977903842926,
-0.06984832882881165,
-0.018590986728668213,
0.03405529633164406,
0.009009228087961674,
-0.06015072017908096,
0.013553014025092125,
0.020386159420013428,
0.0002453558554407209,
0.032936859875917435,
0.015907105058431625,
0.004400821402668953,
-0.024737581610679626,
-0.042080771178007126,
0.034341853111982346,
-0.08185718208551407,
-0.06059033051133156,
0.04722975566983223,
-0.04322829842567444,
0.006334514357149601,
-0.049352239817380905,
-0.04714411124587059,
0.03672163188457489,
0.02236505225300789,
-0.005976953078061342,
-0.0029851198196411133,
0.009888747707009315,
-0.002471738029271364,
0.020526917651295662,
0.06166256591677666,
-0.0016526037361472845,
-0.0012289698934182525,
-0.009986569173634052,
0.013479248620569706,
-0.05930071324110031,
0.0038856181781738997,
-0.07073738425970078,
-0.05503108724951744,
-0.06044890731573105,
-0.027195487171411514,
-0.017147453501820564,
0.02696359157562256,
0.004809659905731678,
0.021465029567480087,
-0.03759964182972908,
0.002909627975896001,
0.0025493386201560497,
-0.040760766714811325,
-0.017526064068078995,
0.01075245812535286,
0.06324885785579681,
0.008761037141084671,
0.045267242938280106,
0.07330285012722015,
0.019256306812167168,
-0.012209814041852951,
0.0015144344652071595,
-0.007569129578769207,
-0.02255956642329693,
-0.004210461862385273,
-0.015502821654081345,
0.034187108278274536,
0.013544825837016106,
-0.018612712621688843,
0.02453378029167652,
0.021614883095026016,
-0.005884579848498106,
-0.016132604330778122,
0.021399838849902153,
-0.024892648681998253,
-0.02214881218969822,
0.03465021029114723,
0.014040138572454453,
0.0700969249010086,
-0.026637181639671326,
0.05069452151656151,
0.015686478465795517,
0.043335411697626114,
0.0031525157392024994,
0.007205870933830738,
-0.0478658564388752,
0.024996642023324966,
0.010476119816303253,
0.0024451755452901125,
0.042555417865514755,
-0.024818923324346542,
-0.022013859823346138,
0.026938268914818764,
0.08317191153764725,
0.0059358952566981316,
0.01894102618098259,
-0.016303343698382378,
-0.000656461575999856,
-0.022819355130195618,
0.016296345740556717,
-0.003082634648308158,
0.012795465067029,
0.04704297333955765,
-0.03702285513281822,
-0.028743330389261246,
0.00302428612485528,
0.030327312648296356,
-0.0038123850245028734,
-0.0264127217233181,
-0.010813785716891289,
0.04152298346161842,
0.005147860385477543,
-0.035343561321496964,
0.023671409115195274,
0.010858298279345036,
0.01751730777323246,
-0.03367926925420761,
0.02938407100737095,
0.054352786391973495,
-0.004665473476052284,
0.06356630474328995,
-0.0000017169396642202628,
0.05932624265551567,
-0.03381584212183952,
0.017514152452349663,
0.004169848281890154,
0.03523363173007965,
0.013694880530238152,
-0.005362981464713812,
0.01179244089871645,
-0.00018631487910170108,
-0.07395204156637192,
-0.0040166196413338184,
0.005221164785325527,
0.02378661185503006,
0.019328005611896515,
0.03185916319489479,
-0.0035627351608127356,
-0.03791351243853569,
-0.031563956290483475,
-0.0305765513330698,
-0.03251442685723305,
0.0812174528837204,
0.045054249465465546,
0.02675585448741913,
-0.023493899032473564,
0.010305111296474934,
-0.0028730081394314766,
-0.0680403858423233,
0.015839215368032455,
-0.007450945675373077,
-0.011313168331980705,
0.016418280079960823,
-0.0695684552192688,
-0.06623894721269608,
0.0369839072227478,
-0.00917266495525837,
-0.04567187279462814,
0.04472164809703827,
0.012288345955312252,
0.0049731372855603695,
-0.02376161329448223,
-0.08252862840890884,
-0.08168430626392365,
0.038924332708120346,
-0.06363677233457565,
-0.0007214425131678581,
0.0004020943306386471,
-0.040127575397491455,
-0.016466818749904633,
0.029898349195718765,
0.03016095981001854,
0.045788269490003586,
0.006333572324365377,
-0.015043186023831367,
-0.07816563546657562,
0.037690192461013794,
-0.018483418971300125,
0.00828487053513527,
-0.004801034461706877,
0.013826793991029263,
-0.021332811564207077,
0.01353843230754137,
0.04062800481915474,
0.024489153176546097,
-0.01603795401751995,
0.005035599693655968,
-0.004389179404824972,
-0.004487285390496254,
0.023099757730960846,
0.004162190016359091,
-0.028775349259376526,
0.08073020726442337,
-0.015999972820281982,
-0.001884358236566186,
0.04432902857661247,
-0.04410048574209213,
0.04349495843052864,
0.005427308846265078,
0.015944745391607285,
0.008113528601825237,
0.016883602365851402,
0.06922714412212372,
-0.039923373609781265,
0.016293840482831,
-0.009229790419340134,
0.08301567286252975,
0.10464449226856232,
0.02732553519308567,
-0.043659768998622894,
-0.01981133036315441,
-0.010833005420863628,
0.034246426075696945,
-0.004506570287048817,
-0.02037927322089672,
0.03995918482542038,
0.08047308772802353,
0.022680217400193214,
0.058296382427215576,
0.030651157721877098,
-0.005476255901157856,
0.022592693567276,
-0.03541715443134308,
0.0460202619433403,
-0.015346546657383442,
0.02952789142727852,
-0.012812849134206772,
0.010476944968104362,
-0.0336960144340992,
0.008694435469806194,
-0.03425274044275284,
0.06675820052623749,
-0.03458251431584358,
-0.016365665942430496,
0.03509070724248886,
-0.0023240314330905676,
-0.027451276779174805,
-0.03565245121717453,
0.002067506080493331,
-0.02864723838865757,
0.01644013822078705,
0.05799669027328491,
0.014225917868316174,
0.017608867958188057,
-0.0013005526270717382,
-0.038569070398807526,
-0.009271437302231789,
0.04813440144062042,
-0.027002917602658272,
-0.022124964743852615,
-0.0062557668425142765,
0.01677222177386284,
-0.04445723071694374,
0.061776384711265564,
0.0017668941291049123,
0.02408386580646038,
0.009292980656027794,
-0.01146326307207346,
-0.007482036482542753,
-0.001918345340527594,
0.007159760221838951,
0.014457064680755138,
-0.01614665612578392,
-0.049094878137111664,
0.03297610208392143,
-0.016393210738897324,
-0.005448617041110992,
0.05633418634533882,
0.0036183439660817385,
-0.04594516381621361,
-0.009221616201102734,
0.000909871538169682,
-0.02918643318116665,
0.09909632802009583,
0.08695964515209198,
0.06631466001272202,
0.008005699142813683,
-0.04659177362918854,
0.07056263089179993,
0.04458272084593773,
-0.0590338371694088,
-0.031035469844937325,
0.05290975794196129,
0.0028633736073970795,
0.013376722112298012,
0.009120539762079716,
-0.0700327530503273,
-0.012037567794322968,
-0.032865650951862335,
-0.01921011507511139,
0.03994207829236984,
-0.043503567576408386,
0.0020210547372698784,
0.03543608635663986,
0.004401189740747213,
-0.0031974026933312416,
-0.007529933471232653,
-0.08590361475944519,
0.01040749903768301,
-0.006127296015620232,
-0.013234401121735573,
-0.0019920242484658957,
-0.01644056662917137,
0.020192915573716164,
0.014634461142122746,
0.04823489487171173,
0.016145862638950348,
-0.07368483394384384,
-0.08635564893484116,
0.014350463636219501,
-0.024471823126077652,
-0.04371240362524986,
0.012592282146215439,
0.01770804263651371,
0.0686548501253128,
-0.05493630841374397,
0.022948337718844414,
-0.05735889449715614,
0.03497789427638054,
-0.02040843293070793,
-0.031086338683962822,
-0.022035013884305954,
0.0017463836120441556,
0.02933265082538128,
0.01143717486411333,
0.006946465000510216,
0.015041256323456764,
-0.07773531228303909,
-0.05387819558382034,
-0.008455559611320496,
-0.005406639538705349,
-0.02989320456981659,
0.044645484536886215,
-0.0532863587141037,
-0.07591445744037628,
-0.0014160253340378404,
-0.00836994405835867,
-0.04585748538374901,
0.05597150698304176,
-0.005493902135640383,
-0.06355097889900208,
-0.014147969894111156,
-0.011187446303665638,
-0.009808343835175037,
0.016737133264541626,
-0.0272248312830925,
-0.0371885672211647,
-0.0021296865306794643,
-0.024733051657676697,
-0.012974685989320278,
0.04869942367076874,
0.025101013481616974,
-0.017523176968097687,
-0.006358235143125057,
-0.01272345520555973,
-0.017933210358023643,
-0.009624693542718887,
-0.01394846010953188,
0.051774900406599045,
-0.02267686277627945,
-0.01705983281135559,
-0.003242294769734144,
-0.03154705837368965,
0.020165767520666122,
0.03457383066415787,
-0.045505769550800323,
0.054662466049194336,
-0.02140667475759983,
-0.011586865410208702,
0.056730952113866806,
-0.03394203633069992,
0.028295164927840233,
0.05123108997941017,
-0.03742343559861183,
-0.050377339124679565,
-0.03800330311059952,
0.00220377161167562,
-0.017910774797201157,
0.053529296070337296,
-0.03941090777516365,
0.015669487416744232,
-0.03134975954890251,
-0.029712604358792305,
-0.06141446903347969,
-0.022971387952566147,
-0.08813004195690155,
-0.010420783422887325,
0.09436634182929993,
-0.011030653491616249,
0.003710080636665225,
0.02008545584976673,
0.07239555567502975,
0.012776845134794712,
0.009888793341815472,
0.002740484429523349,
-0.056503284722566605,
-0.0145088080316782,
0.007883436046540737,
-0.043476611375808716,
0.013412101194262505,
-0.04247848317027092,
0.04800796136260033,
0.07217419147491455,
-0.01825616881251335,
0.030500056222081184,
0.010284466668963432,
-0.01097751036286354,
0.06201239302754402,
0.009172143414616585,
0.027406416833400726,
0.009908648207783699,
0.0006439940771088004,
0.05298665910959244,
0.03505394980311394,
0.022247975692152977,
0.023111840710043907,
0.04549122229218483,
0.029513191431760788,
0.011377568356692791,
0.005758326034992933,
-0.046820055693387985,
-0.009599882178008556,
0.03163246065378189,
-0.03654864802956581,
-0.007601296994835138,
0.0031414118129760027,
0.036337971687316895,
-0.061904311180114746,
-0.004887520335614681,
-0.0673385038971901,
-0.03393260017037392,
0.006418945733457804,
-0.009481888264417648,
-0.001905684475786984,
-0.10046017169952393,
0.01294201985001564,
-0.06050395593047142,
-0.01050532516092062,
-0.01738506555557251,
0.011678783223032951,
-0.019504310563206673,
-0.03851904720067978,
-0.01773262582719326,
-0.0008337186300195754,
-0.01845659874379635,
-0.009153548628091812,
-0.01329042948782444,
-0.02776179648935795,
-0.05156509950757027,
-0.06213287264108658,
-0.03375886380672455,
-0.045428089797496796,
-0.011878162622451782,
-0.004187298472970724,
-0.0158840399235487,
-0.08329249173402786,
0.058816179633140564,
0.04585916921496391,
-0.030312329530715942,
-0.0011448843870311975,
-0.002501267474144697,
0.055994704365730286,
0.006824745796620846,
0.0053367312066257,
-0.01699001155793667,
0.025043435394763947,
-0.038541749119758606,
-0.014870897866785526,
0.025080744177103043,
0.02650746889412403,
0.06205998733639717,
0.022658271715044975,
0.01615135744214058,
0.0030180145986378193,
0.017455486580729485,
0.0203411728143692,
0.019901394844055176,
-0.008558593690395355,
-0.050089333206415176,
-0.020310359075665474,
0.04623691737651825,
-0.004744734149426222,
0.008936422877013683,
-0.009668182581663132,
-0.04499872773885727,
0.013285798951983452,
-0.005243193823844194,
-0.0582064650952816,
-0.01883244328200817,
-0.0023288081865757704,
0.021699324250221252,
0.039345163851976395,
-0.00117496179882437,
-0.031655944883823395,
-0.038717083632946014,
0.028996529057621956,
-0.0037672915495932102,
-0.01484270766377449,
-0.011287309229373932,
-0.01883690245449543,
-0.03816166892647743,
0.010726116597652435,
-0.014148112386465073,
-0.0873241275548935,
-0.005227694287896156,
0.005156638100743294,
0.001192449009977281,
-0.05168752744793892,
-0.05004371330142021,
0.010508687235414982,
0.06483953446149826,
-0.007566940970718861,
-0.00305490312166512,
-0.058683715760707855,
0.02203335613012314,
-0.006949523463845253,
0.008207079954445362,
-0.018478581681847572,
-0.0023178686387836933,
0.04230972006917,
0.029949821531772614,
-0.01803077943623066,
0.0420055016875267,
0.022377140820026398,
0.042864345014095306,
0.028801674023270607,
0.0014273214619606733,
-0.03223470225930214,
-0.07290276885032654,
-0.0019182234536856413
] |
[
16.365341186523438,
-1.1267576217651367
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
na
|
na
|
2007-03-31T02:26:18
|
We describe a new algorithm, the $(k,\ell)$-pebble game with colors, and use
it obtain a characterization of the family of $(k,\ell)$-sparse graphs and
algorithmic solutions to a family of problems concerning tree decompositions of
graphs. Special instances of sparse graphs appear in rigidity theory and have
received increased attention in recent years. In particular, our colored
pebbles generalize and strengthen the previous results of Lee and Streinu and
give a new proof of the Tutte-Nash-Williams characterization of arboricity. We
also present a new decomposition that certifies sparsity based on the
$(k,\ell)$-pebble game with colors. Our work also exposes connections between
pebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and
Westermann and Hendrickson.
|
Sparsity-certifying Graph Decompositions
|
math.CO cs.CG
|
0704.0002
| 2,007
|
[
0.04328163340687752,
0.0778479278087616,
-0.007996815256774426,
-0.04748755320906639,
0.011343740858137608,
-0.012478334829211235,
0.030784882605075836,
-0.0027937362901866436,
0.023982414975762367,
0.04528163745999336,
-0.06803924590349197,
0.02122390642762184,
0.014535598456859589,
0.01858586259186268,
-0.04915421083569527,
-0.003799101337790489,
0.05754535645246506,
-0.011418785899877548,
-0.013341860845685005,
0.005397321190685034,
0.003105905605480075,
0.0036929387133568525,
0.016573837026953697,
-0.030401628464460373,
0.09148195385932922,
0.028443848714232445,
-0.008922937326133251,
-0.021672910079360008,
-0.0224542785435915,
0.03188903257250786,
0.06198343262076378,
0.0009684065007604659,
-0.005258971359580755,
-0.0440354123711586,
0.0062935845926404,
-0.04227302595973015,
0.04316895082592964,
-0.0637347549200058,
0.007416888605803251,
0.05859072506427765,
-0.014435572549700737,
0.012576461769640446,
0.051054034382104874,
-0.02723330818116665,
-0.038372598588466644,
-0.04141530022025108,
0.033769652247428894,
0.05272179841995239,
0.028725314885377884,
-0.029618045315146446,
-0.01265738345682621,
0.027096020057797432,
0.013397490605711937,
-0.09677080065011978,
-0.07066911458969116,
0.057163119316101074,
-0.003903819713741541,
-0.04155603051185608,
0.05508500710129738,
-0.003979638684540987,
-0.01265625562518835,
0.02044565975666046,
-0.048606351017951965,
0.015968063846230507,
0.03497578576207161,
-0.0793694332242012,
-0.04954822361469269,
0.01579734869301319,
0.036967307329177856,
-0.02206081710755825,
0.0031791699584573507,
-0.03906024619936943,
0.05095592141151428,
0.019182385876774788,
-0.04218543693423271,
-0.013418957591056824,
-0.027459822595119476,
-0.0030490874778479338,
0.0009290214511565864,
0.032134201377630234,
0.01877501793205738,
-0.0005172098171897233,
0.029426060616970062,
0.023647086694836617,
0.02229522541165352,
-0.022260552272200584,
0.043170832097530365,
-0.029043344780802727,
-0.0587984137237072,
0.03900541737675667,
0.00745770800858736,
-0.05504497513175011,
0.08087845146656036,
0.06131881847977638,
-0.06623246520757675,
0.006122717633843422,
0.00036840676330029964,
0.022883214056491852,
-0.012163571082055569,
0.007996227592229843,
-0.007605664432048798,
0.004555176943540573,
0.013785173185169697,
-0.014194310642778873,
0.09010319411754608,
0.019336558878421783,
-0.016987985000014305,
-0.000883095373865217,
-0.03783716633915901,
0.030266940593719482,
-0.021978776901960373,
-0.020621884614229202,
0.009060121141374111,
-0.045355603098869324,
-0.006758370902389288,
0.022037651389837265,
0.04581255838274956,
-0.10985028743743896,
0.001128000789321959,
0.07800877094268799,
0.02649054117500782,
-0.009293125942349434,
-0.012647573836147785,
0.012645931914448738,
-0.008805029094219208,
0.05850594863295555,
-0.005715757608413696,
-0.023631757125258446,
-0.027218900620937347,
-0.010770131833851337,
-0.005654422100633383,
0.016288571059703827,
-0.005184832960367203,
-0.0035557341761887074,
0.026909654960036278,
-0.00158646609634161,
-0.06606052070856094,
0.022996358573436737,
0.07377384603023529,
-0.00867371540516615,
-0.01678840070962906,
0.005235190503299236,
-0.06638529151678085,
0.019135862588882446,
0.022883668541908264,
-0.0144611531868577,
0.03091677464544773,
-0.03294331952929497,
0.0014189973007887602,
-0.025341084226965904,
0.037887945771217346,
-0.02249303087592125,
-0.007959781214594841,
-0.005897834897041321,
-0.02920425310730934,
-0.025857582688331604,
0.030662434175610542,
0.06403432041406631,
0.006766085978597403,
0.035969000309705734,
0.024740466848015785,
0.02430613338947296,
-0.02046368271112442,
0.08973725140094757,
-0.012142910622060299,
0.029436271637678146,
0.04607033357024193,
0.012179342098534107,
-0.01589152216911316,
0.052385132759809494,
-0.06545785069465637,
-0.023769324645400047,
-0.011245179921388626,
-0.010125226341187954,
0.008749905042350292,
0.027662087231874466,
0.0056157298386096954,
-0.05636186525225639,
0.021364474669098854,
0.02128738909959793,
0.017978059127926826,
0.03614101558923721,
0.020768381655216217,
0.08732720464468002,
-0.016568563878536224,
0.012367796152830124,
-0.004048318602144718,
-0.038658518344163895,
0.014462902210652828,
-0.0167560912668705,
-0.0004168093728367239,
0.02136254869401455,
-0.05560995638370514,
-0.02101926878094673,
0.014179627411067486,
-0.05964770168066025,
0.08853055536746979,
-0.03815380483865738,
-0.00693459203466773,
-0.08512458950281143,
-0.0006708737346343696,
-0.014027881436049938,
-0.07344086468219757,
-0.0004680048150476068,
-0.03417506068944931,
0.0592581182718277,
-0.03462982177734375,
0.019482823088765144,
0.053421471267938614,
0.024110304191708565,
0.04757241904735565,
0.015150049701333046,
0.053380683064460754,
0.030594447627663612,
0.00058221590006724,
-0.029700366780161858,
-0.020904283970594406,
-0.0277150496840477,
-0.010661494918167591,
0.01633383147418499,
0.044524215161800385,
-0.04376672953367233,
0.004736985079944134,
0.02867855876684189,
0.06229738891124725,
0.013472802005708218,
-0.0029578579124063253,
0.010312488302588463,
-0.04423654079437256,
-0.007677377667278051,
-0.06489687412977219,
-0.05734251067042351,
0.030129022896289825,
-0.03338296711444855,
-0.0075464979745447636,
0.01159160677343607,
0.0026063192635774612,
0.040629997849464417,
0.03505649045109749,
0.0025665739085525274,
0.025565391406416893,
0.010678074322640896,
0.026356449350714684,
0.012448504567146301,
0.0014010441955178976,
0.010410322807729244,
-0.032318487763404846,
-0.02477658912539482,
-0.040361762046813965,
0.05581260472536087,
0.04517044126987457,
0.014842415228486061,
0.019625017419457436,
0.05431287735700607,
0.04935970902442932,
-0.06721893697977066,
-0.00489407405257225,
0.002240169094875455,
0.01523023284971714,
-0.037635304033756256,
0.07335691154003143,
-0.0644586905837059,
-0.03232423961162567,
0.0044333441182971,
-0.04517359659075737,
-0.01863935776054859,
0.06323660165071487,
-0.07177041471004486,
-0.035939861088991165,
-0.031701456755399704,
-0.011679807677865028,
-0.011146881617605686,
0.0649498924612999,
-0.004184621851891279,
-0.02321391925215721,
0.006479460746049881,
0.0673428475856781,
-0.027151819318532944,
-0.03287917748093605,
0.01066422089934349,
-0.009923947975039482,
-0.010171561501920223,
-0.09272585809230804,
-0.0012767509324476123,
-0.04155553877353668,
0.013162892311811447,
0.05391920357942581,
0.02619726024568081,
0.0011323547223582864,
0.04157918691635132,
-0.0020861756056547165,
-0.010024266317486763,
0.024545792490243912,
0.06648002564907074,
0.0059131477028131485,
0.04885176941752434,
-0.0004950555739924312,
-0.04069645330309868,
0.04347262531518936,
-0.0031954313162714243,
-0.06936898082494736,
0.018979458138346672,
0.005479048937559128,
0.011504583992064,
0.052508797496557236,
0.02189900167286396,
-0.018668441101908684,
-0.05359005928039551,
0.031757354736328125,
0.005305280908942223,
0.003973382990807295,
0.07150126993656158,
-0.008797052316367626,
0.05314355716109276,
-0.05170300975441933,
0.04264679551124573,
0.01662156730890274,
-0.0014192586531862617,
0.03770219162106514,
-0.04110821709036827,
-0.008666965179145336,
-0.03758466988801956,
0.05397513136267662,
-0.07989542186260223,
-0.021684082224965096,
0.018959607928991318,
0.006530835293233395,
0.037097834050655365,
-0.014645610935986042,
-0.012942885980010033,
0.00520833907648921,
0.08597942441701889,
-0.007390661630779505,
-0.007727505639195442,
-0.03735795244574547,
-0.026491062715649605,
-0.010696401819586754,
-0.034839190542697906,
-0.0034808400087058544,
-0.04173162952065468,
-0.0040761325508356094,
-0.023941215127706528,
-0.05275464430451393,
-0.017209675163030624,
-0.04107462614774704,
0.029992472380399704,
-0.043293848633766174,
0.004637069068849087,
0.03329675272107124,
-0.04147719219326973,
-0.030438292771577835,
-0.04749272018671036,
0.01219121739268303,
-0.07332314550876617,
-0.028293613344430923,
0.023943722248077393,
-0.028690233826637268,
-0.05325420945882797,
0.02337050996720791,
0.009016619063913822,
0.1137673556804657,
0.0001289377105422318,
-0.012438719160854816,
0.010387623682618141,
0.023843949660658836,
-0.02007397450506687,
0.040431246161460876,
0.035035140812397,
-0.0037043807096779346,
-0.008222073316574097,
-0.014017140492796898,
-0.04712046682834625,
0.028402963653206825,
0.08855295926332474,
0.0110448794439435,
0.010636365972459316,
-0.05295826122164726,
0.026210376992821693,
0.031159967184066772,
-0.03766721487045288,
0.03238789737224579,
0.021196145564317703,
0.0813482403755188,
0.0009866711916401982,
0.03125377744436264,
0.03809092938899994,
-0.056808020919561386,
-0.013749780133366585,
-0.0008861872483976185,
-0.0046040951274335384,
0.0036955419927835464,
-0.009628858417272568,
-0.021462785080075264,
0.01917153038084507,
0.015252194367349148,
-0.019501488655805588,
0.0037225098349153996,
0.0070027681067585945,
-0.03484095633029938,
0.010840347968041897,
-0.05226393789052963,
-0.027543313801288605,
0.017130129039287567,
-0.032049451023340225,
-0.01717107743024826,
0.029724417254328728,
-0.04290388152003288,
-0.016064273193478584,
0.05656149238348007,
-0.013970359228551388,
-0.026583153754472733,
0.016167372465133667,
-0.01898174174129963,
-0.0614105761051178,
-0.003456016769632697,
0.007942911237478256,
0.04711431264877319,
0.0391705222427845,
-0.016000043600797653,
-0.03204413503408432,
-0.0035842189099639654,
0.023733653128147125,
-0.09089541435241699,
-0.019765004515647888,
0.02022719942033291,
0.01928550936281681,
-0.008635848760604858,
0.044174786657094955,
-0.008191879838705063,
-0.07734056562185287,
0.05445181950926781,
0.013563117012381554,
-0.02131219580769539,
0.01352848019450903,
0.005585595965385437,
-0.008286281488835812,
0.0006391933420673013,
0.02385508269071579,
0.03156888857483864,
0.01316306833177805,
0.016615701839327812,
-0.03672738000750542,
0.058615490794181824,
-0.005422261543571949,
0.0236673504114151,
0.03165974095463753,
0.05353955924510956,
-0.024281205609440804,
-0.03914034366607666,
0.02983880788087845,
0.0688602551817894,
0.007978789508342743,
-0.007749292533844709,
0.04413783922791481,
0.09100711345672607,
-0.02180069498717785,
-0.013875381089746952,
-0.03436478599905968,
0.006438469979912043,
0.049842264503240585,
0.03436741605401039,
0.012923607602715492,
0.019732723012566566,
-0.01121868658810854,
-0.023703183978796005,
0.02327497862279415,
-0.03996650129556656,
0.004690306726843119,
0.04397131875157356,
0.030618848279118538,
0.010543285869061947,
0.003871246473863721,
0.05316606163978577,
-0.0037437023129314184,
-0.03229513764381409,
-0.0066449521109461784,
0.03681524842977524,
-0.04756178706884384,
0.039220161736011505,
-0.003694669110700488,
0.03034600242972374,
-0.03460274264216423,
-0.071649931371212,
-0.026920173317193985,
-0.04563817381858826,
0.07753768563270569,
0.015431405045092106,
-0.013450692407786846,
-0.004211836028844118,
0.017319204285740852,
0.012997773475944996,
0.02068278379738331,
0.0024719545617699623,
0.07363520562648773,
-0.06577592343091965,
-0.06905200332403183,
0.007927831262350082,
0.046528078615665436,
0.057347800582647324,
-0.008139997720718384,
-0.02342619001865387,
0.016762398183345795,
0.05822191759943962,
-0.02121102809906006,
0.014566679485142231,
0.03231332078576088,
0.010018276050686836,
-0.07085947692394257,
-0.0018173150019720197,
0.014726085588335991,
-0.010789715684950352,
0.029602428898215294,
0.07689716666936874,
0.07177747786045074,
-0.005501022562384605,
-0.06275973469018936,
0.0035929272416979074,
-0.010102330707013607,
-0.06188995763659477,
0.01863916590809822,
0.035341814160346985,
-0.012411190196871758,
-0.034669503569602966,
-0.04067553952336311,
-0.03938687965273857,
0.03228705748915672,
-0.02848016656935215,
-0.05479803681373596,
0.013964924961328506,
-0.010693153366446495,
0.007506630849093199,
-0.022840401157736778,
-0.05305936932563782,
0.007444605231285095,
0.003175363875925541,
-0.039196114987134933,
-0.0286543145775795,
-0.01265550684183836,
0.01738833449780941,
0.023444650694727898,
-0.010130454786121845,
0.026702964678406715,
0.038626331835985184,
-0.0236921776086092,
-0.01842711865901947,
-0.03878043219447136,
-0.04140402749180794,
-0.00897127017378807,
-0.02508031390607357,
-0.07356414943933487,
0.03978993371129036,
-0.010118489153683186,
0.06996649503707886,
-0.07836002111434937,
-0.029332609847187996,
-0.057119715958833694,
-0.00289203436113894,
-0.07093515247106552,
-0.009731183759868145,
0.006045680493116379,
-0.025411289185285568,
0.018483249470591545,
0.046385254710912704,
-0.01122412458062172,
0.025678323581814766,
-0.08559650927782059,
0.0038355798460543156,
-0.0032143814023584127,
0.009473154321312904,
0.02656257525086403,
-0.016829460859298706,
-0.026081085205078125,
0.04349425062537193,
0.08615349233150482,
-0.026157544925808907,
-0.02162386104464531,
0.04278179258108139,
-0.0393017902970314,
-0.019207587465643883,
0.006720051169395447,
0.016370370984077454,
-0.019683873280882835,
-0.03477142006158829,
0.035006068646907806,
-0.008585788309574127,
0.02062278427183628,
-0.021549347788095474,
-0.04198275879025459,
0.013510409742593765,
-0.03030041977763176,
0.02291063778102398,
-0.020487377420067787,
-0.06552852690219879,
-0.005716283340007067,
-0.028706850484013557,
0.03808731213212013,
-0.0016914530424401164,
0.014346812851727009,
-0.00468944339081645,
0.017891019582748413,
0.022161774337291718,
0.04091988131403923,
0.08046813309192657,
-0.0444067120552063,
-0.015362036414444447,
0.10309118777513504,
0.009496122598648071,
0.022248992696404457,
0.023348215967416763,
-0.023119065910577774,
-0.03043915331363678,
0.027869759127497673,
-0.03101739101111889,
-0.011903361417353153,
0.04578038305044174,
-0.0578550286591053,
0.051904913038015366,
-0.02399384044110775,
0.013757283799350262,
-0.10020953416824341,
-0.021482577547430992,
-0.03587578237056732,
-0.01812519133090973,
-0.03195889666676521,
0.014525271020829678,
0.0073383585549890995,
-0.012970974668860435,
-0.03171805292367935,
0.004294080194085836,
0.016248423606157303,
0.005954160820692778,
-0.014711890369653702,
-0.006154332309961319,
0.020784154534339905,
-0.005127421114593744,
-0.0033190175890922546,
-0.06579165160655975,
0.04252728447318077,
0.0105450339615345,
0.05314300209283829,
0.031492218375205994,
-0.0019249026663601398,
-0.000973843561951071,
0.022065408527851105,
0.026055674999952316,
0.02749023027718067,
0.03802172467112541,
0.053436487913131714,
0.01373255904763937,
0.016428444534540176,
0.02716730535030365,
0.08956634998321533,
-0.020993782207369804,
-0.015087714418768883,
-0.009154227562248707,
0.013272841461002827,
0.041946183890104294,
0.010211162269115448,
0.010194285772740841,
0.03583020344376564,
-0.024108344689011574,
-0.002865829039365053,
-0.04543691501021385,
-0.026919960975646973,
-0.025605827569961548,
-0.04027862474322319,
-0.03058101423084736,
-0.03929009661078453,
-0.06059836596250534,
0.02261504903435707,
-0.03673534095287323,
-0.037388984113931656,
-0.0188575629144907,
-0.011426426470279694,
-0.033187348395586014,
0.042229149490594864,
-0.018972674384713173,
0.03249974921345711,
-0.00009578237950336188,
-0.02603857032954693,
0.03140998259186745,
0.03205188736319542,
0.006640252657234669,
0.013713790103793144,
-0.016401929780840874,
-0.005985766649246216,
0.0027649870608001947,
-0.01774669997394085,
-0.05825258791446686,
-0.03189387172460556,
0.011193592101335526,
0.007929518818855286,
-0.00265310425311327,
-0.04689881205558777,
0.029156813398003578,
-0.0648951604962349,
-0.05723605304956436,
-0.04202784225344658,
0.009937773458659649,
0.04520310088992119,
-0.06387747824192047,
-0.02313224785029888,
-0.04193371161818504,
0.031230024993419647,
-0.000940638710744679,
-0.017759086564183235,
0.004619453568011522,
0.02028406597673893,
-0.025273656472563744,
-0.008904882706701756,
0.016442587599158287,
-0.019814062863588333,
-0.0007902593351900578,
0.029167871922254562,
0.05336036905646324,
-0.049123190343379974,
-0.00022441377223003656,
-0.0671137198805809,
-0.01166860293596983,
-0.027206487953662872,
0.06500870734453201,
-0.031636811792850494,
-0.04699508100748062,
-0.010642782784998417,
0.002820128807798028,
-0.031532470136880875,
0.02494892291724682,
-0.035935211926698685,
0.047950588166713715,
0.055940285325050354,
0.0037469223607331514,
0.019280526787042618,
-0.0014385682297870517,
0.011476784944534302,
-0.023561015725135803,
-0.039648182690143585,
-0.033824801445007324,
-0.02144048735499382,
-0.03304139897227287,
-0.024541959166526794,
-0.02892991714179516,
-0.010358483530580997,
0.015451737679541111,
-0.018014272674918175,
0.02624940313398838,
-0.0725536197423935,
-0.04544481262564659,
0.02871769107878208,
0.018423162400722504,
0.013720187358558178,
-0.033289022743701935,
-0.04369719326496124,
0.013509280979633331,
-0.021285448223352432,
0.012421955354511738,
0.07835227996110916,
0.015032271854579449,
0.0003529006498865783,
0.06450148671865463,
-0.026821602135896683,
-0.028254209086298943,
-0.004607110284268856,
0.019767094403505325,
0.06332501024007797,
-0.014268241822719574,
0.054664693772792816,
0.010719968937337399,
-0.004125681240111589
] |
[
0.7198727130889893,
5.005166530609131
] |
Combinatorics
|
Mathematics
|
math-CO
|
cs-CG
|
na
|
2007-04-01T20:46:54
|
The evolution of Earth-Moon system is described by the dark matter field
fluid model proposed in the Meeting of Division of Particle and Field 2004,
American Physical Society. The current behavior of the Earth-Moon system agrees
with this model very well and the general pattern of the evolution of the
Moon-Earth system described by this model agrees with geological and fossil
evidence. The closest distance of the Moon to Earth was about 259000 km at 4.5
billion years ago, which is far beyond the Roche's limit. The result suggests
that the tidal friction may not be the primary cause for the evolution of the
Earth-Moon system. The average dark matter field fluid constant derived from
Earth-Moon system data is 4.39 x 10^(-22) s^(-1)m^(-1). This model predicts
that the Mars's rotation is also slowing with the angular acceleration rate
about -4.38 x 10^(-22) rad s^(-2).
|
The evolution of the Earth-Moon system based on the dark matter field
fluid model
|
physics.gen-ph
|
0704.0003
| 2,007
|
[
0.013710171915590763,
0.017289698123931885,
0.004148436710238457,
-0.052535586059093475,
0.024260839447379112,
0.07899025082588196,
-0.0056014349684119225,
0.0008843824034556746,
-0.03323475271463394,
-0.017630206421017647,
-0.008760499767959118,
0.03719475865364075,
0.026961617171764374,
0.001393318292684853,
0.027646956965327263,
-0.02719372697174549,
0.01439095288515091,
-0.05841102451086044,
0.010739551857113838,
0.006787040736526251,
0.0027012433856725693,
-0.01256340742111206,
0.0013952674344182014,
-0.04754212871193886,
0.09697631746530533,
-0.0023462616372853518,
0.032283928245306015,
0.006745447870343924,
-0.03981921076774597,
0.021520350128412247,
0.08560795336961746,
-0.07335107773542404,
0.029004588723182678,
-0.023812362924218178,
-0.015795107930898666,
-0.014642787165939808,
0.027022112160921097,
0.006681812461465597,
-0.017077777534723282,
0.03429020941257477,
0.0514104999601841,
-0.01473191287368536,
0.000797748623881489,
0.019043253734707832,
0.03535449877381325,
-0.0115250488743186,
-0.01195786613970995,
-0.03422221541404724,
0.0029368773102760315,
-0.02212989516556263,
-0.00881245732307434,
0.0337279848754406,
-0.0199432410299778,
-0.012422177009284496,
-0.04328793287277222,
0.024200769141316414,
0.0402149073779583,
-0.022320637479424477,
0.026722515001893044,
-0.011305599473416805,
0.026308907195925713,
-0.03150275722146034,
-0.03901597484946251,
-0.027787894010543823,
0.032732728868722916,
-0.06566626578569412,
-0.023897919803857803,
0.04572192579507828,
0.012141797691583633,
-0.027520865201950073,
0.023637881502509117,
-0.0029164431616663933,
-0.016434377059340477,
0.04409118369221687,
-0.04724983870983124,
-0.006236806977540255,
0.018708908930420876,
-0.017876828089356422,
0.028173470869660378,
-0.040475666522979736,
0.003417079569771886,
0.0524141825735569,
0.04737449809908867,
0.019670678302645683,
0.0911397710442543,
-0.022069547325372696,
-0.010354319587349892,
0.02963479980826378,
-0.025765620172023773,
0.07341960072517395,
0.035353727638721466,
-0.023758798837661743,
-0.006996329873800278,
0.017303138971328735,
-0.042841844260692596,
0.028103401884436607,
-0.010194111615419388,
0.05106532573699951,
0.006811713334172964,
-0.01555491890758276,
-0.025106143206357956,
0.01005594152957201,
0.0456276573240757,
0.04718276485800743,
0.09286697953939438,
0.07534748315811157,
0.0003256081254221499,
-0.00002319597297173459,
0.04241662845015526,
-0.01788301207125187,
-0.07636447995901108,
-0.024997396394610405,
-0.01801113225519657,
-0.011225922964513302,
0.009605997242033482,
-0.06652121990919113,
0.050065699964761734,
-0.04536952078342438,
-0.008447321131825447,
0.06627975404262543,
0.012424306944012642,
-0.0016877030720934272,
0.0017524425638839602,
-0.02016480267047882,
-0.046378593891859055,
-0.03799932450056076,
0.001062762807123363,
-0.015470033511519432,
0.000020548532120301388,
0.014151150360703468,
-0.03267304599285126,
0.007946431636810303,
-0.012390493415296078,
-0.02227303385734558,
0.04423610493540764,
0.04565371945500374,
-0.050432853400707245,
-0.03896437957882881,
0.008108860813081264,
-0.024336108937859535,
0.018180323764681816,
-0.05010451003909111,
0.011106561869382858,
-0.00518448930233717,
-0.054042644798755646,
-0.029653726145625114,
0.03619595617055893,
-0.06834142655134201,
-0.004488836042582989,
0.03366394340991974,
0.045830145478248596,
0.05325060710310936,
0.018930677324533463,
0.02672530896961689,
-0.024340879172086716,
-0.01965448446571827,
-0.027880879119038582,
0.01814473420381546,
-0.008937187492847443,
-0.04620898514986038,
0.029122328385710716,
0.032546836882829666,
-0.04025712236762047,
0.03149286285042763,
-0.066375732421875,
-0.01892228238284588,
0.018008612096309662,
0.006555098108947277,
0.011909793131053448,
0.03029461018741131,
-0.06666145473718643,
-0.006627073977142572,
0.0410580113530159,
0.03667784854769707,
-0.0017825820250436664,
0.009138515219092369,
0.08621051162481308,
-0.05342680960893631,
-0.04590970277786255,
-0.0007781359599903226,
0.07868555188179016,
-0.06600433588027954,
-0.01595476269721985,
0.05556619539856911,
0.019365333020687103,
0.003988682758063078,
0.028344616293907166,
-0.03349747508764267,
-0.03030441142618656,
-0.0397675447165966,
0.0008105534943751991,
0.010584652423858643,
-0.01646191067993641,
-0.05548814684152603,
0.038375839591026306,
-0.05316387116909027,
0.06576573848724365,
0.007828102447092533,
-0.011981877498328686,
-0.0010633617639541626,
-0.007916312664747238,
0.029906470328569412,
-0.013024366460740566,
-0.02100968547165394,
0.002991188783198595,
0.014889604412019253,
-0.037392448633909225,
0.023106221109628677,
0.08314576745033264,
0.013209660537540913,
0.06285668909549713,
0.03263149410486221,
-0.018824215978384018,
0.010737944394350052,
-0.04247799143195152,
0.022332509979605675,
-0.037327058613300323,
0.014395100995898247,
-0.021887829527258873,
0.01480596698820591,
-0.004098358564078808,
-0.0009477522689849138,
0.0059766569174826145,
0.04944639652967453,
0.02753753587603569,
0.02067490667104721,
-0.003673484781756997,
0.04184192419052124,
0.009772967547178268,
-0.01004600990563631,
-0.013488228432834148,
-0.04025159031152725,
0.012963577173650265,
0.0053546493873000145,
0.030659982934594154,
0.04262957721948624,
-0.04301883652806282,
-0.02010488137602806,
0.01181208435446024,
0.07054372131824493,
-0.007080262526869774,
0.006553845014423132,
0.029475193470716476,
-0.04022158682346344,
0.004418991506099701,
-0.06282515078783035,
0.02102137915790081,
0.02832183428108692,
-0.03432312607765198,
0.03568439558148384,
0.016727397218346596,
-0.003933013416826725,
0.01481015607714653,
0.04119290038943291,
0.025911405682563782,
-0.06449674814939499,
-0.062237709760665894,
0.09909283369779587,
-0.028236817568540573,
-0.0180612001568079,
0.04133843630552292,
-0.03318339213728905,
0.01080744806677103,
-0.030828727409243584,
-0.03983699157834053,
0.0005398442735895514,
0.008615335449576378,
-0.037884410470724106,
0.015939613804221153,
0.00039241707418113947,
0.057510655373334885,
0.006091885734349489,
0.06347952038049698,
0.06490669399499893,
-0.02490265667438507,
0.042736370116472244,
0.011219947598874569,
-0.02200476825237274,
-0.031022464856505394,
-0.04828133434057236,
-0.0453089140355587,
-0.061446662992239,
-0.0030898633413016796,
-0.010666592977941036,
0.019821370020508766,
-0.006452205125242472,
-0.022006474435329437,
-0.010071259923279285,
-0.02394167333841324,
0.01444909255951643,
-0.06297451257705688,
-0.010909445583820343,
0.01966271921992302,
0.06275429576635361,
0.005023781675845385,
0.07935158908367157,
0.08990103006362915,
-0.028614535927772522,
-0.02473585307598114,
0.02914842776954174,
0.02790045738220215,
-0.053286902606487274,
-0.02032843418419361,
0.014544617384672165,
-0.008159477263689041,
-0.0035718432627618313,
0.004272386431694031,
0.0016153553733602166,
0.023976977914571762,
-0.03813474252820015,
0.006427824962884188,
0.011464988812804222,
-0.027874600142240524,
0.006049968767911196,
-0.07725868374109268,
0.02597765438258648,
0.05764612555503845,
0.03842811658978462,
0.06883218139410019,
0.039314232766628265,
0.04342203214764595,
-0.046773869544267654,
-0.005847539287060499,
-0.10543635487556458,
-0.0075754220597445965,
0.08997473865747452,
-0.020265832543373108,
-0.009063411504030228,
-0.028841467574238777,
0.01845378801226616,
0.015035699121654034,
0.050222478806972504,
-0.043155819177627563,
0.0025294185616075993,
-0.042612362653017044,
0.07064516842365265,
-0.01330584567040205,
0.06331394612789154,
-0.015241586603224277,
0.0359341986477375,
0.006863329093903303,
-0.023902542889118195,
-0.048820532858371735,
-0.04036905989050865,
-0.028371499851346016,
0.01571943424642086,
-0.014827052131295204,
-0.04043104127049446,
0.008963601663708687,
0.01873435452580452,
-0.010441699996590614,
0.0179284755140543,
0.019125064834952354,
-0.010847429744899273,
-0.00843699462711811,
0.007559215184301138,
0.02367631159722805,
-0.016668211668729782,
0.06554938852787018,
-0.013133231550455093,
0.008050893433392048,
-0.02680404670536518,
0.0017184133175760508,
0.0402098223567009,
0.07392190396785736,
0.04618331044912338,
0.006167489103972912,
0.007757219485938549,
-0.01374167948961258,
-0.06699405610561371,
-0.0482821948826313,
0.003338212613016367,
0.02904539741575718,
0.04344320297241211,
0.05108228325843811,
-0.0060718245804309845,
-0.038593392819166183,
0.042865462601184845,
-0.050744954496622086,
-0.019807619974017143,
0.08517974615097046,
0.03005552478134632,
0.0013008053647354245,
0.050000425428152084,
0.0010247168829664588,
0.0134076913818717,
-0.05673399940133095,
-0.022416146472096443,
-0.02854306250810623,
-0.04255930334329605,
0.001651845290325582,
-0.02556869573891163,
-0.038766391575336456,
-0.021399088203907013,
0.01952918991446495,
-0.010218356736004353,
0.022251354530453682,
0.0208957027643919,
0.02925052121281624,
-0.0017677932046353817,
-0.02751157060265541,
-0.06819327175617218,
-0.011246006935834885,
0.01843486912548542,
-0.05933434143662453,
-0.004422725178301334,
-0.0599089153110981,
-0.08252045512199402,
0.062079302966594696,
0.02990870177745819,
0.025781240314245224,
0.06804268062114716,
-0.014259666204452515,
-0.04946725443005562,
0.0023415915202349424,
0.0024002064019441605,
0.015440333634614944,
-0.005062517244368792,
0.041082143783569336,
-0.0032889582216739655,
-0.02423887699842453,
0.06918883323669434,
-0.060422684997320175,
-0.019660482183098793,
-0.013619208708405495,
0.00354816485196352,
0.03778913617134094,
0.020450174808502197,
-0.040578000247478485,
-0.0010421803453937173,
0.046510227024555206,
0.014197110198438168,
0.0005548083572648466,
0.061286959797143936,
-0.05582239478826523,
0.06126655265688896,
0.03743163123726845,
-0.017475154250860214,
-0.021609051153063774,
0.011472362093627453,
0.0029273058753460646,
-0.02660139463841915,
0.06608491390943527,
-0.012815939262509346,
-0.00036296015605330467,
0.09266521781682968,
0.07553800195455551,
-0.019877368584275246,
-0.004155835602432489,
0.004309878684580326,
0.041910506784915924,
0.014512941241264343,
0.015151642262935638,
0.05067380890250206,
0.03253015875816345,
-0.025309979915618896,
-0.010472779162228107,
0.01247474830597639,
0.015060893259942532,
0.0543607734143734,
0.0048766303807497025,
0.06987614184617996,
-0.015076810494065285,
0.03677577152848244,
-0.03529391437768936,
-0.04650816321372986,
-0.02089271880686283,
-0.010770196095108986,
0.003250791458413005,
0.02696116454899311,
-0.043792542070150375,
-0.016661157831549644,
0.0010497375624254346,
0.03340814635157585,
-0.06937197595834732,
0.014095666818320751,
-0.05592299997806549,
-0.08903384208679199,
0.02847818098962307,
0.016533536836504936,
0.022128934040665627,
-0.01869894564151764,
0.016327133402228355,
0.002095688134431839,
-0.05854291468858719,
0.05639416351914406,
-0.018063034862279892,
0.00672488147392869,
-0.03178469464182854,
0.014127171598374844,
-0.023675255477428436,
0.020148929208517075,
-0.02737388201057911,
-0.029199965298175812,
-0.03991030529141426,
0.00308216898702085,
-0.013743323273956776,
-0.004450925160199404,
-0.0035110830795019865,
0.0006251421291381121,
0.008635087870061398,
0.006845592521131039,
-0.022905128076672554,
0.013812758959829807,
-0.007279636338353157,
0.043658751994371414,
-0.04523054137825966,
-0.086800217628479,
0.03798352926969528,
0.006163277197629213,
0.03647509217262268,
0.037265513092279434,
0.039512909948825836,
0.0688088983297348,
0.015149462968111038,
-0.07542842626571655,
0.030177515000104904,
0.060738589614629745,
-0.03951897472143173,
-0.03451823815703392,
-0.024907559156417847,
-0.028704358264803886,
0.06827402114868164,
0.044014450162649155,
-0.025145841762423515,
-0.006142712663859129,
-0.020485861226916313,
-0.07120484858751297,
-0.004555442836135626,
-0.027296660467982292,
0.016892053186893463,
-0.012007711455225945,
0.023265747353434563,
-0.0005405345582403243,
0.005480079911649227,
-0.03114866279065609,
0.005537934135645628,
0.00902527291327715,
0.041677091270685196,
-0.03579413518309593,
-0.009701492264866829,
-0.021883422508835793,
0.04619021341204643,
0.009361372329294682,
0.005196646321564913,
-0.010865986347198486,
-0.07497425377368927,
0.0470677874982357,
0.011559014208614826,
-0.07742179930210114,
0.007079212926328182,
-0.026327086612582207,
0.04046487435698509,
-0.06903846561908722,
0.010997126810252666,
-0.013419592753052711,
-0.03898124024271965,
-0.0399809293448925,
-0.06981167942285538,
0.009213224053382874,
0.010346091352403164,
0.008835342712700367,
0.006852560676634312,
0.02155296318233013,
-0.023745371028780937,
-0.08299460262060165,
0.006246841046959162,
-0.022831575945019722,
0.05255506560206413,
-0.011385695077478886,
0.002219087677076459,
-0.02964504435658455,
-0.03836451843380928,
-0.007255935575813055,
0.013136716559529305,
-0.06661602109670639,
0.04947005212306976,
-0.0014324135845527053,
-0.0763091892004013,
-0.022916367277503014,
0.0062045743688941,
-0.02994852513074875,
-0.021898536011576653,
-0.011336734518408775,
-0.04471803829073906,
0.003388764336705208,
-0.06854952871799469,
-0.016146380454301834,
0.058418504893779755,
-0.07234786450862885,
0.01797940395772457,
-0.00940069742500782,
0.01996886543929577,
-0.022514715790748596,
-0.04604824259877205,
-0.03227325156331062,
-0.016121644526720047,
-0.021194521337747574,
-0.01637532189488411,
-0.06646163761615753,
0.006001072935760021,
0.02287505753338337,
0.05448297783732414,
-0.03598862141370773,
0.0801248699426651,
0.02746196836233139,
-0.041088271886110306,
0.05029823258519173,
0.03733185678720474,
0.01000776793807745,
0.011283334344625473,
0.019847474992275238,
-0.05503528565168381,
-0.0024081526789814234,
-0.01282728835940361,
-0.02133406698703766,
0.05718930810689926,
0.0078101446852087975,
-0.04648752510547638,
-0.011209797114133835,
0.004984586965292692,
0.014756150543689728,
-0.021018553525209427,
-0.10129530727863312,
-0.025343015789985657,
0.03872298821806908,
-0.006337672006338835,
-0.060394078493118286,
-0.010390618816018105,
0.03889526426792145,
0.013653034344315529,
-0.045622214674949646,
-0.022085867822170258,
-0.030070120468735695,
0.005739782005548477,
-0.0190435741096735,
-0.014930765144526958,
0.043975818902254105,
-0.003938424400985241,
0.021890847012400627,
0.07051321864128113,
-0.07180194556713104,
-0.008950174786150455,
0.04001927375793457,
0.04566086828708649,
-0.005008587148040533,
-0.000543429865501821,
0.03344707190990448,
-0.012172725982964039,
-0.002192104235291481,
0.04012930393218994,
-0.006507750600576401,
-0.009039973840117455,
0.023249531164765358,
0.06521811336278915,
0.0373750776052475,
0.017894627526402473,
-0.02881033532321453,
-0.029338961467146873,
-0.024254435673356056,
0.007396867033094168,
-0.038379278033971786,
-0.01075279526412487,
-0.019629064947366714,
-0.003083899850025773,
-0.0650249496102333,
-0.020288687199354172,
-0.05891777202486992,
0.01985592395067215,
0.0017209178768098354,
0.0006856967811472714,
-0.029322437942028046,
-0.03485584259033203,
-0.0013538787607103586,
-0.06580076366662979,
0.006110901944339275,
-0.005791500676423311,
-0.015060337260365486,
0.040605977177619934,
0.006301142740994692,
0.021940143778920174,
0.010697356425225735,
0.011269194073975086,
-0.011246994137763977,
-0.02185162715613842,
0.008895601145923138,
-0.0006700454978272319,
-0.02089829370379448,
-0.05750906467437744,
-0.0218899417668581,
-0.018242869526147842,
0.049734875559806824,
0.004849294666200876,
-0.09924454241991043,
-0.015016118064522743,
-0.0038405240047723055,
-0.01468881405889988,
-0.0009848439367488027,
0.04362998157739639,
0.04309583827853203,
0.015471449121832848,
0.06354633718729019,
-0.01928974688053131,
0.023032132536172867,
0.003336867783218622,
-0.023868843913078308,
0.011957138776779175,
0.06587325781583786,
-0.035499971359968185,
-0.00910577829927206,
-0.007924070581793785,
0.014928611926734447,
0.00615428714081645,
0.017648886889219284,
-0.00046325643779709935,
0.01666695810854435,
0.06782200932502747,
-0.009863193146884441,
-0.026186281815171242,
-0.027871960774064064,
-0.0031880212482064962,
-0.0056200516410171986,
-0.008540082722902298,
-0.003570262109860778,
-0.031912535429000854,
-0.05040609464049339,
0.045503776520490646,
-0.02815079130232334,
0.09379716217517853,
-0.0243986826390028,
0.009024140425026417,
0.0062230173498392105,
-0.04594500735402107,
-0.05432329326868057,
-0.03988867253065109,
0.03247828409075737,
-0.01968015916645527,
0.018889503553509712,
-0.08368416875600815,
0.0018298489740118384,
-0.02445213869214058,
-0.020369235426187515,
0.020321255549788475,
0.016876017674803734,
0.033461324870586395,
-0.026239506900310516,
-0.011414256878197193,
0.06956658512353897,
0.07672435790300369,
-0.018061475828289986,
0.017494751140475273,
0.00004292989251553081,
-0.009492225013673306,
-0.0063382964581251144,
0.002250273246318102,
-0.015900762751698494,
-0.012048511765897274,
0.038745466619729996,
0.026869438588619232,
-0.03509832173585892,
0.01885814778506756,
0.0008535683737136424,
0.06252073496580124,
0.023965561762452126,
0.03826295956969261,
0.021717745810747147,
-0.0463726632297039,
0.04651133716106415
] |
[
12.66603946685791,
7.108608245849609
] |
General Physics
|
General Physics
|
physics-gen-ph
|
na
|
na
|
2007-03-31T03:16:14
|
We show that a determinant of Stirling cycle numbers counts unlabeled acyclic
single-source automata. The proof involves a bijection from these automata to
certain marked lattice paths and a sign-reversing involution to evaluate the
determinant.
|
A determinant of Stirling cycle numbers counts unlabeled acyclic
single-source automata
|
math.CO
|
0704.0004
| 2,007
|
[
-0.032364051789045334,
0.013973338529467583,
-0.016063479706645012,
-0.05970880761742592,
0.036923035979270935,
-0.05083383247256279,
0.03615953028202057,
0.03585187718272209,
-0.02533918060362339,
0.010375839658081532,
-0.08313578367233276,
0.08855132013559341,
0.04965571314096451,
0.014091935940086842,
-0.005996746011078358,
0.0035265274345874786,
0.03943710774183273,
0.00345583725720644,
-0.03190815448760986,
0.04283507540822029,
0.004262375179678202,
0.004912300501018763,
-0.018359553068876266,
-0.03599787876009941,
0.12831665575504303,
-0.02547900564968586,
0.06592436134815216,
-0.012274768203496933,
-0.050127673894166946,
0.04510059952735901,
0.0849650502204895,
-0.03971712291240692,
0.02668442577123642,
-0.0320996455848217,
-0.03965382277965546,
-0.01310202106833458,
0.056862540543079376,
-0.013364456593990326,
0.020363211631774902,
0.03929346427321434,
0.08159696310758591,
-0.006570270750671625,
0.001829621265642345,
0.04632974788546562,
0.021805360913276672,
0.015553698875010014,
-0.006217068526893854,
0.030359234660863876,
0.05968063324689865,
0.009755744598805904,
0.03760935738682747,
0.0014681945322081447,
-0.013629420660436153,
-0.04727477580308914,
-0.05371152609586716,
0.0463373064994812,
-0.01963810995221138,
-0.047450367361307144,
0.0008959297556430101,
0.05132262036204338,
0.0075356364250183105,
0.0479346327483654,
0.034036993980407715,
0.011316617019474506,
-0.006077661644667387,
-0.033639002591371536,
-0.018718240782618523,
0.017661314457654953,
-0.003299929201602936,
-0.008859198540449142,
0.001977063249796629,
-0.01731072925031185,
0.06771846860647202,
-0.007837707176804543,
0.01031606923788786,
0.008105456829071045,
0.0354289710521698,
-0.012508278712630272,
0.004368132911622524,
0.007196671795099974,
-0.024448484182357788,
-0.07224873453378677,
0.015613885596394539,
0.04312798008322716,
0.06922494620084763,
0.019785545766353607,
0.04798905923962593,
-0.0038611681666225195,
-0.07803177833557129,
0.062016554176807404,
-0.017397332936525345,
0.002833043457940221,
0.04343155771493912,
0.04269609600305557,
-0.05707728862762451,
0.012921273708343506,
0.009168718941509724,
0.05632614344358444,
-0.05830676853656769,
-0.036682840436697006,
-0.0231211856007576,
0.042514193803071976,
-0.029578158631920815,
-0.03627912700176239,
0.0262051559984684,
0.014811797998845577,
-0.0062841628678143024,
-0.06960802525281906,
-0.01708216220140457,
-0.05020132660865784,
-0.0353395938873291,
-0.03716373071074486,
-0.009193229489028454,
0.01622770167887211,
-0.04564811661839485,
0.03735409304499626,
0.10085362195968628,
-0.07656199485063553,
-0.003716791979968548,
0.016684258356690407,
-0.04572005569934845,
-0.0563165619969368,
-0.008663671091198921,
0.031618308275938034,
0.042340658605098724,
0.011037776246666908,
-0.016225000843405724,
0.025338010862469673,
-0.05126615986227989,
-0.019402679055929184,
0.023556463420391083,
-0.009849649854004383,
-0.0014379500644281507,
-0.014173909090459347,
0.04017337039113045,
0.03346628323197365,
-0.019562747329473495,
0.002227069577202201,
0.03524262085556984,
-0.031029006466269493,
-0.015695441514253616,
-0.02355246990919113,
0.022220348939299583,
-0.013771205209195614,
0.024387182667851448,
-0.048272017389535904,
0.04340168088674545,
-0.1017170175909996,
-0.0310269296169281,
-0.020582787692546844,
0.06360898166894913,
-0.006857383530586958,
-0.03446624055504799,
0.0013907827669754624,
-0.014298546127974987,
-0.016980014741420746,
-0.013680499978363514,
-0.01213526539504528,
-0.013688668608665466,
0.016647731885313988,
0.0012178196338936687,
-0.05442916974425316,
-0.06240453943610191,
0.013190732337534428,
-0.05453759804368019,
0.0030324708204716444,
-0.024473140016198158,
-0.0035206752363592386,
0.016613349318504333,
0.00879194587469101,
-0.05730791017413139,
0.012434514239430428,
-0.054824985563755035,
-0.011816904880106449,
0.007720337714999914,
-0.04156064987182617,
-0.03701947256922722,
-0.0233045294880867,
0.07149239629507065,
0.00929737277328968,
0.07422482222318649,
-0.03207331523299217,
0.029620148241519928,
0.055659059435129166,
0.0007014477741904557,
0.02469446137547493,
-0.025052376091480255,
-0.029537655413150787,
-0.046276435256004333,
-0.011046456173062325,
0.04813642054796219,
0.029428070411086082,
-0.009366145357489586,
-0.029916873201727867,
-0.006126703694462776,
-0.022487720474600792,
0.026220377534627914,
-0.013662419281899929,
0.04136500507593155,
-0.03095606528222561,
0.028474165126681328,
-0.01673405058681965,
-0.012799863703548908,
-0.0023461400996893644,
-0.05176829174160957,
0.0706574097275734,
0.011157129891216755,
0.00879056565463543,
0.024241359904408455,
-0.043318554759025574,
0.04963328689336777,
-0.021632738411426544,
-0.0241716168820858,
0.041406113654375076,
-0.04419446364045143,
-0.01059200894087553,
-0.005977723281830549,
-0.07081621140241623,
-0.03157695382833481,
-0.028516093268990517,
0.09212271124124527,
-0.016790777444839478,
-0.006602046079933643,
0.02218390814960003,
0.006154016591608524,
0.06344671547412872,
-0.008374945260584354,
0.012532071210443974,
-0.033316366374492645,
-0.016232110559940338,
-0.030449481680989265,
-0.054879650473594666,
0.03954888880252838,
-0.056248024106025696,
-0.015051386319100857,
-0.012364856898784637,
-0.01125276554375887,
0.04649446904659271,
0.041361838579177856,
0.02519953064620495,
0.000009132503691944294,
-0.05147359147667885,
0.03695458546280861,
-0.039183296263217926,
-0.02698376774787903,
-0.025064392015337944,
0.016266735270619392,
-0.0016840839525684714,
-0.04879448562860489,
0.021250583231449127,
-0.0050162747502326965,
0.04642954841256142,
0.009130294434726238,
0.07405709475278854,
0.04660559445619583,
-0.03026008978486061,
-0.00825126189738512,
0.01882067695260048,
-0.002239770721644163,
-0.0020408807322382927,
0.05002874508500099,
-0.04965474084019661,
0.024802247062325478,
-0.03984534367918968,
0.010692272335290909,
-0.034315235912799835,
0.04320985823869705,
-0.07320479303598404,
0.03956383094191551,
-0.01318416278809309,
0.01239289715886116,
0.012017540633678436,
0.05589604750275612,
0.00339798373170197,
-0.013086273334920406,
0.01372215524315834,
0.053575433790683746,
0.005999002605676651,
0.0054407017305493355,
-0.011519941501319408,
-0.04765096679329872,
-0.01320691592991352,
-0.03850452974438667,
-0.0282305758446455,
-0.0313650518655777,
0.012417804449796677,
0.023547004908323288,
-0.027034852653741837,
0.048729535192251205,
0.03523491695523262,
0.005969290155917406,
-0.039851754903793335,
0.006350560579448938,
0.03264038637280464,
0.009965387172996998,
-0.0015565535286441445,
0.01942385919392109,
-0.017317447811365128,
0.009893439710140228,
-0.017605377361178398,
0.022107046097517014,
0.027047401294112206,
0.00020072610641364008,
-0.022130224853754044,
0.04334624484181404,
0.018396208062767982,
0.002628688234835863,
0.019739463925361633,
0.06046334654092789,
-0.004760886076837778,
0.01805361546576023,
0.04568381607532501,
-0.008419082500040531,
-0.025423966348171234,
-0.03651422634720802,
0.05251554772257805,
-0.035296328365802765,
-0.04884732887148857,
0.053305432200431824,
-0.024833133444190025,
0.012319417670369148,
-0.03256041184067726,
0.040567778050899506,
-0.05353258177638054,
-0.006399375852197409,
0.013409199193120003,
0.03155479580163956,
0.05867311730980873,
-0.00476055545732379,
-0.08868301659822464,
0.01637108437716961,
0.06547904014587402,
-0.004229962360113859,
-0.02845349907875061,
-0.04981128126382828,
-0.03142238408327103,
-0.03477314114570618,
0.03405580297112465,
-0.01104115229099989,
0.025066258385777473,
-0.005122531205415726,
0.0635044276714325,
-0.031536251306533813,
-0.05478547886013985,
-0.01601426489651203,
0.02900044061243534,
-0.04330411180853844,
0.005166310351341963,
0.03589579835534096,
-0.00997095089405775,
0.010637599043548107,
-0.007150177378207445,
0.044695716351270676,
-0.018889570608735085,
0.01357385702431202,
0.006080892402678728,
0.04237315058708191,
-0.012332170270383358,
0.05911477655172348,
0.026263084262609482,
0.061488598585128784,
-0.024326372891664505,
-0.009363346733152866,
-0.05939865857362747,
0.05540890991687775,
0.025483042001724243,
0.0006126735243014991,
0.06796135753393173,
0.07866983860731125,
-0.07411269843578339,
-0.037862010300159454,
-0.022888248786330223,
0.03591763973236084,
0.009497435763478279,
-0.033280059695243835,
0.020925037562847137,
-0.038264673203229904,
0.027428504079580307,
-0.017569029703736305,
0.018406638875603676,
0.013908096589148045,
-0.015148135833442211,
0.0462881363928318,
-0.009424707852303982,
-0.020564084872603416,
0.034704819321632385,
-0.04155488684773445,
0.006107419263571501,
-0.012719536200165749,
-0.015608828514814377,
0.02086034044623375,
-0.05206211283802986,
0.0050605833530426025,
0.015289481729269028,
0.025066599249839783,
-0.00034825821057893336,
0.05170753598213196,
0.04576348140835762,
0.03803229704499245,
0.03542400896549225,
-0.05911716818809509,
-0.0613337941467762,
0.011475122533738613,
0.003045527497306466,
0.0035607574973255396,
0.01050644088536501,
-0.00045462753041647375,
-0.070697121322155,
0.05942825600504875,
0.019396701827645302,
-0.022852707654237747,
0.018192235380411148,
0.032705727964639664,
-0.03305062651634216,
0.04540335386991501,
0.014778283424675465,
0.043313924223184586,
0.0202938225120306,
0.012739645317196846,
-0.004628250375390053,
-0.009135759435594082,
0.05602667108178139,
-0.009122914634644985,
0.024577820673584938,
-0.02609955333173275,
-0.0044401464983820915,
-0.017521923407912254,
0.017309917137026787,
-0.04540598392486572,
-0.051940448582172394,
0.043880969285964966,
0.03474394604563713,
-0.01617470569908619,
0.03463103249669075,
-0.05875090882182121,
0.02104020118713379,
0.04266257956624031,
0.03325730934739113,
0.001439966494217515,
-0.02567816711962223,
0.029808228835463524,
-0.0715232789516449,
-0.024234838783740997,
-0.010626915842294693,
0.028020508587360382,
0.038963936269283295,
0.032684892416000366,
-0.024176331236958504,
-0.021676653996109962,
-0.008523603901267052,
0.0642901062965393,
0.0007073492160998285,
0.011200625449419022,
-0.013774268329143524,
0.08762896060943604,
0.006713647395372391,
-0.031045272946357727,
0.03426775336265564,
0.013290059752762318,
0.05170321464538574,
0.05155332386493683,
0.009533829987049103,
-0.05060923472046852,
0.026569655165076256,
-0.01113632507622242,
-0.0015951095847412944,
-0.0053200372494757175,
0.014519274234771729,
-0.003280274337157607,
0.08067622780799866,
0.013154100626707077,
0.014247522689402103,
-0.02676522359251976,
-0.017608363181352615,
-0.02568894810974598,
-0.05474090576171875,
0.027221878990530968,
-0.04723409190773964,
-0.03147101402282715,
0.05951610207557678,
0.03601417690515518,
-0.03396465629339218,
-0.05090545862913132,
-0.01288891863077879,
0.007539004553109407,
0.06111539527773857,
0.009075691923499107,
-0.03998047113418579,
-0.001399545930325985,
-0.02922983281314373,
0.0035619623959064484,
0.023720722645521164,
0.033075351268053055,
0.027408268302679062,
-0.04662517458200455,
-0.04631849378347397,
0.009807582013309002,
0.012119578197598457,
0.02241363562643528,
0.013900455087423325,
-0.03284008055925369,
0.04986453428864479,
0.010676238685846329,
-0.003702215850353241,
0.007072657812386751,
0.029110711067914963,
-0.005250589456409216,
-0.028478840366005898,
-0.004759289789944887,
-0.042141396552324295,
0.061144717037677765,
0.07125706970691681,
0.044595684856176376,
0.04601236805319786,
0.05128777399659157,
-0.04280231520533562,
0.017260806635022163,
-0.007843202911317348,
-0.06051768362522125,
-0.042657673358917236,
-0.026430698111653328,
-0.010538885369896889,
0.01499912515282631,
-0.020638462156057358,
-0.09265837073326111,
-0.02324269339442253,
-0.034904301166534424,
-0.07363232970237732,
0.04204507917165756,
-0.003440065309405327,
-0.009048055857419968,
0.010292218998074532,
-0.028359822928905487,
-0.027308573946356773,
0.04949555918574333,
0.0029693173710256815,
-0.061341676861047745,
0.014223204925656319,
0.013780385255813599,
0.029488375410437584,
0.010205728001892567,
0.002169218147173524,
0.01668495126068592,
-0.007493181619793177,
-0.010989358648657799,
-0.06995585560798645,
-0.08529011160135269,
0.0032498224172741175,
-0.03545859828591347,
-0.10492798686027527,
0.025853758677840233,
0.016633348539471626,
-0.005490447394549847,
-0.08834756165742874,
-0.011711536906659603,
-0.02899518981575966,
0.018200227990746498,
-0.00031497955205850303,
-0.033785317093133926,
0.018392745405435562,
-0.009470401331782341,
0.0745454654097557,
0.043822403997182846,
0.009017880074679852,
0.019946448504924774,
-0.060781627893447876,
-0.023755479604005814,
0.016823209822177887,
-0.00501004746183753,
-0.005118805915117264,
0.035523369908332825,
-0.03655965253710747,
-0.0081126494333148,
0.03773467242717743,
-0.01166980154812336,
-0.025031939148902893,
-0.007030525244772434,
-0.013431526720523834,
0.0014893682673573494,
-0.013671197928488255,
-0.0677662193775177,
-0.029843328520655632,
0.003219296457245946,
-0.020357031375169754,
-0.02452724426984787,
-0.01125679537653923,
0.00037994125159457326,
-0.03774084150791168,
0.030184730887413025,
0.05909661576151848,
0.006545957177877426,
-0.0435829684138298,
-0.01929086074233055,
-0.02216474339365959,
-0.045048024505376816,
0.004485765937715769,
0.0007066951366141438,
0.010852660052478313,
-0.013658962212502956,
-0.07710109651088715,
-0.007946186698973179,
0.07121533900499344,
0.07026145607233047,
-0.04142108932137489,
-0.023435622453689575,
0.045616183429956436,
0.00935025792568922,
0.018792077898979187,
0.027343302965164185,
-0.017872286960482597,
0.020164452493190765,
-0.010564927943050861,
-0.030049990862607956,
0.00266449386253953,
-0.0501466765999794,
-0.04844791442155838,
0.0105205699801445,
-0.017026642337441444,
-0.02031680941581726,
-0.05681831017136574,
0.01943214051425457,
-0.051421914249658585,
-0.002887048525735736,
-0.08353400975465775,
0.05035123601555824,
0.00303099793381989,
-0.000740050571039319,
-0.0014731872361153364,
0.06859971582889557,
0.045656390488147736,
-0.0032700328156352043,
-0.011492716148495674,
-0.060533199459314346,
-0.03344877064228058,
0.01206793263554573,
0.029044227674603462,
-0.024319276213645935,
0.03131217509508133,
0.029623620212078094,
0.019907338544726372,
0.003192944684997201,
-0.00596245052292943,
-0.009079587645828724,
0.013715740293264389,
0.036063943058252335,
-0.03341586887836456,
0.046859387308359146,
0.041433680802583694,
0.04142995551228523,
-0.02673829346895218,
0.04965389147400856,
0.05832642689347267,
-0.033979106694459915,
0.03963625431060791,
-0.01855391077697277,
-0.0017136309761554003,
0.02824953943490982,
0.025418592616915703,
-0.03128733113408089,
0.03105836920440197,
0.004953459836542606,
0.006819408852607012,
-0.018158338963985443,
-0.00606124009937048,
0.061125315725803375,
-0.051689762622117996,
-0.035837773233652115,
-0.0428241565823555,
-0.02830570749938488,
0.009934550151228905,
-0.022220708429813385,
-0.035758234560489655,
-0.002463476499542594,
-0.014419317245483398,
0.01095838937908411,
0.0448518805205822,
-0.004986646585166454,
0.062376298010349274,
-0.004987617488950491,
-0.04878474399447441,
0.00731914397329092,
-0.04805364832282066,
-0.02855459786951542,
-0.03514804691076279,
0.015726203098893166,
0.015146996825933456,
-0.01454397477209568,
-0.02204657718539238,
-0.032496873289346695,
-0.12098649144172668,
0.03130677342414856,
0.021084925159811974,
0.04631485417485237,
-0.042406484484672546,
-0.01781684346497059,
-0.004304563160985708,
-0.03754546120762825,
0.014673369936645031,
-0.027258027344942093,
0.04068561643362045,
0.011901035904884338,
0.07549644261598587,
-0.018360048532485962,
0.09951378405094147,
-0.0486505888402462,
-0.021235154941678047,
-0.023278702050447464,
0.004840602166950703,
-0.002616655780002475,
-0.014136267825961113,
-0.0554797388613224,
0.0075090681202709675,
-0.025606004521250725,
-0.01591450162231922,
0.02533748373389244,
0.012311019003391266,
0.005191545933485031,
-0.022879457101225853,
-0.010299698449671268,
-0.02220294065773487,
0.01790815033018589,
0.004196822643280029,
-0.038565974682569504,
0.047017328441143036,
-0.035984620451927185,
-0.04660420119762421,
0.04417512193322182,
0.007082315161824226,
0.05119042843580246,
0.04925430938601494,
0.014858588576316833,
-0.004916382022202015,
-0.04582872986793518,
0.02210608869791031,
-0.05701710656285286,
-0.01890244148671627,
0.003885549958795309,
0.00673460029065609,
-0.06216171383857727,
-0.01186066959053278,
-0.015297971665859222,
-0.03560584783554077,
0.057014934718608856,
0.002038246253505349,
-0.02190636284649372,
-0.046086493879556656,
-0.06372953951358795,
-0.006210260093212128,
0.030384549871087074,
-0.0010636699153110385,
-0.0021399674005806446,
-0.031715504825115204,
0.00746818957850337,
-0.012860062532126904,
0.02426309883594513,
0.062099527567625046,
0.018786273896694183,
0.030297867953777313,
0.02480863779783249,
0.040663763880729675,
0.0341712050139904,
-0.0015319195808842778,
0.00869778636842966,
0.094097800552845,
-0.0006924649351276457,
0.0035045507829636335,
-0.03472546115517616,
-0.023186422884464264
] |
[
0.37987735867500305,
6.816714763641357
] |
Combinatorics
|
Mathematics
|
math-CO
|
na
|
na
|
2007-04-02T18:09:58
|
In this paper we show how to compute the $\Lambda_{\alpha}$ norm, $\alpha\ge
0$, using the dyadic grid. This result is a consequence of the description of
the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.
|
From dyadic $\Lambda_{\alpha}$ to $\Lambda_{\alpha}$
|
math.CA math.FA
|
0704.0005
| 2,007
|
[
-0.02720588631927967,
0.040897075086832047,
-0.02446940913796425,
-0.004654645919799805,
0.02641661837697029,
-0.02185913920402527,
-0.016616100445389748,
0.036678120493888855,
-0.05678589269518852,
-0.007537512108683586,
-0.04878442734479904,
0.05096667632460594,
0.02939138188958168,
0.00939534418284893,
0.02253095805644989,
-0.011743065901100636,
0.010490594431757927,
-0.021694978699088097,
-0.025530310347676277,
-0.034981150180101395,
-0.041694995015859604,
-0.026098310947418213,
0.0017768911784514785,
-0.08376695960760117,
0.10946393758058548,
-0.013081268407404423,
0.005430801771581173,
0.007545518688857555,
-0.06109684705734253,
-0.000705164682585746,
0.04911455512046814,
-0.02051170915365219,
0.02422083355486393,
-0.03444438800215721,
-0.027874654158949852,
-0.003649819875136018,
0.08048385381698608,
0.028799433261156082,
0.04217531159520149,
0.003944134805351496,
0.027153396978974342,
0.0032893724273890257,
-0.014188159257173538,
-0.00903013814240694,
0.009937051683664322,
-0.0026815321762114763,
0.006393245421350002,
0.013561956584453583,
0.04328656941652298,
0.03644410893321037,
-0.03513053059577942,
0.009140916168689728,
-0.018225450068712234,
-0.06974038481712341,
-0.023542091250419617,
0.038557421416044235,
0.02249409444630146,
-0.066249780356884,
0.056630123406648636,
0.007657483220100403,
-0.009160902351140976,
0.05286024510860443,
-0.026904359459877014,
0.00012863927986472845,
0.025472251698374748,
-0.042323607951402664,
-0.028224360197782516,
-0.007764817215502262,
0.0036132661625742912,
-0.02784336917102337,
0.021209346130490303,
-0.047157954424619675,
0.023309608921408653,
0.02606188878417015,
-0.030631018802523613,
-0.0233551487326622,
0.01932590827345848,
0.018337581306695938,
0.03799332305788994,
0.022043049335479736,
0.002929537557065487,
-0.042159244418144226,
0.07257716357707977,
-0.007875097915530205,
0.03967491537332535,
0.02093554101884365,
0.04306595399975777,
-0.01381076779216528,
-0.040700387209653854,
0.06601507216691971,
0.030849957838654518,
0.018268300220370293,
0.060676030814647675,
0.06917767226696014,
-0.06371773779392242,
0.003496843855828047,
-0.03569026291370392,
0.005007579922676086,
-0.0004215146182104945,
-0.04594216123223305,
-0.0014826569240540266,
0.044442325830459595,
0.02468027174472809,
0.010714514181017876,
0.023518700152635574,
0.044640764594078064,
0.03392016142606735,
-0.008207674138247967,
-0.0007372918189503253,
-0.07870698720216751,
-0.10450176894664764,
0.029936693608760834,
-0.006926573812961578,
-0.06351250410079956,
-0.017509784549474716,
-0.026929764077067375,
0.049723412841558456,
-0.07904183864593506,
0.04669008031487465,
0.06675536930561066,
0.03542253002524376,
0.02603515051305294,
0.001659397385083139,
0.03174389526247978,
0.0293133407831192,
0.03853115439414978,
-0.086564801633358,
0.0060850572772324085,
0.02593894675374031,
-0.05421549081802368,
0.04642412066459656,
0.024804122745990753,
-0.036176398396492004,
0.015239322558045387,
-0.008882499299943447,
0.02156321331858635,
-0.002291808370500803,
0.001318555441685021,
0.023062586784362793,
-0.027801355347037315,
0.015884969383478165,
-0.008405754342675209,
-0.005981348920613527,
-0.09049758315086365,
-0.011666566133499146,
-0.08211949467658997,
0.05163615196943283,
-0.061706747859716415,
-0.029910847544670105,
0.002672330942004919,
0.006152180954813957,
0.06555870175361633,
-0.0026570353657007217,
0.07166954129934311,
-0.03540738299489021,
-0.020336195826530457,
0.006047065835446119,
0.03974936902523041,
0.027300503104925156,
0.014894346706569195,
0.014877225272357464,
0.03623208403587341,
-0.02722332999110222,
-0.001872992841526866,
-0.031274303793907166,
-0.028309248387813568,
0.036410700529813766,
0.014073380269110203,
-0.0031162924133241177,
0.02734673209488392,
-0.05165626108646393,
-0.021546507254242897,
-0.04768485948443413,
-0.009248359128832817,
0.01020791381597519,
0.03643018752336502,
0.00601032841950655,
-0.03809110075235367,
0.036347709596157074,
0.0017241107998415828,
0.04310221970081329,
-0.008391055278480053,
0.06202976778149605,
-0.0022263210266828537,
-0.0008053444908000529,
0.03415578231215477,
-0.0006198926130309701,
-0.036779455840587616,
-0.0547788068652153,
-0.048815321177244186,
0.01002412848174572,
0.06009509786963463,
-0.0005109190242365003,
-0.05152099207043648,
-0.013583828695118427,
-0.022418241947889328,
0.02597762830555439,
0.012301737442612648,
-0.002445956226438284,
-0.06845737993717194,
0.011690718121826649,
-0.05001518875360489,
-0.04731403663754463,
0.02111479826271534,
0.01590079814195633,
0.045558106154203415,
-0.035494424402713776,
0.016589118167757988,
0.0361320823431015,
0.006337024737149477,
0.021308094263076782,
-0.0072226254269480705,
0.004505461547523737,
0.003886317601427436,
-0.004050711169838905,
-0.014016213826835155,
-0.020760564133524895,
-0.006768018007278442,
0.006978954654186964,
0.04155619442462921,
-0.013133794069290161,
-0.017230335623025894,
-0.03692398592829704,
0.009699828922748566,
0.0475979782640934,
0.02896023355424404,
-0.022905299440026283,
0.004198818933218718,
-0.041501160711050034,
0.006033874582499266,
-0.008409188129007816,
-0.04402399808168411,
0.0415198840200901,
-0.05863887071609497,
-0.022251885384321213,
0.007920542731881142,
-0.056366149336099625,
0.07153404504060745,
0.026855597272515297,
0.05854904651641846,
0.026338597759604454,
0.007458411622792482,
0.01320540253072977,
0.032782990485429764,
-0.05430012568831444,
0.018899669870734215,
0.008827940560877323,
-0.04123840481042862,
-0.044739559292793274,
0.02521187998354435,
0.03443673253059387,
0.023348798975348473,
-0.005754427053034306,
0.025819139555096626,
-0.0127188041806221,
-0.0034838011488318443,
-0.03719395399093628,
-0.029114194214344025,
-0.02494765818119049,
-0.10268106311559677,
0.0416884571313858,
-0.06185714900493622,
-0.021363263949751854,
-0.049341462552547455,
-0.024756813421845436,
0.0068275718949735165,
0.03288242965936661,
-0.05722092092037201,
-0.008102013729512691,
-0.043549392372369766,
0.026521878316998482,
0.062067992985248566,
0.12219158560037613,
0.04768935218453407,
-0.029513373970985413,
-0.005543039180338383,
0.01020914688706398,
-0.05775453895330429,
0.021008720621466637,
-0.027568025514483452,
-0.041824087500572205,
0.016762638464570045,
-0.054989732801914215,
0.0011746862437576056,
0.0013648704625666142,
0.023740174248814583,
0.022056730464100838,
0.03375669941306114,
0.001454608398489654,
0.06882040947675705,
-0.06687113642692566,
-0.004152133595198393,
-0.019041556864976883,
0.06836111098527908,
-0.00161801278591156,
0.05072200298309326,
0.09940797835588455,
-0.013683305121958256,
-0.04113129526376724,
0.003256093943491578,
-0.015376364812254906,
0.017181742936372757,
0.01789931207895279,
0.006354895886033773,
0.04031096398830414,
0.0008644858025945723,
0.0015728080179542303,
-0.01488689798861742,
0.024357670918107033,
0.029114294797182083,
0.005766545422375202,
0.025407465174794197,
-0.025826910510659218,
-0.008198750205338001,
-0.022832030430436134,
0.03125343099236488,
0.03110070526599884,
-0.011607007123529911,
0.030263204127550125,
0.008674566633999348,
0.06843508034944534,
-0.10767313092947006,
0.007885513827204704,
-0.05729169026017189,
-0.026086486876010895,
0.04115848243236542,
-0.007019808050245047,
0.04078077897429466,
-0.02726786956191063,
-0.023280423134565353,
0.00036494634696282446,
0.03178681060671806,
0.015167449600994587,
0.018026821315288544,
-0.027658594772219658,
0.006177328992635012,
-0.0525677315890789,
-0.009095121175050735,
-0.0325971357524395,
0.0017940261168405414,
0.03341004624962807,
-0.07070761919021606,
0.0021139997988939285,
-0.041243549436330795,
-0.032368265092372894,
-0.005095291882753372,
0.00861946027725935,
0.0007560770609416068,
0.039563219994306564,
0.005421018227934837,
-0.05870174244046211,
-0.03177235648036003,
0.007434457074850798,
-0.00019371976668480784,
0.03171783313155174,
0.021322421729564667,
0.020868385210633278,
-0.011319269426167011,
0.06861637532711029,
-0.007437499705702066,
-0.028581462800502777,
-0.02892020344734192,
-0.015018646605312824,
0.0023863711394369602,
0.036899201571941376,
0.03173532709479332,
0.004254447761923075,
0.043006885796785355,
0.009785911999642849,
-0.00992274098098278,
-0.029165159910917282,
-0.018910204991698265,
0.07719932496547699,
0.04496678709983826,
0.012395062483847141,
-0.0067976005375385284,
-0.005476372316479683,
-0.03477512672543526,
-0.027833059430122375,
0.019495049491524696,
0.02494046837091446,
0.015754779800772667,
0.04817470908164978,
0.018398478627204895,
0.06614693254232407,
-0.012173487804830074,
0.013316849246621132,
-0.003226581495255232,
0.00629463093355298,
-0.033921126276254654,
-0.013699932023882866,
-0.017871038988232613,
-0.007569488137960434,
0.03582363203167915,
0.023239970207214355,
-0.002003711648285389,
0.07832633703947067,
0.0328700952231884,
-0.07521700859069824,
0.056810054928064346,
-0.01365357544273138,
-0.036924637854099274,
0.0053126392886042595,
0.00006231633597053587,
0.00007838269812054932,
-0.006717886310070753,
-0.026270302012562752,
-0.011076887138187885,
0.09004288911819458,
-0.03766672685742378,
-0.004828033968806267,
-0.027441181242465973,
-0.003915700130164623,
-0.06537619978189468,
0.04857514426112175,
0.018722638487815857,
0.01866198144853115,
-0.011098348535597324,
-0.004702128469944,
-0.011341873556375504,
-0.0076950928196311,
0.05444657802581787,
0.013005776330828667,
0.0008511937921866775,
0.02397739328444004,
-0.015369961969554424,
0.0395980142056942,
0.019266117364168167,
0.025449691340327263,
-0.047657523304224014,
0.021015184000134468,
-0.009057257324457169,
-0.01790071651339531,
0.021893834695219994,
-0.08874090760946274,
-0.07860255986452103,
0.01152268797159195,
0.01941543072462082,
-0.014254743233323097,
0.015052124857902527,
0.01660645194351673,
-0.07152404636144638,
-0.005387013778090477,
0.022836675867438316,
0.002078693825751543,
0.1038866713643074,
0.03018077090382576,
-0.04855852201581001,
-0.03341512009501457,
-0.00843775924295187,
0.03137795999646187,
0.01500913966447115,
0.021304141730070114,
0.030965320765972137,
0.04986929893493652,
0.011679562740027905,
-0.013464828953146935,
0.0008685504435561597,
0.06533285230398178,
0.0707988366484642,
0.011350555345416069,
-0.03285735845565796,
-0.04406585544347763,
-0.00767482491210103,
0.010897524654865265,
-0.0010353553807362914,
-0.046544406563043594,
0.05210419371724129,
-0.03311996906995773,
0.040665723383426666,
0.02204919420182705,
0.012024667114019394,
-0.003518624696880579,
-0.02672991342842579,
-0.04511431232094765,
-0.04843555763363838,
0.0203689131885767,
-0.03635625168681145,
0.020991072058677673,
0.02979229763150215,
0.0017020207596942782,
-0.029617073014378548,
-0.018359940499067307,
-0.009327067993581295,
0.005918810144066811,
0.010307862423360348,
0.01596726104617119,
-0.03432008624076843,
0.022187499329447746,
0.017139626666903496,
-0.038714103400707245,
0.018009359017014503,
0.0014824866084381938,
-0.006707441993057728,
-0.10137125849723816,
-0.06669490039348602,
-0.022602131590247154,
0.017864597961306572,
0.016568763181567192,
-0.026790477335453033,
-0.029063181951642036,
0.07002779096364975,
0.03855689987540245,
-0.030111808329820633,
0.03077854961156845,
0.0031696027144789696,
0.034753620624542236,
-0.04183005541563034,
0.003809048095718026,
-0.025663554668426514,
0.042339492589235306,
0.014689543284475803,
0.07787808775901794,
0.07897210121154785,
0.008730047382414341,
-0.035293105989694595,
0.012867992743849754,
0.015101844444870949,
-0.07743839919567108,
0.0226740799844265,
0.01936873234808445,
-0.0030769859440624714,
0.04015686362981796,
-0.046484120190143585,
-0.05914478376507759,
0.030432647094130516,
-0.03657328709959984,
-0.043254561722278595,
0.024592122063040733,
0.020255785435438156,
0.014743657782673836,
0.03002973087131977,
-0.049674130976200104,
-0.03978212550282478,
0.020394185557961464,
-0.08555660396814346,
-0.04058249294757843,
0.04222126305103302,
0.01783880405128002,
0.03253016993403435,
-0.035167187452316284,
0.003570044180378318,
-0.02556486427783966,
0.009612083435058594,
0.0037179288920015097,
-0.023693343624472618,
-0.09139762073755264,
0.025324204936623573,
-0.023715773597359657,
-0.025991380214691162,
-0.006937598809599876,
-0.059922341257333755,
0.0246344655752182,
-0.06060148775577545,
0.03592703863978386,
-0.04028273746371269,
0.05446247383952141,
-0.016199732199311256,
-0.03886062651872635,
0.03242221102118492,
0.014274593442678452,
0.011459829285740852,
-0.00387937412597239,
0.025621972978115082,
0.015450173988938332,
-0.13730573654174805,
-0.012155135162174702,
-0.03581476956605911,
0.045735713094472885,
-0.0047022197395563126,
0.0005328900879248977,
-0.023157712072134018,
0.03189219534397125,
0.05190885066986084,
0.0011726568918675184,
-0.022855114191770554,
0.030975915491580963,
-0.018004218116402626,
-0.009179795160889626,
0.0008827490382827818,
-0.027748242020606995,
-0.027261147275567055,
0.011515024118125439,
-0.012730528600513935,
-0.034034281969070435,
0.032878611236810684,
-0.017978155985474586,
-0.0228063203394413,
0.06792183965444565,
-0.0006472988752648234,
0.03603304550051689,
-0.015505209565162659,
-0.04048141837120056,
-0.03412685915827751,
-0.0042189923115074635,
0.012599516659975052,
0.027088496834039688,
-0.06137628108263016,
-0.009672116488218307,
-0.024427274242043495,
0.012334607541561127,
0.030581999570131302,
0.04667195677757263,
-0.082763671875,
0.044831532984972,
0.08178550750017166,
0.010462447069585323,
0.03449779748916626,
-0.00794538576155901,
0.00681149959564209,
-0.0021468012128025293,
0.016205206513404846,
-0.015043566934764385,
-0.028280237689614296,
0.010341907851397991,
-0.09136063605546951,
0.060623180121183395,
-0.001549665816128254,
-0.01663052663207054,
-0.007084400858730078,
-0.006195445545017719,
-0.08055365830659866,
0.006483235862106085,
-0.03751768544316292,
0.007861629128456116,
0.02225061133503914,
-0.05727202817797661,
-0.013045161962509155,
-0.0020200409926474094,
0.06468921899795532,
-0.004182958975434303,
-0.02398509718477726,
-0.021934431046247482,
-0.013861425220966339,
-0.03016809932887554,
-0.02029392123222351,
-0.05102839320898056,
0.050227683037519455,
0.04043053463101387,
0.05984250083565712,
0.01633995957672596,
0.0319778136909008,
-0.01768149621784687,
-0.004902257584035397,
0.023938670754432678,
0.003328691003844142,
-0.017162812873721123,
0.02584887482225895,
-0.04078536108136177,
0.013519017957150936,
0.07065540552139282,
0.07989921420812607,
-0.03909149393439293,
0.047952987253665924,
-0.019796116277575493,
0.01431590598076582,
0.025821633636951447,
0.030010053887963295,
-0.04099801182746887,
-0.011406960897147655,
0.0006685387343168259,
0.020729294046759605,
0.049796827137470245,
0.019146617501974106,
0.021205566823482513,
-0.008882181718945503,
0.011124828830361366,
-0.04953302815556526,
-0.028706679120659828,
0.0059295231476426125,
-0.0017628476489335299,
-0.01259753666818142,
0.00030397437512874603,
-0.02425599843263626,
-0.00970656517893076,
0.02619769610464573,
0.05189787596464157,
-0.029613817110657692,
-0.004795867949724197,
-0.062231387943029404,
-0.007452714256942272,
0.0036637885496020317,
-0.0008917071390897036,
-0.049809377640485764,
0.008560452610254288,
-0.015578186139464378,
-0.0006993650458753109,
-0.07254568487405777,
-0.02756226621568203,
-0.01891958899796009,
-0.010486222803592682,
-0.023771459236741066,
-0.004021919798105955,
-0.06015673279762268,
-0.021923409774899483,
-0.013247987255454063,
-0.04414019733667374,
0.0647626742720604,
-0.053013093769550323,
0.021071739494800568,
-0.01671191118657589,
-0.015313645824790001,
-0.0318867452442646,
0.04224023222923279,
-0.0085923345759511,
0.003012728411704302,
-0.013525499030947685,
0.007660092785954475,
0.015121803618967533,
0.009655406698584557,
-0.026929587125778198,
0.04249047860503197,
0.0639384463429451,
0.017891302704811096,
0.07727964222431183,
0.012807466089725494,
-0.013522543013095856,
-0.04500400274991989,
0.04321254789829254,
-0.03306431695818901,
0.03713614493608475,
-0.014396837912499905,
-0.024588538333773613,
0.006012461148202419,
-0.02705623023211956,
-0.044327717274427414,
-0.008124198764562607,
-0.03893797844648361,
0.041803739964962006,
0.03191396966576576,
0.04058273136615753,
-0.0082651162520051,
-0.024799032136797905,
0.06029944494366646,
-0.029945597052574158,
0.009222294203937054,
-0.008018746972084045,
0.007504501845687628,
0.0009050546213984489,
-0.014379417523741722,
-0.0025964316446334124,
-0.03519027680158615,
0.018072791397571564,
0.0186450332403183,
0.03371666371822357,
-0.0380956195294857,
-0.08012472838163376,
-0.007894179783761501,
0.050250910222530365,
-0.017324380576610565,
-0.06536208093166351,
-0.0022170909214764833,
-0.003987473901361227,
-0.015891404822468758,
0.012666638009250164,
0.020948616787791252,
0.0242006815969944,
0.05314779281616211,
0.07700711488723755,
0.005773574113845825,
0.07442308217287064,
0.0019388493383303285,
0.0008087267633527517,
0.05049328878521919,
0.008579098619520664,
0.010244801640510559,
-0.019643038511276245,
-0.0077058738097548485
] |
[
3.040630578994751,
3.4947004318237305
] |
Classical Analysis and ODEs
|
Mathematics
|
math-CA
|
math-FA
|
na
|
2007-03-31T04:24:59
|
We study the two-particle wave function of paired atoms in a Fermi gas with
tunable interaction strengths controlled by Feshbach resonance. The Cooper pair
wave function is examined for its bosonic characters, which is quantified by
the correction of Bose enhancement factor associated with the creation and
annihilation composite particle operators. An example is given for a
three-dimensional uniform gas. Two definitions of Cooper pair wave function are
examined. One of which is chosen to reflect the off-diagonal long range order
(ODLRO). Another one corresponds to a pair projection of a BCS state. On the
side with negative scattering length, we found that paired atoms described by
ODLRO are more bosonic than the pair projected definition. It is also found
that at $(k_F a)^{-1} \ge 1$, both definitions give similar results, where more
than 90% of the atoms occupy the corresponding molecular condensates.
|
Bosonic characters of atomic Cooper pairs across resonance
|
cond-mat.mes-hall
|
0704.0006
| 2,007
|
[
-0.02760763093829155,
0.02958712726831436,
0.008069992996752262,
-0.0634930208325386,
0.038603439927101135,
0.017274878919124603,
-0.04780140519142151,
0.025919824838638306,
-0.024942869320511818,
0.013578553684055805,
-0.06223686411976814,
0.052889615297317505,
0.0010470643173903227,
-0.02260270155966282,
0.03970351442694664,
-0.016518032178282738,
0.025128362700343132,
0.028090886771678925,
-0.006913019344210625,
0.00871628150343895,
0.0030039330013096333,
0.0028948429971933365,
-0.038201410323381424,
-0.023278379812836647,
0.07486919313669205,
-0.03042358160018921,
-0.005745632573962212,
-0.001162958680652082,
-0.048982128500938416,
0.025647412985563278,
0.06875003129243851,
-0.01473027840256691,
0.04255478084087372,
-0.01319038774818182,
0.005182888358831406,
-0.041936736553907394,
0.07558757811784744,
-0.005033587571233511,
0.011052420362830162,
0.012806346639990807,
0.02541118673980236,
-0.02719898149371147,
-0.02329891547560692,
-0.048715829849243164,
0.03784491494297981,
0.028231000527739525,
0.0033726529218256474,
0.005088876001536846,
0.00397311057895422,
-0.04353754594922066,
-0.02816927246749401,
0.026707591488957405,
0.0014540980337187648,
-0.013963596895337105,
0.01350383274257183,
0.04273520037531853,
-0.018312830477952957,
-0.04606981202960014,
0.038177136331796646,
0.002841204172000289,
0.0183480903506279,
0.020225439220666885,
0.013505262322723866,
0.01793818548321724,
0.06296143680810928,
-0.04413505271077156,
-0.033113423734903336,
0.06543929874897003,
0.0010474711889401078,
-0.0639805942773819,
0.04399574175477028,
-0.02273884415626526,
-0.015522204339504242,
0.040852393954992294,
-0.003599820425733924,
0.0010912999277934432,
-0.04631512612104416,
0.00314036151394248,
-0.0023021968081593513,
0.002895906800404191,
-0.013167286291718483,
-0.035557519644498825,
0.024554317817091942,
-0.04323600232601166,
0.028805647045373917,
-0.008666510693728924,
0.010783235542476177,
0.00538922194391489,
-0.044228099286556244,
0.060613907873630524,
0.012868172489106655,
-0.003367878496646881,
0.07670663297176361,
0.056700292974710464,
-0.03913721814751625,
0.017115645110607147,
-0.0013211948098614812,
0.02063690684735775,
0.0023636403493583202,
-0.0039153979159891605,
-0.0635622888803482,
0.10291092842817307,
0.025075344368815422,
-0.012318534776568413,
0.03399117663502693,
0.040433548390865326,
0.029053788632154465,
-0.018540361896157265,
-0.003143246751278639,
-0.03701015189290047,
-0.07218506187200546,
0.0007117201457731426,
0.016171108931303024,
-0.02258361503481865,
-0.01788150519132614,
-0.0379173718392849,
0.002513234270736575,
-0.07143864780664444,
-0.03251839801669121,
0.08142994344234467,
-0.011821652762591839,
-0.0019582186359912157,
0.016344305127859116,
-0.012381413020193577,
-0.024728983640670776,
-0.00021446470054797828,
-0.05626561492681503,
0.023716438561677933,
0.031133221462368965,
-0.03360588848590851,
-0.023564182221889496,
0.01306332740932703,
-0.018198341131210327,
-0.008572361432015896,
0.010710560716688633,
0.0048380023799836636,
-0.01333378255367279,
-0.0067473105154931545,
0.01601436361670494,
-0.010579025372862816,
0.018341489136219025,
-0.010496783070266247,
0.007751106284558773,
-0.06964297592639923,
0.025895699858665466,
-0.06244494020938873,
-0.015182062983512878,
-0.05993301048874855,
-0.06917893886566162,
0.011947465129196644,
0.04766048491001129,
0.007801548577845097,
0.016579309478402138,
0.04621437191963196,
-0.05978158861398697,
-0.053188931196928024,
0.024894211441278458,
0.0023366715759038925,
0.01716722548007965,
0.043756984174251556,
0.0004738134448416531,
0.05493967980146408,
-0.03742004930973053,
0.07204069942235947,
-0.032361287623643875,
0.02067217044532299,
0.09013908356428146,
-0.004516906104981899,
0.0065266950987279415,
0.07843166589736938,
-0.059600796550512314,
-0.0313262864947319,
-0.0696626678109169,
-0.030861126258969307,
0.0389888659119606,
0.04638579487800598,
0.014551373198628426,
-0.06900457292795181,
0.02599642053246498,
0.031546324491500854,
0.0634339451789856,
-0.0326496958732605,
-0.032469309866428375,
0.056376129388809204,
0.002857044106349349,
0.037244077771902084,
-0.00994832906872034,
-0.0066567836329340935,
-0.07820672541856766,
-0.014375907368957996,
0.007175522390753031,
0.023284314200282097,
-0.04177682474255562,
-0.08372678607702255,
0.00822044163942337,
-0.04737910255789757,
0.04581717401742935,
-0.001643971772864461,
0.04846685007214546,
-0.03469618782401085,
-0.06293122470378876,
0.02515672706067562,
-0.031372714787721634,
-0.0014196294359862804,
0.027141056954860687,
0.02220464125275612,
0.030092865228652954,
0.01133659202605486,
0.002923466032370925,
-0.01665446162223816,
0.004258651286363602,
0.0169705580919981,
0.0036238846369087696,
0.02012295089662075,
0.0021933424286544323,
0.00477987015619874,
-0.004283880814909935,
-0.032573167234659195,
-0.06225889176130295,
0.049431003630161285,
0.03989061340689659,
0.007809501141309738,
-0.002002008492127061,
0.021795332431793213,
0.025621743872761726,
-0.030203692615032196,
-0.0001739214640110731,
-0.02360120229423046,
-0.06341968476772308,
0.0275387242436409,
-0.037163473665714264,
0.0009850951610133052,
0.043752528727054596,
-0.010373317636549473,
-0.041356030851602554,
0.022819992154836655,
0.006442925427109003,
0.03162052482366562,
0.05229758843779564,
0.0900544747710228,
0.03141061216592789,
-0.020082106813788414,
-0.0441584475338459,
0.030980629846453667,
-0.05301254615187645,
0.0029508695006370544,
-0.025041766464710236,
-0.021034574136137962,
0.004436589311808348,
-0.004576020408421755,
0.024405157193541527,
-0.0016301509458571672,
-0.015761859714984894,
0.0042304000817239285,
0.031224237754940987,
-0.027673760429024696,
-0.0553799569606781,
0.04791434481739998,
-0.03255971521139145,
-0.10378165543079376,
0.05417574197053909,
-0.04129871726036072,
0.012576506473124027,
-0.02940712496638298,
-0.0363273024559021,
0.000552707992028445,
0.023533476516604424,
-0.023823602125048637,
-0.015316378325223923,
-0.004372850526124239,
-0.00023115855583455414,
0.07754035294055939,
0.04996436461806297,
0.007515902630984783,
-0.01961689442396164,
0.001975448802113533,
0.019236307591199875,
-0.028807250782847404,
0.001342211733572185,
0.0001337092398898676,
-0.08311209827661514,
0.018402576446533203,
-0.04610670730471611,
0.015239640139043331,
-0.012813027948141098,
0.01670745201408863,
0.031038900837302208,
0.03151583671569824,
0.03116282820701599,
0.02878343127667904,
-0.03805945813655853,
0.0014334717998281121,
0.013432600535452366,
0.11432527005672455,
0.01745220646262169,
0.0435461588203907,
0.07810481637716293,
-0.021620173007249832,
-0.01048939861357212,
0.025387203320860863,
0.01409303117543459,
-0.05415290966629982,
-0.005427448078989983,
0.020422369241714478,
0.005724360700696707,
-0.013862050138413906,
-0.01996465027332306,
0.03705918788909912,
-0.01607181318104267,
0.0017472170293331146,
0.01629479229450226,
0.034751929342746735,
0.0055461605079472065,
-0.00590768177062273,
-0.033512044697999954,
0.044506803154945374,
0.03825519233942032,
0.00467642629519105,
0.0682930275797844,
-0.029012924060225487,
0.027307679876685143,
-0.024237029254436493,
0.01467412430793047,
-0.07816579192876816,
0.01548315491527319,
0.035606786608695984,
0.006383288186043501,
0.005467168055474758,
-0.013450685888528824,
-0.013027203269302845,
-0.008141553960740566,
0.004326928872615099,
-0.015644697472453117,
-0.030103055760264397,
-0.061404671519994736,
-0.03789250925183296,
-0.0007869293913245201,
0.019118858501315117,
-0.003948755096644163,
0.018652956932783127,
0.0291435644030571,
-0.02337331511080265,
-0.020768562331795692,
-0.013244963251054287,
-0.012006249278783798,
0.011229121126234531,
-0.041536472737789154,
-0.003519279882311821,
0.0845373272895813,
-0.03166734427213669,
-0.06897380203008652,
0.016288811340928078,
0.06461585313081741,
0.012242957949638367,
-0.02114471234381199,
-0.002597019774839282,
0.11501305550336838,
-0.014832808636128902,
0.05853186920285225,
0.006337877828627825,
0.03303287923336029,
-0.050433725118637085,
0.021921971812844276,
0.005731640383601189,
0.008441480807960033,
-0.038505762815475464,
0.0042031737975776196,
0.026727911084890366,
0.030637221410870552,
-0.03690135106444359,
-0.12142152339220047,
-0.053417716175317764,
0.06095089763402939,
-0.0004297610721550882,
0.055307164788246155,
-0.05881653353571892,
-0.06385673582553864,
-0.027125580236315727,
-0.007505394984036684,
-0.004999063443392515,
0.022744467481970787,
0.03036556765437126,
0.07587707042694092,
0.01371085550636053,
0.013093670830130577,
-0.0076605090871453285,
-0.04376750811934471,
0.004429046995937824,
-0.015281490981578827,
-0.019516721367836,
-0.03303654491901398,
-0.028850676491856575,
-0.03218111768364906,
0.019542735069990158,
0.01270595844835043,
0.007761519402265549,
0.03395182639360428,
-0.0010645304573699832,
-0.008644454181194305,
0.02461078204214573,
-0.08456951379776001,
-0.10422665625810623,
-0.021931342780590057,
-0.02669895999133587,
-0.007004702463746071,
-0.017531445249915123,
0.007494563236832619,
-0.038542069494724274,
0.020183520391583443,
-0.003645342541858554,
0.007027268875390291,
0.028542030602693558,
-0.030873959884047508,
-0.05834966152906418,
0.04703587293624878,
-0.0075112455524504185,
-0.0007127767312340438,
0.013998466543853283,
0.013364935293793678,
0.00851963460445404,
-0.015072889626026154,
0.05088844150304794,
0.04400111362338066,
0.022998498752713203,
-0.01489183958619833,
-0.005405621137470007,
-0.003635284723713994,
0.046810075640678406,
-0.0061995903961360455,
-0.04353126883506775,
0.023972859606146812,
0.017447752878069878,
-0.008303810842335224,
0.04041897505521774,
-0.044245753437280655,
0.02054889127612114,
-0.014020751230418682,
-0.04363865777850151,
0.05296983942389488,
0.09217587858438492,
0.018043871968984604,
-0.042420919984579086,
-0.023807521909475327,
0.021632160991430283,
0.0783882737159729,
0.055305205285549164,
0.027888096868991852,
-0.01761542074382305,
-0.046430449932813644,
-0.04662405699491501,
0.04853038862347603,
0.01180958654731512,
-0.01573803648352623,
0.005328026134520769,
0.053351785987615585,
-0.01591600850224495,
-0.03021722286939621,
0.006175686605274677,
0.030697735026478767,
0.0038728935178369284,
-0.047891054302453995,
0.04655032232403755,
-0.03343721106648445,
-0.016144290566444397,
-0.010012493468821049,
0.02566969208419323,
0.004438819829374552,
-0.015617343597114086,
-0.01816963590681553,
0.046453073620796204,
-0.012900699861347675,
-0.04472263529896736,
0.050810493528842926,
-0.017132563516497612,
0.009273804724216461,
-0.05207917466759682,
0.012546905316412449,
-0.055862896144390106,
0.008764867670834064,
0.024579651653766632,
0.06515885889530182,
-0.015837470069527626,
0.025793910026550293,
-0.04369645193219185,
-0.05754551663994789,
0.019131528213620186,
-0.014803561381995678,
0.020531706511974335,
-0.02090856060385704,
-0.017542267218232155,
0.023612823337316513,
0.050980497151613235,
0.015065737068653107,
0.0062391445972025394,
-0.020720068365335464,
-0.008961762301623821,
-0.0614001601934433,
-0.031800247728824615,
-0.016637781634926796,
0.009451243095099926,
-0.06275127828121185,
0.005400873254984617,
0.0403778962790966,
0.01132305059581995,
-0.042961787432432175,
0.04058053717017174,
-0.004962354898452759,
-0.04362020269036293,
-0.005430057179182768,
-0.004307396709918976,
-0.019364245235919952,
0.0361369289457798,
0.048530299216508865,
0.018578853458166122,
-0.0030107286293059587,
-0.030178816989064217,
0.031736742705106735,
0.007942636497318745,
-0.11476253718137741,
0.005149951204657555,
0.038836732506752014,
0.041370633989572525,
0.007839616388082504,
0.010675971396267414,
-0.0724840834736824,
0.049081504344940186,
0.0030836663208901882,
-0.034345824271440506,
0.029885295778512955,
0.016793804243206978,
-0.01532003190368414,
0.005896644666790962,
0.032954439520835876,
0.012766591273248196,
0.05340885743498802,
-0.03882928937673569,
-0.021261872723698616,
0.03412279859185219,
-0.017185715958476067,
0.036614272743463516,
0.01305784285068512,
-0.0086306631565094,
-0.011777175590395927,
0.010764568112790585,
-0.0049912105314433575,
-0.02072915993630886,
-0.07885777205228806,
0.034423962235450745,
-0.005507369060069323,
-0.03917767107486725,
0.000601020990870893,
-0.047225382179021835,
0.019018033519387245,
-0.06133952736854553,
0.08688652515411377,
-0.04475168511271477,
0.010252801701426506,
0.007080612238496542,
-0.022171292454004288,
0.023246532306075096,
-0.027926508337259293,
-0.02326163835823536,
0.07288986444473267,
0.0023113146889954805,
0.058756276965141296,
-0.0751626193523407,
-0.07329130172729492,
0.03392701596021652,
-0.016606997698545456,
0.0157313235104084,
-0.0013672468485310674,
-0.060917071998119354,
-0.03856825456023216,
0.015137221664190292,
0.0252832118421793,
-0.008743943646550179,
0.02115405537188053,
-0.031420089304447174,
-0.03472891449928284,
-0.014069661498069763,
-0.028405219316482544,
-0.014661802910268307,
-0.040622930973768234,
-0.01053537242114544,
-0.035553984344005585,
0.06674391031265259,
-0.012982700951397419,
-0.002491266466677189,
0.09196408092975616,
0.002244309289380908,
-0.03870144858956337,
-0.046057045459747314,
-0.001982651650905609,
-0.029724547639489174,
-0.030813798308372498,
-0.04343249276280403,
0.0033658810425549746,
0.017990821972489357,
-0.06209961697459221,
-0.03775011748075485,
0.025458799675107002,
0.035226549953222275,
0.053961124271154404,
0.03509141132235527,
0.043794333934783936,
0.04203077033162117,
0.008852058090269566,
0.025211360305547714,
-0.039955709129571915,
0.03334502875804901,
-0.026034193113446236,
-0.013161740265786648,
-0.012606953270733356,
-0.04233070835471153,
0.04133215919137001,
-0.024630196392536163,
0.08142626285552979,
0.005069642327725887,
0.0034615579061210155,
0.010892011225223541,
0.028219642117619514,
-0.08454685658216476,
0.012385673820972443,
-0.07854615896940231,
0.008516666479408741,
0.00797424465417862,
-0.03433072194457054,
-0.022006556391716003,
0.03359132260084152,
0.06163637712597847,
0.017471391707658768,
-0.011948594823479652,
0.01747511886060238,
0.0016578194918110967,
-0.0318143293261528,
0.04659827798604965,
-0.04976410046219826,
0.046976134181022644,
0.013108964078128338,
0.03293726593255997,
-0.02673512138426304,
-0.03592049703001976,
0.02476152963936329,
0.007079644128680229,
-0.02788347192108631,
0.032415736466646194,
0.02646666206419468,
0.0033691534772515297,
-0.042787473648786545,
0.0009942806791514158,
0.050153009593486786,
0.02426660619676113,
-0.004580080509185791,
0.0697953924536705,
-0.0034601811785250902,
-0.017975319176912308,
0.020332034677267075,
-0.004606069531291723,
-0.0016937174368649721,
-0.016173597425222397,
-0.01786479540169239,
-0.03791556879878044,
-0.01812269352376461,
-0.03763195872306824,
0.04085882008075714,
0.03826563432812691,
-0.007602530997246504,
-0.07571786642074585,
-0.036069951951503754,
-0.0018895282410085201,
-0.02906225062906742,
-0.0684863030910492,
-0.05441063269972801,
-0.04188026487827301,
-0.01464184932410717,
-0.004211493767797947,
0.009900134056806564,
0.04242831468582153,
0.016852974891662598,
-0.029706822708249092,
0.02445545233786106,
0.012184282764792442,
0.021672746166586876,
-0.03729306906461716,
-0.005061495583504438,
-0.004542114213109016,
-0.004708611872047186,
-0.010726715438067913,
-0.029253091663122177,
-0.08614742010831833,
0.01839933544397354,
-0.0218665674328804,
0.013284825719892979,
-0.049927543848752975,
-0.00560397794470191,
-0.004783774260431528,
-0.009345798753201962,
0.0035989664029330015,
0.024728691205382347,
0.04900633171200752,
0.015028455294668674,
0.004970658104866743,
-0.04064975678920746,
0.030281657353043556,
0.042458243668079376,
-0.020916271954774857,
0.035650089383125305,
-0.018449801951646805,
-0.002313832985237241,
-0.019863247871398926,
-0.0009062854805961251,
0.0010528285056352615,
0.08217813819646835,
0.026277709752321243,
0.06322935223579407,
-0.01781310699880123,
0.02560485526919365,
-0.00965198315680027,
0.028874393552541733,
-0.004987518768757582,
0.0563349723815918,
-0.01796233095228672,
-0.01671764999628067,
0.03929825499653816,
-0.06149866804480553,
-0.03817402943968773,
-0.01124816294759512,
0.027856551110744476,
0.06255263835191727,
0.037366125732660294,
-0.002189773367717862,
0.0058157057501375675,
-0.044813044369220734,
-0.000292890181299299,
-0.02366892248392105,
0.03031611070036888,
-0.02807222120463848,
0.06584838032722473,
-0.05837548151612282,
0.040337853133678436,
0.026128994300961494,
-0.0478416308760643,
0.03995378687977791,
-0.012726584449410439,
-0.021809354424476624,
-0.03564012050628662,
-0.06875891238451004,
-0.031131470575928688,
0.05967829376459122,
0.020354295149445534,
-0.02290879562497139,
-0.025502394884824753,
-0.006588637363165617,
-0.010742108337581158,
0.029310988262295723,
-0.0008529974729754031,
0.030014723539352417,
0.050148118287324905,
0.04538256302475929,
-0.024964608252048492,
0.025921320542693138,
0.025712991133332253,
0.029265234246850014,
0.02270074561238289,
0.005224548280239105,
0.02601495012640953,
-0.0488552525639534,
0.060315947979688644
] |
[
8.281129837036133,
-1.0779949426651
] |
Mesoscale and Nanoscale Physics
|
Condensed-Matter Physics
|
cond-mat-mes-hall
|
na
|
na
|
2007-03-31T04:27:22
|
A rather non-standard quantum representation of the canonical commutation
relations of quantum mechanics systems, known as the polymer representation has
gained some attention in recent years, due to its possible relation with Planck
scale physics. In particular, this approach has been followed in a symmetric
sector of loop quantum gravity known as loop quantum cosmology. Here we explore
different aspects of the relation between the ordinary Schroedinger theory and
the polymer description. The paper has two parts. In the first one, we derive
the polymer quantum mechanics starting from the ordinary Schroedinger theory
and show that the polymer description arises as an appropriate limit. In the
second part we consider the continuum limit of this theory, namely, the reverse
process in which one starts from the discrete theory and tries to recover back
the ordinary Schroedinger quantum mechanics. We consider several examples of
interest, including the harmonic oscillator, the free particle and a simple
cosmological model.
|
Polymer Quantum Mechanics and its Continuum Limit
|
gr-qc
|
0704.0007
| 2,007
|
[
-0.024828244000673294,
0.020031359046697617,
-0.0007429752731695771,
-0.06428448855876923,
0.01591009832918644,
0.02814851701259613,
-0.0382349006831646,
0.02610725536942482,
0.007408252917230129,
0.000056818251323420554,
-0.02181152068078518,
0.011815229430794716,
0.012188143096864223,
-0.01707819662988186,
0.005003669764846563,
-0.019144242629408836,
0.03229834511876106,
0.014850138686597347,
0.0189109705388546,
0.009132438339293003,
-0.06907898187637329,
-0.02213474176824093,
-0.002024843590334058,
-0.0594489611685276,
0.060075052082538605,
-0.010654963552951813,
0.01598423346877098,
0.00846459437161684,
-0.0477079413831234,
0.01888536475598812,
0.03990447521209717,
-0.03454647958278656,
0.04031279683113098,
-0.03772496432065964,
-0.01383945345878601,
-0.02705319970846176,
0.06941333413124084,
0.006493754219263792,
-0.0060937246307730675,
0.048916444182395935,
0.013680539093911648,
-0.05577385425567627,
0.0038808216340839863,
-0.012062731198966503,
0.0123725151643157,
-0.0049603162333369255,
0.03779749944806099,
0.02663431130349636,
0.02737315371632576,
-0.011367805302143097,
0.004684665706008673,
0.04609732702374458,
-0.025616465136408806,
-0.01829315535724163,
0.008954454213380814,
-0.0007232493371702731,
0.03890515863895416,
-0.03280782699584961,
0.0650046244263649,
-0.030265364795923233,
-0.02269970439374447,
0.03438359871506691,
0.02066887356340885,
0.053428687155246735,
0.02143769897520542,
-0.027483955025672913,
-0.01251626294106245,
0.01116222608834505,
-0.03066263534128666,
-0.0277098398655653,
0.08309664577245712,
-0.0749070942401886,
0.02472730353474617,
0.04351859539747238,
-0.003864513011649251,
0.06997121870517731,
-0.009366205893456936,
-0.02256116271018982,
0.010490664280951023,
0.01442213449627161,
-0.04310368373990059,
-0.02825872227549553,
0.024082278832793236,
0.021257201209664345,
0.1042034700512886,
0.01016577985137701,
0.006611091550439596,
0.002583203837275505,
-0.06314381957054138,
0.05260177701711655,
0.009401220828294754,
-0.04037269204854965,
0.033126428723335266,
0.020061874762177467,
-0.036043647676706314,
-0.011508593335747719,
-0.0435950830578804,
0.03836148604750633,
-0.046696774661540985,
-0.005938160233199596,
-0.04056679457426071,
0.050339940935373306,
0.07321703433990479,
-0.01692473329603672,
0.060187093913555145,
0.04451940953731537,
0.03650406002998352,
-0.018188800662755966,
0.0011879862286150455,
-0.05786076933145523,
-0.06757368892431259,
-0.0289006344974041,
-0.031661760061979294,
-0.031392235308885574,
-0.030576331540942192,
-0.018668483942747116,
0.06727825105190277,
-0.054735664278268814,
0.059253908693790436,
0.08266273140907288,
-0.003952972125262022,
0.005053654778748751,
0.015733078122138977,
0.06952780485153198,
-0.031167689710855484,
0.0038934126496315002,
-0.037335123866796494,
-0.023207437247037888,
0.03526804596185684,
-0.03148902207612991,
0.0223498847335577,
0.0024142777547240257,
-0.05680784583091736,
-0.000418473151512444,
0.014972977340221405,
-0.028979625552892685,
-0.05518099665641785,
-0.05532056838274002,
0.07633260637521744,
0.025474542751908302,
0.010109130293130875,
-0.030870845541357994,
0.014911776408553123,
-0.001924840616993606,
0.015472943894565105,
-0.07098951935768127,
0.029010873287916183,
-0.06908048689365387,
-0.021154792979359627,
-0.04727858304977417,
0.015722360461950302,
0.050763845443725586,
0.006006691604852676,
0.029843876138329506,
-0.021966958418488503,
-0.025841789320111275,
-0.007179348263889551,
0.04618878290057182,
0.04827781394124031,
-0.010212878696620464,
0.013536258600652218,
-0.006197250913828611,
-0.0135479886084795,
0.04159563034772873,
-0.056401289999485016,
0.04986703023314476,
-0.016970502212643623,
0.0029251885134726763,
-0.024167055264115334,
0.007872880436480045,
-0.00402116309851408,
-0.029378531500697136,
-0.056199509650468826,
-0.005935055669397116,
-0.018832668662071228,
0.03738415613770485,
0.004744923207908869,
-0.07527925074100494,
-0.00677581038326025,
-0.023909568786621094,
0.055368173867464066,
-0.022048620507121086,
0.020069332793354988,
0.08493571728467941,
0.008648172952234745,
0.07703607529401779,
0.024698225781321526,
-0.0028919153846800327,
-0.012837005779147148,
-0.04150178283452988,
-0.03626706078648567,
0.058262042701244354,
0.001977745443582535,
-0.03290342167019844,
-0.011499917134642601,
-0.053192559629678726,
0.05863606184720993,
-0.03823970630764961,
-0.012390331365168095,
-0.09619969874620438,
-0.004614576231688261,
-0.004478215705603361,
-0.03786382079124451,
-0.019251380115747452,
0.004375325981527567,
0.052089884877204895,
0.03941594809293747,
0.03736235201358795,
0.00295736500993371,
-0.018431276082992554,
0.06986690312623978,
0.011452860198915005,
-0.003814352210611105,
0.024248916655778885,
-0.021093057468533516,
-0.002634689910337329,
0.043162181973457336,
-0.029756342992186546,
-0.05609869956970215,
0.04364706575870514,
0.06833308190107346,
-0.012462982907891273,
0.039888959378004074,
0.00204574060626328,
0.015561478212475777,
0.053106386214494705,
-0.015603558160364628,
-0.013471271842718124,
-0.04014699533581734,
0.009337326511740685,
-0.052879977971315384,
-0.07852805405855179,
-0.024542639032006264,
0.012679924257099628,
-0.0024052367080003023,
0.0265567097812891,
-0.013432842679321766,
-0.001008655410259962,
0.014473894611001015,
0.000005432227681012591,
0.044087447226047516,
0.03643623739480972,
0.005224954802542925,
-0.009434038773179054,
-0.0466645173728466,
-0.02259586565196514,
-0.022387133911252022,
-0.01917077787220478,
-0.0071087987162172794,
0.02793966606259346,
0.09566012024879456,
-0.019379546865820885,
0.015551317483186722,
0.012037443928420544,
0.055672869086265564,
-0.021328475326299667,
0.023262055590748787,
0.08791539072990417,
-0.01906876638531685,
-0.054510343819856644,
0.05603519082069397,
-0.05646347627043724,
-0.023863596841692924,
0.0059097507037222385,
-0.04839756339788437,
-0.021643584594130516,
0.01713360659778118,
-0.033756088465452194,
-0.04904255270957947,
-0.02953767217695713,
0.01986795850098133,
0.054718345403671265,
0.005472562275826931,
0.03087749145925045,
-0.03075960837304592,
0.03127525374293327,
0.07246491312980652,
-0.0514151006937027,
-0.010988862253725529,
-0.031447287648916245,
-0.03133198246359825,
-0.011380848474800587,
-0.04983634874224663,
-0.021730929613113403,
-0.0015288280555978417,
-0.031799428164958954,
0.006494036875665188,
-0.04291866347193718,
0.05022972449660301,
0.03351692855358124,
-0.03342393413186073,
0.03710183501243591,
0.008390308357775211,
0.0666303038597107,
-0.006420005112886429,
0.09019899368286133,
0.06878968328237534,
-0.028318924829363823,
-0.010845566168427467,
0.06011544167995453,
-0.011902747675776482,
-0.06113974004983902,
0.02223781868815422,
0.03114866092801094,
0.03465595841407776,
-0.009732379578053951,
0.02603364922106266,
0.03837721422314644,
0.06824111193418503,
0.004532076884061098,
0.0024894909001886845,
0.059057340025901794,
0.01776609942317009,
0.0017377880867570639,
-0.030787812545895576,
0.025568243116140366,
0.016614099964499474,
0.0018263846868649125,
0.04158731549978256,
-0.022142162546515465,
0.02664189226925373,
-0.03762299194931984,
-0.004020383581519127,
-0.0017447533318772912,
0.013708291575312614,
0.05054609850049019,
-0.0476883128285408,
-0.009035409428179264,
-0.008948029018938541,
-0.0169515423476696,
0.009522421285510063,
0.05897648259997368,
0.00482900207862258,
-0.012325398623943329,
-0.04990610107779503,
-0.02409166842699051,
-0.05182640627026558,
0.005661853589117527,
-0.0020009379368275404,
-0.021210791543126106,
-0.036197103559970856,
-0.057412609457969666,
-0.003282210323959589,
-0.013004348613321781,
-0.0017010002629831433,
0.006159469485282898,
-0.052763473242521286,
0.0009646516991779208,
0.057296786457300186,
-0.02912118285894394,
-0.03852067515254021,
-0.03360685333609581,
0.0464463084936142,
0.009854983538389206,
-0.04430967569351196,
0.06476597487926483,
0.07571485638618469,
-0.005720589309930801,
0.04349037632346153,
0.022556455805897713,
0.02113410457968712,
-0.05617435649037361,
0.04325547814369202,
0.013247108086943626,
0.052926499396562576,
0.04185061901807785,
0.012046517804265022,
0.015577682293951511,
0.028450842946767807,
-0.09195870161056519,
-0.051302261650562286,
-0.04514465853571892,
0.008691597729921341,
0.05319040268659592,
0.020775634795427322,
0.0011744890362024307,
-0.05500809848308563,
0.008437056094408035,
-0.03617480769753456,
0.0023414900060743093,
0.07501610368490219,
-0.021371282637119293,
0.006904771085828543,
0.022777283564209938,
0.04877803102135658,
-0.0011706232326105237,
-0.05230899527668953,
-0.00333144748583436,
-0.02873055450618267,
-0.0200263150036335,
0.02802039124071598,
-0.059811290353536606,
-0.007127860561013222,
0.039629895240068436,
0.009544722735881805,
0.000249806180363521,
0.030416449531912804,
0.026598112657666206,
0.017681775614619255,
-0.023265184834599495,
-0.04187185317277908,
-0.05609757453203201,
-0.014900720678269863,
-0.016862064599990845,
0.021621176972985268,
0.01749795489013195,
-0.02546086348593235,
-0.06999364495277405,
0.022541668266057968,
-0.02284557931125164,
0.007549192290753126,
0.04616181552410126,
-0.006071863695979118,
-0.0549439936876297,
0.018633516505360603,
0.01993987150490284,
0.08284296840429306,
-0.04529327526688576,
0.00637018121778965,
-0.01015517394989729,
-0.013211195357143879,
0.024731488898396492,
-0.0041998219676315784,
0.00832627434283495,
-0.01969185844063759,
0.00930234044790268,
-0.050483670085668564,
0.02065565064549446,
-0.020999886095523834,
-0.1146637350320816,
0.013476741500198841,
0.028497038409113884,
-0.0008576832478865981,
0.04726139456033707,
-0.06584829837083817,
0.030617058277130127,
0.04841150343418121,
-0.009684265591204166,
-0.05223342031240463,
-0.0005700277397409081,
0.07562632858753204,
-0.03940898925065994,
0.01297694817185402,
-0.0075321076437830925,
0.0017335762968286872,
0.07367178797721863,
0.032866496592760086,
-0.032482996582984924,
-0.0504755973815918,
-0.06654442846775055,
0.04791552200913429,
-0.023156624287366867,
0.01569344475865364,
0.006283999420702457,
0.03495407477021217,
-0.04221966862678528,
-0.016567958518862724,
-0.008848725818097591,
0.03146645426750183,
0.07790320366621017,
-0.03661899268627167,
0.013157889246940613,
-0.03175635263323784,
0.003648024285212159,
0.014568831771612167,
0.0356697179377079,
-0.033876270055770874,
0.040761642158031464,
-0.011455172672867775,
0.037052400410175323,
0.018426531925797462,
0.017610356211662292,
0.010061313398182392,
0.03506789356470108,
-0.052794162184000015,
-0.00653071841225028,
0.01326580997556448,
-0.040842004120349884,
-0.04877268150448799,
-0.01236048899590969,
0.012687656097114086,
-0.030828319489955902,
-0.03617344796657562,
-0.0016040251357480884,
-0.017307382076978683,
0.060510315001010895,
0.0038446399848908186,
0.030530909076333046,
0.01342759933322668,
0.018959548324346542,
0.006942471023648977,
0.03263581544160843,
0.03163924068212509,
0.020093869417905807,
-0.03266977146267891,
0.011615634895861149,
0.013423293828964233,
0.0032301582396030426,
0.019472621381282806,
-0.041034240275621414,
-0.01688837632536888,
0.04618470370769501,
0.04672679305076599,
0.007833111099898815,
-0.019646288827061653,
0.037930894643068314,
-0.02573246881365776,
-0.016934096813201904,
-0.016004422679543495,
0.025813182815909386,
0.020677350461483,
0.03201986104249954,
0.0049978336319327354,
0.09097279608249664,
0.039192620664834976,
-0.03414905071258545,
-0.004332071170210838,
-0.05157850310206413,
-0.02201814576983452,
-0.017399128526449203,
-0.019091736525297165,
0.028666598722338676,
0.015868689864873886,
-0.03393574804067612,
-0.03271758183836937,
0.026043320074677467,
-0.040929459035396576,
-0.04427795857191086,
0.039725374430418015,
0.004869184456765652,
0.06012438237667084,
0.029724108055233955,
0.011661932803690434,
-0.03229936212301254,
0.03164524957537651,
-0.02011888101696968,
-0.044994860887527466,
0.08942008018493652,
0.019439924508333206,
0.0408007875084877,
-0.014242002740502357,
0.02201419696211815,
0.03378165885806084,
0.012284672819077969,
0.03917696326971054,
-0.03532646596431732,
-0.05298222228884697,
0.011101128533482552,
-0.0021777674555778503,
-0.016399089246988297,
-0.05689065530896187,
-0.05766468867659569,
0.027065671980381012,
-0.05904044583439827,
0.003996697720140219,
-0.0142903383821249,
-0.015904385596513748,
-0.04143835976719856,
-0.03581556677818298,
0.05877533182501793,
-0.012886708602309227,
0.020097041502594948,
0.062456164509058,
-0.001919539994560182,
-0.01818171516060829,
-0.03418542817234993,
-0.01233629323542118,
-0.016361545771360397,
0.051717907190322876,
0.011956313624978065,
0.019772345200181007,
-0.04835543408989906,
0.023386534303426743,
0.05374496802687645,
0.0037410901859402657,
-0.02846008725464344,
0.0278245247900486,
-0.06023712828755379,
-0.05786452814936638,
-0.019498467445373535,
-0.051917217671871185,
-0.056410592049360275,
0.004001985304057598,
-0.028530826792120934,
-0.03338202089071274,
0.04337308555841446,
-0.006936613470315933,
-0.09068574011325836,
0.027113482356071472,
0.01659785956144333,
-0.0033092712983489037,
0.02266746386885643,
-0.007174383383244276,
-0.017217343673110008,
0.008868156000971794,
-0.02625161036849022,
0.024558620527386665,
-0.04490252584218979,
-0.046013496816158295,
-0.0393514484167099,
-0.01530645601451397,
-0.021419767290353775,
0.04817163199186325,
-0.036923713982105255,
0.05719476193189621,
0.06616804748773575,
-0.03030320629477501,
0.07260719686746597,
0.013075816445052624,
-0.004978647455573082,
0.018213490024209023,
-0.021993029862642288,
-0.02630455046892166,
-0.022345442324876785,
0.02024839073419571,
-0.01782226748764515,
0.07544516026973724,
0.028281953185796738,
0.041649229824543,
0.004296332597732544,
0.025877274572849274,
-0.03893082216382027,
0.00840036105364561,
-0.04441448301076889,
0.00619187206029892,
0.0023511480540037155,
-0.013888728804886341,
0.0006881709559820592,
0.06730423867702484,
0.04810208082199097,
0.005407705437391996,
-0.055401138961315155,
-0.03358227387070656,
0.05064120143651962,
-0.003561929566785693,
0.03773015737533569,
-0.09767460823059082,
0.008153826929628849,
-0.023884540423750877,
0.03732937574386597,
0.04513130336999893,
-0.05728890374302864,
0.016667073592543602,
0.0160203967243433,
0.013721664436161518,
0.02427767962217331,
0.029668008908629417,
0.02350713685154915,
-0.052358318120241165,
-0.01048940047621727,
0.06259452551603317,
0.05764393135905266,
-0.0483703538775444,
0.026613740250468254,
0.005857166834175587,
0.00010222823766525835,
0.06024683266878128,
0.022060832008719444,
-0.024426454678177834,
-0.025351805612444878,
-0.01705663464963436,
-0.033394478261470795,
-0.01634197123348713,
-0.03977712616324425,
-0.0006396894459612668,
-0.001631826744414866,
0.021611418575048447,
-0.037235699594020844,
-0.03513547033071518,
0.04610692709684372,
-0.0011426924029365182,
-0.05176141858100891,
-0.0271807461977005,
-0.03974564000964165,
-0.024112600833177567,
-0.02825169637799263,
0.014113817363977432,
0.06913720816373825,
-0.03371073678135872,
-0.04186607152223587,
-0.015064994804561138,
0.02311328798532486,
0.009208349511027336,
0.00726202130317688,
-0.02341155894100666,
0.011495836079120636,
0.03093566559255123,
0.009052475914359093,
-0.030732376500964165,
-0.03539910167455673,
0.006027162540704012,
0.007457612082362175,
0.004408948123455048,
-0.056290674954652786,
0.06853380799293518,
0.017270319163799286,
-0.05798054486513138,
0.0029778946191072464,
0.012652621604502201,
0.04329919442534447,
-0.0043884036131203175,
0.002123089274391532,
-0.06300003826618195,
0.009521865285933018,
-0.02163882926106453,
0.008269687183201313,
0.007777485530823469,
-0.01838437095284462,
-0.012541784904897213,
-0.01690838858485222,
-0.05087798088788986,
-0.01167475339025259,
0.019635315984487534,
0.027356160804629326,
0.05003446340560913,
-0.003488038433715701,
-0.016129709780216217,
-0.04683297872543335,
-0.009417233057320118,
-0.02639363333582878,
0.02815391682088375,
0.010982207953929901,
-0.033649545162916183,
-0.024577757343649864,
-0.05970239266753197,
-0.055959831923246384,
-0.025512835010886192,
-0.05204180255532265,
0.014406176283955574,
0.0011224999325349927,
-0.014274723827838898,
0.01883745566010475,
-0.02377060241997242,
-0.0021757115609943867,
-0.05907739698886871,
0.03493437170982361,
-0.024127565324306488,
-0.0153087442740798,
-0.04269149526953697,
-0.016139913350343704,
0.01008162647485733,
-0.05677402392029762,
0.0507655143737793,
0.015805618837475777,
0.02036895602941513,
-0.030973346903920174,
-0.06192484870553017,
0.0051317657344043255,
0.09322920441627502,
-0.011548603884875774,
-0.014913711696863174,
-0.015366061590611935,
-0.019553670659661293,
0.01491913478821516,
0.02362767420709133,
0.017876042053103447,
-0.017858261242508888,
0.01842443458735943,
0.032800693064928055,
-0.051831185817718506,
0.012892983853816986,
0.01776285469532013,
0.009469924494624138,
0.029574986547231674,
-0.00857454165816307,
-0.0024149564560502768,
-0.04827437177300453,
0.025554651394486427
] |
[
12.121484756469727,
1.6009249687194824
] |
General Relativity and Quantum Cosmology
|
General Physics
|
gr-qc
|
na
|
na
|
2007-03-31T04:47:20
|
A general formulation was developed to represent material models for
applications in dynamic loading. Numerical methods were devised to calculate
response to shock and ramp compression, and ramp decompression, generalizing
previous solutions for scalar equations of state. The numerical methods were
found to be flexible and robust, and matched analytic results to a high
accuracy. The basic ramp and shock solution methods were coupled to solve for
composite deformation paths, such as shock-induced impacts, and shock
interactions with a planar interface between different materials. These
calculations capture much of the physics of typical material dynamics
experiments, without requiring spatially-resolving simulations. Example
calculations were made of loading histories in metals, illustrating the effects
of plastic work on the temperatures induced in quasi-isentropic and
shock-release experiments, and the effect of a phase transition.
|
Numerical solution of shock and ramp compression for general material
properties
|
cond-mat.mtrl-sci
|
0704.0008
| 2,007
|
[
0.051005832850933075,
0.028671786189079285,
-0.006167180836200714,
-0.009244587272405624,
0.04395979270339012,
0.004876808729022741,
0.024938618764281273,
0.01530641969293356,
-0.04478691518306732,
0.03667333722114563,
-0.06351089477539062,
-0.006604410242289305,
0.029607074335217476,
-0.00545671209692955,
0.02719712071120739,
-0.03071131370961666,
0.04550395533442497,
-0.01662488467991352,
-0.005617399699985981,
0.03920919448137283,
-0.011973804794251919,
-0.04207390919327736,
-0.008985156193375587,
-0.029237035661935806,
0.09620705246925354,
0.02060292661190033,
0.005044248886406422,
0.030055919662117958,
-0.07792989909648895,
0.0037422527093440294,
0.012890378944575787,
-0.037582576274871826,
-0.0225383173674345,
-0.042024776339530945,
-0.04607062041759491,
-0.04322897642850876,
0.020968571305274963,
-0.03269416466355324,
0.028636731207370758,
0.028710203245282173,
0.04035729542374611,
-0.08288582414388657,
0.049413830041885376,
-0.005098624620586634,
0.0057859825901687145,
0.034915629774332047,
-0.05488916486501694,
-0.039076969027519226,
0.05835586041212082,
0.022356558591127396,
0.010394503362476826,
0.02410994842648506,
0.029515443369746208,
-0.11102685332298279,
0.017021724954247475,
-0.02821229211986065,
0.012823618948459625,
-0.010308746248483658,
0.08780084550380707,
-0.042539507150650024,
-0.061044298112392426,
0.055246345698833466,
-0.04482800140976906,
-0.02284199930727482,
0.027285389602184296,
-0.017154661938548088,
-0.0013526101829484105,
-0.012221606448292732,
0.06538271903991699,
-0.019624989479780197,
0.07284168899059296,
0.0005475498619489372,
0.027786748483777046,
0.00416965689510107,
-0.007902722805738449,
0.018701663240790367,
0.017493929713964462,
-0.00710065383464098,
-0.010992366820573807,
-0.0014255254063755274,
-0.024943988770246506,
-0.015424905344843864,
0.06140764430165291,
0.01000342145562172,
0.010156473144888878,
0.017493603751063347,
-0.0022084650117903948,
0.059955112636089325,
-0.06260082125663757,
0.006265680771321058,
-0.004364922642707825,
0.00897462759166956,
0.009180248714983463,
0.0861465111374855,
-0.07021423429250717,
0.031752683222293854,
-0.029644561931490898,
0.03163463994860649,
0.03223089501261711,
-0.028626997023820877,
0.023714818060398102,
-0.007190977688878775,
-0.02811700850725174,
-0.015326609835028648,
0.012790454551577568,
0.0067186132073402405,
-0.010537004098296165,
0.015432856976985931,
-0.023780956864356995,
-0.021558092907071114,
-0.07103757560253143,
-0.013295793905854225,
-0.003454754827544093,
0.003211736911907792,
0.0062642451375722885,
-0.0357719324529171,
0.03512057662010193,
-0.11106313765048981,
-0.025505758821964264,
0.05210554599761963,
0.010534288361668587,
-0.03867022320628166,
0.014386208727955818,
0.0016129997093230486,
0.04980868101119995,
0.01966775953769684,
-0.07313983887434006,
-0.05240404233336449,
0.0007348032668232918,
-0.003486624686047435,
-0.0199904665350914,
0.0001946442062035203,
-0.03577907383441925,
-0.0018731567542999983,
0.020468536764383316,
0.0165441632270813,
-0.044260405004024506,
-0.03696415200829506,
0.0164751335978508,
0.015048868022859097,
0.03352644667029381,
-0.028890764340758324,
-0.06378626078367233,
0.009087741374969482,
-0.012975675985217094,
-0.02194748818874359,
-0.03619515150785446,
-0.02742888405919075,
-0.03813117370009422,
-0.002223947085440159,
0.009327905252575874,
0.07352349907159805,
0.044215090572834015,
0.028221484273672104,
0.005669528152793646,
-0.023973550647497177,
-0.03991728276014328,
0.01622513122856617,
0.039837777614593506,
0.011821677908301353,
-0.01178011391311884,
-0.023038314655423164,
-0.0751589760184288,
0.09273632615804672,
-0.025878915563225746,
0.021015707403421402,
-0.02851233258843422,
0.012897022068500519,
0.05047087371349335,
0.061248160898685455,
0.0037693202029913664,
-0.04211970791220665,
-0.026714233681559563,
-0.00906267948448658,
0.04851779714226723,
-0.05466770380735397,
0.05939429998397827,
-0.02511533722281456,
0.03918319195508957,
-0.030676091089844704,
0.04850331321358681,
-0.004358937032520771,
0.05532354116439819,
0.0062186638824641705,
0.011347252875566483,
0.048503175377845764,
0.042734138667583466,
0.004868346732109785,
-0.07660220563411713,
0.023556338623166084,
-0.010374530218541622,
0.008431758731603622,
-0.049628160893917084,
-0.02985643409192562,
-0.0181275624781847,
-0.07990307360887527,
0.08188509196043015,
-0.015794388949871063,
-0.012090211734175682,
-0.05848437175154686,
-0.03516240045428276,
0.03489145264029503,
-0.054564692080020905,
0.004854060243815184,
-0.028012612834572792,
0.08802200108766556,
-0.02155815251171589,
0.019064052030444145,
0.05245254561305046,
-0.021670328453183174,
0.09441711008548737,
0.011876587755978107,
0.019964678213000298,
0.07855550199747086,
-0.0376090481877327,
0.0004705179308075458,
0.011098187416791916,
-0.04452870786190033,
-0.029915813356637955,
0.05002681910991669,
0.03405637666583061,
-0.006458291318267584,
-0.033027537167072296,
0.010391189716756344,
0.048469673842191696,
-0.008608182892203331,
-0.019568495452404022,
0.007962181232869625,
0.001120269880630076,
-0.04992673546075821,
-0.040491294115781784,
-0.004308521747589111,
-0.004125729203224182,
-0.01714577153325081,
0.00126466469373554,
0.0027065633330494165,
-0.018677180632948875,
-0.004870896227657795,
0.0148688443005085,
0.040903933346271515,
0.033174529671669006,
0.0016425949288532138,
0.0522628091275692,
-0.03602276369929314,
-0.08030610531568527,
0.005888046696782112,
0.010784435085952282,
0.01573021709918976,
0.04532596096396446,
-0.01585487648844719,
0.0008368820417672396,
0.00009386685997014865,
-0.006138989701867104,
0.04159896448254585,
0.04290685057640076,
-0.02373073622584343,
-0.04980916157364845,
0.019129781052470207,
-0.026845499873161316,
-0.06461308896541595,
0.01770871877670288,
-0.023514296859502792,
-0.013254432007670403,
-0.01817924715578556,
-0.08080941438674927,
-0.002885350026190281,
0.013204088434576988,
-0.03161698207259178,
-0.014417541213333607,
0.01310977153480053,
0.03574654832482338,
-0.0038885350804775953,
0.05685655027627945,
0.07948882132768631,
-0.013570667244493961,
-0.031201859936118126,
0.04301482439041138,
-0.02963709458708763,
-0.026553934440016747,
-0.019841477274894714,
-0.054880283772945404,
-0.048940327018499374,
-0.009687677025794983,
0.0029693704564124346,
0.018878256902098656,
0.04687551036477089,
0.02847503498196602,
-0.019771650433540344,
0.006146888714283705,
0.04335879534482956,
-0.03336767852306366,
-0.03204229474067688,
-0.019774269312620163,
0.029925193637609482,
-0.04056156054139137,
0.053329627960920334,
0.056236978620290756,
-0.041046857833862305,
0.0007121507660485804,
0.01213710568845272,
-0.04473220929503441,
-0.013686642982065678,
0.0579439252614975,
0.00024699221830815077,
0.000036972796806367114,
0.03225835785269737,
0.0016566633712500334,
-0.026065580546855927,
0.055982764810323715,
0.023243645206093788,
-0.041097890585660934,
0.06548871845006943,
0.005880658980458975,
0.02901204116642475,
-0.0873950943350792,
0.020195981487631798,
0.07244385033845901,
-0.023189209401607513,
0.07591164857149124,
0.02510502189397812,
0.005973659455776215,
-0.05439642444252968,
0.04843711480498314,
-0.0285789854824543,
-0.025161879137158394,
0.0729847177863121,
0.016020800918340683,
-0.011535968631505966,
-0.01637045480310917,
-0.027851734310388565,
0.027285009622573853,
0.044890064746141434,
0.013640055432915688,
-0.016967812553048134,
-0.0037387339398264885,
-0.03864467516541481,
-0.021931195631623268,
0.04066414386034012,
0.01088931318372488,
-0.021144280210137367,
0.024127574637532234,
-0.08716127276420593,
-0.009324939921498299,
-0.03406619280576706,
-0.0401512011885643,
-0.029815513640642166,
0.0054043373093008995,
0.02226950414478779,
0.0056046610698103905,
0.001432376797311008,
-0.0005727881216444075,
0.04006148502230644,
-0.0001408745301887393,
-0.022840790450572968,
-0.024619661271572113,
0.053799111396074295,
0.07761058211326599,
-0.004530465230345726,
-0.008920101448893547,
0.06513377279043198,
0.02365032583475113,
-0.039342597126960754,
0.021342866122722626,
0.0014229927910491824,
0.03842349722981453,
0.015443062409758568,
0.06045927107334137,
0.036339081823825836,
0.020180324092507362,
-0.07979712635278702,
-0.002114451490342617,
-0.012842023745179176,
0.012792527675628662,
0.05507805198431015,
0.05151701718568802,
0.029332930222153664,
-0.08093548566102982,
0.027709169313311577,
-0.030349355190992355,
-0.006605152506381273,
0.08031958341598511,
-0.0031088783871382475,
0.039470233023166656,
0.006720959208905697,
-0.019894205033779144,
-0.025258544832468033,
-0.03702354431152344,
-0.003344473661854863,
-0.006294085644185543,
-0.008710279129445553,
0.05063285306096077,
-0.08818811923265457,
-0.04082302749156952,
0.03718365356326103,
0.03679339960217476,
-0.04675031453371048,
0.0233339611440897,
-0.004000284243375063,
-0.02365044876933098,
-0.046447403728961945,
-0.03138650581240654,
-0.035133764147758484,
0.009395156987011433,
-0.020415423437952995,
-0.014247102662920952,
0.017645463347434998,
0.007332752458751202,
-0.05687306076288223,
0.02523336187005043,
0.01146905031055212,
0.023088356480002403,
-0.01813330501317978,
-0.04774417728185654,
-0.04040773957967758,
0.04494953155517578,
-0.048914823681116104,
0.04899498447775841,
0.01740134134888649,
0.0034233727492392063,
0.01000961847603321,
-0.02531537041068077,
0.043566953390836716,
0.017273548990488052,
0.017011862248182297,
0.03445163741707802,
0.02646580897271633,
-0.034735504537820816,
0.007746122777462006,
0.02345716580748558,
-0.04888443276286125,
-0.004167176317423582,
0.009107922203838825,
0.007473161909729242,
0.0009542032494209707,
-0.005346016958355904,
0.03889402002096176,
0.022587958723306656,
-0.014152102172374725,
-0.005725538823753595,
-0.0034440697636455297,
0.02635660022497177,
-0.0005676911678165197,
-0.014368042349815369,
0.00992301944643259,
0.02000032365322113,
0.08957549929618835,
0.02155452035367489,
-0.015606649219989777,
-0.014463872648775578,
-0.015925634652376175,
-0.014499940909445286,
-0.04944977909326553,
0.00301120663061738,
0.00462540565058589,
0.0882473737001419,
-0.04196231812238693,
0.017292803153395653,
-0.014478306286036968,
0.026883652433753014,
0.050376079976558685,
0.022118644788861275,
0.046587441116571426,
-0.05516989901661873,
-0.017307184636592865,
-0.038815684616565704,
-0.022896267473697662,
0.016649147495627403,
0.026179153472185135,
0.03485647588968277,
0.07200179249048233,
-0.06621886789798737,
-0.020337384194135666,
0.029159290716052055,
-0.019317463040351868,
-0.017047205939888954,
0.007931799627840519,
0.018523134291172028,
-0.03823231905698776,
0.02350945770740509,
0.05132129043340683,
0.04201608523726463,
0.01592692919075489,
-0.05392186716198921,
-0.01610846258699894,
0.0074268183670938015,
0.028585392981767654,
-0.04438653588294983,
0.04988102242350578,
0.021520277485251427,
-0.021958446130156517,
0.03680052235722542,
-0.0024895158130675554,
-0.033930983394384384,
0.027834860607981682,
-0.01860623247921467,
-0.01736508123576641,
0.01774917170405388,
0.011344918981194496,
-0.04808778688311577,
-0.0437079519033432,
0.010848307982087135,
-0.009842823259532452,
0.0133734829723835,
-0.0002829496224876493,
-0.002842564834281802,
0.0030730734579265118,
0.0007137709180824459,
-0.04765888303518295,
-0.01636504754424095,
-0.0032774186693131924,
0.0715559795498848,
0.07521387189626694,
0.0671565979719162,
0.03306731954216957,
0.0018913368694484234,
-0.042180608958005905,
0.05696434900164604,
-0.023860633373260498,
-0.0683954656124115,
-0.02568262442946434,
0.006791052874177694,
-0.016524817794561386,
0.052438050508499146,
-0.02015596814453602,
-0.0757816880941391,
0.028409793972969055,
-0.01533666905015707,
-0.08038247376680374,
-0.007048995699733496,
-0.027604997158050537,
-0.04129013791680336,
-0.006833316758275032,
0.03609873354434967,
-0.026098519563674927,
-0.024703416973352432,
-0.06732694804668427,
-0.012312958016991615,
0.02493640035390854,
0.022317221388220787,
-0.004034354351460934,
-0.016061879694461823,
0.019374484196305275,
0.042397789657115936,
0.05445462465286255,
0.02266782335937023,
-0.027118835598230362,
-0.04262867197394371,
0.02043815888464451,
-0.024719832465052605,
-0.07733265310525894,
0.021240899339318275,
-0.027522780001163483,
0.013680115342140198,
-0.07448302209377289,
0.00672505795955658,
-0.007975337095558643,
0.035024262964725494,
-0.07046710699796677,
-0.0070214890874922276,
-0.008582553826272488,
-0.014928718097507954,
-0.003793952753767371,
0.0034782998263835907,
0.006909978110343218,
0.00030760696972720325,
-0.10158348083496094,
-0.015404731035232544,
0.007314492017030716,
0.04450474679470062,
-0.03606029227375984,
0.02320396900177002,
-0.055106669664382935,
0.04599181190133095,
0.02872036024928093,
-0.006894525606185198,
-0.009425392374396324,
-0.0012970191892236471,
-0.004544290713965893,
-0.0377117395401001,
0.012401500716805458,
-0.031237520277500153,
-0.002652270719408989,
0.0013292769435793161,
0.02073490247130394,
-0.03096921741962433,
0.005634772591292858,
-0.02217407152056694,
-0.0587092861533165,
0.029916150495409966,
0.020019592717289925,
0.038251474499702454,
-0.004184011369943619,
-0.006578546948730946,
-0.03656379133462906,
0.006019758526235819,
0.031590353697538376,
0.02152632176876068,
0.004658552818000317,
0.036203209310770035,
0.046947501599788666,
0.0140768988057971,
0.03819696977734566,
0.05052810534834862,
-0.07346297800540924,
0.050456784665584564,
-0.005154971498996019,
0.03443592041730881,
0.029563263058662415,
-0.00642345380038023,
0.007881800644099712,
-0.006994519382715225,
0.028607316315174103,
-0.03906859830021858,
-0.010326243005692959,
0.040836893022060394,
-0.05684737488627434,
0.06372200697660446,
-0.02008124813437462,
0.03368324413895607,
-0.06293836981058121,
-0.020429225638508797,
-0.02577800676226616,
0.029567280784249306,
-0.08371014893054962,
0.00682076858356595,
-0.02284303307533264,
-0.050757646560668945,
0.02348470129072666,
0.05781866982579231,
0.02324759028851986,
0.017950790002942085,
-0.022016435861587524,
-0.028687505051493645,
0.0038677179254591465,
-0.027955474331974983,
0.08170731365680695,
0.03607421740889549,
0.07115700095891953,
0.025357520207762718,
0.06174510717391968,
0.060027897357940674,
-0.04337213560938835,
-0.024673357605934143,
0.02686109021306038,
0.0005374677712097764,
0.0027217864990234375,
-0.0017640766454860568,
0.0017596131656318903,
-0.02260860987007618,
0.025596776977181435,
0.07133623957633972,
0.05719950050115585,
-0.010994927957654,
0.0714857205748558,
-0.0027553485706448555,
0.047325074672698975,
0.011542784981429577,
0.0035275942645967007,
0.0021558585576713085,
0.0101845758035779,
-0.010765092447400093,
-0.027421969920396805,
0.009826760739088058,
-0.026975950226187706,
0.009862232953310013,
-0.03293805941939354,
0.007631606888025999,
-0.07489755749702454,
0.010258934460580349,
0.03866482153534889,
-0.02837345004081726,
0.008107676170766354,
-0.026312021538615227,
0.030185870826244354,
-0.04070284590125084,
-0.008668758906424046,
-0.014833481051027775,
-0.0031104760710150003,
-0.01345578208565712,
-0.014746377244591713,
0.01640760339796543,
0.0456070601940155,
0.003134176367893815,
-0.01978996954858303,
-0.006872274912893772,
-0.023140951991081238,
0.018118908628821373,
-0.021823378279805183,
-0.060752205550670624,
-0.0005204858025535941,
0.030991433188319206,
0.05066657066345215,
0.010693621821701527,
-0.05261487513780594,
0.014597039669752121,
-0.0055190687999129295,
-0.007369826082140207,
-0.0025206725113093853,
0.007769491523504257,
-0.005852026864886284,
0.016299601644277573,
0.03795040026307106,
-0.030681708827614784,
0.016162119805812836,
-0.05047205835580826,
0.0015590386465191841,
-0.0031802395824342966,
0.020083392038941383,
0.017664730548858643,
0.036874715238809586,
-0.006224798504263163,
0.001060241716913879,
0.04364388808608055,
0.03837727755308151,
-0.048652470111846924,
-0.03013395331799984,
-0.006424944847822189,
-0.06435693800449371,
0.015484403818845749,
0.015741167590022087,
0.025932323187589645,
-0.017451878637075424,
-0.06667183339595795,
0.029577532783150673,
0.04330373927950859,
-0.06443848460912704,
-0.014957444742321968,
-0.025241313502192497,
0.0041785272769629955,
0.013803301379084587,
0.04437929764389992,
-0.024955982342362404,
-0.025507578626275063,
0.04085952788591385,
-0.012614257633686066,
0.0033643997740000486,
-0.01236275490373373,
-0.00771482614800334,
-0.0505719855427742,
0.027345171198248863,
0.014250708743929863,
-0.08042646944522858,
-0.006806622724980116,
0.02817642316222191,
-0.015294854529201984,
-0.017959946766495705,
-0.07419916987419128,
0.06722714751958847,
0.028146054595708847,
-0.00834228377789259,
0.0010431824484840035,
-0.05226917937397957,
-0.044229477643966675,
-0.02012026682496071,
-0.017040828242897987,
0.012051411904394627,
-0.08995355665683746,
-0.024026982486248016,
0.03473810479044914,
0.0007821226608939469,
0.02621757611632347,
0.01774914376437664,
-0.014555537141859531,
-0.011228281073272228,
-0.03251348063349724,
0.010487785562872887,
-0.04558115452528,
-0.012171217240393162
] |
[
6.697131156921387,
4.054581165313721
] |
Materials Science
|
Condensed-Matter Physics
|
cond-mat-mtrl-sci
|
na
|
na
|
2007-04-02T19:41:34
|
We discuss the results from the combined IRAC and MIPS c2d Spitzer Legacy
observations of the Serpens star-forming region. In particular we present a set
of criteria for isolating bona fide young stellar objects, YSO's, from the
extensive background contamination by extra-galactic objects. We then discuss
the properties of the resulting high confidence set of YSO's. We find 235 such
objects in the 0.85 deg^2 field that was covered with both IRAC and MIPS. An
additional set of 51 lower confidence YSO's outside this area is identified
from the MIPS data combined with 2MASS photometry. We describe two sets of
results, color-color diagrams to compare our observed source properties with
those of theoretical models for star/disk/envelope systems and our own modeling
of the subset of our objects that appear to be star+disks. These objects
exhibit a very wide range of disk properties, from many that can be fit with
actively accreting disks to some with both passive disks and even possibly
debris disks. We find that the luminosity function of YSO's in Serpens extends
down to at least a few x .001 Lsun or lower for an assumed distance of 260 pc.
The lower limit may be set by our inability to distinguish YSO's from
extra-galactic sources more than by the lack of YSO's at very low luminosities.
A spatial clustering analysis shows that the nominally less-evolved YSO's are
more highly clustered than the later stages and that the background
extra-galactic population can be fit by the same two-point correlation function
as seen in other extra-galactic studies. We also present a table of matches
between several previous infrared and X-ray studies of the Serpens YSO
population and our Spitzer data set.
|
The Spitzer c2d Survey of Large, Nearby, Insterstellar Clouds. IX. The
Serpens YSO Population As Observed With IRAC and MIPS
|
astro-ph
|
0704.0009
| 2,007
|
[
0.003988630138337612,
0.01528525073081255,
-0.01315123401582241,
-0.07136401534080505,
-0.006507189944386482,
0.06443798542022705,
0.041914619505405426,
-0.004568047821521759,
-0.03567326441407204,
-0.02610645443201065,
-0.0953984335064888,
0.060811642557382584,
0.06006233021616936,
-0.01642407849431038,
0.017455244436860085,
-0.04281346872448921,
0.04527854546904564,
-0.020098280161619186,
0.011981277726590633,
0.03100891411304474,
-0.010524694807827473,
-0.050565771758556366,
-0.004332990385591984,
-0.02038027159869671,
0.11162346601486206,
0.03884801268577576,
0.036653440445661545,
-0.0011190881486982107,
-0.048784203827381134,
0.011100276373326778,
0.0794144868850708,
-0.01498498860746622,
0.015468624420464039,
-0.019426217302680016,
0.02194710075855255,
-0.013955377042293549,
0.04613403230905533,
-0.022819848731160164,
0.015955306589603424,
0.05701799690723419,
0.02220899425446987,
-0.0001288105413550511,
0.051178354769945145,
-0.011606541462242603,
-0.003676525317132473,
0.023858865723013878,
0.008276295848190784,
-0.005906345788389444,
0.08201415836811066,
-0.004657665733247995,
0.002476125257089734,
0.015653308480978012,
-0.025817502290010452,
-0.018521267920732498,
-0.05603296682238579,
0.01642739214003086,
-0.0003028297796845436,
-0.050352826714515686,
0.007736347150057554,
-0.058740630745887756,
0.010666937567293644,
0.04583123326301575,
-0.05451212450861931,
-0.007949016988277435,
-0.02009328454732895,
-0.07266184687614441,
-0.03111078403890133,
0.000793627870734781,
-0.0038892636075615883,
-0.047011010348796844,
0.027167804539203644,
0.0205854382365942,
0.020657673478126526,
0.011114181019365788,
-0.05579616501927376,
-0.012796747498214245,
-0.0013481512432917953,
0.00048461160622537136,
-0.010320805013179779,
0.03809627145528793,
0.022608578205108643,
-0.04955646023154259,
-0.0031485978979617357,
0.050265420228242874,
0.06931275874376297,
0.008684640750288963,
-0.0204241331666708,
-0.004640188533812761,
-0.01673378050327301,
0.012407615780830383,
0.0034729877952486277,
0.021424412727355957,
0.05703900754451752,
0.017070511355996132,
-0.00846354104578495,
0.0765356495976448,
0.004567427095025778,
0.018458422273397446,
-0.03526439890265465,
-0.05150563269853592,
0.02479950338602066,
0.04315982013940811,
0.029265398159623146,
0.028434766456484795,
0.0696154460310936,
0.018879873678088188,
0.00527923321351409,
0.02969823032617569,
0.024542175233364105,
-0.006116591859608889,
-0.09215572476387024,
-0.031143782660365105,
0.05442192032933235,
-0.02608782798051834,
-0.03323855251073837,
-0.023844564333558083,
0.01098671555519104,
-0.03567958623170853,
-0.02469564415514469,
0.0932612195611,
0.030915480107069016,
0.0058277971111238,
-0.014540208503603935,
-0.011983921751379967,
-0.016964556649327278,
-0.0379844605922699,
-0.05488169193267822,
-0.03601605072617531,
0.017380867153406143,
-0.00188836723100394,
0.005485451314598322,
0.02115870825946331,
-0.048118818551301956,
0.007503003813326359,
0.07480538636445999,
-0.03715432062745094,
-0.049220968037843704,
-0.04326024278998375,
0.038448553532361984,
-0.02912224642932415,
0.06951206177473068,
0.050139088183641434,
0.06140255182981491,
-0.009534481912851334,
0.015842081978917122,
-0.013173030689358711,
0.02731451392173767,
-0.041165634989738464,
-0.03160737454891205,
-0.03817645460367203,
0.022520285099744797,
0.016291793435811996,
0.011399959214031696,
0.04918696731328964,
-0.048120904713869095,
-0.058829087764024734,
-0.04454231262207031,
-0.03284217417240143,
0.011219856329262257,
-0.0009407343459315598,
-0.0018005585297942162,
0.01830531656742096,
-0.04589156061410904,
0.058178842067718506,
-0.06486260890960693,
0.019823556765913963,
0.025006376206874847,
0.01495728176087141,
-0.003946441225707531,
0.040776293724775314,
-0.021008377894759178,
-0.015492725186049938,
-0.004497968591749668,
-0.05078747123479843,
0.02123117446899414,
-0.02638971619307995,
0.04133833944797516,
-0.023317936807870865,
-0.00660412572324276,
0.016135094687342644,
0.03631715849041939,
-0.04405893757939339,
0.006955951917916536,
0.024123361334204674,
0.043126415461301804,
-0.022782014682888985,
0.012786658480763435,
-0.050667647272348404,
-0.012375591322779655,
0.041857484728097916,
0.012489824555814266,
-0.00023421915830112994,
-0.03364022448658943,
-0.07352112233638763,
-0.0016095328610390425,
-0.03390590474009514,
0.060285784304142,
-0.056094083935022354,
-0.01682269386947155,
0.008718037977814674,
-0.030707987025380135,
0.005407612770795822,
-0.057411015033721924,
-0.022184593603014946,
-0.04580681398510933,
0.05201691389083862,
0.0032220734283328056,
-0.0031680637039244175,
0.009982029907405376,
0.0319221206009388,
0.0206715390086174,
-0.02886558510363102,
0.015437387861311436,
0.026508383452892303,
-0.012266629375517368,
-0.00961090438067913,
0.04129071161150932,
-0.003191020106896758,
0.018416356295347214,
0.0039130388759076595,
0.007213999517261982,
-0.00023529316240455955,
0.0550319068133831,
0.005556715186685324,
0.08918605744838715,
0.05790182948112488,
0.0046596466563642025,
0.036580462008714676,
-0.00152309681288898,
0.02207038551568985,
-0.023294389247894287,
-0.05804421380162239,
0.04872216284275055,
-0.017829278483986855,
0.007602338679134846,
-0.04447343945503235,
-0.004928283859044313,
0.027775125578045845,
0.0599476657807827,
0.039087675511837006,
0.034187592566013336,
0.0014730326365679502,
-0.040443502366542816,
-0.004564803093671799,
-0.0364999957382679,
-0.009007547982037067,
-0.007126517128199339,
0.007340951822698116,
-0.06806077063083649,
0.025893470272421837,
-0.006818345747888088,
0.023641984909772873,
0.025307508185505867,
0.042540986090898514,
0.020128674805164337,
-0.014245295897126198,
-0.03403373807668686,
0.06773217767477036,
-0.05465008690953255,
-0.040659040212631226,
0.029468007385730743,
-0.07134997844696045,
0.006507583428174257,
-0.07770314812660217,
0.009090468287467957,
0.02182908169925213,
-0.02900954708456993,
-0.039840131998062134,
0.046605657786130905,
-0.013132374733686447,
0.014049142599105835,
-0.00747882854193449,
0.022851696237921715,
0.05869297683238983,
0.027306433767080307,
0.07400009036064148,
-0.010819803923368454,
-0.0341605469584465,
-0.02324710413813591,
-0.012465235777199268,
-0.00884583592414856,
-0.003214644966647029,
-0.015875820070505142,
-0.03326084464788437,
0.018132628872990608,
0.027916790917515755,
0.05986405164003372,
0.002142904559150338,
0.03981631249189377,
-0.01591736637055874,
0.0191168375313282,
-0.02369634620845318,
0.023795578628778458,
0.040789373219013214,
0.02472839131951332,
0.03701774775981903,
0.059239305555820465,
-0.017586132511496544,
-0.004929754883050919,
-0.03241351991891861,
0.016044801101088524,
0.006466993596404791,
0.0037524839863181114,
-0.03442632779479027,
0.02298998087644577,
-0.02707969956099987,
-0.020590608939528465,
-0.03645004704594612,
0.023458899930119514,
-0.0625259056687355,
0.012672643177211285,
0.05198989436030388,
-0.0343981608748436,
0.025580598041415215,
-0.029378969222307205,
0.07355614006519318,
0.03633340820670128,
0.02137567102909088,
0.056501030921936035,
0.05181876942515373,
0.029754197224974632,
0.01807301491498947,
0.03547219932079315,
-0.0839344933629036,
0.007971554063260555,
0.03536852449178696,
0.02924164943397045,
-0.008845589123666286,
-0.024572676047682762,
0.015160886570811272,
-0.012326945550739765,
0.041332345455884933,
0.006056345067918301,
-0.021083025261759758,
-0.041436370462179184,
0.0431537888944149,
-0.025940118357539177,
0.023261329159140587,
-0.02120138704776764,
-0.038480862975120544,
-0.0039764405228197575,
-0.022676218301057816,
-0.041612353175878525,
-0.03949682414531708,
-0.06393600255250931,
-0.007261950522661209,
-0.020343219861388206,
0.0011150866048410535,
0.07121075689792633,
0.009132341481745243,
-0.024226881563663483,
-0.03111850842833519,
0.07164289057254791,
-0.013838142156600952,
-0.029287811368703842,
0.04647720605134964,
0.038765303790569305,
-0.041142772883176804,
0.039577189832925797,
0.0047016688622534275,
0.0055753858759999275,
-0.02721351943910122,
0.02583756484091282,
-0.006702110171318054,
0.025271249935030937,
0.03866191580891609,
0.050161510705947876,
-0.008710641413927078,
0.01049443893134594,
-0.03023311123251915,
-0.058941252529621124,
0.0018776031211018562,
0.038616374135017395,
0.04383666440844536,
0.059422675520181656,
-0.025911517441272736,
-0.028755171224474907,
0.02368411235511303,
0.0262973140925169,
0.01680454984307289,
0.06234585866332054,
0.01176814828068018,
0.033590808510780334,
-0.003424322698265314,
0.02099752239882946,
0.02479182742536068,
0.003850494045764208,
0.031925078481435776,
-0.03279947489500046,
-0.044796835631132126,
0.0009236742625944316,
-0.09207931160926819,
-0.0770597904920578,
-0.04544001445174217,
-0.007483944296836853,
-0.021325932815670967,
0.06570905447006226,
-0.03757890686392784,
0.05829473212361336,
0.007758420426398516,
-0.05174276977777481,
-0.04482901096343994,
0.07267122715711594,
-0.03809569776058197,
-0.027504287660121918,
-0.003352646017447114,
-0.05971768870949745,
-0.05275805667042732,
0.0660436600446701,
0.013704120181500912,
0.024828560650348663,
0.016358787193894386,
0.01999773643910885,
-0.08388114720582962,
0.0348312109708786,
-0.03895082324743271,
0.06000504270195961,
-0.0035886119585484266,
0.0318145826458931,
-0.04113128036260605,
0.008051777258515358,
0.02187090739607811,
-0.009597744792699814,
-0.015371871180832386,
0.009626389481127262,
-0.010101402178406715,
0.02313324622809887,
-0.04115516319870949,
-0.009361237287521362,
-0.039107900112867355,
0.05492183193564415,
0.020742570981383324,
0.017269913107156754,
0.07199041545391083,
-0.03863395005464554,
0.011801625601947308,
0.040958985686302185,
-0.04918736591935158,
0.0031280359253287315,
-0.0016824479680508375,
0.024368366226553917,
-0.06769993156194687,
0.002477114088833332,
-0.014800840988755226,
0.04251968488097191,
0.08100400865077972,
0.07200825959444046,
-0.0055476343259215355,
0.002071555471047759,
0.01572500355541706,
0.0282185859978199,
-0.0170249305665493,
-0.00924401544034481,
0.026078617200255394,
0.05875265598297119,
-0.032418105751276016,
-0.022227315232157707,
0.000652001122944057,
0.030991896986961365,
0.045127250254154205,
0.001074435655027628,
0.006011142395436764,
0.015514192171394825,
0.005673606880009174,
0.05631791800260544,
-0.017337532714009285,
-0.032225873321294785,
-0.023288888856768608,
0.006629881449043751,
0.08283525705337524,
-0.07544595748186111,
0.009777674451470375,
0.044548939913511276,
-0.006953498348593712,
-0.056048713624477386,
-0.0025141777005046606,
-0.004657584708184004,
-0.05828841030597687,
0.0015364198479801416,
0.03026994876563549,
0.034946978092193604,
0.016552038490772247,
-0.023322872817516327,
-0.003400832647457719,
0.01006812509149313,
0.07322746515274048,
-0.014603649266064167,
0.03006690740585327,
-0.026579488068819046,
-0.011380918323993683,
-0.007429380435496569,
0.03371338173747063,
0.029137618839740753,
0.016733737662434578,
-0.03185281902551651,
-0.0402376726269722,
0.03328688070178032,
-0.057936057448387146,
0.006451175548136234,
0.017572971060872078,
-0.0014818424824625254,
0.015299627557396889,
0.011380398645997047,
0.028566615656018257,
0.0421367883682251,
0.0000015919035831757355,
-0.041867196559906006,
-0.04146704822778702,
-0.00350254331715405,
0.03417351096868515,
-0.004630511626601219,
0.04527943581342697,
0.05102779343724251,
0.0708451122045517,
0.021827220916748047,
-0.035291094332933426,
0.00958319753408432,
0.06773757934570312,
-0.02657896652817726,
-0.05059739947319031,
-0.024096094071865082,
-0.0119555639103055,
0.017364729195833206,
0.035939160734415054,
-0.02782883681356907,
0.019122419878840446,
-0.04241997376084328,
-0.04056156799197197,
0.05332709848880768,
-0.043684978038072586,
-0.01588093489408493,
0.04203569144010544,
-0.0198447834700346,
-0.022082054987549782,
0.03557123616337776,
-0.024538220837712288,
-0.053320787847042084,
-0.01583198644220829,
0.01921934261918068,
-0.003857062431052327,
0.01697428710758686,
-0.02251039631664753,
0.02255263738334179,
-0.006221503484994173,
-0.01803315430879593,
-0.04321139678359032,
-0.02731570415198803,
0.03286987170577049,
0.019614487886428833,
-0.08186931908130646,
0.04140518605709076,
-0.013645813800394535,
0.08544702082872391,
-0.026026498526334763,
0.000744758581276983,
-0.016711318865418434,
-0.014626869931817055,
-0.015597879886627197,
-0.016530446708202362,
-0.002718901727348566,
-0.05014348775148392,
-0.046801984310150146,
0.03727330267429352,
0.04011499136686325,
0.025716792792081833,
-0.06617797911167145,
0.007488049566745758,
-0.030604267492890358,
0.006822129245847464,
-0.022836968302726746,
0.04660220816731453,
0.002908158814534545,
0.021199747920036316,
0.06742355972528458,
0.021910151466727257,
-0.05585873872041702,
0.04421699792146683,
0.05563434213399887,
-0.00023920551757328212,
-0.03769073635339737,
-0.02969595603644848,
-0.013052577152848244,
0.0022974808234721422,
0.0143899479880929,
-0.032837558537721634,
0.009245481342077255,
-0.0017185217002406716,
-0.01371870469301939,
0.02944330684840679,
-0.018219247460365295,
0.03569473698735237,
-0.07764530181884766,
-0.01048926543444395,
-0.021149808540940285,
-0.03421192616224289,
0.012079386040568352,
-0.03839133679866791,
0.001919723697938025,
-0.02875431440770626,
-0.0776335746049881,
0.014313808642327785,
0.012878582812845707,
0.05775028094649315,
-0.03592880070209503,
-0.020679747685790062,
0.0056769754737615585,
-0.002077193697914481,
0.0634910985827446,
-0.024103501811623573,
-0.005349619314074516,
-0.008554371073842049,
-0.014922477304935455,
-0.07227227836847305,
-0.07953384518623352,
-0.003880472155287862,
-0.02153749391436577,
0.04797862097620964,
0.005661670118570328,
-0.011677226983010769,
-0.055307552218437195,
0.0033291277941316366,
-0.057332441210746765,
-0.0015713094035163522,
-0.11217094957828522,
-0.026858238503336906,
0.010774965398013592,
0.021424973383545876,
-0.052213992923498154,
-0.024541722610592842,
0.08523614704608917,
0.014349639415740967,
0.023301677778363228,
-0.00791177898645401,
-0.06680835783481598,
-0.03359484300017357,
0.019508475437760353,
-0.004892732948064804,
0.00604932801797986,
-0.0032194769009947777,
0.012518457137048244,
0.04887963831424713,
-0.05669581517577171,
-0.025645896792411804,
0.012861821800470352,
0.06068061292171478,
0.008708963170647621,
0.005751766264438629,
0.040282659232616425,
0.038793016225099564,
0.0031066942028701305,
0.07488880306482315,
-0.002446731785312295,
0.001576852286234498,
-0.022022688761353493,
0.02544691599905491,
-0.0006709867739118636,
0.025563225150108337,
-0.004150301218032837,
-0.002892160089686513,
-0.02260543964803219,
-0.04412679374217987,
-0.02518545277416706,
-0.06754669547080994,
-0.023956090211868286,
-0.04273269698023796,
0.006346167530864477,
0.010522584430873394,
-0.044082120060920715,
-0.0696784183382988,
0.015664612874388695,
-0.0163031667470932,
-0.031337905675172806,
-0.06779976189136505,
-0.06582425534725189,
-0.08166392892599106,
0.018293093889951706,
0.028112078085541725,
-0.03006022609770298,
0.06231631338596344,
-0.05768939107656479,
0.019433990120887756,
0.038360532373189926,
-0.004457508679479361,
0.02126503176987171,
0.015075975097715855,
0.0336909256875515,
-0.022727688774466515,
-0.07974397391080856,
-0.019894801080226898,
-0.03557759150862694,
0.04162292182445526,
-0.0044071264564991,
-0.008309769444167614,
-0.0604071319103241,
-0.00678758230060339,
-0.07323013991117477,
-0.035874102264642715,
-0.020168662071228027,
-0.01995682157576084,
0.03394901007413864,
-0.01981557533144951,
0.023677770048379898,
-0.016435660421848297,
-0.019704069942235947,
-0.016447365283966064,
0.0013221553526818752,
-0.018588952720165253,
0.05572250857949257,
-0.02255091443657875,
-0.05250105261802673,
-0.00298118288628757,
-0.0032144521828740835,
0.011906360276043415,
-0.008041146211326122,
0.030640674754977226,
-0.00708739971742034,
-0.007701766211539507,
-0.05123523250222206,
-0.0009126621298491955,
-0.004770949948579073,
0.003303083823993802,
0.028634879738092422,
-0.0065844422206282616,
0.010045323520898819,
-0.008387967012822628,
-0.07700787484645844,
0.023041561245918274,
-0.006403837352991104,
0.08430629223585129,
-0.004114855080842972,
-0.04496459662914276,
0.013905026949942112,
-0.058378566056489944,
0.0352286659181118,
-0.043516844511032104,
-0.006428232882171869,
0.028143245726823807,
0.02082052268087864,
-0.04821360856294632,
-0.008102750405669212,
0.030300790444016457,
-0.05709100142121315,
0.021387087181210518,
-0.011946409940719604,
-0.025303982198238373,
0.0003646795521490276,
-0.018373126164078712,
0.020503932610154152,
0.028187580406665802,
0.05430067703127861,
0.01264868676662445,
0.024189062416553497,
-0.000718918105121702,
-0.006546849850565195,
0.04300966486334801,
0.027257874608039856,
-0.00040875092963688076,
0.008305715397000313,
0.03519630432128906,
-0.037771452218294144,
0.001517805503681302,
0.0007444395450875163,
-0.019274726510047913,
0.053695518523454666,
0.01158058736473322,
-0.007762211840599775,
-0.04251592606306076,
0.03504109010100365
] |
[
14.462421417236328,
7.276159286499023
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
na
|
na
|
2007-03-31T05:10:16
|
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph
defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play
an important role in the theory of partial cubes. These structures are employed
in the paper to characterize bipartite graphs and partial cubes of arbitrary
dimension. New characterizations are established and new proofs of some known
results are given.
The operations of Cartesian product and pasting, and expansion and
contraction processes are utilized in the paper to construct new partial cubes
from old ones. In particular, the isometric and lattice dimensions of finite
partial cubes obtained by means of these operations are calculated.
|
Partial cubes: structures, characterizations, and constructions
|
math.CO
|
0704.0010
| 2,007
|
[
0.015007024630904198,
0.06563875824213028,
0.006585616152733564,
-0.022402925416827202,
-0.017490912228822708,
-0.04014838486909866,
0.018979942426085472,
-0.007990328595042229,
-0.03580107539892197,
0.00011203301255591214,
-0.08036018908023834,
0.016758346930146217,
-0.035266876220703125,
0.005311986897140741,
-0.013994813896715641,
-0.018462661653757095,
-0.010945175774395466,
-0.016665419563651085,
-0.029129380360245705,
0.0355045311152935,
-0.01760786771774292,
-0.006638035178184509,
0.012143776752054691,
-0.00027542642783373594,
0.05164584517478943,
-0.0065268357284367085,
0.03923344612121582,
0.0031926280353218317,
-0.03219703212380409,
0.05096404626965523,
0.04511837661266327,
-0.05185624584555626,
0.013148595578968525,
-0.047719020396471024,
-0.004399201367050409,
-0.015543950721621513,
0.07133358716964722,
-0.010412848554551601,
0.013150465674698353,
0.011997057124972343,
0.024630805477499962,
0.003719428088515997,
-0.023220209404826164,
-0.00534014031291008,
0.020445743575692177,
-0.011743211187422276,
-0.03985670581459999,
0.014721792191267014,
0.02305789664387703,
0.017084360122680664,
0.016047710552811623,
0.03567376360297203,
0.03383661061525345,
-0.06391356885433197,
-0.01150696910917759,
-0.007490634918212891,
0.04442613199353218,
-0.06593881547451019,
0.0897899866104126,
-0.0036939000710844994,
0.04037865623831749,
0.06456638127565384,
-0.031152812764048576,
0.042763881385326385,
0.012323039583861828,
-0.06951119750738144,
-0.03921943157911301,
0.027889184653759003,
-0.011867843568325043,
0.009537758305668831,
0.028516247868537903,
-0.02150188572704792,
0.0743139460682869,
0.02393101528286934,
-0.024187881499528885,
-0.014707044698297977,
0.0248221755027771,
-0.03307357802987099,
0.04224184900522232,
0.02667166292667389,
0.02243788354098797,
-0.03164016455411911,
0.04414919391274452,
0.02095729671418667,
0.09269736707210541,
-0.008335019461810589,
-0.034638531506061554,
0.01637415401637554,
-0.07567798346281052,
0.031167414039373398,
-0.017018988728523254,
0.008717508055269718,
0.03056403435766697,
0.09384975582361221,
-0.03989233449101448,
0.01667427457869053,
0.010847093537449837,
-0.016049901023507118,
-0.02137155644595623,
-0.02591211162507534,
0.015767909586429596,
0.016385572031140327,
0.04474828764796257,
0.037464991211891174,
0.0300606656819582,
0.015477050095796585,
0.02431219257414341,
0.01566408947110176,
0.03876218572258949,
-0.0006024814210832119,
-0.0509382039308548,
0.02100972831249237,
0.009381725452840328,
0.012190562672913074,
-0.008068838156759739,
0.006648292299360037,
0.045572999864816666,
-0.12172900140285492,
-0.017358683049678802,
0.06224792078137398,
0.030258016660809517,
-0.009563532657921314,
0.03912179172039032,
0.006093389820307493,
0.015261637046933174,
0.023777704685926437,
-0.020120207220315933,
-0.0005977643886581063,
-0.004502876196056604,
0.00788307748734951,
0.04167206212878227,
0.01064123585820198,
-0.02255767025053501,
0.01982240006327629,
0.016009464859962463,
0.06643223017454147,
-0.05645408108830452,
-0.006759845186024904,
0.018772806972265244,
-0.015461662784218788,
-0.004917035810649395,
0.017364872619509697,
-0.04175293445587158,
0.0020062411203980446,
0.031935855746269226,
-0.04697638005018234,
-0.004758174996823072,
-0.03466957062482834,
-0.02863149344921112,
-0.01066591590642929,
0.008948505856096745,
0.0710650309920311,
0.009570842608809471,
0.025560639798641205,
-0.06564556062221527,
0.0102959293872118,
0.01559445820748806,
-0.008940165862441063,
0.05531538650393486,
0.021946176886558533,
0.04202809929847717,
0.009396669454872608,
-0.05848396196961403,
0.06371501088142395,
-0.028049668297171593,
0.005538666155189276,
-0.000798560562543571,
0.03090639039874077,
0.027858495712280273,
-0.004246289376169443,
-0.06007483974099159,
-0.013300514779984951,
-0.026504643261432648,
0.046582214534282684,
0.00014919295790605247,
-0.007787302602082491,
-0.02650381252169609,
-0.020797619596123695,
0.06670296937227249,
-0.004111189395189285,
-0.0077169365249574184,
-0.016810664907097816,
-0.0017816928448155522,
0.04247325658798218,
-0.069699227809906,
0.00930964108556509,
0.038115810602903366,
-0.059899527579545975,
-0.013674944639205933,
0.035344671458005905,
-0.0048867082223296165,
0.03839235007762909,
-0.03198755159974098,
-0.0596243180334568,
0.027298375964164734,
-0.06285186856985092,
0.03369029611349106,
0.0022936540190130472,
0.0075298938900232315,
-0.05457214638590813,
0.025048451498150826,
-0.04596761614084244,
-0.015526148490607738,
0.05539508908987045,
-0.01510767824947834,
0.06279472261667252,
0.01104002632200718,
0.0393420048058033,
0.07742726802825928,
0.020033035427331924,
0.026433072984218597,
0.02428017370402813,
0.01953904889523983,
0.04808051139116287,
-0.006969037931412458,
-0.026028068736195564,
-0.02973458170890808,
-0.05372414365410805,
-0.027429962530732155,
-0.0021492885425686836,
-0.011287217028439045,
-0.0633913055062294,
-0.06275994330644608,
0.029297230765223503,
0.05393408238887787,
0.008743698708713055,
-0.015062244608998299,
0.030001746490597725,
-0.021725721657276154,
0.02147124707698822,
-0.053255077451467514,
-0.07936785370111465,
0.05634506419301033,
-0.017336798831820488,
-0.014280080795288086,
-0.006739210803061724,
-0.04262150079011917,
0.007218226324766874,
0.024344095960259438,
0.021616723388433456,
0.08123466372489929,
-0.009477601386606693,
0.03216348960995674,
-0.033392421901226044,
-0.020272506400942802,
-0.006466518621891737,
0.01573031209409237,
-0.03264842554926872,
-0.016256459057331085,
0.028239570558071136,
0.017302697524428368,
0.023824060335755348,
-0.006125167477875948,
0.06203757971525192,
0.01884089782834053,
0.014855806715786457,
-0.055888425558805466,
0.036559537053108215,
-0.019653722643852234,
-0.06570491939783096,
0.046753160655498505,
-0.039670467376708984,
-0.02288197912275791,
-0.025849666446447372,
-0.030577732250094414,
-0.006569577381014824,
-0.01279675867408514,
-0.03732678294181824,
0.021106407046318054,
-0.006524031050503254,
0.009747914038598537,
0.02824835292994976,
0.06110096350312233,
0.03481576591730118,
-0.023891083896160126,
-0.03952927887439728,
0.036430731415748596,
-0.058865681290626526,
-0.055854301899671555,
-0.0009832297218963504,
0.007211429066956043,
-0.008770176209509373,
-0.039663366973400116,
-0.002692817710340023,
-0.022137032821774483,
0.04375055432319641,
0.0345345214009285,
0.0018326012650504708,
-0.01675376482307911,
0.03949100524187088,
-0.050838910043239594,
0.014300612732768059,
0.050353825092315674,
0.016462532803416252,
0.028786389157176018,
0.04071681573987007,
0.05131158232688904,
-0.009037292562425137,
-0.006287552881985903,
0.0019478012109175324,
-0.03770213946700096,
0.02749718725681305,
-0.010401721112430096,
-0.007247047498822212,
0.03173144534230232,
0.016852254047989845,
0.02603604644536972,
-0.02783096581697464,
-0.014229433611035347,
0.04354419186711311,
-0.05218815803527832,
0.04939543828368187,
-0.026905279606580734,
-0.014946423470973969,
-0.06631245464086533,
0.04610803350806236,
0.036818359047174454,
0.020197421312332153,
0.018264619633555412,
-0.012302078306674957,
0.01685921475291252,
-0.020512692630290985,
0.026342997327446938,
-0.0321209616959095,
0.04058272764086723,
0.023322829976677895,
0.014322838746011257,
0.058782804757356644,
-0.037029020488262177,
0.008800323121249676,
-0.0018731924938037992,
0.027938472107052803,
-0.009181925095617771,
-0.02542494796216488,
-0.015750296413898468,
-0.030372926965355873,
-0.030916759744286537,
0.00934407114982605,
-0.04303412884473801,
0.006565909832715988,
0.01851036585867405,
-0.035024240612983704,
-0.054078683257102966,
-0.06380786001682281,
-0.001635801512748003,
0.009791864082217216,
-0.018265368416905403,
0.001167095615528524,
0.04128739982843399,
-0.007644944358617067,
-0.025387177243828773,
0.026260532438755035,
-0.009993402287364006,
0.012202737852931023,
-0.0217724796384573,
0.045456353574991226,
0.007097724359482527,
-0.006222570780664682,
-0.011097942478954792,
0.03389134258031845,
0.03347392380237579,
-0.05221248418092728,
0.03491872549057007,
-0.017555436119437218,
0.01787836104631424,
0.023439131677150726,
0.06832823902368546,
0.04429177939891815,
0.013673031702637672,
-0.023100173100829124,
-0.020658064633607864,
-0.05150928348302841,
0.025257285684347153,
0.02561328001320362,
0.04780707135796547,
-0.02014557458460331,
-0.053247638046741486,
-0.007770392578095198,
-0.004246382508426905,
-0.020411673933267593,
0.08927369117736816,
0.029373830184340477,
0.052192289382219315,
0.008995012380182743,
0.0034435444977134466,
-0.012665124610066414,
-0.04272047057747841,
0.02724195457994938,
-0.03629725053906441,
0.011714404448866844,
-0.01821545884013176,
0.0037669746670871973,
-0.034820206463336945,
0.007591730915009975,
-0.01769108511507511,
-0.02803768590092659,
-0.027214376255869865,
-0.009015083312988281,
-0.0072045405395329,
-0.02829550765454769,
-0.03524608910083771,
-0.06412369012832642,
0.01363880094140768,
-0.04085236415266991,
0.018684569746255875,
-0.003888383274897933,
-0.03870173171162605,
-0.045367397367954254,
0.07487522810697556,
-0.01918836496770382,
-0.010827461257576942,
0.029774704948067665,
0.025802653282880783,
-0.05371853709220886,
0.028384536504745483,
0.0010747594060376287,
0.025319093838334084,
-0.009089162573218346,
0.03903152793645859,
-0.01489400677382946,
0.01296196784824133,
0.04516851156949997,
-0.03330786153674126,
0.026924949139356613,
0.04418396204710007,
0.024490848183631897,
-0.0022868087980896235,
-0.03759239986538887,
-0.0137820178642869,
-0.07103754580020905,
-0.013779805973172188,
0.07221142202615738,
-0.0018357782391831279,
0.039552148431539536,
-0.08647482842206955,
-0.03438812494277954,
0.03054521232843399,
-0.013586782850325108,
-0.003261474659666419,
0.019287919625639915,
0.03128283843398094,
-0.00901544839143753,
0.01322006992995739,
0.005525587126612663,
0.07532947510480881,
0.02603444829583168,
0.02385587804019451,
-0.03184294328093529,
-0.022781113162636757,
-0.04678751155734062,
0.079600989818573,
0.05265766754746437,
0.0004551310557872057,
-0.0032865693792700768,
0.0589611642062664,
-0.00020757262245751917,
0.005018943455070257,
-0.004954216070473194,
0.06859816610813141,
0.03675182908773422,
0.007795582991093397,
0.0001866974198492244,
0.013416757807135582,
0.017079990357160568,
-0.007740220986306667,
-0.0022906234953552485,
-0.027675719931721687,
0.012627892196178436,
-0.0017704005585983396,
0.06674665957689285,
-0.022762635722756386,
0.03306526690721512,
0.00001955857442226261,
0.020222395658493042,
0.01674150489270687,
-0.01796679012477398,
0.01614224538207054,
0.004827856086194515,
-0.03545447066426277,
0.0668121948838234,
0.02828974463045597,
-0.04167838767170906,
-0.060481686145067215,
-0.059969328343868256,
0.018527422100305557,
0.05314057320356369,
-0.0025220410898327827,
-0.011296648532152176,
0.0025969238486140966,
-0.024150652810931206,
0.010731156915426254,
0.020122990012168884,
0.008451923727989197,
0.06191478669643402,
-0.07751256227493286,
-0.07497674226760864,
0.03734887018799782,
0.01611056737601757,
0.06109604239463806,
0.017154511064291,
-0.018799809738993645,
-0.0033995001576840878,
0.035891253501176834,
-0.001607038313522935,
-0.005088603124022484,
0.02234766073524952,
-0.000023728131054667756,
-0.1316058188676834,
-0.016239888966083527,
-0.0041649676859378815,
-0.01384598296135664,
0.038534976541996,
0.05278053879737854,
0.057932522147893906,
0.001037759124301374,
-0.014858962036669254,
0.022007547318935394,
-0.010044523514807224,
-0.06534635275602341,
0.013473235070705414,
0.02940109372138977,
-0.01329310704022646,
0.014020434580743313,
0.004407751839607954,
-0.07085233181715012,
0.07168847322463989,
-0.049462057650089264,
-0.052054207772016525,
0.04702368006110191,
0.0029364638030529022,
-0.029826324433088303,
0.0068016997538506985,
-0.007144901901483536,
-0.03376975655555725,
-0.030569525435566902,
-0.04414736479520798,
-0.10642421245574951,
0.03710460290312767,
0.0361311174929142,
0.022145964205265045,
-0.03796029090881348,
0.007679142989218235,
-0.017016658559441566,
0.030031032860279083,
0.013720269314944744,
-0.033404916524887085,
-0.04200820252299309,
0.0063225990161299706,
-0.016694113612174988,
0.0095727713778615,
0.027180010452866554,
-0.011411279439926147,
0.003620036179199815,
-0.0836329311132431,
0.04196390509605408,
-0.023692823946475983,
0.03652356564998627,
-0.0193551667034626,
-0.012452478520572186,
-0.027671629562973976,
0.011815336532890797,
0.04674072191119194,
-0.011830396950244904,
-0.018821420148015022,
0.033654168248176575,
-0.11339779943227768,
-0.03566933050751686,
-0.005408713594079018,
0.03311082348227501,
-0.012279550544917583,
0.013785777613520622,
-0.0538809597492218,
0.002384790452197194,
0.056558139622211456,
-0.033697593957185745,
-0.02706550434231758,
0.062586210668087,
-0.023267116397619247,
0.0038735962007194757,
0.0015828422037884593,
-0.011534844525158405,
-0.017787456512451172,
-0.016202492639422417,
0.03655827417969704,
-0.058682672679424286,
-0.003846141044050455,
0.012370545417070389,
0.010810669511556625,
-0.0037704359274357557,
-0.016663504764437675,
0.0032022136729210615,
-0.012286164797842503,
-0.051622528582811356,
0.006009284872561693,
-0.029712732881307602,
0.036901265382766724,
0.015324866399168968,
0.03662285581231117,
-0.0017593569355085492,
-0.04947444796562195,
-0.0019445025827735662,
0.033891987055540085,
0.019413474947214127,
-0.05960402637720108,
0.028274230659008026,
0.038683947175741196,
-0.02696678228676319,
0.0455348864197731,
-0.019538551568984985,
-0.027423137798905373,
-0.027235791087150574,
0.04362202808260918,
-0.018178878352046013,
-0.0570015013217926,
0.02041381597518921,
-0.10734257847070694,
0.02217925526201725,
-0.08633774518966675,
0.03778325393795967,
-0.10334596782922745,
-0.03684024140238762,
-0.06849175691604614,
-0.02213093265891075,
-0.052329037338495255,
0.03413873165845871,
0.014390367083251476,
0.00300240539945662,
-0.03611530736088753,
0.02480878122150898,
0.0636858195066452,
0.04710264503955841,
-0.029626403003931046,
-0.04958139359951019,
-0.025107309222221375,
0.02002507448196411,
0.02513468824326992,
-0.03630679473280907,
0.05619502440094948,
0.03471624478697777,
0.01253601722419262,
0.01927371136844158,
-0.04823162406682968,
-0.041188064962625504,
-0.010840518400073051,
0.0472453273832798,
0.0005464894347824156,
0.014135036617517471,
0.011829455383121967,
-0.01034576166421175,
0.007784721441566944,
0.10523086041212082,
0.0522601380944252,
-0.0443764366209507,
0.026912052184343338,
-0.026743484660983086,
-0.020523784682154655,
0.01907917484641075,
-0.027344046160578728,
-0.036031827330589294,
-0.012373663485050201,
-0.03545524552464485,
0.05227472633123398,
0.0028400614392012358,
0.011979588307440281,
-0.02550172433257103,
-0.05883742868900299,
-0.006011979188770056,
-0.0084800124168396,
-0.06799303740262985,
0.01579149253666401,
-0.06391911953687668,
-0.018282681703567505,
0.02213886007666588,
-0.013470864854753017,
-0.017689298838377,
0.033076316118240356,
0.01521215122193098,
-0.017724519595503807,
0.004901242908090353,
-0.04812469333410263,
-0.038546767085790634,
0.051163408905267715,
0.0025287128519266844,
-0.006334226578474045,
-0.027148691937327385,
0.0010375697165727615,
-0.006958759855479002,
-0.014853681437671185,
-0.039029669016599655,
-0.017968513071537018,
0.023879947140812874,
0.00035264191683381796,
-0.017495160922408104,
-0.04329570382833481,
0.04207007959485054,
0.02531241998076439,
-0.03955887630581856,
0.009077277034521103,
-0.02546650543808937,
-0.00005917128510191105,
0.00846827682107687,
0.004825186915695667,
-0.021023333072662354,
-0.0119713069871068,
-0.05288270488381386,
-0.026894092559814453,
-0.0019392367685213685,
0.0440630167722702,
-0.007261097896844149,
0.024453656747937202,
-0.014969006180763245,
0.020402859896421432,
0.07531291246414185,
-0.022568464279174805,
0.06263367086648941,
0.0013970318250358105,
-0.015264017507433891,
-0.06786328554153442,
0.02879529632627964,
-0.06499473750591278,
-0.005300652701407671,
-0.02922712452709675,
-0.08254814893007278,
-0.04719381779432297,
-0.015342159196734428,
-0.0370936393737793,
-0.02562253549695015,
-0.013946270570158958,
0.04109865054488182,
0.07108301669359207,
0.05593307316303253,
0.03819500282406807,
-0.014509226195514202,
0.009282605722546577,
-0.013535559177398682,
-0.012021246366202831,
0.009107564575970173,
-0.0002741193457040936,
0.024992629885673523,
-0.012049478478729725,
-0.05991213023662567,
-0.016432546079158783,
0.008402226492762566,
0.031457483768463135,
-0.0009356182417832315,
-0.06545516103506088,
-0.07305803894996643,
0.02719133347272873,
0.04006524011492729,
0.0397581048309803,
-0.10239739716053009,
-0.012353441677987576,
0.04126356169581413,
-0.041060224175453186,
-0.04292013496160507,
0.0456753633916378,
-0.014891828410327435,
0.045163195580244064,
0.0644058883190155,
-0.036899082362651825,
0.02114677242934704,
0.07115720957517624,
0.02988729067146778,
0.06174474582076073,
-0.007944882847368717,
0.03296167775988579,
-0.0236497949808836,
-0.012499584816396236
] |
[
0.6369844079017639,
4.840635776519775
] |
Combinatorics
|
Mathematics
|
math-CO
|
na
|
na
|
2007-03-31T05:32:49
|
In this paper we present an algorithm for computing Hecke eigensystems of
Hilbert-Siegel cusp forms over real quadratic fields of narrow class number
one. We give some illustrative examples using the quadratic field
$\Q(\sqrt{5})$. In those examples, we identify Hilbert-Siegel eigenforms that
are possible lifts from Hilbert eigenforms.
|
Computing genus 2 Hilbert-Siegel modular forms over $\Q(\sqrt{5})$ via
the Jacquet-Langlands correspondence
|
math.NT math.AG
|
0704.0011
| 2,007
|
[
-0.013102318160235882,
0.010296490974724293,
0.005686193238943815,
-0.03381418436765671,
-0.006474705878645182,
0.012599548324942589,
0.028640955686569214,
0.0009555962169542909,
-0.02684945985674858,
0.02605072781443596,
-0.09501585364341736,
0.02478155493736267,
0.0556299202144146,
0.0035664623137563467,
-0.03243567422032356,
-0.026125621050596237,
0.006879851222038269,
-0.003503186162561178,
-0.021905766800045967,
0.006111090537160635,
-0.011119826696813107,
-0.00923073012381792,
-0.030384765937924385,
-0.02967946231365204,
0.11800897121429443,
0.030603701248764992,
0.05534952133893967,
0.012024223804473877,
-0.04448763653635979,
0.023691458627581596,
0.05530788004398346,
0.028216416016221046,
0.07831481099128723,
-0.026194898411631584,
-0.02518961951136589,
0.00486300652846694,
0.07442126423120499,
0.036470577120780945,
0.011691578663885593,
0.04342621937394142,
0.04795984551310539,
-0.06147238612174988,
0.01652735471725464,
0.03211741894483566,
0.03549525886774063,
0.009021366015076637,
0.05602862685918808,
0.023829324170947075,
0.015099008567631245,
0.04681801050901413,
-0.010217647068202496,
-0.00035039012436755,
-0.005332860164344311,
-0.05555066093802452,
-0.029606888070702553,
-0.004504765383899212,
0.04478701576590538,
-0.03609072417020798,
0.01059593167155981,
-0.01645730808377266,
-0.00557486480101943,
0.024058716371655464,
-0.03928850591182709,
0.04059876129031181,
-0.0018156233709305525,
0.011023168452084064,
-0.00904963817447424,
0.008370715193450451,
-0.0150079894810915,
-0.0034795808605849743,
-0.016616588458418846,
0.014655709266662598,
0.04797437787055969,
0.04250447824597359,
-0.017932234331965446,
0.008297721855342388,
0.06087898463010788,
-0.03390031307935715,
-0.009958894923329353,
0.026611335575580597,
0.048194967210292816,
-0.014581396244466305,
0.020023956894874573,
0.019270678982138634,
-0.003914662171155214,
0.04077744483947754,
0.0441155768930912,
0.061316534876823425,
-0.06686105579137802,
0.018314475193619728,
-0.0019187614088878036,
0.012409311719238758,
0.02440919540822506,
0.06617146730422974,
-0.03757687658071518,
0.00955803319811821,
-0.02535458654165268,
-0.028034022077918053,
-0.0077173360623419285,
-0.00973963737487793,
0.050814151763916016,
0.04040791094303131,
0.0490109920501709,
-0.0162760391831398,
0.04223690181970596,
0.04128444567322731,
0.053748659789562225,
-0.026357276365160942,
0.045897092670202255,
-0.008115822449326515,
-0.08022879809141159,
0.0056909602135419846,
0.010709807276725769,
-0.03672897443175316,
-0.031755849719047546,
-0.0067881192080676556,
0.03067498654127121,
-0.05086514726281166,
-0.0347849577665329,
0.04665874317288399,
-0.005497315898537636,
-0.06332471966743469,
0.04624032601714134,
0.042675621807575226,
0.04680383577942848,
0.0010280839633196592,
-0.051916129887104034,
0.019152402877807617,
0.027645576745271683,
-0.025749024003744125,
0.030985912308096886,
0.006994153838604689,
-0.005994050297886133,
0.010646671056747437,
0.05902589112520218,
0.04168212041258812,
-0.014655906707048416,
0.009268081746995449,
0.014664862304925919,
-0.05589697137475014,
0.03732869774103165,
-0.026699215173721313,
-0.0005742862122133374,
-0.014583738520741463,
0.07674656808376312,
-0.045936841517686844,
0.02048318274319172,
-0.07347230613231659,
-0.0011655999114736915,
-0.023779338225722313,
0.011433063074946404,
0.02994089014828205,
0.016810428351163864,
-0.01774938590824604,
-0.03856823965907097,
-0.027151061221957207,
-0.037378087639808655,
-0.023695383220911026,
0.03959551826119423,
0.01655723713338375,
-0.02407122775912285,
0.01244860328733921,
-0.03569215536117554,
0.06619575619697571,
-0.018652785569429398,
0.027107637375593185,
-0.004275957588106394,
0.01973700523376465,
-0.01325206644833088,
0.04525931552052498,
0.0034399337600916624,
-0.025174429640173912,
-0.0040903533808887005,
-0.03635450452566147,
0.03774010390043259,
0.0032738957088440657,
-0.012378284707665443,
-0.0011213128454983234,
0.08236011862754822,
0.008292822167277336,
0.018851405009627342,
-0.031038695946335793,
0.010409771464765072,
0.06864288449287415,
-0.029851092025637627,
0.02358793467283249,
0.03628874942660332,
-0.04215094819664955,
-0.0030913958325982094,
0.017658624798059464,
-0.01613324135541916,
0.015001863241195679,
-0.03384660556912422,
-0.10369038581848145,
0.011919930577278137,
-0.012432636693120003,
0.05702698603272438,
0.019962383434176445,
-0.013799878768622875,
-0.03715970367193222,
-0.0038512672763317823,
0.000048161691665882245,
-0.059055671095848083,
0.02431683987379074,
0.0078306645154953,
0.05409975349903107,
0.023460345342755318,
-0.033115286380052567,
-0.0010260140988975763,
-0.022707685828208923,
-0.0002497121458873153,
0.003875038120895624,
0.005822674371302128,
0.0025439977180212736,
0.013520722277462482,
0.04179016873240471,
-0.0107449721544981,
-0.05119655281305313,
-0.05002216622233391,
0.044153351336717606,
0.00976940430700779,
0.008158338256180286,
-0.013703206554055214,
0.016892535611987114,
0.07049619406461716,
0.01660512387752533,
-0.02715447172522545,
0.00018718207138590515,
-0.04732196778059006,
-0.03699333965778351,
-0.016981733962893486,
-0.07577448338270187,
0.021891150623559952,
-0.002857227111235261,
-0.03141072392463684,
0.003508485620841384,
-0.014636426232755184,
0.029320141300559044,
0.11501568555831909,
0.07769136875867844,
0.013911481015384197,
0.05220329761505127,
0.015823842957615852,
-0.02010011486709118,
-0.03770037740468979,
-0.02089577727019787,
-0.0009500306332483888,
-0.01973777636885643,
-0.08464599400758743,
0.02353658340871334,
-0.007896794006228447,
-0.040085528045892715,
0.02875007502734661,
0.044225987046957016,
0.0013265794841572642,
-0.012914937920868397,
-0.00116637849714607,
-0.003051776671782136,
0.02237609028816223,
-0.0498407781124115,
0.03174629807472229,
-0.03961660712957382,
-0.01859164610505104,
0.01982838846743107,
-0.0328829251229763,
-0.0302472822368145,
0.007734573911875486,
-0.09117699414491653,
0.009357119910418987,
-0.017405614256858826,
0.001895437715575099,
0.031696200370788574,
0.03257197514176369,
-0.0009714314364828169,
-0.04775388166308403,
-0.07220935821533203,
0.0031796987168490887,
-0.0426245778799057,
-0.029498180374503136,
-0.012293621897697449,
-0.012569501996040344,
-0.07644301652908325,
-0.0272538959980011,
-0.029270226135849953,
0.002932800678536296,
-0.03251633048057556,
-0.011405717581510544,
0.018982738256454468,
-0.019689219072461128,
-0.0066892788745462894,
-0.060627806931734085,
-0.0652533695101738,
-0.007697856519371271,
0.023751040920615196,
-0.016099393367767334,
0.03588630259037018,
0.04501226916909218,
-0.037528350949287415,
-0.028931662440299988,
0.016893822699785233,
0.0033103327732533216,
0.02613505721092224,
-0.016461847350001335,
-0.01889859139919281,
-0.020167212933301926,
-0.030677681788802147,
0.056745413690805435,
-0.0008250271785072982,
0.04209114611148834,
-0.025260234251618385,
-0.020869817584753036,
0.007460158318281174,
-0.03176072984933853,
-0.0011857472127303481,
-0.025376111268997192,
0.015265651978552341,
0.05252572521567345,
-0.0005851315218023956,
0.061370935291051865,
0.009203038178384304,
-0.02454407513141632,
-0.05712803453207016,
0.07148824632167816,
-0.023135192692279816,
-0.003992501646280289,
0.03484080359339714,
-0.04599693417549133,
0.0564262829720974,
-0.018543513491749763,
-0.06785769760608673,
0.0037683944683521986,
0.036089811474084854,
0.004817426670342684,
-0.02223207801580429,
0.03251197561621666,
0.0018891931977123022,
-0.023745493963360786,
0.026621144264936447,
-0.019247008487582207,
0.013288788497447968,
0.016819585114717484,
0.005321762524545193,
-0.04664440453052521,
-0.04059422388672829,
-0.013442900963127613,
-0.0011698551243171096,
-0.01397476065903902,
-0.03583263233304024,
0.008753139525651932,
-0.0245344378054142,
-0.12406717985868454,
0.007378847803920507,
0.07320854812860489,
-0.021275091916322708,
0.017384929582476616,
0.044716835021972656,
0.04413091018795967,
-0.011236493475735188,
0.09363807737827301,
-0.033632103353738785,
0.00973848719149828,
-0.001404499402269721,
0.06552231311798096,
0.031458642333745956,
0.058584753423929214,
0.016715077683329582,
0.0343148410320282,
0.00873728096485138,
0.009763219393789768,
0.029783159494400024,
-0.05241943523287773,
-0.033891711384058,
0.04721442610025406,
-0.01609562337398529,
-0.018046140670776367,
0.008871614001691341,
-0.08002215623855591,
-0.06250051409006119,
0.006295574363321066,
-0.04217630624771118,
0.003719144267961383,
0.0020477704238146544,
0.08189046382904053,
-0.011379086412489414,
-0.006015182472765446,
0.03245927393436432,
-0.01790885627269745,
0.040226299315690994,
0.0032714013941586018,
0.02903931774199009,
0.008855490945279598,
-0.03987610712647438,
-0.05011218786239624,
0.004472763277590275,
-0.05786607414484024,
0.032716333866119385,
0.03074575401842594,
0.025678062811493874,
-0.020061807706952095,
-0.004971376620233059,
-0.009920916520059109,
-0.10834015160799026,
0.02194312773644924,
0.0037420711014419794,
-0.030023887753486633,
0.00984970759600401,
-0.013867628760635853,
-0.029527150094509125,
0.04305308312177658,
-0.006917597260326147,
0.018427977338433266,
-0.017544858157634735,
0.031037313863635063,
-0.02168552577495575,
0.03139663115143776,
0.02861456386744976,
0.04984641075134277,
0.006723595783114433,
-0.035623613744974136,
-0.0495104044675827,
-0.015800075605511665,
0.014781761914491653,
-0.06370993703603745,
0.02739601582288742,
-0.003938098903745413,
0.000898735539522022,
-0.009398909285664558,
0.012176744639873505,
0.004151731263846159,
-0.036193326115608215,
0.020993711426854134,
0.04151162505149841,
0.010061514563858509,
0.03146607056260109,
-0.05446943640708923,
-0.017164357006549835,
0.00209942483343184,
0.006275946740061045,
-0.020105117931962013,
0.0017780519556254148,
0.0633147656917572,
-0.02030220627784729,
-0.0016025437507778406,
-0.011145729571580887,
0.04379720613360405,
-0.0152217922732234,
0.04860633984208107,
-0.013955806382000446,
-0.015085944905877113,
-0.02371312864124775,
0.09505901485681534,
0.004433665424585342,
0.00501444423571229,
0.0017698387382552028,
0.06777315586805344,
-0.007530038710683584,
-0.03162475302815437,
0.003026107791811228,
0.060605235397815704,
0.0343007817864418,
0.05404110252857208,
0.0002802673843689263,
-0.0011732443235814571,
0.05434001237154007,
0.00947930570691824,
0.011795463971793652,
-0.04732883721590042,
0.02297648973762989,
-0.034132879227399826,
-0.021125104278326035,
0.007743181195110083,
0.0479067787528038,
0.042838145047426224,
-0.0770052894949913,
0.011398290283977985,
-0.031184708699584007,
-0.019245877861976624,
-0.0907047763466835,
-0.03072798252105713,
0.017778046429157257,
0.017733091488480568,
-0.01131267100572586,
-0.012099044397473335,
0.0016124938847497106,
-0.0136113865301013,
0.014999756589531898,
0.03567398712038994,
0.012392121367156506,
-0.05642753466963768,
-0.03551039099693298,
0.027106674388051033,
0.03323761001229286,
0.002607270609587431,
0.060117240995168686,
-0.011977063491940498,
-0.03233810514211655,
0.05670003592967987,
0.038089051842689514,
0.013476595282554626,
-0.05813896656036377,
-0.017989138141274452,
0.03683353587985039,
-0.006085977889597416,
0.09234534949064255,
0.021557115018367767,
0.017226170748472214,
0.03964494168758392,
-0.025892212986946106,
0.014544573612511158,
-0.018307609483599663,
0.00503022875636816,
-0.026270663365721703,
0.04465227201581001,
-0.0039941491559147835,
0.07087992131710052,
-0.010547585785388947,
-0.014523676596581936,
0.03061353601515293,
-0.04309876263141632,
-0.0002942805294878781,
0.035028472542762756,
-0.02887624315917492,
0.006049817427992821,
-0.05272909626364708,
-0.0350630097091198,
0.0754740983247757,
0.009924723766744137,
-0.10980153828859329,
0.038636427372694016,
0.03188003972172737,
0.028093533590435982,
0.005789745599031448,
-0.030297791585326195,
0.015835538506507874,
0.03842838481068611,
0.0017038312507793307,
0.02185044251382351,
-0.04425550997257233,
-0.03143209591507912,
0.07637844979763031,
-0.005804907996207476,
-0.0026004137471318245,
0.035216547548770905,
0.010833557695150375,
0.03983916714787483,
-0.050150226801633835,
-0.046577468514442444,
-0.0057494500651955605,
-0.010395576246082783,
-0.013917960226535797,
-0.005292074754834175,
-0.06647056341171265,
0.010480927303433418,
-0.061077479273080826,
0.024657098576426506,
-0.06016182154417038,
-0.015904603525996208,
-0.061405282467603683,
-0.025653650984168053,
0.002622088650241494,
0.0037204979453235865,
-0.027137713506817818,
-0.01752709038555622,
-0.011401087045669556,
-0.0084998132660985,
-0.08327022939920425,
-0.016267497092485428,
0.07843317836523056,
0.0752803385257721,
0.03543853759765625,
0.001600355957634747,
-0.03754234313964844,
0.006270202342420816,
0.05984487012028694,
-0.006205947138369083,
-0.07411471754312515,
0.06549336761236191,
-0.0346619188785553,
-0.0015792332123965025,
-0.0051531316712498665,
-0.034666355699300766,
-0.02527090534567833,
-0.029890278354287148,
-0.009456602856516838,
-0.059682268649339676,
0.058123357594013214,
-0.0003808084293268621,
-0.022352004423737526,
0.07662998139858246,
0.01982598565518856,
-0.010258466005325317,
-0.019867923110723495,
-0.02048340067267418,
-0.0069343228824436665,
-0.04107746481895447,
0.004953321535140276,
0.017648978158831596,
0.07738117128610611,
-0.03452420234680176,
-0.034528765827417374,
0.046159978955984116,
-0.023653868585824966,
0.05793447047472,
-0.020696984604001045,
0.006671958137303591,
0.06281998753547668,
-0.04532656446099281,
0.03160112723708153,
-0.003126283176243305,
0.013055161572992802,
0.0026200050488114357,
-0.011177103035151958,
-0.04306057468056679,
-0.05574173107743263,
-0.023719104006886482,
-0.08986262232065201,
0.0271851047873497,
-0.012780429795384407,
-0.013234352692961693,
-0.08991154283285141,
0.01542217843234539,
-0.01862393692135811,
-0.010663635097444057,
-0.08759650588035583,
-0.03076840192079544,
-0.015429133549332619,
-0.024189108982682228,
-0.014013150706887245,
0.022781992331147194,
0.03049325756728649,
0.00009688493446446955,
-0.04887981340289116,
0.013275069184601307,
-0.061289623379707336,
-0.01516246609389782,
0.00831065233796835,
-0.07988777756690979,
-0.0014225904596969485,
-0.013601596467196941,
0.04876246303319931,
0.06771329790353775,
-0.0008745212107896805,
0.02028321847319603,
0.012325769290328026,
0.060838524252176285,
0.002851401921361685,
0.02681020461022854,
0.04405861720442772,
-0.012240239419043064,
-0.009446453303098679,
0.13422724604606628,
0.03724033012986183,
-0.03068723902106285,
0.0004942988161928952,
0.019848737865686417,
-0.00327305868268013,
0.011220069602131844,
-0.01740073785185814,
0.00024987818324007094,
0.024675622582435608,
0.007077853195369244,
-0.003177712205797434,
0.011389018967747688,
-0.021342486143112183,
-0.00899659562855959,
0.00730258971452713,
-0.03245801851153374,
-0.0334789901971817,
-0.0183354914188385,
0.038243368268013,
-0.050317294895648956,
-0.008230251260101795,
-0.020446302369236946,
-0.06383419036865234,
-0.024855315685272217,
0.0037146415561437607,
-0.01142839901149273,
0.02932504005730152,
0.019602233543992043,
-0.03333353251218796,
0.009235331788659096,
-0.021654263138771057,
-0.022613296285271645,
-0.02551482431590557,
0.005076293833553791,
-0.004431101493537426,
0.02359798364341259,
-0.03992047160863876,
-0.03136473521590233,
0.005912076216191053,
0.016588501632213593,
-0.004154034424573183,
-0.04131678119301796,
-0.03137252479791641,
0.007067528087645769,
-0.00589884165674448,
-0.01942235603928566,
0.014581342227756977,
0.0017309071263298392,
0.07278124988079071,
-0.012971307151019573,
0.05747082084417343,
-0.028357962146401405,
-0.00030668964609503746,
-0.028931818902492523,
-0.045125097036361694,
-0.02143610082566738,
0.014443591237068176,
-0.025929847732186317,
-0.004916113335639238,
-0.03694638982415199,
-0.002143649850040674,
0.010679504834115505,
0.016587667167186737,
0.07035276293754578,
0.004853044170886278,
0.0243076179176569,
-0.01435976941138506,
-0.024886762723326683,
-0.04867185279726982,
0.00954804290086031,
-0.01534233521670103,
-0.05555297061800957,
0.019561156630516052,
-0.041703250259160995,
-0.04332003369927406,
-0.006740243639796972,
-0.010289505124092102,
0.02469732239842415,
0.010975337587296963,
-0.009231307543814182,
-0.0017203191528096795,
-0.007301583886146545,
0.011909897439181805,
-0.025999901816248894,
0.00235047098249197,
-0.08340143412351608,
-0.05330391600728035,
0.00463842460885644,
0.016074230894446373,
-0.05873982235789299,
-0.040164388716220856,
0.02661406807601452,
0.036675769835710526,
-0.00035244636819697917,
-0.024612847715616226,
-0.037453364580869675,
-0.004449072293937206,
0.05493701621890068,
0.033263906836509705,
-0.031989872455596924,
0.010267700999975204,
-0.012054131366312504,
0.08602628856897354,
0.044192325323820114,
-0.009809816256165504,
-0.00499738659709692,
0.07880515605211258,
0.03912457451224327,
0.00339759374037385,
-0.031130744144320488,
0.00602283701300621,
-0.0211136844009161,
0.0706329271197319,
-0.012597988359630108,
-0.0122715188190341,
0.013645184226334095,
0.011364005506038666
] |
[
-0.5564212203025818,
2.0130093097686768
] |
Number Theory
|
Mathematics
|
math-NT
|
math-AG
|
na
|
2007-03-31T05:48:51
|
Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty}
a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does
not satisfy a certain distribution property for modulo odd primes $p$. In this
paper, using Rankin-Cohen Bracket, we extend this result to modular forms of
half integral weight for primes $p \geq 5$. As applications of our main theorem
we derive distribution properties, for modulo primes $p\geq5$, of traces of
singular moduli and Hurwitz class number. We also study an analogue of Newman's
conjecture for overpartitions.
|
Distribution of integral Fourier Coefficients of a Modular Form of Half
Integral Weight Modulo Primes
|
math.NT
|
0704.0012
| 2,007
|
[
-0.01994185894727707,
0.0011107996106147766,
0.0031916815787553787,
-0.0786307230591774,
0.02752760238945484,
-0.0052095456048846245,
-0.0008628232753835618,
-0.012260083109140396,
-0.012718860991299152,
-0.026102053001523018,
-0.13243575394153595,
0.003226205939427018,
-0.010316583327949047,
0.035416748374700546,
0.031446076929569244,
-0.025174003094434738,
0.0368431881070137,
0.015494298189878464,
-0.03314470872282982,
0.04763185605406761,
-0.04613146930932999,
0.007610345724970102,
-0.006246085278689861,
-0.010839492082595825,
0.10198810696601868,
0.01876121759414673,
0.00581200560554862,
-0.009047728963196278,
-0.03839186578989029,
0.011252433992922306,
0.014699875377118587,
-0.039383724331855774,
0.013389404863119125,
-0.013972625136375427,
-0.0861450582742691,
-0.029318779706954956,
0.09063033014535904,
0.013641981407999992,
0.029863065108656883,
0.0123128117993474,
0.0007817642181180418,
-0.019971167668700218,
0.023988746106624603,
-0.018243400380015373,
0.0060892365872859955,
0.056464001536369324,
0.0006407395703718066,
0.06326363235712051,
0.009698934853076935,
0.015001766383647919,
0.0014219768345355988,
0.00836272444576025,
-0.001241748221218586,
-0.06153213605284691,
-0.023297596722841263,
0.006769617088139057,
0.01811848022043705,
-0.04883958771824837,
0.05406998470425606,
0.02381688728928566,
0.021803118288517,
0.05186476185917854,
-0.06736838072538376,
0.012244935147464275,
-0.011682777665555477,
-0.007828135043382645,
-0.0034333255607634783,
-0.008915532380342484,
0.012898284010589123,
-0.028230829164385796,
-0.013671972788870335,
0.021596994251012802,
0.018611527979373932,
-0.006313840858638287,
-0.0452742725610733,
-0.0018916672561317682,
0.02918160893023014,
0.0019373249961063266,
-0.009911863133311272,
0.02645910531282425,
0.019769873470067978,
-0.034305840730667114,
0.03134595975279808,
0.046518050134181976,
-0.0001227598258992657,
-0.03593684732913971,
0.051317960023880005,
0.0424659438431263,
-0.03672190010547638,
0.011038499884307384,
0.011681641452014446,
0.006390097085386515,
-0.008601361885666847,
0.0535086989402771,
-0.027352195233106613,
0.04243665561079979,
-0.04342569783329964,
-0.03032905049622059,
-0.05887944623827934,
-0.05387713015079498,
0.022404368966817856,
0.07480569183826447,
0.052411921322345734,
-0.02947979047894478,
0.04899994283914566,
0.06391061842441559,
0.02620301954448223,
-0.0037558123003691435,
0.003462450113147497,
-0.0030771763995289803,
-0.0848725289106369,
0.012601267546415329,
0.028487984091043472,
-0.040608540177345276,
-0.01913771964609623,
-0.03392411395907402,
0.03421671688556671,
-0.08560682088136673,
-0.0018268608255311847,
0.07409557700157166,
-0.012631449848413467,
-0.04856875538825989,
0.0013627908192574978,
0.04862998053431511,
-0.006516617257148027,
0.010384679771959782,
-0.0007073928136378527,
0.019780784845352173,
0.021070610731840134,
-0.016362814232707024,
0.03950139880180359,
0.009339447133243084,
-0.0671597346663475,
-0.01073550432920456,
0.06796079874038696,
0.030699914321303368,
-0.03983654826879501,
-0.02327224425971508,
0.018228013068437576,
-0.03071533516049385,
0.032628849148750305,
-0.029960723593831062,
0.035214200615882874,
-0.025488153100013733,
0.06635638326406479,
-0.03187526762485504,
0.016673995181918144,
-0.07925769686698914,
-0.08652419596910477,
-0.046097688376903534,
0.018765823915600777,
0.047384291887283325,
-0.009342284873127937,
0.019623519852757454,
-0.05124124512076378,
-0.026747729629278183,
-0.008095073513686657,
0.0059698838740587234,
0.024483559653162956,
0.001388152944855392,
-0.016686705872416496,
0.059414006769657135,
-0.058136001229286194,
0.03460053354501724,
-0.0033036163076758385,
0.0438523106276989,
-0.005576504860073328,
0.020029636099934578,
-0.008683023042976856,
0.011408671736717224,
0.00847865454852581,
0.004353788681328297,
0.004134416580200195,
-0.027530036866664886,
0.03931032121181488,
-0.017115607857704163,
-0.0032199970446527004,
-0.000036491437640506774,
0.11259856820106506,
0.047867342829704285,
0.01669473573565483,
0.013098949566483498,
0.01255597360432148,
0.02130281552672386,
-0.006853969767689705,
-0.024951063096523285,
0.04018160700798035,
-0.012971825897693634,
-0.041720543056726456,
0.0371217243373394,
-0.02717798575758934,
0.05546729639172554,
-0.03409199416637421,
-0.04891122877597809,
-0.024004053324460983,
-0.03252628818154335,
0.03325270488858223,
-0.01237026508897543,
0.009026462212204933,
-0.044877536594867706,
0.006073365919291973,
-0.008946027606725693,
0.007951921783387661,
0.0041895778849720955,
0.0006380030536092818,
0.040022727102041245,
-0.0031080208718776703,
0.011828124523162842,
0.029013628140091896,
-0.025209374725818634,
0.023392843082547188,
-0.07062996178865433,
-0.013973113149404526,
0.04837489500641823,
-0.017877714708447456,
0.045317936688661575,
0.024223461747169495,
-0.03139311447739601,
-0.014208605512976646,
0.04903466999530792,
0.05269337445497513,
-0.004509346093982458,
-0.03219250962138176,
0.004116124473512173,
0.03523048013448715,
0.04782189801335335,
0.00721570523455739,
-0.041007332503795624,
-0.038543857634067535,
0.028008796274662018,
-0.02151608094573021,
-0.06356393545866013,
0.047511208802461624,
0.031721021980047226,
-0.030087986961007118,
-0.012925454415380955,
-0.03451623395085335,
0.06366069614887238,
0.059885792434215546,
0.07136837393045425,
-0.008917971514165401,
0.01646297425031662,
0.0582931786775589,
-0.01489420235157013,
-0.043506935238838196,
0.00944944005459547,
-0.02735467441380024,
-0.030020391568541527,
-0.03168907016515732,
0.031321682035923004,
0.011054694652557373,
-0.005705215502530336,
0.07424292713403702,
0.01664838194847107,
0.008590558543801308,
-0.006879265420138836,
-0.029042406007647514,
0.0027569178491830826,
0.008063718676567078,
-0.019846975803375244,
0.00866415724158287,
-0.06019451469182968,
0.0048308102414011955,
-0.04050302505493164,
-0.03322311490774155,
0.013382656499743462,
0.03650056570768356,
-0.045510705560445786,
-0.02073478512465954,
-0.0017212118254974484,
0.006967743393033743,
0.0869515910744667,
0.07625333219766617,
0.02828213945031166,
-0.02654699794948101,
-0.03678363561630249,
0.05289177596569061,
-0.05892311409115791,
-0.02098183147609234,
-0.007502763066440821,
-0.037865906953811646,
-0.03286825492978096,
-0.018864568322896957,
-0.03201758489012718,
0.0009969056118279696,
-0.033162835985422134,
0.020327802747488022,
-0.012174475006759167,
0.018389340490102768,
-0.004514525178819895,
-0.05826270580291748,
-0.020275047048926353,
0.004702280275523663,
0.0287840124219656,
0.036958158016204834,
0.06357287615537643,
0.06407622992992401,
-0.025171661749482155,
-0.019066521897912025,
-0.025067154318094254,
0.02989068068563938,
-0.004950674716383219,
-0.003920321352779865,
-0.014698255807161331,
0.013626223430037498,
0.014852247200906277,
0.021681159734725952,
0.0015057025011628866,
0.01610483229160309,
0.0008212093380279839,
-0.004489880986511707,
0.02974042110145092,
0.031238360330462456,
-0.04736393317580223,
-0.05794195085763931,
0.02720465138554573,
0.015317641198635101,
-0.007972532883286476,
0.10359670221805573,
-0.0057211462408304214,
0.0020764528308063745,
-0.07341403514146805,
-0.00753232603892684,
-0.06634072959423065,
0.03116190806031227,
0.052388910204172134,
0.022708572447299957,
0.06859856843948364,
-0.0004639908147510141,
-0.011969277635216713,
0.013389271683990955,
0.04659218341112137,
-0.023204177618026733,
-0.03115471825003624,
0.01299227960407734,
0.028507834300398827,
-0.007512192241847515,
0.05237589776515961,
-0.030456315726041794,
0.022948110476136208,
-0.016205700114369392,
-0.025171684101223946,
-0.03324456885457039,
-0.01962379924952984,
-0.023782406002283096,
-0.021949101239442825,
-0.008302469737827778,
0.037438537925481796,
0.021998951211571693,
0.0211508609354496,
-0.0725582167506218,
0.008493056520819664,
0.04836314544081688,
-0.030760997906327248,
0.04169682040810585,
0.07658533751964569,
0.04735514521598816,
-0.03714371845126152,
0.05860775709152222,
0.02460877038538456,
0.06241271272301674,
-0.047865625470876694,
0.06239045411348343,
-0.00749598303809762,
0.09370242804288864,
0.007132933009415865,
0.04400394856929779,
0.015493745915591717,
-0.0010343263857066631,
0.001745083136484027,
-0.021818961948156357,
-0.018688036128878593,
0.09824883192777634,
0.002385310595855117,
0.0010247861500829458,
-0.030671872198581696,
-0.07993026822805405,
0.009275145828723907,
-0.014459209516644478,
-0.02831316739320755,
0.035635437816381454,
-0.019533276557922363,
0.03783092647790909,
-0.0034882696345448494,
0.02619241736829281,
-0.017117999494075775,
-0.0273087490350008,
-0.02785491570830345,
0.009915790520608425,
-0.050332311540842056,
0.031414806842803955,
-0.06450217962265015,
-0.012049050070345402,
0.02516116201877594,
0.001269922242499888,
-0.01077941618859768,
0.023600919172167778,
-0.018710734322667122,
0.03125152364373207,
-0.00565218273550272,
-0.06753838807344437,
-0.06934314966201782,
0.0193607360124588,
-0.0037278577219694853,
-0.0013329440262168646,
0.08924606442451477,
-0.043449174612760544,
-0.07305952906608582,
0.05538487434387207,
-0.04127716273069382,
-0.0021469092462211847,
-0.00855317059904337,
0.01940409280359745,
-0.027332140132784843,
0.05307282507419586,
0.0135950967669487,
0.033954743295907974,
0.013496090658009052,
-0.002800480928272009,
-0.0158546082675457,
-0.016994250938296318,
0.03966661915183067,
-0.05386244133114815,
0.03844527527689934,
-0.008239436894655228,
0.011773690581321716,
0.010889570228755474,
0.0022293427027761936,
0.026574447751045227,
-0.04250796511769295,
0.00261650956235826,
0.062120355665683746,
-0.0042260270565748215,
0.0480864942073822,
-0.06791575253009796,
0.020559480413794518,
0.0026517510414123535,
-0.025724131613969803,
0.0179376732558012,
0.03650987520813942,
0.03967277705669403,
-0.045605193823575974,
-0.03011179156601429,
0.02362198568880558,
0.09455878287553787,
0.01931011490523815,
0.03874717280268669,
-0.03763319551944733,
0.014401170425117016,
-0.02171812392771244,
0.04986166954040527,
-0.014885668642818928,
-0.013026912696659565,
-0.010912365280091763,
0.057727985084056854,
0.024649761617183685,
0.006706160493195057,
-0.014372582547366619,
0.09258487820625305,
0.019127948209643364,
-0.006971742957830429,
-0.00788271613419056,
-0.024563932791352272,
0.01752028986811638,
0.0036730312276631594,
0.008416647091507912,
-0.029231712222099304,
-0.008105302229523659,
-0.02505303919315338,
0.09897914528846741,
0.0063994997180998325,
0.0036621091421693563,
0.03417712077498436,
-0.044433508068323135,
-0.03726061433553696,
-0.006475725211203098,
0.03532770648598671,
-0.036981165409088135,
-0.04748949408531189,
0.05529140681028366,
0.01748531684279442,
-0.014215469360351562,
-0.06281272321939468,
-0.01376007217913866,
0.001492087496444583,
0.020272353664040565,
0.009950496256351471,
-0.05288014933466911,
-0.011069678701460361,
-0.08804745227098465,
0.014451034367084503,
0.021732686087489128,
-0.012961974367499352,
0.02215622551739216,
0.005046190228313208,
-0.02583610638976097,
0.0023258656729012728,
0.007068650797009468,
0.06849004328250885,
-0.050961464643478394,
0.028771035373210907,
0.0295182503759861,
-0.004833650775253773,
0.03163750842213631,
0.014114711433649063,
-0.02246641367673874,
-0.002893229713663459,
-0.031789541244506836,
-0.008095593191683292,
0.008015505038201809,
0.05034827068448067,
0.015748821198940277,
0.08442790806293488,
0.013687585480511189,
0.0459064319729805,
-0.012616590596735477,
-0.03201458975672722,
-0.015166698023676872,
-0.05658237636089325,
-0.014990012161433697,
0.01808888092637062,
-0.04740422964096069,
-0.01826026849448681,
0.020049262791872025,
0.0013022483326494694,
-0.020071620121598244,
-0.03968299180269241,
-0.115657277405262,
0.011958198621869087,
0.00017282557382714003,
0.031213684007525444,
-0.011937630362808704,
0.02870277129113674,
-0.024573437869548798,
0.0018023992888629436,
-0.006378591060638428,
-0.005169129464775324,
-0.016567887738347054,
-0.01646999455988407,
0.052345260977745056,
0.003495988203212619,
-0.010659553110599518,
0.000741862750146538,
0.031083552166819572,
-0.004217959474772215,
-0.006819296162575483,
-0.02507525123655796,
0.012662079185247421,
-0.017066409811377525,
-0.09115617722272873,
0.06406472623348236,
0.0028233882039785385,
0.008455948904156685,
-0.05789845809340477,
-0.008275887928903103,
0.013907617889344692,
0.014707631431519985,
-0.05072716996073723,
-0.03949525207281113,
-0.004909623879939318,
-0.020482493564486504,
-0.023894304409623146,
0.02352115325629711,
0.005748922936618328,
0.02131243795156479,
-0.11720512807369232,
-0.010859774425625801,
-0.004539620131254196,
0.02401444874703884,
0.008172749541699886,
0.01789897494018078,
-0.016199437901377678,
0.016216978430747986,
0.030633561313152313,
0.014162733219563961,
-0.042113929986953735,
0.025664936751127243,
-0.03669247776269913,
-0.03306848928332329,
-0.009448532946407795,
-0.034457288682460785,
-0.02175126224756241,
-0.014204202219843864,
-0.0066544185392558575,
-0.06848524510860443,
0.03811727836728096,
0.004874023608863354,
0.007780194748193026,
0.05736806243658066,
0.0042201741598546505,
0.004032733850181103,
0.004224667325615883,
-0.010092662647366524,
-0.026293471455574036,
-0.05100492015480995,
0.014007498510181904,
0.03578055277466774,
0.009525194764137268,
0.0018620388582348824,
-0.06288895010948181,
0.037162311375141144,
-0.017139587551355362,
0.07654089480638504,
-0.023472005501389503,
0.03787599131464958,
0.044921182096004486,
0.0033306183759123087,
-0.0008103196159936488,
0.020543847233057022,
0.05142664164304733,
0.018377985805273056,
-0.0026342871133238077,
-0.010820760391652584,
-0.030110187828540802,
-0.012382366694509983,
-0.0573979988694191,
0.0028482568450272083,
-0.04650110378861427,
-0.03532278537750244,
-0.058044612407684326,
0.03275632858276367,
-0.03416351601481438,
-0.03051520325243473,
-0.031070120632648468,
0.04762914776802063,
0.02171969972550869,
0.009024233557283878,
-0.024222074076533318,
0.013297708705067635,
0.016072267666459084,
0.02240012213587761,
-0.03364298865199089,
0.0018682138761505485,
-0.01599818840622902,
-0.03534994274377823,
0.01411433145403862,
-0.09083174169063568,
-0.0010140887461602688,
-0.0002521823043935001,
0.0820493996143341,
0.0400901697576046,
-0.04386525601148605,
0.001034481800161302,
-0.03351661562919617,
0.013517205603420734,
0.009880316443741322,
0.03249088302254677,
0.024625049903988838,
-0.04722542688250542,
-0.013683358207345009,
0.10212916135787964,
0.06476973742246628,
-0.01262066699564457,
0.03314409777522087,
0.014692752622067928,
-0.007277804426848888,
0.05002392828464508,
-0.01649976149201393,
0.01711650751531124,
-0.008568373508751392,
-0.03067842684686184,
0.010697931982576847,
0.024206608533859253,
-0.01035118754953146,
-0.016898062080144882,
0.018839918076992035,
-0.018059270456433296,
-0.06738610565662384,
-0.07208650559186935,
0.02059723436832428,
-0.020555144175887108,
-0.017957430332899094,
-0.013218807056546211,
-0.0683249831199646,
-0.02023676037788391,
-0.010484610684216022,
-0.014738098718225956,
-0.005239991471171379,
-0.003487665904685855,
-0.02712824195623398,
-0.021046452224254608,
-0.03019469417631626,
-0.01916472613811493,
-0.01080856379121542,
-0.0016068177064880729,
-0.0023588896729052067,
0.003455742262303829,
-0.024804510176181793,
-0.0016295848181471229,
-0.012349666096270084,
0.00947658997029066,
-0.0263872891664505,
0.042996641248464584,
-0.05146843567490578,
-0.01634000614285469,
0.02250438928604126,
-0.011474013328552246,
0.0392250157892704,
-0.00663059251382947,
0.10397003591060638,
0.015286250039935112,
0.034924592822790146,
-0.04867575690150261,
0.0072900946252048016,
-0.03182672709226608,
-0.02823803201317787,
0.012204594910144806,
0.0014532357454299927,
-0.046338241547346115,
-0.0010889917612075806,
0.05519901216030121,
-0.01079049427062273,
0.011503838934004307,
0.00720156729221344,
0.04337310045957565,
-0.0037904398050159216,
-0.009192602708935738,
-0.10690052807331085,
0.010542026720941067,
-0.05303093045949936,
0.02271224558353424,
-0.02116614207625389,
-0.05941717326641083,
-0.004053198732435703,
-0.03457517921924591,
-0.05162492394447327,
-0.04496702924370766,
0.02066989243030548,
0.04732557386159897,
0.055886782705783844,
0.03649131953716278,
-0.006820598617196083,
-0.03746126592159271,
-0.005685597658157349,
-0.002156693721190095,
-0.024413680657744408,
-0.010320390574634075,
-0.006974964402616024,
-0.013217486441135406,
0.006231929641216993,
-0.024773143231868744,
-0.02349989488720894,
0.01908561773598194,
0.005576931871473789,
-0.004663309548050165,
-0.007837395183742046,
-0.08866390585899353,
-0.012722100131213665,
0.012818521820008755,
0.053531721234321594,
-0.06476161628961563,
-0.004148771055042744,
-0.048062145709991455,
0.054882995784282684,
0.005276509094983339,
-0.004947283770889044,
0.06060926988720894,
0.055224452167749405,
0.02234332077205181,
-0.04007260501384735,
0.004976608790457249,
-0.041025057435035706,
0.008945138193666935,
0.07637953758239746,
-0.04470168426632881,
0.012888681143522263,
0.004273981787264347,
-0.03902094066143036
] |
[
-0.6114268898963928,
2.4092397689819336
] |
Number Theory
|
Mathematics
|
math-NT
|
na
|
na
|
2007-03-31T06:21:49
|
Serre obtained the p-adic limit of the integral Fourier coefficient of
modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend
the result of Serre to weakly holomorphic modular forms of half integral weight
on $\Gamma_{0}(4N)$ for $N=1,2,4$. A proof is based on linear relations among
Fourier coefficients of modular forms of half integral weight. As applications
we obtain congruences of Borcherds exponents, congruences of quotient of
Eisentein series and congruences of values of $L$-functions at a certain point
are also studied. Furthermore, the congruences of the Fourier coefficients of
Siegel modular forms on Maass Space are obtained using Ikeda lifting.
|
$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral
Weight
|
math.NT
|
0704.0013
| 2,007
|
[
-0.004228043369948864,
0.0016981072258204222,
-0.014036959037184715,
-0.030935073271393776,
0.028508516028523445,
-0.028163818642497063,
0.01917107403278351,
-0.017986992374062538,
-0.05573727935552597,
-0.0019190210150554776,
-0.09956817328929901,
0.010272941552102566,
0.0013395457062870264,
-0.0013842341722920537,
0.02094278857111931,
-0.01862732693552971,
0.0345069095492363,
0.020225392654538155,
-0.016199205070734024,
0.05268583446741104,
-0.005650356411933899,
-0.02398897334933281,
-0.01116073876619339,
-0.0008073971839621663,
0.09244270622730255,
0.03417643532156944,
0.07456140965223312,
0.009212304838001728,
-0.0626690611243248,
0.023458726704120636,
0.03275853395462036,
-0.0028465171344578266,
0.04916849359869957,
-0.051600225269794464,
-0.07208691537380219,
-0.046381838619709015,
0.10882913321256638,
0.008178560063242912,
0.002521468559280038,
0.021386219188570976,
0.034413889050483704,
-0.016895093023777008,
0.021649634465575218,
-0.0004341040039435029,
0.022320132702589035,
0.030990639701485634,
-0.014858095906674862,
0.04428429156541824,
0.02957936003804207,
0.01554607879370451,
-0.0009858376579359174,
-0.0016694210935384035,
0.0024984085466712713,
-0.052866652607917786,
-0.04953281953930855,
-0.0015297367936000228,
-0.01496990118175745,
-0.0745035707950592,
0.031574323773384094,
0.01140574086457491,
0.006794441491365433,
0.0020739866886287928,
-0.08497820794582367,
0.01867811381816864,
0.015447214245796204,
-0.06151574105024338,
0.015870224684476852,
-0.024848470464348793,
-0.006696431431919336,
-0.002591101685538888,
0.028480317443609238,
-0.0005182782770134509,
0.021245915442705154,
-0.035233691334724426,
-0.04181940108537674,
-0.020379601046442986,
0.020370585843920708,
-0.025494864210486412,
-0.02408059500157833,
0.027105161920189857,
0.055934175848960876,
-0.03072749823331833,
0.031128713861107826,
0.0431484654545784,
0.02157135121524334,
-0.015026497654616833,
0.06470388919115067,
0.02980170212686062,
-0.043912388384342194,
0.03989198058843613,
0.03703896701335907,
0.018713947385549545,
-0.016781741753220558,
0.05069536343216896,
-0.05304710194468498,
0.02466944418847561,
-0.0178361888974905,
-0.029033014550805092,
-0.05923975259065628,
-0.04616647586226463,
0.02184317447245121,
0.03389383479952812,
0.013150671496987343,
-0.008934949524700642,
0.07568904757499695,
0.04742846265435219,
0.024200743064284325,
-0.013201753608882427,
-0.0011399294016882777,
-0.014420227147638798,
-0.07889198511838913,
0.014303676784038544,
0.050456248223781586,
0.004755182191729546,
-0.023992683738470078,
-0.031978487968444824,
0.032936546951532364,
-0.06759984791278839,
-0.012297208420932293,
0.03467243164777756,
0.015026072040200233,
-0.011126063764095306,
0.054558414965867996,
0.016842860728502274,
-0.00474803801625967,
-0.005977566819638014,
-0.041766274720430374,
0.032676488161087036,
0.033378150314092636,
-0.0402558259665966,
0.024839388206601143,
0.03632274270057678,
-0.05510476231575012,
-0.03923260420560837,
0.011796396225690842,
0.0780550017952919,
-0.035053230822086334,
-0.06698565185070038,
0.030227044597268105,
-0.03575572371482849,
-0.001509135589003563,
-0.03086414746940136,
0.04653037711977959,
-0.034580446779727936,
0.025025278329849243,
-0.0184993464499712,
0.03259991854429245,
-0.07072854042053223,
-0.06699757277965546,
-0.00015446690667886287,
-0.00120266224257648,
0.0243583545088768,
-0.01034171786159277,
0.009455223567783833,
-0.04478153958916664,
-0.017156096175312996,
0.013286939822137356,
0.03242354467511177,
0.053140319883823395,
0.020927784964442253,
-0.022454237565398216,
0.07618822157382965,
0.008276180364191532,
-0.002739331917837262,
-0.06999389827251434,
0.051654644310474396,
-0.025042884051799774,
0.030246293172240257,
-0.021036166697740555,
-0.017173463478684425,
-0.05635880306363106,
0.011665292084217072,
0.027977975085377693,
-0.059390097856521606,
0.0465860590338707,
0.022381773218512535,
-0.01729414239525795,
-0.039060719311237335,
0.04086469113826752,
0.025813637301325798,
-0.010739095509052277,
-0.038075536489486694,
0.014431711286306381,
0.010511442087590694,
0.015104937367141247,
-0.009509991854429245,
0.0434480756521225,
-0.032597173005342484,
-0.014651445671916008,
0.006758640520274639,
-0.020629577338695526,
0.07533086091279984,
-0.07364167273044586,
-0.01638220064342022,
0.015478232875466347,
-0.007194029167294502,
0.01959792524576187,
-0.013109241612255573,
0.019223134964704514,
-0.009968827478587627,
0.008865461684763432,
-0.029569221660494804,
0.002228892408311367,
-0.0008843381656333804,
-0.0272228941321373,
0.07232698798179626,
-0.024588296189904213,
0.03926431015133858,
0.037762317806482315,
0.0017181204166263342,
0.037619221955537796,
-0.050832271575927734,
0.012275774031877518,
0.04706110805273056,
-0.010934973135590553,
0.04054756090044975,
0.013358951546251774,
0.011036946438252926,
-0.037187278270721436,
0.02716374583542347,
0.05626164376735687,
0.007923063822090626,
-0.010600350797176361,
-0.022949889302253723,
0.03368387743830681,
0.02101808786392212,
-0.07066219300031662,
-0.0017018468352034688,
-0.02827158011496067,
-0.024940647184848785,
-0.017432009801268578,
-0.052307844161987305,
0.022770894691348076,
0.02250344306230545,
-0.03433840349316597,
0.017324455082416534,
-0.010723627172410488,
0.014762568287551403,
0.04792783036828041,
0.0385383665561676,
0.01640547253191471,
0.021941669285297394,
0.0710681900382042,
-0.025340955704450607,
-0.03537851944565773,
0.03792129456996918,
-0.047881945967674255,
-0.0041037690825760365,
-0.049394454807043076,
0.02282453142106533,
0.0027487757615745068,
0.01065316703170538,
0.06089872866868973,
0.06131185591220856,
-0.00871327705681324,
-0.0199715755879879,
-0.03355298936367035,
-0.005897071678191423,
0.004483153577893972,
-0.040529217571020126,
0.022059887647628784,
-0.06789567321538925,
0.023371342569589615,
0.011469024233520031,
-0.05275948718190193,
0.010773933492600918,
0.030795622617006302,
-0.05890531837940216,
0.02615249529480934,
0.0001952151651494205,
0.016532503068447113,
0.032370638102293015,
0.05000320449471474,
0.06398763507604599,
-0.035793229937553406,
-0.07083530724048615,
0.03690226003527641,
-0.052125368267297745,
0.016336286440491676,
-0.013125902973115444,
-0.02516588382422924,
-0.04987313225865364,
-0.012408537790179253,
-0.031172577291727066,
-0.002777620917186141,
-0.00948613416403532,
-0.003846760606393218,
0.007512961979955435,
-0.003805455518886447,
0.026512818410992622,
-0.06413804739713669,
-0.01762869954109192,
0.01519877091050148,
0.021207891404628754,
0.030974028632044792,
0.06396570056676865,
0.017284588888287544,
-0.011137976311147213,
-0.022576821967959404,
-0.019841523841023445,
0.03688821196556091,
0.009905818849802017,
0.011793856509029865,
-0.03661172837018967,
0.02432720735669136,
0.00013160939852241427,
0.037515074014663696,
-0.001261158031411469,
0.026257386431097984,
0.038036104291677475,
-0.0047693755477666855,
0.0027752607129514217,
-0.0052256532944738865,
-0.020144464448094368,
-0.0779915601015091,
0.031122300773859024,
0.06854122132062912,
-0.03397032618522644,
0.04389852285385132,
-0.0064427778124809265,
0.0008108995971269906,
-0.06915731728076935,
-0.029807310551404953,
-0.0824403464794159,
-0.015324876643717289,
-0.0017326408997178078,
0.016214793547987938,
0.02179781347513199,
-0.05066227167844772,
-0.033815499395132065,
-0.019991418346762657,
0.07708767801523209,
-0.026177827268838882,
-0.041043564677238464,
0.008194131776690483,
0.01607886701822281,
-0.04454422369599342,
0.055802639573812485,
-0.05875765532255173,
0.01295959111303091,
-0.025293497368693352,
0.003433328354731202,
-0.004275434650480747,
-0.03220595791935921,
-0.0036251237615942955,
-0.0489262156188488,
-0.00045946656609885395,
-0.013610396534204483,
0.02808236889541149,
-0.0222766250371933,
-0.06975983828306198,
-0.027258949354290962,
0.029717542231082916,
-0.013521064072847366,
0.021561788395047188,
0.039390165358781815,
0.04018421471118927,
-0.007809073198586702,
0.08270876854658127,
-0.01139436848461628,
0.041422560811042786,
-0.018607646226882935,
0.034004222601652145,
-0.01213918998837471,
0.04736271873116493,
0.036779310554265976,
0.04864111170172691,
0.047007039189338684,
-0.003030781401321292,
0.017044752836227417,
0.005929289851337671,
-0.07236512005329132,
0.09464762359857559,
-0.00948288757354021,
-0.0065731266513466835,
-0.006309492513537407,
-0.06809091567993164,
-0.01141777727752924,
-0.022486185654997826,
-0.00936775840818882,
0.05846346169710159,
-0.011609982699155807,
0.037033919245004654,
0.03163396567106247,
0.038064613938331604,
-0.0029507603030651808,
-0.030362136662006378,
-0.021783921867609024,
0.006248248275369406,
-0.029516765847802162,
0.03988967835903168,
-0.04487594589591026,
-0.011816452257335186,
0.017539266496896744,
0.0012038290733471513,
-0.0434703528881073,
0.04512070119380951,
0.007631093263626099,
0.02292812615633011,
0.0002602571330498904,
-0.09302882105112076,
-0.052704084664583206,
0.015883618965744972,
-0.004092560615390539,
-0.05555136874318123,
0.058492131531238556,
-0.02610098570585251,
-0.06063738092780113,
0.08233103901147842,
-0.04832617938518524,
0.008260638453066349,
-0.00035423069493845105,
-0.0035843413788825274,
-0.07198672741651535,
0.0216636061668396,
0.031062178313732147,
0.0440606065094471,
-0.010410486720502377,
0.0013773291138932109,
0.014354804530739784,
-0.030825691297650337,
0.024138659238815308,
-0.10142435133457184,
0.009082320146262646,
0.015601113438606262,
0.030500655993819237,
0.00612771138548851,
0.009015594609081745,
0.045450516045093536,
-0.01772932894527912,
0.02412674017250538,
0.038387756794691086,
-0.006955060642212629,
0.04336746409535408,
-0.06568395346403122,
0.013151425868272781,
0.012522703967988491,
0.004312901757657528,
-0.012505518272519112,
0.03834705427289009,
0.04098766669631004,
-0.03814321756362915,
-0.009285613894462585,
0.009281326085329056,
0.04284054785966873,
0.018088264390826225,
0.023436354473233223,
-0.03271949291229248,
0.02776808850467205,
-0.019691074267029762,
0.014771477319300175,
-0.026952190324664116,
0.015697678551077843,
0.0022936745081096888,
0.09529540687799454,
-0.007516866084188223,
-0.010538375936448574,
-0.006613683421164751,
0.029329979792237282,
0.0107699790969491,
0.028502367436885834,
-0.01934121735394001,
-0.038666851818561554,
-0.001937373774126172,
0.017594732344150543,
-0.008354412391781807,
-0.04528177157044411,
-0.006362284533679485,
-0.044929828494787216,
0.05745450779795647,
0.0024044096935540438,
0.04996130242943764,
0.05451694875955582,
-0.03631099686026573,
-0.03073258325457573,
0.0167414378374815,
0.060489751398563385,
-0.023544585332274437,
-0.023652803152799606,
0.06109332665801048,
0.02346285805106163,
-0.01675322651863098,
-0.06033401936292648,
-0.0356154702603817,
-0.0355277955532074,
0.003207825357094407,
0.04980017989873886,
-0.030401887372136116,
-0.006376889534294605,
-0.06784000247716904,
-0.028855668380856514,
0.06272094696760178,
-0.0059459698386490345,
0.0045357863418757915,
-0.022230977192521095,
0.005576135590672493,
-0.01888463646173477,
0.033978793770074844,
0.04517369344830513,
0.00380073138512671,
0.01903342641890049,
0.010218363255262375,
0.02222764492034912,
0.04337119683623314,
0.004546470940113068,
-0.011782568879425526,
-0.011184905655682087,
-0.034253694117069244,
-0.0005118976696394384,
0.024756718426942825,
0.0074728564359247684,
0.04972795024514198,
0.05061298608779907,
0.02695726603269577,
0.007202888838946819,
0.007488885894417763,
0.02478860691189766,
0.024694621562957764,
-0.048842813819646835,
0.008168061263859272,
0.014687907882034779,
-0.050326697528362274,
0.01355613861232996,
-0.007391111925244331,
-0.016633223742246628,
0.017557192593812943,
-0.04002100229263306,
-0.13091520965099335,
0.03935842216014862,
0.006093435920774937,
0.012629173696041107,
0.004665665328502655,
0.06763479858636856,
-0.012172309681773186,
0.035895489156246185,
-0.019650273025035858,
-0.017864692956209183,
0.00876785907894373,
-0.013203619979321957,
0.052750635892152786,
0.01727474108338356,
-0.030410470440983772,
0.044002603739500046,
0.0550166592001915,
0.0388147346675396,
-0.03175792098045349,
-0.03343355283141136,
-0.034970249980688095,
-0.015833936631679535,
-0.03361910209059715,
0.04064197838306427,
-0.003272237488999963,
0.023437505587935448,
-0.06312921643257141,
0.01708710566163063,
-0.029268158599734306,
0.018352165818214417,
-0.02473217062652111,
-0.019861431792378426,
-0.0029430983122438192,
0.02209463343024254,
-0.03569158911705017,
-0.009639265015721321,
-0.001334751839749515,
0.017124980688095093,
-0.13460707664489746,
-0.02270817756652832,
0.01091027818620205,
0.05589267611503601,
0.025049922987818718,
0.02485794387757778,
-0.020170466974377632,
0.0159895196557045,
0.06654787808656693,
0.000778449117206037,
-0.024507148191332817,
0.04641477018594742,
-0.03585630655288696,
-0.006714732386171818,
-0.027870599180459976,
-0.04737691208720207,
-0.020845254883170128,
-0.0032735499553382397,
-0.010378346778452396,
-0.08036474883556366,
0.039785586297512054,
0.03118785284459591,
0.03258688747882843,
0.023458106443285942,
-0.015275212936103344,
-0.010524413548409939,
0.011300116777420044,
-0.022645719349384308,
0.019358234480023384,
-0.031774044036865234,
0.01485635619610548,
-0.00039936762186698616,
0.002829961711540818,
-0.026583010330796242,
-0.06578230112791061,
0.04323076829314232,
0.041413649916648865,
0.07591186463832855,
-0.013120848685503006,
0.0017571670468896627,
0.048319630324840546,
-0.016295932233333588,
0.017240500077605247,
0.004782434087246656,
0.045691125094890594,
-0.015709394589066505,
0.050056081265211105,
-0.015314440242946148,
-0.014244092628359795,
-0.029808782041072845,
-0.06883560866117477,
0.01605933904647827,
-0.02035890333354473,
-0.007476316299289465,
-0.07402646541595459,
0.027682693675160408,
-0.029667582362890244,
-0.0031543620862066746,
-0.014116869308054447,
0.012236964888870716,
-0.007758365944027901,
0.015269231051206589,
-0.032751988619565964,
-0.015888256952166557,
0.033747993409633636,
0.021963153034448624,
-0.0007827450754120946,
-0.038895491510629654,
-0.026935629546642303,
0.01759597286581993,
0.035725876688957214,
-0.08075521141290665,
-0.02790212072432041,
-0.024631885811686516,
0.06276918947696686,
0.04404289275407791,
-0.06192993000149727,
-0.01266598328948021,
-0.01194785162806511,
0.029413506388664246,
0.0066044386476278305,
0.009639686904847622,
0.014242819510400295,
-0.02227640710771084,
-0.043614234775304794,
0.12323859333992004,
0.05740336701273918,
-0.020760679617524147,
0.002088914392516017,
-0.006067704875022173,
-0.0011673870030790567,
0.014922252856194973,
0.014760076068341732,
0.004219653084874153,
0.020477058365941048,
-0.029526783153414726,
0.004280295222997665,
0.029593273997306824,
-0.0013959859497845173,
-0.018387988209724426,
0.03848065808415413,
-0.014447481371462345,
-0.019500399008393288,
-0.05220459774136543,
0.032123737037181854,
-0.023374274373054504,
-0.01034463569521904,
-0.04622850567102432,
-0.05132273957133293,
-0.019069047644734383,
0.029839584603905678,
-0.032304368913173676,
-0.029691364616155624,
0.004003846552222967,
0.005753546953201294,
-0.023232074454426765,
-0.006637681275606155,
-0.006466882303357124,
-0.026223333552479744,
0.002875502919778228,
0.009531012736260891,
-0.015526975505053997,
-0.028950674459338188,
-0.0020339456386864185,
-0.0031854650005698204,
0.03390989452600479,
0.023603161796927452,
0.035438813269138336,
-0.07573141157627106,
-0.02926327846944332,
-0.0001606591249583289,
-0.036638591438531876,
0.05727124214172363,
-0.02217816561460495,
0.08891931176185608,
-0.015194629319012165,
0.03148482367396355,
-0.03899383544921875,
-0.0023770553525537252,
-0.018905825912952423,
-0.002102288417518139,
-0.018635377287864685,
0.06033137068152428,
-0.0364186130464077,
0.001281768549233675,
-0.001798681216314435,
0.021046239882707596,
0.01694999262690544,
0.009278402663767338,
0.03259894251823425,
0.037758968770504,
0.007967835292220116,
-0.12252246588468552,
-0.04894588515162468,
-0.01924496702849865,
0.056318558752536774,
-0.0632021427154541,
-0.06699706614017487,
-0.021750347688794136,
-0.04341556876897812,
-0.045195773243904114,
-0.029242578893899918,
-0.0026704431511461735,
0.12310975790023804,
0.035776183009147644,
0.007621018216013908,
0.013814895413815975,
-0.07291829586029053,
-0.010267498902976513,
-0.03150098770856857,
0.01184904482215643,
-0.04878951609134674,
0.020865697413682938,
0.0033651087433099747,
-0.008093475364148617,
-0.015195047482848167,
-0.04887769743800163,
0.030968228355050087,
0.022585831582546234,
0.028288327157497406,
-0.00455835135653615,
-0.027996141463518143,
-0.006018605548888445,
0.03891098126769066,
0.0622815303504467,
-0.06555238366127014,
0.007350154221057892,
-0.009617944248020649,
0.0425877682864666,
0.006144029553979635,
0.014041926711797714,
-0.0203134436160326,
0.023647669702768326,
0.009960764087736607,
-0.01301399152725935,
0.008548904210329056,
-0.021735649555921555,
0.011417348869144917,
0.07557979971170425,
-0.036371249705553055,
0.0152659360319376,
-0.003352407133206725,
0.006679463665932417
] |
[
-0.6433110237121582,
2.286226987838745
] |
Number Theory
|
Mathematics
|
math-NT
|
na
|
na
|
2007-04-01T12:04:13
|
In this article we discuss a relation between the string topology and
differential forms based on the theory of Chen's iterated integrals and the
cyclic bar complex.
|
Iterated integral and the loop product
|
math.CA math.AT
|
0704.0014
| 2,007
|
[
-0.007069278042763472,
0.05266990512609482,
-0.015040204860270023,
-0.025559332221746445,
0.057217709720134735,
0.020796891301870346,
0.025035040453076363,
-0.04397355765104294,
-0.04504213109612465,
-0.014391143806278706,
-0.09866857528686523,
0.013438046909868717,
0.031623724848032,
0.015608363784849644,
0.06195875629782677,
-0.060871683061122894,
-0.0028893204871565104,
-0.00015034487296361476,
-0.019851913675665855,
-0.035920917987823486,
-0.04283449053764343,
-0.046937551349401474,
0.0001771727838786319,
-0.04551221802830696,
0.09489881992340088,
0.005043894052505493,
0.07301922887563705,
-0.0012399837141856551,
-0.07084529846906662,
0.0444219633936882,
0.07630626857280731,
-0.005735915154218674,
0.015456194058060646,
0.012468045577406883,
-0.0379837229847908,
-0.018458833917975426,
0.07221508026123047,
0.0364568792283535,
0.05259942635893822,
0.039282698184251785,
0.025017164647579193,
0.005063256248831749,
-0.021123861894011497,
-0.026805784553289413,
0.00300136161968112,
0.014220946468412876,
-0.03251270949840546,
0.044304173439741135,
0.043409381061792374,
0.003942498005926609,
-0.001928490586578846,
0.014551217667758465,
-0.011031106114387512,
-0.07674551010131836,
-0.016341498121619225,
0.019476668909192085,
0.01598263718187809,
-0.03743097186088562,
0.07291635125875473,
-0.014613419771194458,
-0.0001637290552025661,
0.03252075985074043,
-0.00034428367507644,
0.045870501548051834,
0.0523209348320961,
-0.09639545530080795,
0.04650439694523811,
0.007596926297992468,
0.009387725964188576,
-0.023682819679379463,
0.03203057125210762,
-0.021812861785292625,
0.06437177956104279,
0.02250516414642334,
-0.006384486332535744,
0.019427042454481125,
0.039454638957977295,
-0.05211245268583298,
0.0031950881239026785,
0.006905906833708286,
-0.05137486010789871,
-0.040459044277668,
0.0237397663295269,
0.023096494376659393,
0.03210229054093361,
-0.02397366613149643,
0.04395681992173195,
-0.012554807588458061,
-0.061429403722286224,
0.08017838001251221,
0.07000903785228729,
-0.04992204159498215,
0.01173730194568634,
0.02833275869488716,
-0.057808831334114075,
0.020949212834239006,
0.020254654809832573,
0.04072659835219383,
-0.04906900227069855,
-0.06740400195121765,
0.017911361530423164,
0.05304066464304924,
0.03718142211437225,
-0.0035055819898843765,
0.05475929006934166,
0.04387208819389343,
0.013643158599734306,
-0.06926903128623962,
0.00020504363055806607,
-0.02735711634159088,
-0.04265408217906952,
-0.015629807487130165,
-0.008100737817585468,
0.022952046245336533,
-0.04248974099755287,
0.007616173941642046,
0.0261641014367342,
-0.0988636463880539,
-0.021864043548703194,
0.04078071936964989,
-0.008138208650052547,
-0.026118896901607513,
0.02100507542490959,
0.01488527562469244,
0.041107576340436935,
0.004450750537216663,
-0.055061571300029755,
-0.033407069742679596,
0.0036529633216559887,
-0.058872006833553314,
-0.010494093410670757,
0.016083601862192154,
-0.0039323437958955765,
-0.0111704021692276,
0.05864190682768822,
0.04020087420940399,
-0.04218415543437004,
-0.05922193080186844,
0.01738276146352291,
-0.004095379263162613,
0.046347327530384064,
-0.028851505368947983,
-0.05713888630270958,
-0.006873434875160456,
0.013874408788979053,
-0.017820343375205994,
0.0018243513768538833,
-0.058148667216300964,
-0.020364662632346153,
-0.07744698226451874,
0.03338351845741272,
0.0348673090338707,
-0.010239210911095142,
0.022803204134106636,
-0.011962939985096455,
-0.0025914120487868786,
0.026460153982043266,
-0.036189038306474686,
0.06422602385282516,
0.03419502079486847,
0.0006312115001492202,
0.03061835654079914,
-0.015309169888496399,
0.003952162805944681,
-0.06583408266305923,
-0.03566716983914375,
0.017100581899285316,
0.01883971318602562,
-0.020831411704421043,
0.015649493783712387,
-0.0016073343576863408,
0.027429655194282532,
0.0051421113312244415,
-0.02455938048660755,
0.044407498091459274,
0.0017560729756951332,
-0.0381939671933651,
-0.008358909748494625,
0.013472536578774452,
0.021629439666867256,
-0.011862490326166153,
-0.05200345069169998,
-0.006588486488908529,
0.05147837847471237,
0.05974411964416504,
0.04778485372662544,
-0.015965737402439117,
-0.037302978336811066,
-0.009552493691444397,
-0.05628421902656555,
0.008916566148400307,
0.010168883949518204,
-0.0025522655341774225,
0.0009318034281022847,
-0.01392569299787283,
-0.008038254454731941,
0.0387994684278965,
0.005627843551337719,
0.06345393508672714,
-0.010846101678907871,
-0.031024429947137833,
0.006949639413505793,
0.016269586980342865,
-0.02010626159608364,
-0.07161545753479004,
0.05355631560087204,
0.006406668573617935,
0.029643310233950615,
0.014706305228173733,
0.0029155975207686424,
0.065119169652462,
-0.06061916798353195,
0.021416518837213516,
0.050685420632362366,
-0.08256807923316956,
-0.0035826629027724266,
0.014291729778051376,
-0.028733637183904648,
0.013415839523077011,
0.007667203433811665,
0.07929889112710953,
-0.007410062942653894,
0.010439942590892315,
-0.007134482730180025,
0.006275962106883526,
0.016370320692658424,
0.00574092473834753,
-0.027674509212374687,
-0.02149312198162079,
-0.038977719843387604,
0.009013156406581402,
-0.05743182823061943,
0.015073866583406925,
-0.03361339122056961,
0.01860138587653637,
0.003174187382683158,
0.023262595757842064,
0.015376250259578228,
0.02143835835158825,
0.07644689828157425,
0.010568167082965374,
-0.022481203079223633,
0.07969144731760025,
-0.04674980416893959,
-0.03621402755379677,
0.01221022941172123,
-0.0034959143958985806,
0.03343195468187332,
-0.07238315045833588,
0.0131769310683012,
0.06038018688559532,
-0.010168613865971565,
-0.04332370683550835,
0.04405050724744797,
0.061193399131298065,
-0.027894839644432068,
-0.027555027976632118,
0.0010119648650288582,
0.006437636911869049,
-0.05489663407206535,
0.014489931985735893,
-0.031646616756916046,
-0.0035855905152857304,
-0.02145211212337017,
-0.10821373015642166,
0.01602996699512005,
0.042729198932647705,
-0.08897071331739426,
0.010053228586912155,
-0.04925702512264252,
-0.010418964549899101,
-0.0071046543307602406,
0.023512892425060272,
-0.009479347616434097,
-0.00851350836455822,
-0.028067246079444885,
0.017335936427116394,
-0.030439626425504684,
-0.0583265945315361,
-0.0534239262342453,
-0.004324878100305796,
0.0017721230397000909,
-0.02814008668065071,
-0.019331950694322586,
-0.008957893587648869,
0.02318221889436245,
-0.017398709431290627,
0.02781197801232338,
0.0269797183573246,
0.07516256719827652,
-0.013420765288174152,
-0.004868758376687765,
0.03284110501408577,
0.035512618720531464,
0.007210209034383297,
0.08638745546340942,
0.026533573865890503,
-0.012043421156704426,
-0.0253921952098608,
-0.007059319410473108,
0.00024361233226954937,
0.03302328661084175,
0.02180095762014389,
-0.014516882598400116,
0.05723016336560249,
-0.01116697583347559,
-0.019589608535170555,
0.048711419105529785,
0.07836852967739105,
-0.01624760404229164,
0.0007936437032185495,
-0.0075912680476903915,
0.04922647029161453,
-0.0463770292699337,
-0.06246718019247055,
0.07534826546907425,
0.046575408428907394,
0.011585979722440243,
0.05240946263074875,
-0.0026199158746749163,
-0.009039762429893017,
-0.02419232949614525,
0.01339611317962408,
-0.047444481402635574,
-0.02725181356072426,
-0.010356639511883259,
-0.024866526946425438,
0.019190317019820213,
0.0012272326275706291,
-0.039844006299972534,
-0.04764421284198761,
0.035999566316604614,
-0.023147568106651306,
-0.011361068114638329,
-0.020887287333607674,
-0.015406244434416294,
-0.04571269825100899,
0.009222297929227352,
-0.042547401040792465,
0.029094558209180832,
0.0007955716573633254,
-0.0004771724052261561,
0.007458976004272699,
-0.028552625328302383,
0.017742982134222984,
0.025622425600886345,
-0.02168186940252781,
0.04028608649969101,
0.037162214517593384,
-0.013528113253414631,
-0.05705573782324791,
-0.011148260906338692,
0.007731171790510416,
0.0040636686608195305,
-0.016509519889950752,
0.04581357166171074,
0.04607576131820679,
-0.00029183606966398656,
0.03257817029953003,
0.026273353025317192,
0.051321644335985184,
0.01554884109646082,
-0.0018847823375836015,
-0.01055114809423685,
0.005477393511682749,
0.04802851751446724,
-0.017295610159635544,
0.012704771012067795,
-0.04743362218141556,
0.017617402598261833,
-0.04692582041025162,
0.0009391570929437876,
0.03366789594292641,
-0.03681454062461853,
0.03496856987476349,
-0.002876634942367673,
-0.07836354523897171,
0.038426127284765244,
-0.007495086640119553,
0.012821602635085583,
0.050359684973955154,
0.012067338451743126,
0.030588336288928986,
0.042442310601472855,
0.01107695046812296,
0.011857906356453896,
-0.04866920784115791,
0.024510029703378677,
-0.03545786812901497,
-0.03229783847928047,
0.003757008584216237,
0.019286807626485825,
-0.02088715136051178,
0.011141343973577023,
0.023657189682126045,
-0.017830604687333107,
0.061473116278648376,
0.03844521567225456,
0.0031910594552755356,
-0.004996425472199917,
-0.00337520195171237,
-0.09232346713542938,
0.034002408385276794,
-0.011588798835873604,
-0.04306714981794357,
0.053000349551439285,
0.008131814189255238,
-0.07598572224378586,
0.054123423993587494,
-0.0005826431442983449,
-0.012186259031295776,
-0.03255035728216171,
0.03380352258682251,
-0.05083763226866722,
0.04140906408429146,
0.03569020330905914,
0.0493265837430954,
-0.04045527055859566,
0.03432505577802658,
-0.0411984957754612,
-0.04710172861814499,
0.04204513505101204,
-0.03822078928351402,
-0.00999884121119976,
-0.015616164542734623,
0.05694787576794624,
0.0094666238874197,
0.04682014510035515,
-0.000578173843678087,
-0.04587351530790329,
-0.001412662910297513,
0.027341146022081375,
-0.03841668367385864,
0.05669362097978592,
-0.11918754130601883,
0.03595888242125511,
0.05468631908297539,
0.01601049117743969,
-0.03788003697991371,
-0.0061617507599294186,
0.04533015191555023,
-0.022814534604549408,
-0.037305980920791626,
0.024410158395767212,
0.018955672159790993,
0.05661031976342201,
0.03950025513768196,
-0.013437860645353794,
-0.06472572684288025,
-0.04456239938735962,
-0.006404868792742491,
0.005038006231188774,
-0.0026033050380647182,
-0.004146614111959934,
0.06057099625468254,
0.03935801237821579,
0.022545350715517998,
-0.005418982822448015,
-0.005789575632661581,
-0.03212032467126846,
0.03560377657413483,
0.008994362317025661,
-0.03958398476243019,
0.040266405791044235,
0.02081965282559395,
-0.024948306381702423,
-0.026924801990389824,
0.005148828960955143,
-0.004234244581311941,
0.07672514766454697,
0.015916503965854645,
0.0341702476143837,
0.02440009079873562,
-0.019715555012226105,
0.026371372863650322,
-0.0401357039809227,
0.06394872069358826,
-0.01172085851430893,
0.008963963016867638,
0.015319183468818665,
-0.03625931963324547,
-0.01130617968738079,
-0.07933451235294342,
-0.027091605588793755,
-0.015537353232502937,
0.0132062379270792,
-0.048991430550813675,
-0.0354241207242012,
-0.015238313004374504,
0.02971840649843216,
0.04696617275476456,
0.04365486279129982,
0.04227970913052559,
0.022081006318330765,
-0.019219236448407173,
-0.0035971631295979023,
-0.013186092488467693,
-0.03238777071237564,
0.05535842478275299,
-0.04157344996929169,
-0.053272880613803864,
-0.004322050139307976,
-0.019719574600458145,
0.05061464011669159,
-0.0012416874524205923,
0.058150842785835266,
0.0003275602648500353,
-0.02790178917348385,
-0.003670815611258149,
-0.02903210185468197,
0.018286623060703278,
0.03422427549958229,
0.0085211843252182,
0.04782431945204735,
-0.0031292494386434555,
-0.007666861172765493,
0.004650721326470375,
0.011106103658676147,
-0.0280863419175148,
0.021461915224790573,
0.02945094369351864,
0.04889422282576561,
0.023722896352410316,
-0.039528895169496536,
0.016252592206001282,
0.03990914672613144,
-0.07349657267332077,
-0.07721628993749619,
0.021643156185746193,
0.006670775823295116,
0.026803266257047653,
0.013120216317474842,
-0.01039445586502552,
-0.015524550341069698,
0.03502628579735756,
-0.051684390753507614,
-0.005747593939304352,
0.04751111939549446,
0.04806052893400192,
0.030108321458101273,
-0.03970947489142418,
-0.019673220813274384,
0.013333593495190144,
0.024301493540406227,
0.06272022426128387,
-0.053630340844392776,
-0.049362584948539734,
0.02948351390659809,
0.019745631143450737,
-0.04047852009534836,
-0.006641232408583164,
-0.030121030285954475,
0.012312281876802444,
-0.05394132807850838,
-0.008487479761242867,
-0.02310904674232006,
0.06522919982671738,
-0.02435472048819065,
-0.03895460441708565,
0.028855497017502785,
0.024591103196144104,
0.0213492251932621,
-0.01654612272977829,
0.013770410791039467,
0.02071305736899376,
-0.04770129919052124,
0.012404096312820911,
0.031111519783735275,
0.018407067283988,
-0.009844944812357426,
0.013460489921271801,
-0.0281473770737648,
-0.032648321241140366,
0.03370240703225136,
-0.016204960644245148,
-0.049568887799978256,
0.04224911704659462,
-0.07221401482820511,
0.013674993067979813,
-0.03552859276533127,
-0.034205883741378784,
-0.07284816354513168,
0.054822299629449844,
-0.09254448115825653,
-0.05250933766365051,
0.015908852219581604,
-0.028957221657037735,
-0.03182288259267807,
0.04397554323077202,
0.02909003756940365,
0.010152876377105713,
0.05093761906027794,
-0.04832109808921814,
0.03663284331560135,
-0.01909806579351425,
0.026374932378530502,
-0.006805308163166046,
0.04171086102724075,
-0.0039005286525934935,
-0.054757632315158844,
0.007749014999717474,
0.01945972442626953,
0.08753565698862076,
-0.05186024308204651,
0.04507708176970482,
0.0587058924138546,
0.04590766504406929,
0.002730732783675194,
-0.030300509184598923,
0.012980555184185505,
0.043205246329307556,
0.027772309258580208,
-0.013675549998879433,
-0.030250119045376778,
0.033612847328186035,
-0.015096059069037437,
0.04487341269850731,
-0.025631016120314598,
0.0027451813220977783,
-0.05790649354457855,
0.05538494139909744,
-0.06582298874855042,
-0.007073909044265747,
-0.05297446250915527,
0.022159159183502197,
0.009059838950634003,
-0.028336962684988976,
-0.03485658019781113,
-0.037677861750125885,
0.057132937014102936,
-0.03667593374848366,
0.013660330325365067,
-0.025944430381059647,
-0.011073516681790352,
-0.031558193266391754,
0.032578565180301666,
-0.03411256894469261,
0.03853246942162514,
0.010690273717045784,
0.02395227923989296,
0.01490110158920288,
-0.003284134902060032,
0.03271133080124855,
0.005274239927530289,
0.03625161200761795,
-0.0034461270552128553,
0.017483605071902275,
-0.00021987775107845664,
-0.018045620992779732,
0.030785370618104935,
0.05568816885352135,
0.08629066497087479,
0.008404426276683807,
0.02181016281247139,
0.040989525616168976,
-0.08137703686952591,
-0.006481257267296314,
-0.04865939915180206,
-0.017219144850969315,
-0.007410889491438866,
-0.024787798523902893,
0.024555273354053497,
0.017926262691617012,
-0.01602049171924591,
0.0016110268188640475,
0.018891042098402977,
0.010486827231943607,
-0.028928296640515327,
-0.02640955150127411,
0.022052181884646416,
-0.029818806797266006,
-0.023023951798677444,
-0.01581801474094391,
-0.024987854063510895,
-0.034328948706388474,
-0.010166316293179989,
-0.06295537948608398,
-0.027484074234962463,
-0.06604447215795517,
0.01471793930977583,
-0.021577315405011177,
0.013555488549172878,
-0.023961151018738747,
-0.017972296103835106,
-0.0031733661890029907,
-0.04291488975286484,
-0.03852158412337303,
-0.07242751121520996,
-0.05267205089330673,
-0.02438899502158165,
0.03372059389948845,
0.023936891928315163,
-0.06410329788923264,
-0.0584491491317749,
0.045402444899082184,
0.013933118432760239,
-0.0494101345539093,
0.02811393514275551,
-0.04216926544904709,
0.04835093766450882,
0.005146969575434923,
0.022062765434384346,
-0.02945251390337944,
0.009202434681355953,
0.04559045284986496,
-0.014661747962236404,
-0.002087482949718833,
0.002572094788774848,
-0.012610028497874737,
0.01936269924044609,
0.002485672477632761,
-0.0157774668186903,
-0.021307513117790222,
-0.017135409638285637,
-0.03169548884034157,
0.018642935901880264,
0.012457570992410183,
-0.051808081567287445,
-0.07299390435218811,
0.015394060872495174,
0.0346481129527092,
-0.03316890820860863,
-0.00820092111825943,
-0.006093975156545639,
-0.007850038819015026,
-0.037435129284858704,
-0.019863810390233994,
-0.03613298386335373,
0.044108033180236816,
0.03457580879330635,
-0.028454521670937538,
0.009968751110136509,
-0.03743807598948479,
0.03441143035888672,
-0.032056115567684174,
0.014822949655354023,
-0.03021879494190216,
-0.003550406778231263,
-0.03303477540612221,
-0.014667428098618984,
-0.0336870402097702,
-0.04515274614095688,
-0.022294379770755768,
0.046432867646217346,
0.012502066791057587,
0.004431968554854393,
-0.04847894608974457,
0.05089224502444267,
0.053776565939188004,
0.007360477466136217,
-0.00774666853249073,
0.021274508908391,
-0.009218952618539333,
0.04080263897776604,
0.0608980730175972,
-0.01045138668268919,
-0.01024611759930849,
0.04406978562474251,
0.02693210542201996,
-0.004851954989135265,
-0.0007005996303632855,
0.031667422503232956,
-0.028606263920664787,
0.03355688974261284,
-0.008805828168988228,
0.003093643579632044,
-0.017710020765662193,
0.011225239373743534
] |
[
1.3562570810317993,
1.3984668254852295
] |
Classical Analysis and ODEs
|
Mathematics
|
math-CA
|
math-AT
|
na
|
2007-04-02T18:10:09
|
The pure spinor formulation of the ten-dimensional superstring leads to
manifestly supersymmetric loop amplitudes, expressed as integrals in pure
spinor superspace. This paper explores different methods to evaluate these
integrals and then uses them to calculate the kinematic factors of the one-loop
and two-loop massless four-point amplitudes involving two and four Ramond
states.
|
Fermionic superstring loop amplitudes in the pure spinor formalism
|
hep-th
|
0704.0015
| 2,007
|
[
0.011520120315253735,
0.025732403621077538,
-0.009357927367091179,
-0.04135053977370262,
0.02056361362338066,
-0.002780766226351261,
-0.011316743679344654,
0.05029457435011864,
-0.001394241931848228,
-0.019814828410744667,
-0.11624600738286972,
0.013184960931539536,
0.042846519500017166,
0.03317129239439964,
0.04387718066573143,
-0.011732573620975018,
0.012071038596332073,
-0.005355057772248983,
0.023009147495031357,
-0.05749906599521637,
-0.0040549528785049915,
-0.047387268394231796,
-0.03941504284739494,
-0.023134078830480576,
0.07355599850416183,
-0.03254666551947594,
0.016451647505164146,
-0.015562188811600208,
-0.062035731971263885,
0.006812402047216892,
-0.0019040880724787712,
-0.021945303305983543,
0.0029548665042966604,
-0.06774593144655228,
-0.035720374435186386,
-0.037723615765571594,
0.09628026187419891,
0.02691865898668766,
-0.0030145335476845503,
0.036321207880973816,
0.02777164801955223,
-0.04548521339893341,
-0.02477065660059452,
0.004602570086717606,
0.016851451247930527,
0.03766515105962753,
0.01639297604560852,
-0.0033411094918847084,
-0.005209564696997404,
0.027689341455698013,
-0.03717914968729019,
0.00709746265783906,
0.022110728546977043,
-0.024758867919445038,
-0.010340817272663116,
0.04605000093579292,
-0.01297535840421915,
-0.03690512478351593,
0.03763144835829735,
0.044793542474508286,
0.07831601053476334,
0.0047617158852517605,
0.014738052152097225,
0.024463346228003502,
0.0469299778342247,
0.004495995119214058,
0.004729569423943758,
0.03274068608880043,
-0.005622030235826969,
0.01891126111149788,
0.0735829770565033,
-0.01670503430068493,
0.039688125252723694,
0.0022397295106202364,
-0.03785725310444832,
0.03057359904050827,
-0.006427799351513386,
-0.033450037240982056,
-0.0033795442432165146,
-0.008946100249886513,
0.015007808804512024,
-0.06265593320131302,
0.04230586439371109,
-0.016472533345222473,
0.012734844349324703,
-0.019479643553495407,
0.03756679967045784,
0.014013903215527534,
-0.07246989756822586,
0.028227537870407104,
0.02904784493148327,
0.012215572409331799,
0.024080052971839905,
0.08538959920406342,
-0.03619018569588661,
0.005141271743923426,
-0.003370883408933878,
0.0526309497654438,
-0.04349024221301079,
-0.08009620010852814,
-0.030541736632585526,
0.0842992514371872,
0.00821586512029171,
0.037353988736867905,
0.07057807594537735,
0.00371622946113348,
0.005444586742669344,
-0.045396849513053894,
-0.004779805429279804,
-0.02539871446788311,
-0.09139304608106613,
-0.05047372356057167,
-0.00236453372053802,
-0.006614358630031347,
-0.04853695258498192,
-0.0013071243884041905,
0.07345869392156601,
-0.09103803336620331,
-0.007395127322524786,
0.0688527524471283,
0.01375829242169857,
-0.03497694060206413,
0.04152463376522064,
0.061640121042728424,
0.02426910400390625,
0.013114876113831997,
-0.062395162880420685,
-0.02727452665567398,
0.007242068648338318,
-0.004770826082676649,
0.0069657075218856335,
0.02546839788556099,
-0.009207685478031635,
-0.010132534429430962,
-0.004302504006773233,
0.0503830723464489,
-0.02655205689370632,
-0.06423236429691315,
0.02601168490946293,
-0.0441620908677578,
0.00295687816105783,
0.002449417719617486,
-0.026007089763879776,
-0.012960421852767467,
0.01728234812617302,
-0.083807572722435,
0.039482422173023224,
-0.04300280287861824,
-0.06289777904748917,
0.008153306320309639,
0.0604516938328743,
0.014270845800638199,
0.037962403148412704,
0.029500342905521393,
-0.01035471074283123,
-0.03724725916981697,
0.0023685183841735125,
-0.012126290239393711,
0.05620695650577545,
0.037427954375743866,
0.0045224823988974094,
0.03431026637554169,
-0.02951768785715103,
0.062178805470466614,
-0.10531199723482132,
0.0191873237490654,
0.06864654272794724,
0.0685821920633316,
-0.032634977251291275,
0.020846543833613396,
-0.029229719191789627,
0.00797178503125906,
-0.017126094549894333,
-0.03899963200092316,
-0.006758132949471474,
0.011328954249620438,
-0.02190435864031315,
-0.01316552609205246,
0.0043132612481713295,
0.007365441415458918,
0.0671820342540741,
-0.000031172494345810264,
-0.02062295936048031,
0.009338886477053165,
0.024122370406985283,
-0.0250924713909626,
-0.004917712416499853,
0.02487955242395401,
-0.02404189668595791,
-0.04222498834133148,
0.02795945666730404,
0.019930735230445862,
-0.030675772577524185,
-0.05041985958814621,
-0.06480392068624496,
-0.01937371864914894,
0.05398429185152054,
-0.058276209980249405,
0.009523187763988972,
-0.011385221965610981,
-0.008632163517177105,
-0.020762545987963676,
-0.038842782378196716,
-0.027835117653012276,
0.00010510985157452524,
0.052767787128686905,
0.018414076417684555,
0.06969179958105087,
0.0014732680283486843,
0.027956359088420868,
0.036857374012470245,
0.02945113740861416,
-0.013876119628548622,
0.05726676434278488,
-0.019913792610168457,
0.00431188615038991,
0.03848625347018242,
-0.054165780544281006,
-0.023254387080669403,
0.06417216360569,
0.025427890941500664,
-0.038068097084760666,
0.02422785386443138,
0.04792322590947151,
0.04261836037039757,
0.04875095933675766,
-0.03394661098718643,
0.022475043311715126,
-0.008362666703760624,
0.010026267729699612,
-0.06579689681529999,
-0.036405351012945175,
0.0012912721140310168,
-0.030521998181939125,
-0.04772736877202988,
-0.005999588407576084,
0.003975842613726854,
0.008479357697069645,
0.03364448621869087,
0.05667145177721977,
0.08557183295488358,
0.05387939512729645,
0.015685847029089928,
-0.011668168008327484,
-0.07299364358186722,
-0.005190838593989611,
-0.008676278404891491,
0.017342282459139824,
-0.03823942318558693,
0.023271329700946808,
0.011483750306069851,
0.036754060536623,
0.006223582196980715,
0.07176760584115982,
-0.015323663130402565,
-0.010474607348442078,
-0.009364751167595387,
0.04995301365852356,
-0.07283288985490799,
-0.050278082489967346,
0.044961027801036835,
-0.030843587592244148,
0.0054677617736160755,
-0.0473647303879261,
-0.0661020502448082,
0.023035306483507156,
0.01278354600071907,
-0.03178411349654198,
-0.022370358929038048,
-0.059332337230443954,
-0.015038438141345978,
0.05515405908226967,
0.005386116914451122,
0.01336029451340437,
0.004355712793767452,
0.0026594200171530247,
0.0504840724170208,
0.007585425395518541,
-0.03145776689052582,
0.0031334718223661184,
-0.0829928070306778,
-0.025122035294771194,
-0.04648727551102638,
-0.008929266594350338,
-0.0037071409169584513,
-0.005034222267568111,
0.04898068308830261,
0.00035269843647256494,
-0.007601112127304077,
0.03808600455522537,
-0.05458272248506546,
0.0058726235292851925,
0.025787686929106712,
0.02647973969578743,
-0.020394057035446167,
0.04788785055279732,
0.013797728344798088,
-0.02499183639883995,
0.04538374021649361,
0.06006820872426033,
0.014233284629881382,
0.026783879846334457,
0.014273779466748238,
-0.03321816399693489,
-0.027993232011795044,
-0.01678275875747204,
-0.0060918089002370834,
-0.0007011198904365301,
0.03602622449398041,
0.006376002915203571,
0.01313017774373293,
0.04450995475053787,
0.017460210248827934,
0.021435987204313278,
-0.036164212971925735,
0.023015717044472694,
0.027728460729122162,
0.02347712591290474,
0.10623450577259064,
-0.004172082059085369,
-0.014313451014459133,
-0.043772902339696884,
0.04159674048423767,
-0.015962544828653336,
0.011500037275254726,
0.009195348247885704,
0.019822267815470695,
-0.024450263008475304,
-0.03857157751917839,
-0.03600901737809181,
-0.06921762973070145,
0.04239213094115257,
-0.044831499457359314,
-0.004399048164486885,
-0.033030178397893906,
-0.021773837506771088,
-0.061086781322956085,
0.04255639761686325,
-0.03413928672671318,
-0.011503960005939007,
-0.012399609200656414,
-0.06268487125635147,
-0.026166465133428574,
-0.02345968782901764,
-0.0014099770924076438,
-0.00094547652406618,
-0.036004386842250824,
0.006172227673232555,
0.06930908560752869,
0.0014625864569097757,
-0.03140263631939888,
0.01831509731709957,
-0.006063264328986406,
0.008249223232269287,
-0.024713803082704544,
0.031819600611925125,
0.05801811069250107,
-0.009496607817709446,
0.05831660330295563,
0.037244100123643875,
0.047665826976299286,
0.004657386336475611,
-0.001130486256442964,
-0.05359262600541115,
0.00038835586747154593,
0.024004727602005005,
0.019854489713907242,
-0.025089619681239128,
0.01708866097033024,
-0.01084001176059246,
-0.01905386708676815,
-0.05140119045972824,
0.025708241388201714,
0.020684178918600082,
0.03371109440922737,
0.011271056719124317,
-0.04678115248680115,
0.024208614602684975,
-0.036997370421886444,
0.04839232563972473,
0.06943310052156448,
0.023100832477211952,
0.013246835209429264,
0.03887175768613815,
0.005601370241492987,
0.00916533824056387,
-0.05892067775130272,
0.016515415161848068,
-0.0305889081209898,
-0.0350395143032074,
0.05958840623497963,
-0.035873331129550934,
0.007034022361040115,
-0.020602071657776833,
0.03851981833577156,
-0.013094151392579079,
0.045707590878009796,
-0.048094142228364944,
0.008741088211536407,
0.022396216168999672,
-0.0590183362364769,
-0.06189609318971634,
0.0491890087723732,
-0.030889270827174187,
-0.043998681008815765,
0.002143658697605133,
-0.028088003396987915,
-0.017382478341460228,
0.07088813185691833,
0.028991226106882095,
0.025381535291671753,
0.0569433867931366,
0.036999836564064026,
-0.07332271337509155,
0.0804944559931755,
0.04815109446644783,
0.053798288106918335,
-0.03276113048195839,
0.022399503737688065,
-0.03176221624016762,
-0.023559460416436195,
0.06766261160373688,
-0.00407909881323576,
-0.016701078042387962,
0.015614476054906845,
-0.03267541900277138,
-0.035665858536958694,
0.025544632226228714,
0.023628856986761093,
-0.04510556533932686,
0.023302767425775528,
0.013526665978133678,
0.00458719814196229,
0.04771743714809418,
-0.08672413229942322,
0.05103752017021179,
-0.023503480479121208,
-0.017776207998394966,
-0.01754065230488777,
0.05075676366686821,
0.02303151786327362,
-0.05808398127555847,
0.012048754841089249,
0.026014577597379684,
0.010999930091202259,
0.0830255001783371,
0.02883307822048664,
-0.027487553656101227,
-0.03975757583975792,
-0.06349165737628937,
0.0028053049463778734,
0.0030113819520920515,
-0.002137009287253022,
0.047543663531541824,
0.01248977705836296,
-0.02120223082602024,
-0.0022664563730359077,
0.008870157413184643,
0.034891415387392044,
0.020156225189566612,
0.018704071640968323,
0.01619051583111286,
-0.038022663444280624,
-0.02624574303627014,
-0.023301200941205025,
-0.03372775763273239,
0.0035553383640944958,
-0.008849408477544785,
0.00478248530998826,
0.06021471321582794,
0.007978140376508236,
-0.030329890549182892,
0.006361796986311674,
-0.007440394256263971,
0.020770957693457603,
-0.009829753078520298,
0.010962449945509434,
-0.05389856919646263,
-0.009729080833494663,
0.10043300688266754,
0.00015445427561644465,
-0.02217056229710579,
-0.008611515164375305,
-0.040463320910930634,
-0.031461674720048904,
-0.0013289032503962517,
0.014273502863943577,
-0.011438058689236641,
0.006103077437728643,
0.017736544832587242,
-0.024605922400951385,
0.07597469538450241,
0.0150264548137784,
-0.03969525173306465,
0.012362188659608364,
0.023540841415524483,
-0.025116784498095512,
-0.04765613377094269,
-0.002001728629693389,
0.006003400310873985,
-0.0025758016854524612,
0.016665128991007805,
0.05122777074575424,
0.05437280982732773,
-0.01714078150689602,
0.04147019237279892,
-0.020593376830220222,
-0.06485231220722198,
-0.004666432738304138,
-0.031685929745435715,
0.017117707058787346,
0.07719719409942627,
0.025005215778946877,
0.01591068133711815,
-0.030674193054437637,
-0.046810995787382126,
0.04721586033701897,
-0.01837540604174137,
-0.05271865054965019,
0.03574375435709953,
0.020957889035344124,
0.05496567487716675,
-0.02221699431538582,
-0.03899185359477997,
-0.055339328944683075,
0.05907784402370453,
-0.012058952823281288,
-0.058008935302495956,
0.04731791466474533,
-0.009831497445702553,
0.033853624016046524,
0.0033103020396083593,
0.029751768335700035,
-0.009628177620470524,
0.035510722547769547,
-0.10382194817066193,
0.025377731770277023,
0.023116353899240494,
-0.007043013349175453,
0.003558224532753229,
-0.012083920650184155,
-0.00487894844263792,
0.0015887634363025427,
0.04128042981028557,
-0.017051564529538155,
-0.05817170813679695,
-0.0537661574780941,
-0.02464381419122219,
0.0010608116863295436,
-0.06975863128900528,
-0.03954262658953667,
-0.016087902709841728,
0.0437028631567955,
-0.06098334491252899,
0.0345110259950161,
0.008704540319740772,
-0.011370396241545677,
-0.004839641973376274,
-0.041042231023311615,
0.015190999023616314,
0.007847581058740616,
-0.012968304567039013,
0.026301100850105286,
0.025103449821472168,
-0.0062235500663518906,
-0.08465495705604553,
-0.019065041095018387,
-0.02089092507958412,
0.02327175997197628,
0.011668229475617409,
-0.00616562832146883,
-0.02302200347185135,
-0.06546115130186081,
0.05043580383062363,
-0.025823969393968582,
-0.013559576123952866,
0.014100589789450169,
0.008056027814745903,
-0.026902489364147186,
0.0024727305863052607,
-0.024062037467956543,
0.02062065526843071,
-0.03363552317023277,
-0.00808699894696474,
-0.027060944586992264,
0.05215398222208023,
-0.04569849744439125,
-0.06475804001092911,
0.05045096203684807,
0.04003787040710449,
-0.015157556161284447,
0.007836641743779182,
-0.0006466129561886191,
-0.020069360733032227,
-0.022709090262651443,
0.014945851638913155,
-0.020726121962070465,
0.016651298850774765,
-0.01817276142537594,
-0.015111207030713558,
0.01348789595067501,
0.02338266186416149,
0.07072377949953079,
-0.021876182407140732,
0.037508051842451096,
0.04676372930407524,
-0.024323320016264915,
0.015498214401304722,
-0.045910075306892395,
-0.00389377074316144,
0.039856236428022385,
0.023821566253900528,
-0.043108440935611725,
-0.02339194528758526,
0.014321171678602695,
-0.007868066430091858,
0.04654547572135925,
-0.014336359687149525,
-0.004128195345401764,
-0.04354454204440117,
0.06916452199220657,
-0.007293691858649254,
0.006585333496332169,
-0.04727001488208771,
0.003696618601679802,
0.027727801352739334,
-0.0011367079569026828,
-0.030878223478794098,
-0.008278287015855312,
0.010178640484809875,
0.010431287810206413,
-0.010646850802004337,
-0.004890847019851208,
-0.04750070348381996,
-0.026471365243196487,
0.03999043256044388,
0.0012508979998528957,
0.049033019691705704,
-0.019654013216495514,
0.08281762152910233,
0.0413384810090065,
-0.05323987081646919,
-0.0021838638931512833,
-0.001237988588400185,
0.018099311739206314,
0.020757991820573807,
-0.00458538206294179,
0.030867228284478188,
-0.016420723870396614,
0.034520890563726425,
0.0876646414399147,
0.022941095754504204,
0.008259560912847519,
0.0621049664914608,
-0.02411152794957161,
0.0002838335349224508,
0.054660338908433914,
0.059178270399570465,
-0.00125147495418787,
-0.01618889905512333,
0.0036135404370725155,
-0.036346085369586945,
-0.02305951900780201,
-0.015152242965996265,
0.02152831293642521,
0.00045888961176387966,
-0.02411889284849167,
-0.03090120479464531,
-0.037656236439943314,
0.012995115481317043,
-0.02467632107436657,
-0.02037651091814041,
-0.021727226674556732,
-0.014342008158564568,
-0.03325439617037773,
-0.00912349484860897,
-0.013889146968722343,
-0.004837920889258385,
0.0035433084703981876,
-0.015437232330441475,
-0.017093496397137642,
-0.006249327678233385,
-0.03390803933143616,
0.005841000005602837,
0.0029273955151438713,
0.038075972348451614,
-0.0006799111724831164,
-0.059612520039081573,
-0.07612206786870956,
-0.03307974338531494,
0.06255263835191727,
0.01871033012866974,
-0.0028235360514372587,
-0.07229389250278473,
-0.008815828710794449,
-0.006190661806613207,
-0.0577726848423481,
-0.02399316430091858,
0.005022983532398939,
0.036949917674064636,
-0.006063204258680344,
-0.0003158906183671206,
-0.021703915670514107,
0.05434177443385124,
0.03345106542110443,
-0.01054389588534832,
0.0008258085581474006,
0.006205450277775526,
-0.008955013006925583,
0.0280750822275877,
0.0010591117898002267,
0.015541096217930317,
0.036450520157814026,
0.020994171500205994,
-0.020021317526698112,
0.008809177204966545,
-0.013391660526394844,
-0.029333896934986115,
0.006786624900996685,
-0.03886336088180542,
0.04785606637597084,
-0.0201273076236248,
-0.06044595316052437,
0.03103337250649929,
-0.027051623910665512,
-0.05207815766334534,
0.005983253475278616,
0.0007584594422951341,
0.0644095316529274,
-0.00921596772968769,
0.012303833849728107,
0.0016214869683608413,
-0.06410415470600128,
0.03517424315214157,
-0.012247581034898758,
0.024032624438405037,
-0.07103416323661804,
0.008674572221934795,
-0.06990588456392288,
0.017866259440779686,
0.02995959296822548,
-0.07970912754535675,
-0.0077256555669009686,
-0.004122133832424879,
-0.045154958963394165,
-0.016821477562189102,
-0.059754401445388794,
0.0030607779044657946,
0.02264646254479885,
-0.03505193814635277,
-0.029945502057671547,
-0.02861318364739418,
-0.016544196754693985,
0.004203815013170242,
0.03898430988192558,
0.01337803341448307,
-0.014025015756487846,
-0.03156592324376106,
0.09061531722545624,
0.005626303609460592,
0.05735982954502106,
0.027011876925826073,
-0.013729375787079334,
0.057685695588588715,
0.004483927506953478,
-0.028100157156586647,
-0.06165607273578644,
0.04274753853678703
] |
[
13.409040451049805,
0.378653347492218
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-03-31T07:04:26
|
In this work, we evaluate the lifetimes of the doubly charmed baryons
$\Xi_{cc}^{+}$, $\Xi_{cc}^{++}$ and $\Omega_{cc}^{+}$. We carefully calculate
the non-spectator contributions at the quark level where the Cabibbo-suppressed
diagrams are also included. The hadronic matrix elements are evaluated in the
simple non-relativistic harmonic oscillator model. Our numerical results are
generally consistent with that obtained by other authors who used the diquark
model. However, all the theoretical predictions on the lifetimes are one order
larger than the upper limit set by the recent SELEX measurement. This
discrepancy would be clarified by the future experiment, if more accurate
experiment still confirms the value of the SELEX collaboration, there must be
some unknown mechanism to be explored.
|
Lifetime of doubly charmed baryons
|
hep-ph
|
0704.0016
| 2,007
|
[
-0.0027349821757525206,
0.01969260908663273,
-0.0029545770958065987,
-0.029647881165146828,
0.0502755381166935,
0.01317377109080553,
0.0378359854221344,
0.03617381304502487,
0.0026851880829781294,
-0.008903310634195805,
-0.07821130752563477,
0.030019249767065048,
0.007243622560054064,
0.008936962112784386,
0.013266636058688164,
-0.046329986304044724,
0.023126371204853058,
0.02499651163816452,
-0.021200081333518028,
-0.0074708773754537106,
-0.03022289089858532,
-0.0024205800145864487,
-0.026195965707302094,
-0.04331519082188606,
0.07956857234239578,
0.0057424455881118774,
0.030726537108421326,
0.0585903525352478,
-0.08700304478406906,
0.07322871685028076,
0.004706428851932287,
-0.06143666431307793,
0.041221365332603455,
-0.026002172380685806,
-0.02603728696703911,
0.008417903445661068,
0.08753553777933121,
0.027123119682073593,
-0.011751614511013031,
0.04365577548742294,
-0.006884580943733454,
-0.016665220260620117,
0.0563957653939724,
-0.04868673160672188,
0.010040217079222202,
0.042621172964572906,
0.03443184867501259,
-0.028142040595412254,
0.059738632291555405,
-0.03608810156583786,
-0.05442561209201813,
0.031252458691596985,
0.04278435558080673,
-0.010284424759447575,
-0.014482306316494942,
0.03823167458176613,
0.05379185453057289,
-0.03769835829734802,
0.02882533147931099,
-0.007013096008449793,
0.014110417105257511,
0.03451857343316078,
-0.0258211400359869,
0.042132459580898285,
0.049187202006578445,
-0.050830282270908356,
0.002569840755313635,
0.03817977011203766,
-0.04668700322508812,
-0.027087407186627388,
0.02352689765393734,
-0.012279043905436993,
-0.016856377944350243,
0.03962453454732895,
0.017744315788149834,
0.012187708169221878,
-0.03587540239095688,
0.0248054601252079,
-0.02110283449292183,
-0.03345174342393875,
0.03499148413538933,
-0.0004848205717280507,
-0.004359686281532049,
0.02011401578783989,
0.06817590445280075,
0.007833307608962059,
-0.01709112897515297,
0.018751023337244987,
-0.10441579669713974,
0.03109397180378437,
0.07133929431438446,
-0.03551635518670082,
0.025963395833969116,
0.03709951415657997,
-0.006447412073612213,
0.001273928675800562,
0.004848596639931202,
0.027748551219701767,
0.014718038029968739,
-0.0041199978440999985,
0.03162363916635513,
0.06995473057031631,
-0.007695423439145088,
0.052209168672561646,
0.03125559538602829,
0.05755678564310074,
-0.0009310746099799871,
-0.0009156769374385476,
0.024545080959796906,
-0.011523842811584473,
-0.11287122964859009,
0.008703161031007767,
0.031075874343514442,
0.006812710780650377,
0.01349844690412283,
-0.019274195656180382,
0.036428552120923996,
-0.06728155165910721,
-0.01683814637362957,
0.04286797717213631,
0.0045715621672570705,
0.011774291284382343,
-0.02733180858194828,
0.030635464936494827,
0.003199751954525709,
0.01329008862376213,
-0.02734025940299034,
0.01828160136938095,
0.004171194974333048,
-0.01033447403460741,
-0.026461347937583923,
0.02391045168042183,
-0.014041636139154434,
0.033830225467681885,
0.016792912036180496,
0.022863315418362617,
0.008003519847989082,
-0.03214948996901512,
0.0211340244859457,
0.002369210822507739,
0.04235651344060898,
-0.019106874242424965,
0.004737150855362415,
-0.031938254833221436,
0.026417287066578865,
-0.0536782443523407,
0.03926251828670502,
-0.06392297148704529,
-0.02872522361576557,
0.0035620457492768764,
0.04384272173047066,
0.0010227831080555916,
0.033524274826049805,
0.03578963503241539,
-0.04400401562452316,
-0.05181333050131798,
-0.05238981917500496,
-0.0008083421853370965,
-0.05752227455377579,
0.05907730385661125,
-0.01266014575958252,
0.03908390924334526,
-0.027058525010943413,
-0.006599696818739176,
-0.032818399369716644,
-0.023507898673415184,
0.009956764057278633,
0.007495226804167032,
0.00011914824426639825,
0.01822632923722267,
-0.054281044751405716,
-0.0375051274895668,
-0.001092641963623464,
-0.02291225828230381,
0.007271142210811377,
-0.002827353309839964,
-0.03376908600330353,
-0.02734356001019478,
-0.01884293183684349,
0.016062278300523758,
0.0503736287355423,
-0.03212307021021843,
0.01811344176530838,
0.02044779434800148,
-0.02200269140303135,
-0.014160605147480965,
-0.012199857272207737,
-0.030503926798701286,
0.00924772210419178,
-0.008242799900472164,
0.004993988201022148,
-0.002303248504176736,
0.010464556515216827,
-0.018174251541495323,
-0.028080543503165245,
-0.03161884471774101,
0.09280382841825485,
-0.0277935229241848,
-0.01267477497458458,
-0.00029233694658614695,
-0.063325896859169,
-0.026604389771819115,
-0.04095222428441048,
-0.028945043683052063,
0.026616737246513367,
0.02968202903866768,
0.011117671616375446,
-0.010970117524266243,
0.01354314386844635,
-0.03849329054355621,
0.08044520765542984,
-0.004412275739014149,
-0.03821895271539688,
0.033855415880680084,
-0.0028705555014312267,
0.029227398335933685,
-0.017497321590781212,
-0.043278083205223083,
-0.007807060610502958,
0.03112105466425419,
-0.003262704238295555,
0.004550931975245476,
-0.006045525893568993,
-0.06714826077222824,
0.003574228612706065,
0.03949901461601257,
-0.004370119422674179,
0.020826095715165138,
-0.003484223037958145,
-0.031010093167424202,
-0.0003601944481488317,
-0.06988508254289627,
-0.03088674321770668,
0.002808284480124712,
-0.021613100543618202,
0.0017516022780910134,
-0.04516955465078354,
-0.010228870436549187,
0.039930809289216995,
0.041450005024671555,
0.0672147125005722,
-0.00785892829298973,
0.040580395609140396,
-0.039435144513845444,
-0.05488675832748413,
0.002396024763584137,
0.015635520219802856,
0.033914223313331604,
-0.07113423198461533,
0.009921496734023094,
0.018697120249271393,
0.02466495707631111,
0.013966647908091545,
0.06715790927410126,
0.04213354364037514,
0.0015634947922080755,
-0.031126901507377625,
0.02613297663629055,
-0.03306318074464798,
-0.04461277648806572,
-0.010161325335502625,
-0.04304680973291397,
-0.028411291539669037,
-0.06277836859226227,
-0.014160583727061749,
0.004354954697191715,
0.01386537030339241,
0.002603295026347041,
-0.017599603161215782,
-0.011054439470171928,
0.02141810767352581,
0.02931642159819603,
0.04520155116915703,
0.04233540967106819,
-0.015725338831543922,
0.00873404648154974,
0.03384547680616379,
0.029385551810264587,
-0.02466164529323578,
-0.022349746897816658,
-0.04152192175388336,
-0.031212199479341507,
-0.038089774549007416,
-0.012339380569756031,
0.02119852602481842,
0.036759279668331146,
0.02520175464451313,
-0.010666824877262115,
0.02135169506072998,
0.044605206698179245,
-0.049224480986595154,
-0.01538760308176279,
-0.0008215113775804639,
0.05537676811218262,
0.02069760486483574,
0.043971288949251175,
0.0872155949473381,
-0.02289726212620735,
0.001264564460143447,
0.045811012387275696,
0.03306804969906807,
0.040472742170095444,
-0.057648301124572754,
-0.005574296228587627,
0.036106519401073456,
0.014584764838218689,
-0.01224176399409771,
0.03052728809416294,
0.09971670806407928,
0.01014669332653284,
0.030822986736893654,
0.04652257263660431,
0.004625252448022366,
0.03927040472626686,
-0.04294491186738014,
0.0421924963593483,
-0.02324388548731804,
0.024647559970617294,
0.039553090929985046,
-0.02890525572001934,
0.05544014275074005,
-0.011269099079072475,
0.041564878076314926,
-0.010458179749548435,
0.021091604605317116,
0.0004521966620814055,
0.0067851063795387745,
0.02355032227933407,
-0.005949953105300665,
-0.03832549974322319,
-0.030565936118364334,
0.050530217587947845,
0.026774179190397263,
-0.01716829277575016,
-0.05208417400717735,
-0.024297066032886505,
-0.04453825205564499,
0.008247057907283306,
-0.025921490043401718,
0.029876092448830605,
-0.008235742338001728,
-0.03729977086186409,
-0.043961431831121445,
-0.013666104525327682,
-0.03191922605037689,
-0.02350258082151413,
-0.08488933742046356,
0.012953190132975578,
0.003181495936587453,
0.00821316335350275,
-0.031831495463848114,
0.027002597227692604,
-0.05230880156159401,
0.028515592217445374,
-0.03563743829727173,
0.0326995849609375,
0.002314924029633403,
0.0049285488203167915,
0.05003401264548302,
0.009709601290524006,
0.031202996149659157,
-0.0327204130589962,
0.06232842057943344,
-0.005302730947732925,
0.04682544991374016,
0.06776086986064911,
0.042053814977407455,
0.030374832451343536,
0.03889263793826103,
-0.04790366068482399,
-0.07847524434328079,
-0.03090081363916397,
0.023927757516503334,
0.019875017926096916,
0.018464725464582443,
0.020138392224907875,
-0.03939720615744591,
-0.007893660105764866,
-0.021870795637369156,
0.025409802794456482,
0.02993827313184738,
-0.027076708152890205,
0.05275633558630943,
-0.023525573313236237,
0.00777149572968483,
-0.0052747828885912895,
-0.0062964195385575294,
-0.010226324200630188,
-0.05148106813430786,
-0.026622626930475235,
0.01910395734012127,
-0.05116669461131096,
-0.0283794142305851,
0.04377196356654167,
-0.012652615085244179,
-0.08326847851276398,
0.06032302975654602,
-0.02998312935233116,
0.031115615740418434,
-0.0016327907796949148,
-0.08196365833282471,
-0.044787269085645676,
-0.01778678223490715,
-0.0352766327559948,
-0.025174332782626152,
0.06633639335632324,
-0.03189840540289879,
-0.024750659242272377,
0.06721991300582886,
0.00834223534911871,
0.03014826402068138,
0.0367816686630249,
0.0008003098773770034,
-0.10250996798276901,
0.04016265273094177,
0.004880229942500591,
-0.008116956800222397,
-0.028592286631464958,
0.013973993249237537,
0.003690974088385701,
-0.01444636844098568,
0.05138716101646423,
-0.0399126335978508,
0.045043401420116425,
0.025442007929086685,
0.029128169640898705,
-0.013938709162175655,
0.04268693923950195,
0.01232986245304346,
-0.042579296976327896,
0.04580939933657646,
-0.015015185810625553,
-0.01193629764020443,
0.03456456959247589,
-0.08136136084794998,
0.007904944010078907,
0.060951992869377136,
0.051308006048202515,
-0.05303099378943443,
0.0010714350501075387,
0.060395676642656326,
-0.0290771946310997,
0.024734167382121086,
-0.04742498695850372,
0.08039747923612595,
0.07836739718914032,
0.004816469736397266,
-0.03527535870671272,
-0.02211305871605873,
-0.004902706015855074,
0.06810334324836731,
0.012820444069802761,
0.0020246687345206738,
0.021131211891770363,
0.0679413229227066,
-0.036675576120615005,
0.06220618635416031,
0.036251943558454514,
0.018461095169186592,
0.08541055023670197,
-0.0705924928188324,
-0.03406220301985741,
0.04264551401138306,
0.025876406580209732,
-0.029346223920583725,
0.014974712394177914,
0.030175630003213882,
-0.028570368885993958,
-0.004634804558008909,
0.057502683252096176,
-0.043654464185237885,
-0.03132501244544983,
0.070400170981884,
-0.008198969066143036,
-0.08445601165294647,
-0.08588021993637085,
-0.021852334961295128,
-0.026485219597816467,
0.012509873136878014,
0.0810735896229744,
0.003582901321351528,
-0.01969187520444393,
-0.034197863191366196,
0.008701926097273827,
-0.05148788541555405,
-0.00583517225459218,
-0.01159476675093174,
-0.044204533100128174,
-0.008694951422512531,
0.02397724613547325,
0.033446721732616425,
0.08076781779527664,
-0.018626853823661804,
0.010542946867644787,
0.025082146748900414,
-0.006972339935600758,
-0.007202009670436382,
0.0010783695615828037,
0.010741498321294785,
-0.0011614528484642506,
-0.016615072265267372,
0.027923984453082085,
-0.0030215431470423937,
0.00809085089713335,
0.026372522115707397,
0.019923347979784012,
-0.03264477849006653,
-0.05055490881204605,
0.009772982448339462,
-0.04854012280702591,
-0.02082047052681446,
0.023772714659571648,
0.052075717598199844,
0.07822839170694351,
-0.026786234229803085,
0.012596643529832363,
-0.006865481846034527,
0.011922480538487434,
-0.03677593171596527,
-0.03489777445793152,
-0.02193492092192173,
0.014219547621905804,
0.013030926696956158,
-0.026451529935002327,
-0.02299382910132408,
-0.01796180009841919,
0.021169884130358696,
-0.05049959942698479,
0.0628284439444542,
-0.023432830348610878,
0.019118504598736763,
0.016794875264167786,
-0.00687377480790019,
-0.010584048926830292,
0.02361680194735527,
-0.02318967692553997,
-0.004248588811606169,
-0.012214645743370056,
-0.03993768244981766,
0.012109643779695034,
-0.00020034215413033962,
0.017096199095249176,
0.03212786465883255,
0.06879507005214691,
-0.0012609005207195878,
0.006751521490514278,
-0.08003800362348557,
0.029247812926769257,
0.017960799857974052,
0.028446849435567856,
-0.0010189592139795423,
-0.03769335523247719,
0.09229342639446259,
-0.016276231035590172,
0.054061904549598694,
-0.024516139179468155,
0.022780871018767357,
-0.014275886118412018,
-0.03543154522776604,
-0.002806002041324973,
0.0016856525326147676,
0.007780417334288359,
0.013833876699209213,
0.0468464232981205,
0.007345646619796753,
-0.08711551129817963,
-0.00520140677690506,
0.01250777579843998,
0.015462248586118221,
0.004680915270000696,
0.0383879691362381,
-0.020987851545214653,
-0.06400004774332047,
0.009450887329876423,
-0.02346622943878174,
-0.008001679554581642,
0.019189005717635155,
-0.0033098580315709114,
-0.017906539142131805,
-0.016283277422189713,
-0.051051829010248184,
-0.013751331716775894,
-0.021447602659463882,
0.03525519371032715,
-0.020197968930006027,
0.019191814586520195,
-0.010374065488576889,
-0.003992034122347832,
0.061142973601818085,
-0.0329853817820549,
0.009523150511085987,
-0.02750050090253353,
-0.02420494705438614,
0.001254327013157308,
-0.04893070459365845,
0.005328922066837549,
0.03270309790968895,
-0.05030226334929466,
-0.02294217050075531,
-0.05966499075293541,
-0.027145642787218094,
-0.004552350379526615,
0.05740814656019211,
0.003953299950808287,
0.09435955435037613,
0.025943556800484657,
-0.003840632736682892,
-0.006200304254889488,
-0.005368932615965605,
0.07128241658210754,
0.001271441811695695,
0.001842201454564929,
0.011686515063047409,
-0.0803777351975441,
0.0091886967420578,
-0.06309982389211655,
0.07950074970722198,
-0.022630468010902405,
-0.01643027551472187,
0.014238226227462292,
-0.020308226346969604,
-0.013607664965093136,
-0.01781432330608368,
-0.025088049471378326,
-0.046551790088415146,
0.05079854279756546,
0.0034201894886791706,
-0.046295322477817535,
-0.0175669863820076,
0.04142839461565018,
-0.012821845710277557,
-0.033346179872751236,
0.01863895356655121,
-0.051270533353090286,
-0.022649666294455528,
0.03759623318910599,
-0.07038149982690811,
0.007909830659627914,
0.000035725708585232496,
-0.014781848527491093,
0.031814560294151306,
0.022496609017252922,
0.019130924716591835,
0.007564039900898933,
-0.02064361423254013,
-0.004355594981461763,
0.021017108112573624,
0.021994877606630325,
0.02100694552063942,
0.006786314304918051,
0.04219374060630798,
0.0443415492773056,
-0.022342929616570473,
0.06454451382160187,
-0.0028585384134203196,
-0.026576006785035133,
0.046842850744724274,
0.012252389453351498,
-0.05938785895705223,
-0.001916919369250536,
-0.013186421245336533,
-0.0911208912730217,
-0.03806578740477562,
0.01551771443337202,
0.05902766063809395,
-0.03306838497519493,
0.011499744839966297,
-0.08091676980257034,
-0.035702403634786606,
0.02792312204837799,
0.002781510818749666,
-0.04072342813014984,
-0.03977733850479126,
-0.06565071642398834,
-0.05330323427915573,
-0.009064947254955769,
-0.004072878044098616,
-0.0028381405863910913,
0.026932572945952415,
-0.014414649456739426,
0.004913228563964367,
0.0065191700123250484,
-0.0586513914167881,
0.009580965153872967,
-0.016787586733698845,
0.038982219994068146,
0.01017464604228735,
-0.08187977969646454,
0.003132943529635668,
-0.010779540985822678,
0.023378582671284676,
0.01989920064806938,
-0.038648489862680435,
-0.05626276135444641,
0.018531005829572678,
-0.03087623603641987,
-0.07613251358270645,
0.02880144491791725,
0.0018500651931390166,
0.049450892955064774,
0.011906095780432224,
0.0344521589577198,
-0.005489668343216181,
-0.0011536725796759129,
0.002384680090472102,
-0.008718174882233143,
-0.01548471674323082,
0.03246211260557175,
-0.00010952894808724523,
-0.0037494231946766376,
-0.018851803615689278,
-0.004319622181355953,
0.02715214528143406,
-0.016989413648843765,
0.07439697533845901,
-0.039904508739709854,
0.007856848649680614,
-0.0582028403878212,
0.05660317465662956,
0.005840168800204992,
0.0028990409336984158,
-0.03677350655198097,
-0.06461873650550842,
0.03662322089076042,
0.005327600985765457,
-0.05413835868239403,
-0.03722753748297691,
-0.011479661799967289,
0.0371776707470417,
0.056812647730112076,
-0.033763594925403595,
0.012654037214815617,
-0.10335195809602737,
0.043073538690805435,
-0.03741668537259102,
-0.020944485440850258,
-0.053976576775312424,
0.023471033200621605,
-0.0413367934525013,
-0.004283620044589043,
-0.0010498787742108107,
-0.07312047481536865,
0.006913910154253244,
0.014400636777281761,
-0.028669724240899086,
-0.008149757981300354,
-0.06663001328706741,
-0.03607730567455292,
0.06520538032054901,
0.03847447782754898,
0.03867042064666748,
-0.006343300919979811,
-0.04451712220907211,
0.024491701275110245,
0.014778833836317062,
0.0014742010971531272,
-0.004531616345047951,
-0.03037969022989273,
0.029861917719244957,
-0.01442534290254116,
0.06036043539643288,
-0.010650823824107647,
0.03145958110690117,
0.03214327245950699,
-0.008513553068041801,
-0.0070271617732942104,
-0.04467526450753212,
0.02445577271282673
] |
[
15.238005638122559,
-3.026965618133545
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
na
|
na
|
2007-03-31T07:38:48
|
Results from spectroscopic observations of the Intermediate Polar (IP) EX Hya
in quiescence during 1991 and 2001 are presented. Spin-modulated radial
velocities consistent with an outer disc origin were detected for the first
time in an IP. The spin pulsation was modulated with velocities near ~500-600
km/s. These velocities are consistent with those of material circulating at the
outer edge of the accretion disc, suggesting corotation of the accretion
curtain with material near the Roche lobe radius. Furthermore, spin Doppler
tomograms have revealed evidence of the accretion curtain emission extending
from velocities of ~500 km/s to ~1000 km/s. These findings have confirmed the
theoretical model predictions of King & Wynn (1999), Belle et al. (2002) and
Norton et al. (2004) for EX Hya, which predict large accretion curtains that
extend to a distance close to the Roche lobe radius in this system. Evidence
for overflow stream of material falling onto the magnetosphere was observed,
confirming the result of Belle et al. (2005) that disc overflow in EX Hya is
present during quiescence as well as outburst. It appears that the hbeta and
hgamma spin radial velocities originated from the rotation of the funnel at the
outer disc edge, while those of halpha were produced due to the flow of
material along the field lines far from the white dwarf (narrow component) and
close to the white dwarf (broad-base component), in agreement with the
accretion curtain model.
|
Spectroscopic Observations of the Intermediate Polar EX Hydrae in
Quiescence
|
astro-ph
|
0704.0017
| 2,007
|
[
-0.014510762877762318,
0.033229611814022064,
-0.004124447703361511,
-0.043676406145095825,
0.023756006732583046,
0.024381257593631744,
0.024897832423448563,
0.004733431618660688,
-0.03992573171854019,
-0.024098675698041916,
-0.020242970436811447,
0.06721338629722595,
0.05241136625409126,
-0.007864696905016899,
0.07211735844612122,
-0.05280308052897453,
-0.021383272483944893,
-0.03137445077300072,
0.01180399488657713,
0.026719212532043457,
-0.02213919162750244,
-0.03418116271495819,
-0.0283335130661726,
-0.03036290593445301,
0.1207246258854866,
0.04538845643401146,
-0.014072710648179054,
-0.005296263378113508,
-0.04576478153467178,
0.02861724980175495,
0.026339415460824966,
-0.09544476866722107,
-0.0012015729444101453,
-0.016284631565213203,
-0.003748882096260786,
-0.03381669893860817,
0.054721150547266006,
0.012483877129852772,
-0.015710461884737015,
0.03978489711880684,
0.030092483386397362,
-0.039692532271146774,
0.033077288419008255,
-0.017450736835598946,
0.0243198461830616,
-0.0003510441747494042,
0.017881149426102638,
-0.018425416201353073,
0.004501983057707548,
0.04388649761676788,
0.014443985186517239,
0.01936519518494606,
0.03096110187470913,
-0.023802747949957848,
-0.03280148282647133,
0.055466845631599426,
0.023082124069333076,
-0.06760897487401962,
0.015545744448900223,
-0.05637058615684509,
-0.020742150023579597,
0.036226045340299606,
-0.05798069387674332,
0.006277311127632856,
0.009220906533300877,
-0.08481021225452423,
-0.04781690612435341,
0.010714706964790821,
-0.032595936208963394,
-0.0076499637216329575,
0.0613706149160862,
-0.013315051794052124,
0.013850891031324863,
0.047405779361724854,
-0.037622757256031036,
0.025474656373262405,
0.018750036135315895,
-0.034500401467084885,
-0.02064543403685093,
0.022020140662789345,
-0.02042900212109089,
-0.008399908430874348,
-0.01998922787606716,
0.032660797238349915,
0.016054315492510796,
0.036550916731357574,
-0.04396558925509453,
0.017499713227152824,
-0.006967512425035238,
0.0307087954133749,
0.041555311530828476,
-0.007698036730289459,
0.02374502271413803,
-0.011105460114777088,
-0.00756915844976902,
0.04422242194414139,
0.005028113257139921,
0.05463316664099693,
-0.019653020426630974,
0.0022105518728494644,
-0.005545471329241991,
-0.00261324062012136,
0.008239243179559708,
-0.004585087765008211,
0.09904500097036362,
0.02748055011034012,
0.01448647677898407,
-0.024182496592402458,
-0.003554070834070444,
-0.007082642056047916,
-0.08623658865690231,
-0.017462078481912613,
0.0073180412873625755,
0.01811264641582966,
0.013375598005950451,
-0.05076087266206741,
0.008202055469155312,
-0.014411206357181072,
0.016342753544449806,
0.06041858717799187,
0.02420749142765999,
-0.01430597621947527,
-0.06164649873971939,
0.05766424164175987,
0.01704169437289238,
-0.01554109901189804,
-0.020640842616558075,
-0.05964164808392525,
0.004015170969069004,
0.028298791497945786,
-0.06574974954128265,
-0.006341821514070034,
-0.04637640342116356,
0.01915428414940834,
0.04731018468737602,
0.003123400267213583,
-0.01627124659717083,
-0.054643888026475906,
-0.0008051083423197269,
-0.0357755646109581,
0.03812108188867569,
-0.042706482112407684,
0.036027103662490845,
-0.032123614102602005,
0.049533165991306305,
-0.04853807017207146,
0.030836712568998337,
-0.013424603268504143,
-0.059087496250867844,
-0.016917627304792404,
-0.01686585135757923,
0.06513503193855286,
0.02427983656525612,
0.06302327662706375,
-0.05373605340719223,
-0.01737954467535019,
-0.02298370935022831,
0.013893332332372665,
0.006983866449445486,
0.007023397833108902,
-0.0016067437827587128,
-0.001070139231160283,
-0.005523041356354952,
0.03019596077501774,
-0.05544043332338333,
0.03103630803525448,
0.05855383351445198,
0.05956206098198891,
0.0541735514998436,
0.05656960979104042,
-0.05838990956544876,
-0.043434448540210724,
-0.03025234304368496,
-0.017776692286133766,
0.022158494219183922,
-0.02819288708269596,
0.05115586146712303,
-0.05606379359960556,
-0.03441561013460159,
0.02030445821583271,
0.05182259529829025,
-0.037074942141771317,
0.03880695626139641,
0.03997821360826492,
0.030518680810928345,
0.023371269926428795,
0.04183482751250267,
-0.0346250981092453,
-0.07662516832351685,
0.02428172156214714,
0.020707402378320694,
0.014618153683841228,
-0.022318176925182343,
-0.046394117176532745,
0.025237182155251503,
-0.02454969473183155,
0.04389264062047005,
-0.06506549566984177,
-0.06301932781934738,
-0.01532879751175642,
-0.0023982012644410133,
-0.032929785549640656,
-0.026627810671925545,
0.0094909043982625,
-0.00500307185575366,
0.02630803920328617,
0.0249040424823761,
0.02628597803413868,
0.06364166736602783,
0.008195845410227776,
0.08604362607002258,
0.050593677908182144,
-0.032171402126550674,
0.03169823810458183,
-0.032947201281785965,
0.002256448846310377,
0.012005769647657871,
-0.0013155651977285743,
-0.012598139233887196,
0.016110500320792198,
0.001074713421985507,
-0.0126635218039155,
0.0608552023768425,
-0.008739128708839417,
0.01917850226163864,
0.01235671155154705,
-0.05832682549953461,
-0.00573338195681572,
-0.040080681443214417,
-0.023998340591788292,
-0.01287014875560999,
-0.06841041147708893,
0.05985791236162186,
0.012298895046114922,
-0.0214792862534523,
-0.028237292543053627,
-0.031392548233270645,
-0.0197635218501091,
-0.002734049689024687,
0.012190697714686394,
0.0514669306576252,
0.02313379757106304,
-0.005614199675619602,
-0.05118250101804733,
-0.008059014566242695,
-0.0043799695558846,
-0.013138365931808949,
0.008963599801063538,
-0.015525121241807938,
0.028770973905920982,
0.0729188472032547,
-0.032298289239406586,
0.05667061358690262,
0.026565425097942352,
0.036995161324739456,
-0.021702447906136513,
-0.057556796818971634,
0.07085616886615753,
-0.03593111410737038,
-0.05757249891757965,
0.0047994921915233135,
-0.055887963622808456,
0.02455051988363266,
-0.03890404477715492,
-0.04471132159233093,
0.02600798010826111,
0.008556323125958443,
-0.06351309269666672,
0.00505099119618535,
-0.03349008411169052,
0.01234222948551178,
0.005088054109364748,
0.029987774789333344,
0.0286746546626091,
-0.030373355373740196,
0.024268923327326775,
0.03039100579917431,
0.014996885322034359,
-0.016865840181708336,
-0.010949903167784214,
-0.05507083609700203,
-0.07144777476787567,
0.01533521432429552,
0.001830508466809988,
-0.06970097124576569,
0.02943740226328373,
0.010437946766614914,
0.0248404610902071,
0.009248008020222187,
0.04584658145904541,
-0.04084162414073944,
-0.08277401328086853,
0.0007187269511632621,
0.07882538437843323,
0.04494849964976311,
0.07353418320417404,
0.08958382159471512,
0.04314308986067772,
0.012945685535669327,
0.0011581659782677889,
0.006709299981594086,
0.007809478789567947,
-0.03844480961561203,
0.007721655536442995,
-0.007478191051632166,
0.011611845344305038,
0.016459358856081963,
-0.06821727752685547,
0.010167784988880157,
-0.022010063752532005,
-0.014143147505819798,
0.0059999641962349415,
-0.03298842906951904,
0.06104819104075432,
0.02075146697461605,
0.03877093642950058,
-0.005895310081541538,
0.011572519317269325,
0.12276603281497955,
0.05464673042297363,
0.01640891097486019,
0.005147945135831833,
0.02326548844575882,
-0.05657744035124779,
0.00389128178358078,
0.018414637073874474,
0.013141385279595852,
-0.028468292206525803,
-0.02176826447248459,
0.02371068298816681,
-0.006963526364415884,
0.05112254247069359,
-0.057227835059165955,
-0.016334298998117447,
-0.03195696324110031,
0.05602530762553215,
-0.010976660996675491,
0.09332825988531113,
-0.025459757074713707,
0.013270720839500427,
0.03789014369249344,
-0.04872205853462219,
-0.04320608079433441,
-0.049446992576122284,
-0.039879243820905685,
-0.012548374012112617,
-0.03875134140253067,
-0.030868591740727425,
0.03904636204242706,
0.014816675335168839,
-0.027900170534849167,
0.013921508565545082,
0.001696710824035108,
-0.035689596086740494,
-0.011448360048234463,
0.07565049827098846,
0.05257830768823624,
-0.033703021705150604,
0.03087427280843258,
0.008769070729613304,
0.014081543311476707,
-0.04374853894114494,
0.015161989256739616,
0.000611416413448751,
0.014642360620200634,
0.024222709238529205,
0.01573074795305729,
0.022756241261959076,
0.0035564249847084284,
-0.022532224655151367,
-0.058807723224163055,
-0.01605192944407463,
-0.025691241025924683,
0.04225281998515129,
0.008493964560329914,
-0.027780329808592796,
-0.04117100313305855,
0.03427737206220627,
0.015072175301611423,
0.03731239587068558,
0.07314999401569366,
0.028504718095064163,
0.009670395404100418,
0.02711527980864048,
-0.0025663014966994524,
-0.013675776310265064,
-0.03687667474150658,
0.003948351833969355,
-0.01189112477004528,
-0.06217603757977486,
-0.007041679695248604,
-0.02864324115216732,
0.004633184988051653,
0.008290043100714684,
-0.008637753315269947,
0.0072705866768956184,
0.03564867004752159,
-0.04832343012094498,
0.023044398054480553,
-0.031421955674886703,
-0.08039852976799011,
-0.03655226528644562,
0.016958709806203842,
0.004513245541602373,
-0.026880886405706406,
0.03086836449801922,
-0.020686179399490356,
-0.052899591624736786,
0.032541438937187195,
-0.025348039343953133,
0.014413398690521717,
0.05155262351036072,
-0.027002133429050446,
-0.045554932206869125,
0.027314092963933945,
0.008766585029661655,
0.05055354908108711,
0.010287292301654816,
-0.012748293578624725,
-0.04108262434601784,
-0.0007063890807330608,
0.03207145631313324,
0.007903049699962139,
0.01444204617291689,
-0.0032883959356695414,
0.031975310295820236,
0.015378355979919434,
-0.03537966310977936,
-0.023383326828479767,
-0.050155334174633026,
0.0010178774828091264,
-0.035617027431726456,
0.043997760862112045,
0.033681340515613556,
-0.0529698021709919,
-0.021379642188549042,
-0.008912959136068821,
-0.012259695678949356,
0.0032143585849553347,
-0.01307868305593729,
0.08949676901102066,
-0.08072594553232193,
-0.0023833143059164286,
-0.00714223925024271,
0.012863044627010822,
0.08612619340419769,
0.0965280830860138,
-0.010691609233617783,
0.017268389463424683,
-0.002892863005399704,
0.006341577973216772,
-0.01451547909528017,
-0.02990756742656231,
0.03456685692071915,
0.0704297125339508,
-0.04221324995160103,
-0.004547682590782642,
-0.012165559455752373,
0.05455206334590912,
0.04695241525769234,
0.012932918034493923,
0.03129704296588898,
-0.03703553229570389,
0.0096164271235466,
0.023496566340327263,
0.025304442271590233,
0.0052343555726110935,
-0.042245976626873016,
0.02356777898967266,
0.030550654977560043,
-0.01714104600250721,
-0.0029451006557792425,
0.061984725296497345,
-0.015230578370392323,
-0.05275926738977432,
-0.01941896602511406,
-0.01259505096822977,
-0.06899441033601761,
-0.0068052359856665134,
0.02942000888288021,
0.0011980931740254164,
0.010138346813619137,
-0.016493279486894608,
-0.03785417601466179,
0.019785305485129356,
0.011557817459106445,
-0.020447975024580956,
-0.035659607499837875,
-0.0019660047255456448,
-0.008972512558102608,
-0.012972459197044373,
0.033178381621837616,
0.02153923176229,
0.015360035002231598,
-0.051671694964170456,
-0.04073534905910492,
0.025094425305724144,
-0.012521432712674141,
0.024778543040156364,
0.000319462240440771,
0.007471761666238308,
0.005032296292483807,
-0.03869316726922989,
0.004288157913833857,
0.0069020031951367855,
0.05892087146639824,
-0.0822591781616211,
-0.054210513830184937,
0.0256092119961977,
0.01651288941502571,
0.003495569573715329,
0.06981263309717178,
0.01931806094944477,
0.07313045114278793,
0.04069920629262924,
0.017471203580498695,
0.03893069922924042,
0.024248355999588966,
-0.02785709872841835,
-0.013004237785935402,
-0.041664961725473404,
-0.046315643936395645,
0.02191094309091568,
0.011596010997891426,
-0.024576641619205475,
0.015214487910270691,
0.016586219891905785,
-0.0697907879948616,
0.023793185129761696,
-0.007327353581786156,
0.003457313869148493,
0.01778770238161087,
0.010146597400307655,
0.040471069514751434,
0.0143545251339674,
-0.04708284139633179,
-0.03744234889745712,
0.01746840961277485,
0.03663517162203789,
0.02095184102654457,
-0.0128632178530097,
0.012864382937550545,
0.037263572216033936,
-0.005453391466289759,
0.010827495716512203,
-0.002050786279141903,
-0.013920415192842484,
0.04071258008480072,
0.023724423721432686,
-0.040728479623794556,
0.01082935743033886,
-0.0013298664707690477,
0.04813537001609802,
-0.06181654334068298,
0.011750503443181515,
0.017093488946557045,
0.03736085444688797,
-0.0547056682407856,
-0.05349762365221977,
-0.0007948828861117363,
-0.031082719564437866,
-0.021040670573711395,
0.053521931171417236,
0.023454491049051285,
-0.02203958109021187,
-0.0932973325252533,
-0.017602864652872086,
-0.030367877334356308,
0.04101761430501938,
-0.020227614790201187,
-0.034291937947273254,
-0.05356442928314209,
-0.04930731654167175,
0.06179991364479065,
0.02929040789604187,
0.0015323390252888203,
0.07161640375852585,
0.0316321961581707,
-0.04155690222978592,
-0.014466986060142517,
-0.06957875937223434,
-0.026521628722548485,
0.042425572872161865,
0.06793264299631119,
0.005263252183794975,
-0.01619209162890911,
-0.01922152191400528,
-0.021804070100188255,
0.06784408539533615,
-0.0032933412585407495,
0.004941343795508146,
-0.027139753103256226,
-0.034937817603349686,
-0.038322143256664276,
-0.021445851773023605,
0.02809256687760353,
-0.024503104388713837,
-0.03486244007945061,
-0.05910828709602356,
-0.09802914410829544,
-0.009622757323086262,
0.0033970384392887354,
0.03933968394994736,
-0.04809614270925522,
-0.010352079756557941,
-0.017301740124821663,
0.005008731968700886,
0.028946254402399063,
-0.022530606016516685,
0.025478865951299667,
0.023937202990055084,
0.03138413652777672,
-0.01509062945842743,
-0.07100522518157959,
-0.040200892835855484,
0.0055240364745259285,
0.0214203093200922,
0.0031769475899636745,
0.010082091204822063,
-0.015220293775200844,
-0.0073170773684978485,
-0.05635342001914978,
0.0038039847277104855,
-0.09027577191591263,
0.01306010689586401,
0.00377743411809206,
-0.0028218114748597145,
0.008665707893669605,
0.007088320329785347,
0.045608486980199814,
0.02138415351510048,
-0.01756836101412773,
-0.0027495939284563065,
-0.018100997433066368,
-0.0059763528406620026,
-0.01503279060125351,
0.020097916945815086,
0.025002431124448776,
0.06483253091573715,
0.04910561069846153,
0.06474952399730682,
-0.02477913908660412,
-0.04180010408163071,
-0.012884501367807388,
0.009752319194376469,
0.015978075563907623,
-0.007925009354948997,
0.00207339134067297,
-0.004664761945605278,
0.008553602732717991,
0.047241102904081345,
-0.0015635895542800426,
-0.0020587246399372816,
0.03795704245567322,
0.043567705899477005,
0.037666693329811096,
0.017753250896930695,
0.02432212233543396,
-0.007357422728091478,
-0.024126768112182617,
-0.02706826850771904,
0.004529507365077734,
0.018038393929600716,
0.00018465770699549466,
-0.017925506457686424,
-0.05426662787795067,
0.0043420265428721905,
-0.057766158133745193,
-0.04664717987179756,
0.04805533587932587,
-0.03375115245580673,
-0.020123986527323723,
-0.0713639110326767,
-0.05682097002863884,
-0.07079765200614929,
-0.02191942371428013,
0.022319750860333443,
-0.05104789137840271,
0.020828600972890854,
-0.000033312895538983867,
0.018919676542282104,
0.00954527035355568,
-0.0016904863296076655,
0.03246031329035759,
-0.004418386146426201,
0.018589764833450317,
-0.061068616807460785,
-0.027835790067911148,
-0.013615996576845646,
0.03505469486117363,
0.00250454293563962,
0.009778589941561222,
0.07095307856798172,
-0.06434058398008347,
-0.013856986537575722,
0.021950600668787956,
-0.05972913280129433,
-0.020711038261651993,
-0.012979565188288689,
0.019419662654399872,
0.024014975875616074,
0.08870361000299454,
0.00047948103747330606,
-0.004246701020747423,
-0.04240017011761665,
0.025535540655255318,
0.023261556401848793,
0.05908888578414917,
0.027600403875112534,
-0.003783100750297308,
-0.04249877855181694,
0.03087203949689865,
0.05721784383058548,
-0.014849508181214333,
0.02560672163963318,
0.01208202913403511,
-0.004535135347396135,
-0.041525665670633316,
0.007253570016473532,
-0.002050733659416437,
-0.007619387470185757,
0.0026018661446869373,
-0.05839555338025093,
0.0021906006149947643,
-0.03612025827169418,
-0.058333076536655426,
0.04122086614370346,
-0.004511861130595207,
0.0629425197839737,
-0.009600329212844372,
0.025011690333485603,
0.05758729204535484,
-0.06750214844942093,
0.011129342950880527,
-0.06506827473640442,
-0.040520403534173965,
0.007399516645818949,
-0.02765868790447712,
-0.08631037175655365,
0.00884842686355114,
0.005895230453461409,
-0.016702184453606606,
0.05540820583701134,
0.008354848250746727,
-0.03427642956376076,
-0.03202783316373825,
0.00018964930495712906,
0.030902022495865822,
0.06175702437758446,
0.0064897616393864155,
0.04409116879105568,
-0.019537249580025673,
-0.0013153599575161934,
-0.010474841110408306,
-0.009175390936434269,
-0.0020217513665556908,
-0.05530649796128273,
0.051907218992710114,
0.011514239013195038,
-0.04046246409416199,
-0.0037669639568775892,
-0.02408163994550705,
0.05350271984934807,
0.0004484230885282159,
0.035922400653362274,
0.01157375331968069,
-0.038065824657678604,
0.03114677034318447
] |
[
14.825446128845215,
8.622700691223145
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
na
|
na
|
2007-04-02T08:58:27
|
We give a prescription for how to compute the Callias index, using as
regulator an exponential function. We find agreement with old results in all
odd dimensions. We show that the problem of computing the dimension of the
moduli space of self-dual strings can be formulated as an index problem in
even-dimensional (loop-)space. We think that the regulator used in this Letter
can be applied to this index problem.
|
In quest of a generalized Callias index theorem
|
hep-th
|
0704.0018
| 2,007
|
[
-0.04940589517354965,
0.048607293516397476,
-0.008045841008424759,
-0.04833115637302399,
-0.02996048331260681,
0.007094068452715874,
0.01385229267179966,
-0.03164304420351982,
0.005525942891836166,
0.035541754215955734,
-0.0924924686551094,
0.0833013579249382,
0.04751034080982208,
0.00687117176130414,
0.012301458977162838,
-0.05534522980451584,
0.07006560266017914,
0.012257326394319534,
-0.014064031653106213,
0.007591353729367256,
0.03648269921541214,
-0.04869343712925911,
-0.04902417212724686,
-0.0565568245947361,
0.11701404303312302,
-0.025473712012171745,
0.010891453363001347,
0.0021291787270456553,
-0.037735842168331146,
0.02741216868162155,
0.08203011006116867,
-0.014610681682825089,
-0.009749926626682281,
-0.03866094350814819,
-0.05276605114340782,
0.0006982520571909845,
0.050968848168849945,
0.0076495264656841755,
0.06400136649608612,
0.06820225715637207,
0.015794310718774796,
0.007089043501764536,
-0.01651768386363983,
-0.02065758779644966,
0.005570270586758852,
0.00920503307133913,
-0.023950427770614624,
0.034423358738422394,
0.1215725913643837,
-0.040207359939813614,
-0.017657523974776268,
0.03864431008696556,
0.03162898123264313,
-0.05335737019777298,
-0.016463520005345345,
0.014956020750105381,
-0.00468065869063139,
-0.007017016410827637,
0.06349080801010132,
0.004866370931267738,
0.012855163775384426,
0.012034176848828793,
-0.011019544675946236,
0.006564196199178696,
0.013300787657499313,
-0.014973847195506096,
0.004491930827498436,
0.0011901961406692863,
-0.0074579487554728985,
-0.002826122799888253,
0.08442189544439316,
0.010197663679718971,
0.0342850498855114,
-0.018321756273508072,
-0.0581541545689106,
0.01847905106842518,
-0.004874809179455042,
-0.030399145558476448,
-0.02682187408208847,
-0.006976239383220673,
-0.001787484739907086,
-0.03261546045541763,
0.03412988781929016,
-0.025570424273610115,
-0.010687687434256077,
-0.0016945007955655456,
0.04157211259007454,
0.022969866171479225,
-0.04341071844100952,
0.026325328275561333,
0.01455988921225071,
0.008023926988244057,
0.07330746203660965,
0.06906015425920486,
0.0014626457123085856,
0.0425419881939888,
-0.0004243100993335247,
0.019647639244794846,
-0.01900901086628437,
-0.01170537993311882,
0.03556797653436661,
0.07888960093259811,
0.03971582278609276,
-0.005725830793380737,
0.05294620990753174,
0.049212612211704254,
0.07009284198284149,
-0.0559861995279789,
-0.01801563985645771,
-0.014853518456220627,
-0.07387492805719376,
-0.021255388855934143,
-0.0023321581538766623,
-0.05522238463163376,
-0.01815752126276493,
-0.0228668674826622,
0.023632097989320755,
-0.1031644195318222,
-0.03695529326796532,
0.04930499568581581,
-0.013857891783118248,
-0.04434249922633171,
0.07542045414447784,
-0.0075597153045237064,
0.03873797133564949,
-0.00016922915528994054,
-0.014122797176241875,
0.06028645113110542,
0.0518450029194355,
-0.026871902868151665,
-0.024760272353887558,
-0.00936787761747837,
-0.023396320641040802,
0.010384767316281796,
0.01895713619887829,
0.012580778449773788,
-0.0535447858273983,
-0.05092817172408104,
-0.016700271517038345,
-0.004948748741298914,
0.011203446425497532,
-0.015649165958166122,
-0.013960316777229309,
0.019332805648446083,
0.0070399753749370575,
-0.06702463328838348,
0.03548591956496239,
-0.06835688650608063,
0.01292282436043024,
-0.03436959162354469,
0.0307789146900177,
0.057492695748806,
0.00005807734851259738,
0.04476305469870567,
-0.022403396666049957,
-0.00032809414551593363,
0.011517506092786789,
0.026591502130031586,
0.0374085009098053,
0.04900183528661728,
0.012587985023856163,
0.02379128523170948,
-0.019463898614048958,
0.0684095099568367,
-0.05987260118126869,
-0.049650877714157104,
0.018453244119882584,
0.015054652467370033,
0.002054275246337056,
0.0054995352402329445,
-0.009441173635423183,
0.011420752853155136,
0.002632005140185356,
0.01298360526561737,
-0.0018424246227368712,
0.009312977083027363,
-0.002033431548625231,
0.013782964088022709,
0.009270275011658669,
0.0011061264667659998,
0.07120296359062195,
-0.028668027371168137,
0.009162808768451214,
0.02525503747165203,
0.026702184230089188,
0.014572921209037304,
0.028361421078443527,
-0.01791374199092388,
-0.03768317773938179,
-0.040122948586940765,
0.0058643207885324955,
0.050574060529470444,
-0.0025560015346854925,
0.010280312970280647,
0.013709230348467827,
-0.0817895457148552,
0.07226250320672989,
-0.07179947197437286,
0.01570594124495983,
-0.019118430092930794,
0.014812037348747253,
0.014524636790156364,
0.009876503609120846,
0.02162683941423893,
-0.03178311139345169,
0.03843768686056137,
0.015029573813080788,
-0.023626426234841347,
0.05472474545240402,
-0.01543350238353014,
0.09446679055690765,
-0.007618675008416176,
-0.012630789540708065,
-0.00046272363397292793,
-0.0710175484418869,
-0.02569502592086792,
0.01764766499400139,
-0.030626079067587852,
-0.03997445106506348,
-0.01558109000325203,
0.027000321075320244,
-0.024555929005146027,
0.005703985225409269,
0.02832474559545517,
0.003497630124911666,
0.009748351760208607,
-0.010007261298596859,
0.05003151670098305,
0.002351482165977359,
-0.01986943744122982,
-0.0631582960486412,
-0.051205459982156754,
0.03242713212966919,
-0.0042723799124360085,
-0.06532909721136093,
0.043335091322660446,
-0.02795911207795143,
0.03283129632472992,
0.08086355030536652,
0.06279134750366211,
0.037875592708587646,
-0.02055729180574417,
0.10107588768005371,
-0.003526050131767988,
-0.048635147511959076,
0.025968758389353752,
0.004063193686306477,
0.010739868506789207,
-0.009720079600811005,
0.030328456312417984,
-0.023546529933810234,
0.008703429251909256,
0.019437292590737343,
0.06914713978767395,
0.03462933748960495,
-0.01574028469622135,
-0.005017582792788744,
0.013920455239713192,
0.02244110032916069,
-0.06413032114505768,
0.023277726024389267,
-0.00418568029999733,
0.04675539210438728,
-0.013179123401641846,
-0.06308536231517792,
-0.00494337547570467,
0.01883971504867077,
-0.06021732836961746,
-0.008655315265059471,
-0.0321933813393116,
0.027181873098015785,
0.009437442757189274,
0.024155251681804657,
0.02496775984764099,
-0.013148776255548,
-0.003528314409777522,
0.023538338020443916,
-0.019508909434080124,
0.008403358981013298,
-0.05401542782783508,
-0.0563606321811676,
0.009699665009975433,
-0.0616297647356987,
-0.025059306994080544,
-0.01732189767062664,
0.014229247346520424,
0.03794350475072861,
0.017710262909531593,
0.006787428166717291,
0.05934871360659599,
-0.007533420342952013,
-0.028164805844426155,
0.0073460182175040245,
0.037908751517534256,
0.04088689386844635,
0.08281989395618439,
0.02759478986263275,
-0.008613971062004566,
-0.0012026955373585224,
0.0008354639285244048,
0.0176079198718071,
-0.0046442290768027306,
0.02060956507921219,
-0.03870202228426933,
0.04504590854048729,
-0.007859325967729092,
-0.0035643691662698984,
0.002632121555507183,
0.033023614436388016,
0.031841766089200974,
0.004423377104103565,
0.041292380541563034,
-0.016115326434373856,
-0.05070307478308678,
-0.016777697950601578,
0.05338580906391144,
0.015814362093806267,
-0.021488623693585396,
0.08203121274709702,
-0.036259040236473083,
0.010002095252275467,
-0.09475527703762054,
0.035385001450777054,
-0.0193171463906765,
-0.04503525421023369,
-0.034402910619974136,
-0.041661713272333145,
0.04014990106225014,
-0.02097436413168907,
0.02207646705210209,
-0.026161396875977516,
0.03397177904844284,
-0.03528008610010147,
-0.048468463122844696,
0.031045669689774513,
-0.03691181167960167,
-0.02234111726284027,
0.0027494013775140047,
-0.019990550354123116,
-0.01056066807359457,
-0.029966523870825768,
-0.0439312681555748,
0.02152855694293976,
-0.05058930069208145,
-0.014823909848928452,
0.021700741723179817,
-0.029315782710909843,
0.020929811522364616,
0.030091123655438423,
-0.011143266223371029,
-0.05541940778493881,
-0.04631776362657547,
0.029155205935239792,
0.017769809812307358,
0.018653931096196175,
0.04721515625715256,
0.06461451947689056,
-0.0029221957083791494,
0.037434790283441544,
0.027978768572211266,
0.031774476170539856,
0.014239105395972729,
-0.01674726977944374,
0.017876094207167625,
0.04846392571926117,
0.008944351226091385,
0.05394429340958595,
0.02521556429564953,
-0.04166213050484657,
0.007945682853460312,
-0.004856403451412916,
-0.024107694625854492,
0.04697832465171814,
0.0005655974382534623,
0.03141644597053528,
0.007288826629519463,
-0.10448586195707321,
0.010558614507317543,
-0.008981751278042793,
0.00937825720757246,
0.03563816100358963,
-0.04987858980894089,
0.038436248898506165,
0.008757760748267174,
-0.014455456286668777,
-0.0190171767026186,
-0.028295224532485008,
0.01914985105395317,
-0.0030692811124026775,
-0.08754375576972961,
0.02804439328610897,
-0.016682973131537437,
-0.012414839118719101,
-0.003343589836731553,
0.02342173457145691,
-0.02741084434092045,
0.06404531747102737,
0.02200762741267681,
0.015063418075442314,
0.003421059576794505,
-0.012445117346942425,
-0.08749088644981384,
0.03150549903512001,
-0.022465385496616364,
-0.006751148961484432,
0.04048318788409233,
0.01689203456044197,
-0.026260968297719955,
0.023933585733175278,
-0.0099598104134202,
0.02341761253774166,
0.03411739692091942,
-0.028044158592820168,
-0.04546535387635231,
0.04644668847322464,
0.03097323514521122,
0.03944184631109238,
0.00841250829398632,
0.030799007043242455,
-0.01694398745894432,
0.0041110157035291195,
0.04405352473258972,
-0.03767401725053787,
-0.05488009378314018,
-0.047176532447338104,
0.0075123799033463,
-0.0030042515136301517,
0.011798939667642117,
-0.0019504758529365063,
-0.022917719557881355,
0.03310704603791237,
0.03453243896365166,
0.0011089235777035356,
0.050365786999464035,
-0.05356026068329811,
0.011768244206905365,
0.012079823762178421,
-0.020311176776885986,
0.03456170856952667,
0.03327876329421997,
0.07088647037744522,
-0.05671759322285652,
-0.013112911023199558,
0.04026653245091438,
-0.025806736201047897,
0.05695272609591484,
0.008397525176405907,
0.04273690655827522,
-0.035695161670446396,
0.026006363332271576,
0.050831232219934464,
-0.021378401666879654,
0.011660981923341751,
-0.03367874398827553,
0.028157686814665794,
-0.007971560582518578,
0.006784964352846146,
0.01925470121204853,
0.08649980276823044,
0.005852291360497475,
0.029429346323013306,
-0.011595260351896286,
-0.036425188183784485,
0.07474186271429062,
0.05039968341588974,
0.000208378754905425,
-0.03008122742176056,
0.0022283040452748537,
-0.009298231452703476,
0.0916813537478447,
0.004031481686979532,
0.0028682115953415632,
-0.013699010945856571,
-0.03738974779844284,
-0.041995178908109665,
-0.00007057439506752416,
-0.005136515479534864,
-0.05036327242851257,
-0.025696199387311935,
0.030934588983654976,
-0.016179945319890976,
-0.0437220074236393,
-0.03055969998240471,
-0.03702472150325775,
-0.004229659680277109,
-0.0038225743919610977,
-0.037132859230041504,
-0.013963748700916767,
-0.022619564086198807,
0.006456148810684681,
-0.006813450250774622,
0.05476601421833038,
0.005733848549425602,
0.023181023076176643,
-0.07525448501110077,
-0.06608043611049652,
0.04835468903183937,
-0.02206363156437874,
-0.017504507675766945,
-0.10265043377876282,
-0.018612978979945183,
0.015243382193148136,
-0.0064179375767707825,
0.03194064646959305,
-0.02690248377621174,
-0.0013910072157159448,
-0.031203998252749443,
-0.05637571960687637,
0.04020674154162407,
-0.03504391387104988,
-0.00923608336597681,
0.03589059039950371,
0.07422881573438644,
0.02782529965043068,
0.0779167041182518,
-0.046560995280742645,
0.01637168973684311,
-0.02109571173787117,
-0.009245431050658226,
-0.008748245425522327,
0.019011609256267548,
-0.0061784530989825726,
0.03337765485048294,
-0.029303815215826035,
-0.05161282420158386,
0.01611298881471157,
-0.032868992537260056,
-0.0729849636554718,
0.014614117331802845,
-0.00835972186177969,
0.024184715002775192,
0.005241875071078539,
-0.08056250959634781,
-0.028382668271660805,
-0.00042252562707290053,
-0.05705568194389343,
-0.02083013579249382,
0.03372136875987053,
0.02770932950079441,
-0.010736317373812199,
-0.02826610580086708,
-0.010242599993944168,
-0.0038664538878947496,
-0.011954004876315594,
0.017977669835090637,
-0.06585902720689774,
-0.0392255038022995,
-0.0014988849870860577,
0.04401077702641487,
-0.018678082153201103,
-0.0023679661098867655,
-0.034554850310087204,
0.030548488721251488,
-0.06848426163196564,
-0.019349468871951103,
-0.023879878222942352,
0.03531371057033539,
-0.004799744579941034,
-0.03772714361548424,
0.000796634703874588,
0.02445736713707447,
-0.01405287068337202,
0.008899705484509468,
-0.019531691446900368,
0.041297975927591324,
-0.06317310035228729,
-0.010181715711951256,
0.041591111570596695,
0.08118270337581635,
0.019891953095793724,
-0.012690364383161068,
-0.06632044911384583,
0.027634119614958763,
0.09210097789764404,
0.005909606348723173,
-0.016955364495515823,
0.011172915808856487,
-0.011900586076080799,
0.020783554762601852,
-0.014302589930593967,
-0.029017895460128784,
-0.019318215548992157,
-0.021076736971735954,
-0.028418337926268578,
-0.042942337691783905,
0.006895486265420914,
-0.0008486627484671772,
-0.05097699537873268,
0.057722147554159164,
-0.010421518236398697,
-0.03722669184207916,
-0.008259099908173084,
-0.03212710842490196,
-0.0578412301838398,
-0.015787288546562195,
0.001469115260988474,
0.019659847021102905,
-0.0031667642761021852,
0.011437537148594856,
-0.027123374864459038,
-0.005799529608339071,
-0.017613574862480164,
0.08409235626459122,
-0.03793976083397865,
0.02643837034702301,
0.04266840219497681,
0.02023974433541298,
0.012659273110330105,
0.020774461328983307,
0.004020771011710167,
0.04595154896378517,
-0.007602762430906296,
-0.034190140664577484,
-0.012436646036803722,
-0.005222355481237173,
-0.06013430282473564,
0.04727492108941078,
-0.030318250879645348,
0.013260004110634327,
-0.013187938369810581,
0.0029601543210446835,
-0.02489546127617359,
0.019463766366243362,
-0.0482332780957222,
-0.008659685961902142,
-0.0035288650542497635,
-0.042436860501766205,
-0.04047746583819389,
0.019026191905140877,
0.030245577916502953,
-0.02944822609424591,
-0.028899597004055977,
-0.010182217694818974,
-0.028420744463801384,
-0.010438126511871815,
-0.0008954451186582446,
-0.057282011955976486,
0.02375941164791584,
-0.026938792318105698,
0.05020102486014366,
-0.009316160343587399,
-0.03635760396718979,
-0.024841682985424995,
0.012388063594698906,
0.07044199109077454,
-0.020245719701051712,
-0.0009587291278876364,
-0.0019201976247131824,
-0.013393813744187355,
0.05075136944651604,
0.07455477863550186,
0.06976907700300217,
-0.010744504630565643,
0.029031410813331604,
-0.012047700583934784,
-0.03834578022360802,
0.05054974555969238,
-0.04047932103276253,
-0.036663081496953964,
-0.0015020432183519006,
-0.03716283664107323,
-0.029751507565379143,
0.021668218076229095,
-0.03845619037747383,
-0.0007875300361774862,
-0.02475236915051937,
-0.01007346622645855,
-0.05516456067562103,
-0.023152461275458336,
0.03400421887636185,
-0.0442434586584568,
-0.014978410676121712,
0.006889558397233486,
-0.002990327775478363,
-0.033661138266325,
0.02646329253911972,
-0.01909964345395565,
-0.01013367809355259,
-0.0488191694021225,
-0.01871158368885517,
0.017906654626131058,
-0.011959491297602654,
0.016179457306861877,
-0.031096044927835464,
-0.03737718239426613,
-0.010934839956462383,
-0.03937879577279091,
-0.028149181976914406,
-0.02082372084259987,
-0.011465740390121937,
0.033855535089969635,
-0.004358251113444567,
0.025500206276774406,
-0.09548155218362808,
0.05303940549492836,
-0.015891050919890404,
-0.04626191034913063,
0.01302350778132677,
-0.058091163635253906,
0.05764400213956833,
0.035239752382040024,
0.02385866828262806,
-0.020758764818310738,
0.05079090595245361,
-0.039391834288835526,
-0.027774157002568245,
0.022911839187145233,
0.020515944808721542,
-0.07103913277387619,
0.027166426181793213,
-0.07123137265443802,
0.029693102464079857,
-0.0020321051124483347,
-0.004100257996469736,
0.04030404984951019,
-0.025416487827897072,
-0.0031929523684084415,
-0.07010696083307266,
0.032175250351428986,
-0.034724388271570206,
-0.012080855667591095,
-0.013282667845487595,
-0.056702908128499985,
0.022681891918182373,
-0.049955349415540695,
-0.06692452728748322,
-0.010169540531933308,
-0.025193573907017708,
0.031018564477562904,
0.032036781311035156,
0.036867640912532806,
0.012300007045269012,
0.006608945783227682,
0.06409791857004166,
-0.003823816543444991,
0.0006937485304661095,
-0.04113426059484482,
-0.04377623647451401,
-0.04839995130896568,
0.02866355888545513,
0.012562909163534641,
-0.02451813593506813,
0.014829525724053383,
-0.012636054307222366,
0.029946431517601013,
-0.023285144940018654,
-0.05904332920908928,
0.03660140186548233,
-0.003022949444130063,
-0.014056675136089325,
-0.02054888755083084,
-0.031203940510749817,
-0.019158676266670227,
0.038139741867780685,
0.004794768989086151,
0.05055975541472435,
0.023355115205049515,
0.024040045216679573,
0.012020398862659931,
0.020391441881656647,
0.01654006540775299,
0.03025680035352707,
0.03198154270648956,
0.07034340500831604,
0.02375902235507965,
-0.06409705430269241,
-0.017084406688809395,
0.057477474212646484
] |
[
2.4928946495056152,
1.9491060972213745
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-03-31T08:12:35
|
In this note we give a new method for getting a series of approximations for
the extinction probability of the one-dimensional contact process by using the
Gr\"obner basis.
|
Approximation for extinction probability of the contact process based on
the Gr\"obner basis
|
math.PR math.AG
|
0704.0019
| 2,007
|
[
0.009777710773050785,
-0.007435332052409649,
-0.001736794481985271,
-0.05042191594839096,
0.017055805772542953,
0.034505899995565414,
0.043717630207538605,
0.015511469915509224,
-0.041524309664964676,
0.011903408914804459,
-0.03675112500786781,
0.043491072952747345,
0.033444736152887344,
0.027516024187207222,
-0.01364404521882534,
-0.04131736233830452,
0.05410052090883255,
-0.019104141741991043,
-0.03757954761385918,
0.008022606372833252,
-0.005988359451293945,
-0.053052280098199844,
-0.013807704672217369,
-0.02679794654250145,
0.029171762987971306,
0.00037073486601002514,
0.0013144973199814558,
0.01604769378900528,
-0.033494070172309875,
-0.0342770554125309,
0.0358894057571888,
-0.03469475731253624,
0.01756425015628338,
-0.05168874189257622,
-0.03790875896811485,
-0.026535319164395332,
0.0706484466791153,
0.021128876134753227,
0.06587696075439453,
0.0010140271624550223,
0.06966648995876312,
-0.0699879452586174,
0.04197286441922188,
-0.05623345077037811,
0.010817558504641056,
0.016526993364095688,
0.02319476380944252,
-0.032208748161792755,
0.07337270677089691,
-0.027702152729034424,
-0.0073299650102853775,
0.04620005190372467,
-0.003676569787785411,
-0.038465239107608795,
-0.02311723306775093,
0.05965515226125717,
-0.0023312359116971493,
-0.055196452885866165,
0.018547089770436287,
-0.01752404309809208,
0.003550203051418066,
0.03803633898496628,
-0.041762031614780426,
0.03023068979382515,
0.029724469408392906,
-0.0413854718208313,
-0.034544769674539566,
0.0008840937516652048,
0.04011999070644379,
-0.00835692510008812,
0.0011011689202859998,
0.018257075920701027,
-0.04826446250081062,
0.006535439286381006,
-0.026737796142697334,
0.009563126601278782,
0.00488763814792037,
0.011341158300638199,
-0.02266041561961174,
0.05866140499711037,
-0.03218341991305351,
-0.06456192582845688,
0.04744827747344971,
0.042310163378715515,
0.07627774029970169,
0.01552534755319357,
0.04177149757742882,
0.04828253760933876,
-0.022425703704357147,
0.042624104768037796,
-0.016121838241815567,
0.03144736588001251,
0.015452905558049679,
0.04648558795452118,
-0.03699938952922821,
0.054091677069664,
-0.05009348690509796,
0.03281771391630173,
0.02925623022019863,
-0.032374583184719086,
0.025774948298931122,
0.028942150995135307,
0.028000982478260994,
-0.00022600295778829604,
0.017504503950476646,
0.036410484462976456,
-0.011482587084174156,
-0.026764532551169395,
0.03835635259747505,
0.012703856453299522,
-0.08027512580156326,
0.004432444926351309,
-0.019889233633875847,
-0.05227769911289215,
0.011960064060986042,
-0.014946561306715012,
0.07637915760278702,
-0.09899833053350449,
0.051794152706861496,
0.03217153251171112,
0.01974811777472496,
-0.020727381110191345,
0.011821490712463856,
0.005367832724004984,
-0.020506903529167175,
0.019059929996728897,
-0.051687587052583694,
0.016404863446950912,
0.03287089616060257,
-0.000480280548799783,
0.03887685015797615,
-0.016180772334337234,
0.010087731294333935,
-0.0022766164038330317,
0.0401969812810421,
0.029045678675174713,
-0.020808903500437737,
-0.01523516234010458,
0.029825717210769653,
-0.01335135381668806,
-0.021014386788010597,
-0.0019230791367590427,
-0.03155778348445892,
-0.046509649604558945,
-0.027842560783028603,
-0.004955892916768789,
-0.013727458193898201,
-0.06389642506837845,
-0.01375870406627655,
-0.05102807655930519,
0.07494699209928513,
0.034539222717285156,
0.02542617917060852,
0.02362939342856407,
-0.015162676572799683,
-0.027481937780976295,
-0.06090521812438965,
-0.039122324436903,
0.025551771745085716,
0.022205209359526634,
0.03889196738600731,
-0.015602052211761475,
-0.017590761184692383,
0.013701953925192356,
-0.05106330290436745,
0.02144695073366165,
0.0168401300907135,
-0.0284197349101305,
0.029490403831005096,
-0.0345972403883934,
0.013555037789046764,
-0.04733120650053024,
-0.018596040084958076,
-0.023524107411503792,
-0.022022243589162827,
-0.007597204763442278,
0.013708935119211674,
-0.03015972673892975,
0.02644205093383789,
0.030032092705368996,
0.0675002783536911,
-0.04753550514578819,
0.021462876349687576,
0.01948469690978527,
-0.004067988600581884,
0.0012659297790378332,
0.059021469205617905,
0.02159116230905056,
0.012708361260592937,
-0.022759269922971725,
-0.04401712492108345,
-0.019230473786592484,
-0.034859947860240936,
-0.0046121953055262566,
-0.027925780043005943,
-0.013275843113660812,
0.0884920135140419,
-0.028460372239351273,
-0.013723297044634819,
-0.03715384006500244,
-0.04469425231218338,
0.05543864518404007,
-0.05303487181663513,
0.0328211672604084,
-0.025100668892264366,
-0.007293299771845341,
0.03227202594280243,
0.03016672097146511,
0.03459315001964569,
-0.029514528810977936,
0.02388039417564869,
0.00039642027695663273,
0.01497733499854803,
0.010607744567096233,
-0.04901081696152687,
-0.02503746934235096,
0.0038723493926227093,
0.0015223213704302907,
-0.023113558068871498,
0.027492957189679146,
0.05723969265818596,
-0.007668560370802879,
-0.024013657122850418,
0.04732487350702286,
0.04669453203678131,
0.07825963199138641,
-0.029307547956705093,
0.01928056962788105,
-0.04352215304970741,
0.005146139767020941,
-0.05838111415505409,
-0.0455060675740242,
-0.012030604295432568,
-0.04217344895005226,
-0.017450232058763504,
0.03383117541670799,
-0.011984148994088173,
0.028083685785531998,
-0.011667776852846146,
0.08025577664375305,
0.046424753963947296,
-0.019547685980796814,
0.051985710859298706,
-0.04261302947998047,
-0.04393674433231354,
-0.0004457133181858808,
-0.03902110084891319,
-0.021168041974306107,
-0.03042580746114254,
-0.004160899668931961,
-0.018343988806009293,
0.020998366177082062,
0.028384197503328323,
0.04227399453520775,
0.01931537128984928,
-0.011779263615608215,
-0.030458686873316765,
-0.0023779310286045074,
-0.0055932579562067986,
-0.03268446773290634,
0.003872315166518092,
-0.04155877232551575,
0.0502859503030777,
-0.052323922514915466,
-0.06755755841732025,
-0.005690001416951418,
-0.008820910006761551,
-0.05108995735645294,
0.0007980084628798068,
-0.02294505015015602,
-0.025108225643634796,
0.0115073686465621,
0.05017527565360069,
0.09702672809362411,
0.016006603837013245,
0.006231809034943581,
0.0883966013789177,
-0.03663540631532669,
-0.014664717018604279,
-0.0016332096420228481,
-0.06915471702814102,
-0.027678586542606354,
-0.02573046274483204,
-0.037878744304180145,
0.018897822126746178,
-0.029944701120257378,
0.07247042655944824,
0.016449788585305214,
0.006438023876398802,
0.010591178201138973,
-0.0021857628598809242,
-0.039906833320856094,
-0.027156373485922813,
0.041644055396318436,
-0.032484639436006546,
0.07453619688749313,
0.06354151666164398,
-0.03677714988589287,
-0.013644438236951828,
0.029811860993504524,
0.010610035620629787,
-0.008525513112545013,
-0.0006374559598043561,
-0.016794025897979736,
0.025760319083929062,
0.0018889970378950238,
-0.020748525857925415,
-0.014090362936258316,
0.03649057820439339,
0.020295273512601852,
-0.018931405618786812,
0.03659014776349068,
0.008835063315927982,
-0.059959638863801956,
-0.055509649217128754,
0.02052980288863182,
0.05468418076634407,
-0.007135580759495497,
0.04198078811168671,
0.03406999260187149,
0.004984742496162653,
-0.05663081258535385,
0.0548962838947773,
-0.06128964200615883,
0.005238824058324099,
0.029366327449679375,
-0.03561585769057274,
0.05595792829990387,
0.017506342381238937,
0.006361875217407942,
-0.013251152820885181,
0.05195828899741173,
0.008287598378956318,
-0.004119056276977062,
-0.07758136838674545,
-0.03620753809809685,
-0.010139836929738522,
-0.020638665184378624,
-0.05653148517012596,
0.020413236692547798,
0.0007040207274258137,
-0.00022082356736063957,
0.017591826617717743,
-0.026945386081933975,
-0.025249239057302475,
0.013306398876011372,
-0.01927567645907402,
0.0357251912355423,
0.006898369174450636,
-0.01427343301475048,
-0.034505750983953476,
-0.03705313056707382,
0.033080555498600006,
0.005354110151529312,
-0.013859598897397518,
0.045988067984580994,
0.01714637130498886,
0.00019459494797047228,
0.06419634073972702,
0.0488683320581913,
0.060953330248594284,
-0.0034325954038649797,
0.03480854257941246,
0.03213747590780258,
0.058451294898986816,
-0.04072680324316025,
-0.0167460385710001,
0.04015761986374855,
0.016087641939520836,
-0.013177595101296902,
-0.034643109887838364,
-0.03370523452758789,
0.053124990314245224,
0.060856711119413376,
0.06845799833536148,
0.042740028351545334,
-0.010793262161314487,
0.0367966964840889,
-0.009095767512917519,
0.002661344362422824,
0.0370124951004982,
-0.026428425684571266,
0.061176300048828125,
-0.010761869139969349,
0.05510818213224411,
-0.003389471210539341,
-0.012728934176266193,
0.005287290085107088,
-0.03707682341337204,
-0.018628671765327454,
0.024432118982076645,
-0.059737835079431534,
-0.016730422154068947,
0.017817193642258644,
0.020056791603565216,
-0.08385128527879715,
0.02742721326649189,
0.02836610935628414,
0.022282348945736885,
-0.0210405420511961,
-0.0002826443233061582,
-0.0995437428355217,
0.019274093210697174,
0.01911243610084057,
-0.01690569892525673,
0.037733547389507294,
-0.016363179311156273,
-0.03247462213039398,
0.033409398049116135,
0.028863918036222458,
-0.025624873116612434,
0.031315743923187256,
-0.01644626073539257,
-0.06053370609879494,
0.0849556177854538,
-0.003967053722590208,
0.08221866190433502,
0.014409962110221386,
0.03470175713300705,
-0.01647792011499405,
0.024951020255684853,
0.01747313141822815,
-0.011323748156428337,
-0.003680971683934331,
-0.02816816419363022,
0.0017238561995327473,
-0.013372690416872501,
0.0014538466930389404,
0.022511925548315048,
-0.08488185703754425,
0.003959733061492443,
0.008257681503891945,
0.020351482555270195,
0.04713006317615509,
-0.08104266971349716,
0.03954166918992996,
0.009614589624106884,
-0.0013039238983765244,
0.04390815272927284,
0.012956773862242699,
0.019555237144231796,
-0.03954378515481949,
-0.0008633674588054419,
-0.010430548340082169,
0.05289637669920921,
0.06667270511388779,
0.05256907641887665,
-0.04163992404937744,
0.024521682411432266,
-0.011841367930173874,
0.01408334169536829,
0.020211167633533478,
-0.011146802455186844,
0.006593513302505016,
0.07071778178215027,
-0.017775915563106537,
0.002152025466784835,
-0.0013039804762229323,
0.05224267393350601,
0.028899209573864937,
0.01373365055769682,
0.05016566440463066,
-0.048810940235853195,
-0.00021300255320966244,
0.009335648268461227,
-0.027586456388235092,
0.003751808311790228,
0.03299945965409279,
0.0014913277700543404,
0.013450032100081444,
-0.0030734376050531864,
-0.011613819748163223,
0.03642924129962921,
-0.006647085305303335,
-0.054431892931461334,
-0.0013859695754945278,
0.02293495647609234,
-0.049143169075250626,
0.005286643281579018,
0.047539643943309784,
0.00040005132905207574,
-0.07030152529478073,
-0.00905185379087925,
0.0007092470186762512,
-0.032100219279527664,
0.01982535794377327,
0.04670889675617218,
-0.037033285945653915,
-0.03396489471197128,
-0.0015901185106486082,
-0.008201937191188335,
0.036114539951086044,
0.017398865893483162,
0.01848525181412697,
-0.011786166578531265,
-0.005277629941701889,
0.005314507521688938,
0.01124140527099371,
-0.017471695318818092,
-0.014893255196511745,
-0.049567218869924545,
-0.02024848386645317,
-0.056328244507312775,
0.007200303487479687,
-0.013647550716996193,
0.001006344798952341,
0.014236148446798325,
-0.09490961581468582,
-0.012040020897984505,
0.010316596366465092,
0.02948424220085144,
0.03459355980157852,
0.09561032801866531,
0.043092165142297745,
0.0028927314560860395,
-0.01593784987926483,
0.012449496425688267,
0.006345607340335846,
-0.09130149334669113,
0.004587867297232151,
0.08739503473043442,
0.0039314026944339275,
0.011532288044691086,
0.0015669198473915458,
-0.0949886366724968,
0.0007555627962574363,
-0.057603172957897186,
-0.0647239238023758,
0.027992773801088333,
-0.015132240951061249,
0.02273706905543804,
0.016034763306379318,
-0.06835978478193283,
-0.049341894686222076,
-0.01993301883339882,
-0.060752417892217636,
-0.037404678761959076,
0.013128046877682209,
0.007815632037818432,
-0.0177353136241436,
-0.017897499725222588,
0.05718018859624863,
0.014515443705022335,
0.016191674396395683,
0.02054741233587265,
-0.01484836544841528,
-0.05433562025427818,
0.07845630496740341,
-0.04086408391594887,
-0.05469907075166702,
0.063070148229599,
-0.06422196328639984,
0.049181994050741196,
-0.09868857264518738,
0.018189940601587296,
0.027454691007733345,
0.0038592431228607893,
-0.043004054576158524,
0.01817736215889454,
0.025693506002426147,
-0.03550991415977478,
0.005040935706347227,
0.004676134791225195,
0.0038936336059123278,
0.029132070019841194,
-0.10452833026647568,
-0.055803995579481125,
0.001650237012654543,
0.008501353673636913,
-0.03290502354502678,
0.0019726587925106287,
-0.041720274835824966,
-0.010403539054095745,
-0.004408006090670824,
0.008131662383675575,
-0.005783273838460445,
0.02536337450146675,
-0.06094249710440636,
0.004149342887103558,
-0.0020876987837255,
-0.01481499895453453,
-0.0331190750002861,
-0.0005548037588596344,
0.0027987537905573845,
-0.030139125883579254,
-0.02175496146082878,
-0.061173584312200546,
0.015256336890161037,
0.04130450636148453,
0.01853112503886223,
0.011776911094784737,
-0.012453832663595676,
0.025620386004447937,
-0.037867989391088486,
-0.03307043015956879,
-0.013964323326945305,
-0.044967178255319595,
-0.017056643962860107,
-0.022169072180986404,
-0.03427766636013985,
0.005147474352270365,
0.005004062782973051,
0.05901937186717987,
-0.03151324391365051,
0.01744164153933525,
0.04269087687134743,
-0.01184823364019394,
0.0034489398822188377,
0.019351776689291,
0.016102831810712814,
0.02067537233233452,
0.01943729631602764,
-0.015072233974933624,
0.00961027480661869,
0.040264762938022614,
-0.10671085119247437,
0.05818840116262436,
-0.021602358669042587,
0.060138292610645294,
-0.036891184747219086,
-0.01219658087939024,
-0.022672006860375404,
0.06451918184757233,
-0.053671739995479584,
-0.020068515092134476,
0.04409068822860718,
-0.029597083106637,
-0.08217692375183105,
0.011848983354866505,
0.024030698463320732,
-0.0016447165980935097,
-0.02310011349618435,
-0.0049437303096055984,
-0.039957672357559204,
-0.01262873038649559,
0.07504694908857346,
-0.023464826866984367,
0.012738357298076153,
-0.013892904855310917,
0.03452690318226814,
0.0025101955980062485,
-0.028156736865639687,
-0.0030535301193594933,
-0.01020897924900055,
0.019411450251936913,
0.015560404397547245,
0.008392153307795525,
0.035798925906419754,
0.02090615965425968,
0.006789019331336021,
0.09624093025922775,
0.07778310030698776,
0.06027359515428543,
0.024926457554101944,
0.014094910584390163,
0.01172521524131298,
0.031972791999578476,
0.005113137420266867,
-0.02747943252325058,
0.019477155059576035,
-0.02400246448814869,
-0.10828423500061035,
-0.01345766056329012,
-0.0355043038725853,
0.02448071539402008,
-0.02980244904756546,
0.01443252619355917,
-0.09666747599840164,
-0.008347365073859692,
0.030432458966970444,
-0.026423024013638496,
-0.051154159009456635,
-0.01710331067442894,
0.0012582199415192008,
-0.03617320582270622,
0.025283414870500565,
0.014270630665123463,
0.018698709085583687,
-0.012395323254168034,
0.02740863896906376,
-0.020869772881269455,
0.01460010651499033,
-0.010059218853712082,
-0.0333782434463501,
0.016260256990790367,
-0.0012079904554411769,
0.0059718480333685875,
-0.004198688548058271,
-0.024453796446323395,
-0.006595795974135399,
-0.028855884447693825,
0.032694339752197266,
0.024075224995613098,
-0.05536127835512161,
0.044615618884563446,
-0.02219409868121147,
-0.04195534810423851,
-0.0022536872420459986,
-0.004700665827840567,
0.0710231214761734,
0.0021115117706358433,
0.014310861006379128,
-0.010992234572768211,
0.023699462413787842,
-0.017963029444217682,
-0.06577650457620621,
-0.04360582306981087,
0.0017495849169790745,
0.05847404897212982,
-0.004315333440899849,
0.04119911789894104,
0.058101437985897064,
0.024150602519512177,
0.005984652321785688,
-0.050198838114738464,
-0.0017536761006340384,
-0.007024961523711681,
-0.0370902493596077,
-0.003306951140984893,
-0.005030913278460503,
0.026066554710268974,
-0.022261742502450943,
-0.04816627874970436,
0.030687320977449417,
-0.03948899358510971,
-0.00761660560965538,
-0.012990877032279968,
0.010021792724728584,
0.04510720819234848,
0.014643779024481773,
-0.008497241884469986,
-0.03622645512223244,
-0.08767469972372055,
0.026857899501919746,
0.027934294193983078,
0.022481093183159828,
-0.0624767504632473,
0.023424647748470306,
-0.04355328157544136,
-0.004981771111488342,
-0.017804738134145737,
-0.041980963200330734,
0.038527823984622955,
-0.0005974352825433016,
-0.015673663467168808,
-0.07655631005764008,
-0.029527300968766212,
0.05089374631643295,
0.032431017607450485,
0.0404629148542881,
-0.054344139993190765,
0.025294175371527672,
-0.0028870960231870413,
-0.010533667169511318,
0.07525547593832016,
-0.013217857107520103,
-0.011444448493421078,
0.007042358163744211,
0.04297686368227005,
-0.019870862364768982,
0.035098422318696976,
-0.009027300402522087,
-0.010476463474333286,
0.02867911569774151,
-0.011562107130885124,
0.04299216717481613,
-0.0437232106924057,
0.04633230343461037
] |
[
5.233858108520508,
5.12327766418457
] |
Probability
|
Mathematics
|
math-PR
|
math-AG
|
na
|
2007-03-31T09:49:10
|
The shape of the hadronic form factor f+(q2) in the decay D0 --> K- e+ nue
has been measured in a model independent analysis and compared with theoretical
calculations. We use 75 fb(-1) of data recorded by the BABAR detector at the
PEPII electron-positron collider. The corresponding decay branching fraction,
relative to the decay D0 --> K- pi+, has also been measured to be RD = BR(D0
--> K- e+ nue)/BR(D0 --> K- pi+) = 0.927 +/- 0.007 +/- 0.012. From these
results, and using the present world average value for BR(D0 --> K- pi+), the
normalization of the form factor at q2=0 is determined to be f+(0)=0.727 +/-
0.007 +/- 0.005 +/- 0.007 where the uncertainties are statistical, systematic,
and from external inputs, respectively.
|
Measurement of the Hadronic Form Factor in D0 --> K- e+ nue Decays
|
hep-ex
|
0704.0020
| 2,007
|
[
-0.03518064320087433,
0.035845670849084854,
0.007933560758829117,
-0.006387704983353615,
0.027882488444447517,
0.029663529247045517,
-0.00686968769878149,
0.04439491406083107,
-0.03328924998641014,
-0.05075858160853386,
-0.06612429022789001,
0.05318397656083107,
0.05010951682925224,
0.026089392602443695,
0.08679107576608658,
-0.05431987717747688,
0.040747396647930145,
-0.028482405468821526,
-0.0020168886985629797,
-0.003077634610235691,
-0.06504294276237488,
-0.011711973696947098,
0.0016749020433053374,
-0.0340404212474823,
0.1162349283695221,
-0.04310760647058487,
-0.019031774252653122,
0.04777824878692627,
-0.08958057314157486,
0.0005578771233558655,
0.025863179937005043,
-0.0300546083599329,
0.049400605261325836,
-0.02615738846361637,
-0.03184931352734566,
-0.05594535171985626,
0.048197660595178604,
-0.023893754929304123,
0.010709411464631557,
0.035390108823776245,
-0.006875840947031975,
-0.04502027481794357,
-0.013329925015568733,
0.03034663014113903,
0.018662892282009125,
0.008175298571586609,
0.01938989758491516,
-0.0018492155941203237,
-0.01999904215335846,
-0.0035874363966286182,
-0.03847454488277435,
0.001029578736051917,
0.0356459878385067,
-0.05366542562842369,
-0.006679274141788483,
0.0477309487760067,
-0.0037287059240043163,
0.0040041785687208176,
0.09486626833677292,
-0.007756877690553665,
0.009037227369844913,
0.025232726708054543,
-0.022849837318062782,
0.02636994607746601,
0.05025380477309227,
-0.0477403923869133,
-0.041613105684518814,
0.0237876046448946,
0.008381422609090805,
-0.02972872368991375,
0.02480405569076538,
-0.03528274968266487,
0.011818399652838707,
0.05215591937303543,
-0.012913930229842663,
0.002965802326798439,
0.006751793436706066,
-0.024059254676103592,
0.007381883915513754,
0.038194239139556885,
0.010071906261146069,
-0.01748540997505188,
0.020934173837304115,
0.029919609427452087,
0.05622302368283272,
-0.028056249022483826,
0.029963040724396706,
0.06752102077007294,
-0.026069626212120056,
0.04252229258418083,
0.018294325098395348,
-0.020816946402192116,
0.027606964111328125,
0.0064999875612556934,
-0.026447433978319168,
0.016856195405125618,
-0.015643399208784103,
0.05748450756072998,
-0.03693636134266853,
-0.025969740003347397,
0.0224173441529274,
0.0686986967921257,
-0.009640445932745934,
0.05392741039395332,
0.0020436716731637716,
0.03755507990717888,
-0.031162500381469727,
-0.002323262859135866,
0.04317223280668259,
-0.055358558893203735,
-0.11133772879838943,
-0.02695164829492569,
-0.00006029250653227791,
0.01043280865997076,
-0.01932067796587944,
-0.024586793035268784,
0.014889472164213657,
-0.05887599661946297,
-0.0028302122373133898,
0.020624522119760513,
0.014416287653148174,
0.0021090484224259853,
-0.004685508087277412,
0.03311728686094284,
-0.02624361403286457,
-0.01576744206249714,
-0.04280414432287216,
0.008429689332842827,
0.046049926429986954,
-0.010526549071073532,
0.023372003808617592,
-0.0064283376559615135,
-0.06646722555160522,
-0.01614570803940296,
0.0407516174018383,
0.08927976340055466,
-0.05292300507426262,
-0.02032315358519554,
0.017709463834762573,
-0.04529719427227974,
-0.005927486345171928,
0.055082548409700394,
0.030248982831835747,
-0.029573142528533936,
0.007704596966505051,
-0.06215131655335426,
0.044257961213588715,
-0.011317632161080837,
-0.033759359270334244,
0.03816511854529381,
0.05478274077177048,
-0.022809596732258797,
0.006667153909802437,
0.03159312158823013,
-0.03164079040288925,
-0.056587837636470795,
-0.009553673677146435,
0.0035027293488383293,
0.004160323180258274,
-0.004336358048021793,
0.01411453541368246,
0.029768753796815872,
-0.05714469775557518,
-0.016154661774635315,
0.010080548003315926,
-0.009134333580732346,
0.06362133473157883,
0.026678208261728287,
0.002759820781648159,
0.0255037322640419,
-0.05468396842479706,
-0.013866600580513477,
0.027284938842058182,
-0.03230318799614906,
-0.022921251133084297,
0.03161637485027313,
-0.0014114764053374529,
-0.06867200881242752,
0.04132029041647911,
0.014855513349175453,
0.040866509079933167,
0.051917560398578644,
0.06499166041612625,
0.02387099899351597,
-0.0006241993978619576,
0.0169171541929245,
0.06635980308055878,
-0.03500836715102196,
-0.007901111617684364,
-0.022162655368447304,
0.01836804486811161,
-0.027414793148636818,
-0.007786499336361885,
-0.052175652235746384,
0.02133159525692463,
-0.011549931019544601,
0.033430639654397964,
-0.05084910988807678,
0.012457500211894512,
0.0011980144772678614,
-0.07401714473962784,
-0.009972412139177322,
-0.07834187895059586,
-0.007617462892085314,
0.04496603086590767,
-0.010128509253263474,
0.02036159485578537,
0.040678296238183975,
0.024675728753209114,
0.02947845309972763,
0.04668448865413666,
0.04368652030825615,
-0.060341477394104004,
0.03698423504829407,
-0.0024838370736688375,
0.00000774318050389411,
0.011503159068524837,
-0.014854776673018932,
-0.03747310861945152,
0.028797822073101997,
-0.014802183955907822,
-0.0013643736019730568,
0.015302060171961784,
0.03453933447599411,
0.006158968433737755,
0.06390202045440674,
-0.01043992955237627,
-0.0010426060762256384,
-0.01929234154522419,
0.007387127261608839,
-0.04828720539808273,
-0.02996806986629963,
0.0035674695391207933,
0.03876927122473717,
-0.04006905481219292,
0.03249890357255936,
0.01418733038008213,
-0.022193027660250664,
0.01589871756732464,
0.03847324848175049,
0.02406194433569908,
0.02505890093743801,
0.032480113208293915,
-0.019199317321181297,
-0.04248417913913727,
-0.026623938232660294,
-0.03722015395760536,
0.0028683142736554146,
-0.044585783034563065,
0.007879507727921009,
0.002479879418388009,
-0.007555559277534485,
0.03630682826042175,
0.04533987119793892,
-0.01146200206130743,
-0.05869201198220253,
-0.0628582313656807,
0.05591461807489395,
-0.044498033821582794,
-0.06408520042896271,
0.019414853304624557,
-0.024804962798953056,
-0.0044414889998734,
-0.02586260996758938,
-0.042597878724336624,
-0.00440952880308032,
0.023446647450327873,
0.0023932172916829586,
0.010516286827623844,
-0.03792446851730347,
0.025494350120425224,
0.034091342240571976,
0.004245733842253685,
0.04919566959142685,
0.0045552062802016735,
-0.04654984921216965,
0.05131473392248154,
-0.018550856038928032,
-0.020986709743738174,
0.0027818968519568443,
-0.05011993646621704,
0.0384071059525013,
-0.032853443175554276,
-0.009425058029592037,
-0.037263255566358566,
0.03835175558924675,
0.037017934024333954,
-0.013291039504110813,
-0.02260422706604004,
0.05607740953564644,
-0.04594087973237038,
-0.01566167175769806,
0.01754658669233322,
0.006683932617306709,
0.026574578136205673,
0.11707776039838791,
0.09202966094017029,
-0.031880445778369904,
0.03683917969465256,
-0.01672183722257614,
-0.0004897890612483025,
-0.023311002179980278,
-0.0246120598167181,
-0.05255419760942459,
-0.008497866801917553,
-0.02503047324717045,
-0.009260093793272972,
0.0015054475516080856,
-0.010351178236305714,
0.02111205831170082,
-0.0557585284113884,
0.039728205651044846,
-0.020695120096206665,
-0.016723118722438812,
-0.019703233614563942,
-0.02340441197156906,
0.020213760435581207,
0.03955569118261337,
0.08124004304409027,
0.025429600849747658,
0.05008005350828171,
-0.043131545186042786,
0.054472677409648895,
-0.059304967522621155,
0.04393451288342476,
0.06790746748447418,
0.043672479689121246,
0.05643368512392044,
-0.026752648875117302,
-0.01709085889160633,
-0.0006668387213721871,
0.052383918315172195,
-0.026745684444904327,
0.005914642009884119,
-0.0008339486084878445,
0.05199180915951729,
-0.013252979144454002,
0.07062295079231262,
-0.02529938891530037,
0.0035570424515753984,
0.01392156258225441,
-0.0489601269364357,
-0.025509752333164215,
-0.03306964039802551,
0.022216906771063805,
-0.037322018295526505,
-0.004263946786522865,
-0.028383702039718628,
0.041521601378917694,
0.02993280254304409,
-0.033519044518470764,
0.012385232374072075,
-0.01706809364259243,
0.008673740550875664,
0.005733173806220293,
0.0452008917927742,
0.016169507056474686,
-0.0466054305434227,
-0.018179960548877716,
0.018667060881853104,
0.045800384134054184,
-0.05814101919531822,
0.05544126033782959,
-0.011509677395224571,
-0.002441163407638669,
-0.0022645092103630304,
0.0004226625896990299,
0.01750159077346325,
0.00753414910286665,
-0.024920742958784103,
-0.02717668190598488,
-0.016251588240265846,
0.05714812129735947,
0.06047734245657921,
0.015853429213166237,
0.01936919614672661,
-0.02152187190949917,
-0.002289785072207451,
-0.04603306204080582,
-0.007375482935458422,
0.03552995249629021,
0.060459889471530914,
0.0464392751455307,
0.006316716317087412,
0.007977746427059174,
-0.05314594507217407,
-0.07139439880847931,
-0.03261668607592583,
0.011133451946079731,
-0.014417771250009537,
0.028140634298324585,
-0.04245167598128319,
-0.031878821551799774,
0.0164286270737648,
-0.019645337015390396,
-0.02134937234222889,
0.06455063819885254,
-0.01578994281589985,
-0.01214780192822218,
0.020528530701994896,
-0.05019908770918846,
-0.03419254347681999,
0.0325547456741333,
-0.01853974722325802,
-0.004883753135800362,
0.002081827027723193,
-0.061426032334566116,
-0.05482735484838486,
0.05605265498161316,
-0.029342150315642357,
0.0037542025092989206,
0.06194400414824486,
-0.007073977496474981,
-0.0531638078391552,
0.04054823890328407,
-0.001391113270074129,
0.04303424805402756,
0.012929192744195461,
0.00498812785372138,
-0.06998616456985474,
0.02701914869248867,
0.031748779118061066,
-0.03490864858031273,
0.02404213882982731,
0.017400186508893967,
0.01996641978621483,
-0.00464054336771369,
0.00600840337574482,
0.029388491064310074,
-0.0230864305049181,
0.06478960067033768,
-0.001677984488196671,
0.021434200927615166,
0.03782474622130394,
-0.08750065416097641,
0.02770931087434292,
0.04773539677262306,
0.024802962318062782,
-0.03891441226005554,
0.05312751978635788,
0.017658358439803123,
-0.07883337885141373,
0.05211573466658592,
0.038107819855213165,
0.03798429295420647,
0.07732090353965759,
0.022783642634749413,
-0.03613844886422157,
-0.039402540773153305,
0.004830221179872751,
0.06833314150571823,
-0.009440101683139801,
0.015061824582517147,
0.012218142859637737,
0.02500767633318901,
-0.015243020839989185,
0.005775123368948698,
-0.0004170614993199706,
0.046847615391016006,
0.08306966722011566,
-0.00850257370620966,
-0.015205971896648407,
-0.051126252859830856,
0.0064419936388731,
-0.022231988608837128,
-0.040484726428985596,
-0.03215167298913002,
0.017747927457094193,
0.007737442385405302,
0.018494373187422752,
-0.024514859542250633,
-0.03276248648762703,
0.040200669318437576,
-0.011684507131576538,
-0.021192776039242744,
-0.0053926026448607445,
-0.020516542717814445,
-0.0657029002904892,
-0.015083692036569118,
0.053633395582437515,
0.02508402429521084,
0.004483246244490147,
-0.056866709142923355,
0.017905088141560555,
-0.02228921465575695,
0.013044841587543488,
0.02806667797267437,
0.016146546229720116,
0.004829208366572857,
-0.03778425231575966,
-0.005081469658762217,
0.0932222455739975,
0.08754336833953857,
-0.028463397175073624,
0.027077341452240944,
0.029762810096144676,
-0.03872573375701904,
0.010450524277985096,
0.02393423765897751,
0.027438241988420486,
-0.03408465161919594,
0.01713823899626732,
0.02010497823357582,
0.010772096924483776,
0.015236111357808113,
0.0486614890396595,
-0.07913843542337418,
-0.04582957923412323,
0.0025475206784904003,
-0.014803056605160236,
0.008279082365334034,
0.03282196819782257,
0.0665205642580986,
0.014628502540290356,
-0.011631105095148087,
-0.010202772915363312,
-0.007790711242705584,
0.0036958621349185705,
-0.04444921761751175,
0.0287080816924572,
-0.003982767462730408,
0.0011713047279044986,
0.027594640851020813,
-0.01440621167421341,
-0.056323885917663574,
-0.01975437067449093,
-0.008960438892245293,
-0.07608310133218765,
0.027019765228033066,
-0.029788663610816002,
0.055100951343774796,
0.030598104000091553,
-0.004168846178799868,
0.0013962365919724107,
-0.02327915094792843,
-0.00504102511331439,
-0.02050423063337803,
0.03411431983113289,
0.013451793231070042,
0.007636412512511015,
0.031768616288900375,
0.04213511571288109,
0.007843438535928726,
0.019450334832072258,
-0.010793889872729778,
-0.020002758130431175,
-0.01008889451622963,
0.018174638971686363,
-0.027941714972257614,
-0.0817069411277771,
0.02316500060260296,
-0.018004924058914185,
0.011416265740990639,
-0.08001981675624847,
0.0385890007019043,
-0.043618347495794296,
0.06121844798326492,
-0.023516615852713585,
-0.09260528534650803,
-0.07346227765083313,
-0.025107039138674736,
-0.024641992524266243,
0.02984633855521679,
0.01447325013577938,
-0.008243710733950138,
-0.10641679167747498,
-0.01201575342565775,
0.0031879073940217495,
0.01051885262131691,
0.0037057590670883656,
-0.016682440415024757,
-0.06933414191007614,
-0.028606323525309563,
-0.0007941917865537107,
-0.006082470528781414,
-0.02863260731101036,
-0.003809226443991065,
0.007132479455322027,
-0.04528021067380905,
0.0036689655389636755,
-0.01904277503490448,
0.03074423409998417,
0.03437399864196777,
-0.019041508436203003,
-0.020358435809612274,
0.06454133242368698,
0.008274667896330357,
-0.057546645402908325,
0.01886226423084736,
-0.010441642254590988,
-0.009568541310727596,
0.002438892377540469,
-0.025211868807673454,
-0.05236348509788513,
-0.01800653524696827,
0.004867512732744217,
-0.005493747070431709,
-0.033724937587976456,
-0.009426962584257126,
-0.019459018483757973,
-0.04380391910672188,
0.03135642781853676,
0.036781907081604004,
-0.013795632869005203,
0.02898719720542431,
0.019876543432474136,
0.007417112588882446,
0.059845659881830215,
-0.03897511214017868,
-0.019210994243621826,
0.04594390466809273,
0.022572161629796028,
-0.041196558624506,
-0.048046596348285675,
0.0002554284001234919,
-0.06940893828868866,
0.08174443989992142,
-0.0011289527174085379,
0.0016738737467676401,
0.00924662034958601,
0.029239920899271965,
-0.05719943717122078,
-0.0153318140655756,
-0.08710244297981262,
-0.021073084324598312,
0.0709591805934906,
-0.006021725479513407,
-0.04646150767803192,
-0.022451741620898247,
0.033649418503046036,
-0.008907484821975231,
0.01571447029709816,
0.009759940207004547,
-0.02634435147047043,
-0.014586090110242367,
-0.006362380459904671,
-0.016743823885917664,
0.04808300733566284,
0.04032868519425392,
0.05980488285422325,
0.039238687604665756,
-0.027345003560185432,
0.005306855775415897,
-0.0066794236190617085,
-0.014145010150969028,
0.016883207485079765,
-0.015892192721366882,
0.04199017584323883,
-0.0374470129609108,
0.008282968774437904,
0.06981679797172546,
0.04101449251174927,
0.0047441814094781876,
0.040029142051935196,
0.03395969793200493,
0.008058268576860428,
0.024501798674464226,
0.038632504642009735,
-0.03733671456575394,
-0.042562372982501984,
-0.0067117405124008656,
-0.06127170845866203,
0.0364600345492363,
-0.008565006777644157,
0.03588254004716873,
-0.011980435810983181,
-0.0295544546097517,
-0.04113228619098663,
-0.06536930799484253,
-0.0044233789667487144,
-0.0031759648118168116,
-0.02529691532254219,
-0.039655596017837524,
-0.03734152764081955,
-0.02527650259435177,
0.017484350129961967,
-0.009511797688901424,
-0.023120179772377014,
0.004476264119148254,
-0.012759959325194359,
0.05005534365773201,
0.005674792919307947,
-0.024644458666443825,
0.008907419629395008,
-0.05454197898507118,
0.03954974189400673,
-0.012182367965579033,
-0.026463601738214493,
-0.057479336857795715,
0.017155060544610023,
0.0186723954975605,
0.019706422463059425,
0.018655922263860703,
-0.0857849270105362,
-0.028775373473763466,
0.010578762739896774,
-0.055705830454826355,
-0.010280968621373177,
-0.02916521020233631,
-0.01677757129073143,
0.016784051433205605,
0.05707378685474396,
-0.02561497502028942,
0.014825823716819286,
0.01033019833266735,
-0.012265568599104881,
0.018081748858094215,
0.002022599335759878,
-0.008470755070447922,
-0.025289859622716904,
0.030706051737070084,
-0.0014265314675867558,
0.05363411828875542,
0.04487069323658943,
0.007151896134018898,
-0.02711191214621067,
-0.03825082629919052,
-0.07055570185184479,
0.050432879477739334,
-0.024433676153421402,
-0.020169436931610107,
-0.03394785150885582,
-0.0242510624229908,
0.018640371039509773,
-0.006679427344352007,
-0.06771261245012283,
-0.04702406004071236,
0.03547937422990799,
0.05736590549349785,
0.05790221691131592,
-0.04523004591464996,
0.02201688662171364,
-0.044393688440322876,
0.029893310740590096,
0.0043964930810034275,
-0.016099480912089348,
0.03656496852636337,
0.004679468460381031,
-0.12282592058181763,
-0.009269033558666706,
-0.009462282061576843,
-0.010020972229540348,
-0.0035289532970637083,
0.05553385242819786,
-0.01960659772157669,
-0.06387913227081299,
-0.05749344453215599,
0.036029912531375885,
0.04764288291335106,
-0.002308136783540249,
-0.021707413718104362,
-0.007838426157832146,
0.003122632624581456,
0.030575010925531387,
0.010412588715553284,
-0.021877512335777283,
-0.03444867208600044,
0.020855026319622993,
0.041685160249471664,
-0.03159857913851738,
0.039797164499759674,
-0.014027182944118977,
-0.014489363878965378,
0.05971090495586395,
0.009615509770810604,
-0.0013088298728689551,
-0.03285534307360649,
0.042932089418172836
] |
[
15.38412094116211,
-3.313856363296509
] |
High Energy Physics - Experiment
|
General Physics
|
hep-ex
|
na
|
na
|
2007-03-31T12:57:59
|
Spatiotemporal pattern formation in a product-activated enzymic reaction at
high enzyme concentrations is investigated. Stochastic simulations show that
catalytic turnover cycles of individual enzymes can become coherent and that
complex wave patterns of molecular synchronization can develop. The analysis
based on the mean-field approximation indicates that the observed patterns
result from the presence of Hopf and wave bifurcations in the considered
system.
|
Molecular Synchronization Waves in Arrays of Allosterically Regulated
Enzymes
|
nlin.PS physics.chem-ph q-bio.MN
|
0704.0021
| 2,007
|
[
-0.026254145428538322,
0.02915380150079727,
-0.022480973973870277,
0.0053808484226465225,
0.05731385201215744,
-0.015581022948026657,
0.008223965764045715,
0.06212712824344635,
-0.02863508090376854,
0.006257790140807629,
-0.0706419050693512,
0.0705643892288208,
0.028496047481894493,
0.014214062131941319,
0.004777842201292515,
-0.04160558804869652,
0.020023729652166367,
0.04613079875707626,
-0.04674655571579933,
0.025868387892842293,
-0.0497310496866703,
0.02347373589873314,
-0.030735792592167854,
-0.03833922743797302,
0.07271970808506012,
0.013279374688863754,
0.03127196803689003,
-0.04238244146108627,
-0.00855649821460247,
0.008257224224507809,
0.039228200912475586,
-0.047584306448698044,
-0.012518586590886116,
-0.030492985621094704,
-0.004702799953520298,
-0.0012665853137150407,
0.027891237288713455,
-0.007235890254378319,
-0.009074901230633259,
0.05488620325922966,
0.03642437234520912,
-0.029398540034890175,
-0.006724023260176182,
-0.059502013027668,
0.03700796514749527,
0.003118222113698721,
0.013507688418030739,
0.002932053990662098,
0.023205023258924484,
0.015195949003100395,
-0.006800721865147352,
0.0027874906081706285,
-0.025200875476002693,
-0.050118472427129745,
0.029698604717850685,
0.05692974105477333,
0.02002744749188423,
-0.006785953417420387,
0.06262648850679398,
0.013405965641140938,
0.019625408574938774,
0.06036991998553276,
0.0017859520157799125,
0.003735265228897333,
0.057864222675561905,
-0.03842407837510109,
-0.03807046264410019,
0.011699344031512737,
-0.009225787594914436,
-0.04628114402294159,
-0.004863817244768143,
-0.01713620126247406,
-0.037414394319057465,
0.0639214739203453,
0.030204851180315018,
0.012709000147879124,
-0.011751364916563034,
0.02276826649904251,
-0.018357738852500916,
-0.02168312668800354,
0.0029971329495310783,
-0.027573170140385628,
0.015295096673071384,
0.08034677803516388,
0.040131933987140656,
-0.001784868654794991,
0.01882292330265045,
0.008712081238627434,
-0.09344625473022461,
0.027742823585867882,
0.021857937797904015,
0.011339275166392326,
0.03621853515505791,
0.036329206079244614,
-0.0851467102766037,
0.03318975120782852,
-0.034801241010427475,
0.0316396988928318,
-0.03741316497325897,
-0.016412150114774704,
-0.006200352683663368,
0.04355849698185921,
-0.0016033488791435957,
-0.06706269830465317,
0.007820743136107922,
0.027748744934797287,
0.02072550728917122,
-0.01913430355489254,
-0.007668267469853163,
-0.006073928438127041,
-0.059034887701272964,
0.006839475128799677,
-0.0708310604095459,
0.02024129033088684,
-0.024148279801011086,
-0.029966525733470917,
0.033180102705955505,
-0.06190513074398041,
-0.007183301728218794,
0.00590834254398942,
-0.004058691672980785,
-0.07309851050376892,
-0.05989791080355644,
0.023309223353862762,
0.02537013590335846,
0.06839494407176971,
-0.0648847222328186,
0.011577614583075047,
0.009893090464174747,
-0.02202862873673439,
0.024667734280228615,
0.010265812277793884,
-0.053253304213285446,
0.008643240667879581,
0.02063482254743576,
0.012158097699284554,
-0.05271492153406143,
-0.07058496028184891,
0.0186860803514719,
0.008378203958272934,
0.01197529025375843,
-0.03767525404691696,
0.028438763692975044,
-0.03770820051431656,
-0.021648451685905457,
-0.04430089145898819,
0.036841392517089844,
-0.0464036650955677,
0.019864249974489212,
-0.06312309205532074,
-0.02902986854314804,
0.04600090906023979,
0.008136109448969364,
0.03538590297102928,
-0.02272552065551281,
-0.005585397128015757,
-0.021515987813472748,
0.013052125461399555,
0.024432765319943428,
-0.010415766388177872,
0.05113885551691055,
-0.008842294104397297,
-0.03067976050078869,
0.036283187568187714,
-0.08480963110923767,
0.006115340162068605,
0.05236321687698364,
0.011749857105314732,
0.022712569683790207,
0.0591888464987278,
-0.007115992251783609,
-0.02518497407436371,
-0.0816870778799057,
-0.02122170478105545,
0.01486455649137497,
0.06017214059829712,
-0.017885306850075722,
-0.03629733994603157,
0.06282966583967209,
0.0008955103694461286,
0.051946163177490234,
-0.03469466790556908,
0.008144340477883816,
-0.01463207509368658,
0.061951473355293274,
-0.000740970834158361,
-0.0040670353919267654,
-0.020221693441271782,
-0.08079559355974197,
-0.017399637028574944,
0.05883016809821129,
0.01078110747039318,
-0.02319057658314705,
-0.062453869730234146,
-0.00023609600611962378,
0.003944065887480974,
0.06204941123723984,
-0.016224531456828117,
0.03156841918826103,
-0.016351597383618355,
-0.03278491273522377,
-0.03213345259428024,
0.00022460492618847638,
0.024000653997063637,
-0.019977398216724396,
0.019255034625530243,
0.021162573248147964,
0.0545506551861763,
-0.03046010620892048,
0.039963219314813614,
0.07154139131307602,
0.024236667901277542,
-0.02327805943787098,
0.012938144616782665,
-0.020868269726634026,
0.007989303208887577,
-0.0022158657666295767,
-0.07389552146196365,
-0.009630262851715088,
0.046556755900382996,
0.0063278996385633945,
-0.005924442317336798,
-0.01701134815812111,
0.006203087512403727,
0.057760290801525116,
0.016802765429019928,
-0.036370616406202316,
-0.049141138792037964,
-0.062077026814222336,
-0.03855090215802193,
-0.0032568643800914288,
0.006360335741192102,
0.0569927841424942,
-0.00856692623347044,
0.021011410281062126,
0.006359882187098265,
-0.03912925347685814,
0.05521601065993309,
-0.0071146138943731785,
-0.00006805110024288297,
0.02549743466079235,
0.02120286412537098,
0.009881767444312572,
-0.005319955293089151,
-0.03864797577261925,
-0.027944272384047508,
-0.004434753209352493,
0.0026903608813881874,
-0.04268430545926094,
0.011106017976999283,
0.04733344167470932,
0.008678494952619076,
0.04184774309396744,
0.03688802197575569,
0.010783955454826355,
-0.050401028245687485,
-0.027000106871128082,
0.06379257142543793,
-0.0004056149919051677,
-0.00012779365351889282,
0.03545736148953438,
-0.011910812929272652,
0.03743835166096687,
-0.050858139991760254,
0.003275619586929679,
-0.017133207991719246,
0.03440985083580017,
-0.030123207718133926,
-0.048656828701496124,
-0.04188868775963783,
-0.05537617579102516,
0.03298594057559967,
0.055546991527080536,
0.057916149497032166,
-0.06502112001180649,
0.03879125416278839,
0.022481407970190048,
-0.0024706751573830843,
-0.03914423659443855,
-0.030774232000112534,
-0.0694223940372467,
0.004587586037814617,
0.001060790498740971,
-0.012041781097650528,
-0.011242096312344074,
0.014534050598740578,
0.04012586176395416,
0.014024577103555202,
0.03342370688915253,
0.04568900540471077,
0.01748986355960369,
-0.036050256341695786,
0.024158762767910957,
0.06825491786003113,
-0.03030584007501602,
0.03665349259972572,
0.06308259814977646,
-0.05962858721613884,
0.0099195446819067,
0.05217859521508217,
-0.005771482829004526,
-0.0108834533020854,
0.0339849516749382,
0.008447227999567986,
0.007968922145664692,
0.030607927590608597,
-0.03146229311823845,
0.020631399005651474,
-0.0039495243690907955,
0.031070450320839882,
-0.0026962084230035543,
-0.029220206663012505,
-0.021807074546813965,
-0.03208574652671814,
-0.038088057190179825,
0.03332091495394707,
-0.0005118991830386221,
-0.019179269671440125,
0.07318370044231415,
-0.014801687560975552,
-0.022731324657797813,
-0.014906374737620354,
-0.02341589890420437,
-0.07123365253210068,
0.0136947613209486,
0.031116269528865814,
0.002431139349937439,
0.009053132496774197,
-0.05034960061311722,
0.006714328657835722,
0.016149425879120827,
0.03059268929064274,
-0.011240567080676556,
-0.014620011672377586,
0.06602822244167328,
0.001597564434632659,
-0.05706853047013283,
0.040230363607406616,
-0.03803404048085213,
0.01087893359363079,
-0.009328776970505714,
0.016731809824705124,
0.02019643969833851,
-0.11459002643823624,
-0.022333625704050064,
0.04482000693678856,
-0.023301824927330017,
-0.04467958211898804,
0.04501595348119736,
-0.0786084458231926,
-0.04292275756597519,
0.009479801170527935,
-0.009810768067836761,
0.0010735144605860114,
-0.03154569864273071,
0.06193967163562775,
0.03478879854083061,
-0.05386102944612503,
0.08574028313159943,
0.014582413248717785,
0.003995529841631651,
-0.04378128424286842,
-0.006668407469987869,
0.014967788942158222,
0.020707447081804276,
0.04442497342824936,
-0.0200546532869339,
0.03267042711377144,
0.0465904138982296,
-0.07310265302658081,
-0.04028010740876198,
0.0048827058635652065,
0.037589363753795624,
0.02332667075097561,
0.010235920548439026,
0.016343025490641594,
-0.06260040402412415,
-0.0023672140669077635,
-0.0036071310751140118,
-0.018720310181379318,
0.046834301203489304,
0.01821688748896122,
0.0011091575725004077,
-0.017588431015610695,
0.04125078022480011,
0.02061677910387516,
-0.04611751809716225,
0.012638820335268974,
-0.0271284282207489,
0.01267131045460701,
0.008240148425102234,
-0.045590683817863464,
-0.04771632328629494,
-0.0032787173986434937,
-0.01661832444369793,
-0.044933244585990906,
0.029489412903785706,
0.02895362675189972,
0.0395842008292675,
0.03150884807109833,
0.041359227150678635,
-0.07190588861703873,
-0.06600186973810196,
-0.049367450177669525,
0.010692854411900043,
0.005915137939155102,
-0.0109889917075634,
-0.042956896126270294,
0.051407426595687866,
0.0048492723144590855,
0.003300363663583994,
0.0035667922347784042,
0.006399756297469139,
-0.07014663517475128,
-0.00030300061916932464,
0.05095108225941658,
0.05049213767051697,
-0.006907016504555941,
-0.016015904024243355,
0.008762473240494728,
0.01288984902203083,
0.06677211076021194,
0.006252877879887819,
-0.0034518351312726736,
-0.020448075607419014,
-0.02182147279381752,
0.037334609776735306,
-0.004162121564149857,
-0.007519254926592112,
-0.09950420260429382,
-0.003532682079821825,
0.026842020452022552,
-0.00530307786539197,
0.010460619814693928,
-0.03522977977991104,
-0.005476572550833225,
0.048042308539152145,
-0.03328564763069153,
0.03824136406183243,
0.06826091557741165,
0.03226639702916145,
-0.017186792567372322,
-0.0039435215294361115,
0.028429022058844566,
0.04062813147902489,
0.1176532506942749,
0.08770494908094406,
-0.0323873870074749,
-0.01917235553264618,
-0.04523325338959694,
-0.010515819303691387,
0.054096661508083344,
-0.019659483805298805,
0.008887800388038158,
0.10794588178396225,
-0.006186303216964006,
-0.055037032812833786,
0.052921637892723083,
0.016612673178315163,
0.024231964722275734,
0.0029705832712352276,
0.014696775004267693,
-0.08619233220815659,
0.026579953730106354,
0.0037670014426112175,
-0.012388529255986214,
0.02253899537026882,
-0.01733488403260708,
-0.0222906693816185,
0.03457958996295929,
0.03165585920214653,
-0.021302521228790283,
0.015049166977405548,
0.031158076599240303,
-0.011632603593170643,
0.001752259791828692,
0.02903633378446102,
-0.024122122675180435,
0.020762253552675247,
0.07004447281360626,
0.0026492394972592592,
-0.031600095331668854,
-0.0018376711523160338,
-0.013737672008574009,
-0.003971097990870476,
0.019078724086284637,
0.017814578488469124,
0.011078765615820885,
0.004629415925592184,
-0.009808747097849846,
-0.02990770898759365,
0.025329995900392532,
-0.028748581185936928,
-0.008521565236151218,
-0.02142326533794403,
-0.035007450729608536,
-0.0000882456952240318,
-0.021988296881318092,
-0.004423718433827162,
-0.0033658307511359453,
-0.043195515871047974,
0.024122148752212524,
-0.03992129862308502,
-0.01660456322133541,
-0.01794070564210415,
0.0449422262609005,
-0.03700698912143707,
-0.05843047425150871,
0.009148100391030312,
0.047163378447294235,
0.048225581645965576,
0.08694994449615479,
0.0015726190758869052,
0.055641379207372665,
0.02049103192985058,
-0.089810810983181,
0.04400894045829773,
0.004944578278809786,
-0.06318923085927963,
-0.025577859953045845,
0.011354892514646053,
0.017580244690179825,
-0.01577855460345745,
0.035839296877384186,
-0.08014531433582306,
0.03919563442468643,
-0.019270386546850204,
0.0011421657400205731,
0.017239917069673538,
0.011939833872020245,
0.00441319216042757,
0.003062215633690357,
-0.00931067019701004,
0.026512961834669113,
0.040731750428676605,
-0.042815323919057846,
-0.008274300023913383,
0.03346651419997215,
0.0341179184615612,
0.019439533352851868,
-0.0010199676034972072,
0.0026598453987389803,
0.007271254900842905,
-0.004721533972769976,
0.013639618642628193,
-0.057694051414728165,
-0.04498793184757233,
0.008061960339546204,
-0.01992034539580345,
-0.04552360624074936,
0.06743808835744858,
-0.014752581715583801,
0.04512203857302666,
-0.09247874468564987,
-0.0005484530702233315,
0.0264748465269804,
-0.006729397457093,
-0.025092048570513725,
-0.04652004316449165,
-0.03184690698981285,
0.017911696806550026,
0.07105545699596405,
0.04159131273627281,
-0.05539880320429802,
0.06612539291381836,
-0.04860784113407135,
-0.03813471272587776,
0.008763677440583706,
0.03590666875243187,
0.038341231644153595,
0.043167635798454285,
-0.03589225932955742,
-0.02441694214940071,
0.038973238319158554,
-0.007603296544402838,
-0.04947895556688309,
0.021761426702141762,
0.02585640177130699,
-0.040072374045848846,
0.002119690179824829,
-0.03375618904829025,
-0.05708286911249161,
0.00943700410425663,
0.0006367210880853236,
0.00028904297505505383,
-0.01558448001742363,
-0.028177641332149506,
0.014458656311035156,
0.07330022752285004,
0.00764326099306345,
-0.02769279293715954,
-0.01162328477948904,
-0.04648037254810333,
-0.0007477516774088144,
-0.0031138225458562374,
-0.04139414057135582,
-0.017002904787659645,
0.028707152232527733,
-0.015681017190217972,
-0.022846749052405357,
-0.03867354989051819,
0.02366384118795395,
0.035006437450647354,
-0.037371210753917694,
-0.03396458551287651,
0.07023824751377106,
-0.0025788627099245787,
0.042946312576532364,
-0.015204278752207756,
0.029756028205156326,
0.010284913703799248,
-0.04513442888855934,
0.0039968425408005714,
-0.037732869386672974,
0.01055806316435337,
-0.03907441347837448,
0.07118425518274307,
-0.014197306707501411,
0.027008233591914177,
0.008201795630156994,
0.016614072024822235,
-0.03963543474674225,
0.02898009866476059,
-0.054959531873464584,
-0.032524995505809784,
0.005660166498273611,
0.019922908395528793,
-0.07450152188539505,
0.02367803454399109,
0.047950007021427155,
0.05583983287215233,
0.026757603511214256,
-0.03442951664328575,
0.03257565200328827,
-0.0263497494161129,
-0.0004986030980944633,
-0.047998201102018356,
0.03260533884167671,
0.026543427258729935,
0.03169754520058632,
0.07864989340305328,
0.013077745214104652,
0.016192631796002388,
0.019944870844483376,
0.032934270799160004,
0.017138220369815826,
0.031262435019016266,
0.00032503396505489945,
0.023199275135993958,
-0.015939028933644295,
0.04028461128473282,
0.036487191915512085,
-0.032258231192827225,
0.025491761043667793,
0.028874672949314117,
-0.021691802889108658,
0.03599308431148529,
-0.0034555946476757526,
-0.08896909654140472,
-0.030331484973430634,
-0.016068851575255394,
-0.02130671590566635,
0.012364762835204601,
-0.020540978759527206,
0.03175332024693489,
-0.026604343205690384,
-0.04127461463212967,
-0.01541929505765438,
-0.025230810046195984,
-0.04106663167476654,
-0.013638298027217388,
0.008147167041897774,
-0.039797063916921616,
-0.030050477012991905,
-0.050018373876810074,
-0.002810850040987134,
0.006293200887739658,
-0.001440956722944975,
0.004645762499421835,
-0.0129279475659132,
0.02781728468835354,
0.008630400523543358,
-0.00011461813846835867,
-0.001498567289672792,
0.01243110466748476,
0.03299825266003609,
-0.019897228106856346,
0.004671706352382898,
-0.04171457141637802,
-0.04323651269078255,
0.008007828146219254,
0.05885739624500275,
-0.02109728939831257,
-0.0637311264872551,
0.015709731727838516,
0.03931039944291115,
-0.041360657662153244,
-0.004195529501885176,
-0.023141896352171898,
0.011213636957108974,
0.016549086198210716,
0.11171257495880127,
-0.00857787486165762,
0.04466042295098305,
-0.003837980329990387,
-0.0015444207238033414,
0.019661160185933113,
-0.07162624597549438,
0.04010983183979988,
0.0012196395546197891,
-0.03692201152443886,
0.035703886300325394,
-0.02047102339565754,
-0.004789263475686312,
0.017001593485474586,
0.0014792296569794416,
-0.0037729546893388033,
-0.045995261520147324,
-0.04039289802312851,
0.028063958510756493,
-0.0025744340382516384,
0.012342260219156742,
-0.07186564803123474,
0.04952958971261978,
0.021591249853372574,
-0.042977362871170044,
0.049253176897764206,
-0.007070266641676426,
0.08517635613679886,
-0.00886954553425312,
-0.008796950802206993,
-0.024071339517831802,
-0.06215420365333557,
0.002417154610157013,
-0.02186351828277111,
0.03838329762220383,
-0.04797619953751564,
0.033740654587745667,
-0.07876293361186981,
-0.059815287590026855,
0.00793233048170805,
-0.053989771753549576,
0.011963286437094212,
-0.028561590239405632,
-0.013503918424248695,
-0.01823795959353447,
-0.010115251876413822,
-0.0008586448966525495,
0.04848634451627731,
-0.025567280128598213,
-0.04935833811759949,
-0.021671820431947708,
0.0002723384532146156,
-0.009938051924109459,
0.0321599543094635,
0.007051035761833191,
0.0030978466384112835,
0.03484344109892845,
0.10565479844808578,
-0.02860662341117859,
0.04224661737680435,
-0.027929460629820824,
0.0018584474455565214,
-0.023827679455280304,
-0.024783795699477196,
0.0006770792533643544,
-0.03821495920419693,
0.015428008511662483
] |
[
6.43058967590332,
5.499793529510498
] |
Pattern Formation and Solitons
|
Nonlinear Sciences
|
nlin-PS
|
physics-chem-ph
|
q-bio-MN
|
2007-03-31T11:05:53
|
We present Lie group integrators for nonlinear stochastic differential
equations with non-commutative vector fields whose solution evolves on a smooth
finite dimensional manifold. Given a Lie group action that generates transport
along the manifold, we pull back the stochastic flow on the manifold to the Lie
group via the action, and subsequently pull back the flow to the corresponding
Lie algebra via the exponential map. We construct an approximation to the
stochastic flow in the Lie algebra via closed operations and then push back to
the Lie group and then to the manifold, thus ensuring our approximation lies in
the manifold. We call such schemes stochastic Munthe-Kaas methods after their
deterministic counterparts. We also present stochastic Lie group integration
schemes based on Castell--Gaines methods. These involve using an underlying
ordinary differential integrator to approximate the flow generated by a
truncated stochastic exponential Lie series. They become stochastic Lie group
integrator schemes if we use Munthe-Kaas methods as the underlying ordinary
differential integrator. Further, we show that some Castell--Gaines methods are
uniformly more accurate than the corresponding stochastic Taylor schemes.
Lastly we demonstrate our methods by simulating the dynamics of a free rigid
body such as a satellite and an autonomous underwater vehicle both perturbed by
two independent multiplicative stochastic noise processes.
|
Stochastic Lie group integrators
|
math.NA
|
0704.0022
| 2,007
|
[
-0.001430674223229289,
0.011359358206391335,
-0.003607881488278508,
-0.02487955242395401,
-0.01105395145714283,
-0.0065024481154978275,
0.03353298082947731,
-0.005570901557803154,
-0.07079336047172546,
0.01895306445658207,
-0.035071808844804764,
0.028823716565966606,
0.03301321342587471,
0.03054744191467762,
-0.040747981518507004,
-0.024471234530210495,
0.023757586255669594,
0.04048075154423714,
-0.050657160580158234,
0.018245724961161613,
-0.00814506970345974,
0.012351498939096928,
0.026288561522960663,
-0.021045414730906487,
0.10672005265951157,
-0.03693697974085808,
0.022878095507621765,
-0.002120138378813863,
-0.04348098859190941,
0.020193500444293022,
0.10172481089830399,
-0.05815800651907921,
0.025383148342370987,
-0.040074434131383896,
-0.027940941974520683,
0.02601955272257328,
0.04496685415506363,
-0.0328344888985157,
0.02335670217871666,
-0.0018724326509982347,
0.030811090022325516,
-0.009789521805942059,
0.030603768303990364,
-0.00905081070959568,
-0.016310932114720345,
0.0350884385406971,
-0.0072192177176475525,
0.008972535841166973,
0.04341635853052139,
-0.019435858353972435,
-0.002369960304349661,
0.05857564136385918,
-0.0065671103075146675,
-0.05053155869245529,
-0.028497770428657532,
0.015942919999361038,
0.008808419108390808,
0.003914088010787964,
0.039579372853040695,
0.009865237399935722,
-0.022293968126177788,
0.022273601964116096,
-0.0528947077691555,
-0.014730693772435188,
0.018866756930947304,
-0.06093185022473335,
0.0013301778817549348,
-0.04138297587633133,
-0.003260989673435688,
0.025175414979457855,
0.04403891786932945,
0.026842547580599785,
0.012813952751457691,
0.02697623148560524,
-0.009127919562160969,
0.031075941398739815,
0.03421463444828987,
0.024337995797395706,
-0.00949073489755392,
0.006767862476408482,
0.025898635387420654,
-0.04594596475362778,
0.04635542631149292,
0.02169429138302803,
0.019940661266446114,
0.008916633203625679,
0.023452414199709892,
0.0678602010011673,
-0.05636543408036232,
-0.002552323043346405,
0.01890408620238304,
-0.004341162741184235,
0.04660531133413315,
0.05238024517893791,
-0.01747949607670307,
-0.010844238102436066,
-0.07455798238515854,
0.034684617072343826,
-0.03426036238670349,
-0.04021241143345833,
-0.02738633193075657,
0.07877122610807419,
-0.0021338281221687794,
-0.017029520124197006,
0.016135862097144127,
-0.0034135098103433847,
0.021781016141176224,
0.03723623976111412,
0.021867536008358,
-0.02222185954451561,
-0.06381043046712875,
0.006817695684731007,
0.04349574074149132,
-0.011451694183051586,
0.015716243535280228,
-0.03861953690648079,
0.012488598003983498,
-0.04721815139055252,
0.0072430954314768314,
0.01629251055419445,
0.011010228656232357,
-0.020438821986317635,
0.04751170054078102,
0.00980681274086237,
0.015200380235910416,
0.07635032385587692,
-0.034939855337142944,
-0.007469781208783388,
0.023943347856402397,
-0.05151652544736862,
-0.0007374786073341966,
0.004471225664019585,
-0.012112843804061413,
0.03256401792168617,
0.043673042207956314,
-0.011164535768330097,
-0.08257035911083221,
-0.06996041536331177,
0.04251272231340408,
0.04957196116447449,
-0.007067588623613119,
-0.012063085101544857,
-0.011002122424542904,
-0.025206737220287323,
-0.019155556336045265,
-0.0435260534286499,
0.01563851535320282,
-0.11325852572917938,
-0.04215417429804802,
-0.05779102072119713,
0.01801241748034954,
0.058470387011766434,
0.03196849673986435,
0.05099902302026749,
0.01526714488863945,
0.003752735909074545,
0.01742749661207199,
0.014041096903383732,
0.04308090731501579,
-0.008069286122918129,
0.01299781259149313,
0.06715968996286392,
0.008004182949662209,
0.019229892641305923,
-0.029475899413228035,
0.014586718752980232,
0.0016878133174031973,
-0.004506125580519438,
-0.017049644142389297,
0.044348109513521194,
-0.008344311267137527,
-0.04834572225809097,
-0.0220864936709404,
0.013046073727309704,
0.003364108968526125,
-0.006795668974518776,
-0.029090294614434242,
-0.06435438245534897,
-0.03141416981816292,
0.014767473563551903,
0.0509159117937088,
0.014693981036543846,
0.04989247024059296,
-0.005208468530327082,
0.02750563807785511,
0.058029159903526306,
-0.02792150154709816,
0.009243563748896122,
-0.0197497196495533,
-0.04501330107450485,
0.06844304502010345,
0.0006498342263512313,
-0.03211083263158798,
-0.050695907324552536,
-0.002570009557530284,
0.0228629931807518,
0.06522433459758759,
-0.06958936899900436,
0.003976990934461355,
-0.016041666269302368,
-0.02484806440770626,
0.03327091410756111,
-0.01496436633169651,
-0.01308334618806839,
0.007917755283415318,
0.044676925987005234,
-0.026851985603570938,
-0.02237716317176819,
-0.004916670266538858,
-0.029410766437649727,
0.09857536107301712,
0.0254860520362854,
0.006161617115139961,
0.004551152233034372,
-0.00964359287172556,
0.004614623729139566,
-0.00815060269087553,
-0.060154881328344345,
-0.021805742755532265,
-0.046089984476566315,
0.042831338942050934,
-0.022231027483940125,
0.02378358505666256,
0.007234437856823206,
-0.00807478278875351,
0.016880083829164505,
-0.021779431030154228,
-0.03111734613776207,
-0.031269609928131104,
-0.021021058782935143,
-0.021045753732323647,
-0.05420082435011864,
0.002493235282599926,
-0.003277314594015479,
-0.02219429239630699,
0.029106250032782555,
-0.016716357320547104,
0.0496210902929306,
0.03927631676197052,
0.08801045268774033,
0.059063930064439774,
0.03209390118718147,
0.026143405586481094,
-0.011342447251081467,
-0.09106845408678055,
-0.02234380692243576,
0.02754194103181362,
-0.004494090098887682,
-0.062255945056676865,
0.024428987875580788,
0.018241586163640022,
-0.030787432566285133,
0.017598681151866913,
-0.014569997787475586,
0.03500331565737724,
-0.008433518931269646,
-0.05940020829439163,
0.059858839958906174,
-0.0011286026565358043,
0.0024654665030539036,
-0.0067618791945278645,
0.012189858593046665,
0.0191297996789217,
-0.0066611613146960735,
-0.04927464947104454,
0.008991291746497154,
0.03998834639787674,
-0.0441526398062706,
0.008074135519564152,
-0.02503623254597187,
0.00095195765607059,
0.033734388649463654,
0.09886473417282104,
0.0729607492685318,
0.013457848690450191,
0.028967082500457764,
-0.009819112718105316,
-0.020344208925962448,
-0.06959284096956253,
-0.004816691391170025,
-0.05228867009282112,
-0.003867875784635544,
-0.018827995285391808,
0.0013583794934675097,
-0.014123248867690563,
-0.011587968096137047,
0.08608365803956985,
-0.026033438742160797,
-0.0024934131652116776,
0.024904770776629448,
-0.004774725995957851,
-0.024025090038776398,
0.005601644050329924,
0.030008923262357712,
0.026890117675065994,
0.07116734981536865,
0.0491660051047802,
-0.03797917813062668,
0.005412223748862743,
0.040364328771829605,
-0.016797928139567375,
-0.014900398440659046,
0.045632608234882355,
-0.006467907223850489,
0.03727831318974495,
-0.011278137564659119,
-0.020874710753560066,
-0.01986268162727356,
0.04768110811710358,
0.012288102880120277,
-0.014953987672924995,
-0.0054580350406467915,
-0.0003140969492960721,
-0.03762298822402954,
-0.025031281635165215,
0.00996506679803133,
0.02897155098617077,
-0.02894454076886177,
0.028814803808927536,
-0.03404603525996208,
0.010394955985248089,
-0.09240557998418808,
0.022883474826812744,
-0.018736111000180244,
0.010757459327578545,
0.03739860653877258,
-0.009785087779164314,
0.0072547015734016895,
0.013765738345682621,
-0.0730295181274414,
0.013776926323771477,
0.06332126259803772,
-0.002479855902493,
0.008699730038642883,
0.004366560839116573,
-0.04905441030859947,
-0.005887179635465145,
0.046244047582149506,
-0.04190150648355484,
-0.012431072071194649,
-0.012937145307660103,
-0.07173710316419601,
-0.007937374524772167,
-0.019777944311499596,
-0.09534744918346405,
-0.012768437154591084,
-0.006771234795451164,
-0.000914280884899199,
0.007823335006833076,
-0.016075419262051582,
-0.013443403877317905,
-0.014362451620399952,
0.042574286460876465,
-0.0006058180006220937,
-0.029061447829008102,
0.027327243238687515,
0.025213459506630898,
-0.0416947677731514,
0.03332749754190445,
0.06646156311035156,
0.03287419304251671,
-0.02766958437860012,
-0.01195517648011446,
0.06485287845134735,
0.031147750094532967,
0.015532486140727997,
0.044434159994125366,
0.02131742052733898,
-0.009791944175958633,
-0.017547091469168663,
-0.014919173903763294,
-0.020957009866833687,
0.007938502356410027,
0.06098778545856476,
-0.02797383815050125,
0.009665213525295258,
-0.06855633854866028,
0.01278891321271658,
-0.008938662707805634,
-0.044763676822185516,
0.08285018056631088,
-0.019320446997880936,
0.05208205059170723,
-0.042674094438552856,
0.007635433226823807,
0.043123528361320496,
-0.030600402504205704,
0.04765212908387184,
-0.025296689942479134,
0.015138414688408375,
0.0451204851269722,
-0.013400154188275337,
-0.028613554313778877,
0.0382421500980854,
-0.009577078744769096,
-0.05062403529882431,
0.04366808384656906,
0.0514337383210659,
0.031949643045663834,
-0.04781932383775711,
-0.013421469368040562,
-0.04156983643770218,
-0.013695911504328251,
-0.03861301392316818,
0.008359212428331375,
0.02534732222557068,
-0.010203730314970016,
-0.06890030205249786,
0.05340069904923439,
-0.0001483991218265146,
0.00024868821492418647,
0.005736674182116985,
-0.008418607525527477,
-0.09329793602228165,
0.03053376078605652,
0.013577631674706936,
0.024092819541692734,
-0.012465525418519974,
-0.005946940276771784,
0.04722180217504501,
-0.009136039763689041,
0.009977569803595543,
-0.006210270803421736,
0.02234506607055664,
-0.07147245109081268,
-0.030489539727568626,
0.036912478506565094,
0.01781274750828743,
0.0141203124076128,
-0.075860396027565,
0.011563325300812721,
0.03213677555322647,
-0.018339216709136963,
0.03509107977151871,
-0.059623099863529205,
0.03149488940834999,
0.06607195734977722,
-0.00038332692929543555,
-0.017394056543707848,
0.02613506093621254,
0.03165211156010628,
-0.04650748521089554,
0.012284033931791782,
-0.012643014080822468,
0.056823842227458954,
0.14213725924491882,
0.09873370081186295,
-0.03995685651898384,
-0.02006639912724495,
0.0405895970761776,
-0.002036638092249632,
-0.002120010554790497,
-0.01171666570007801,
0.062235597521066666,
0.0673539862036705,
0.005618450231850147,
-0.03769930079579353,
-0.0016422152984887362,
0.012816520407795906,
0.03181907534599304,
0.027015333995223045,
0.021508604288101196,
-0.0016648301389068365,
0.016964294016361237,
-0.03960246220231056,
-0.018564842641353607,
-0.021469421684741974,
-0.00481216236948967,
0.08494287729263306,
0.043312981724739075,
-0.002147465944290161,
0.014163645915687084,
0.009131617844104767,
0.011225385591387749,
-0.0546686053276062,
-0.008377783000469208,
0.04553123563528061,
-0.03818027675151825,
-0.02179904654622078,
0.007893458940088749,
0.04080742970108986,
-0.040446847677230835,
-0.015699686482548714,
0.01001150906085968,
-0.014417367987334728,
0.0625654086470604,
-0.0034392268862575293,
-0.005911995656788349,
0.027366893365979195,
-0.046386417001485825,
-0.03589959442615509,
0.030872777104377747,
0.0080059003084898,
0.029649147763848305,
-0.03410007432103157,
-0.04366134852170944,
0.006569921970367432,
-0.03592650964856148,
0.008044959045946598,
-0.06805191934108734,
-0.03367271646857262,
0.011986570432782173,
0.0154441948980093,
-0.03327261283993721,
0.0398518368601799,
0.03930480033159256,
-0.018369145691394806,
-0.03979571908712387,
-0.0020455834455788136,
0.056658677756786346,
0.017236195504665375,
0.03064125031232834,
0.041842203587293625,
0.044666748493909836,
-0.029310405254364014,
-0.022106822580099106,
0.023822447285056114,
-0.01887642964720726,
-0.022468330338597298,
-0.0024709433782845736,
0.02964918687939644,
-0.010520677082240582,
-0.0013220175169408321,
0.020977765321731567,
-0.034670863300561905,
0.005550542380660772,
-0.04472345858812332,
-0.051812585443258286,
-0.010198323987424374,
0.0057031880132853985,
-0.033840734511613846,
-0.026751453056931496,
-0.027715103700757027,
-0.0785430446267128,
0.01052494440227747,
-0.02931145206093788,
-0.00642843171954155,
0.011748727411031723,
0.0022136445622891188,
0.005050672683864832,
-0.027671625837683678,
-0.004086943343281746,
0.04529373347759247,
0.018385935574769974,
0.00939401425421238,
-0.01919764280319214,
-0.03745439276099205,
0.06427032500505447,
-0.04640651121735573,
-0.06869156658649445,
0.002135578077286482,
-0.050309788435697556,
0.030499374493956566,
-0.07016754895448685,
0.009755244478583336,
-0.02400454878807068,
-0.013379193842411041,
-0.007715826854109764,
-0.051388196647167206,
0.048657212406396866,
-0.031649503856897354,
-0.04298405721783638,
0.060024578124284744,
-0.04646909236907959,
0.024657713249325752,
-0.05377661809325218,
-0.016422662883996964,
-0.02263413555920124,
0.012434416450560093,
0.018797747790813446,
0.0011727048549801111,
-0.011396270245313644,
-0.00997740589082241,
0.027316056191921234,
-0.013686858117580414,
-0.054483190178871155,
0.012697656638920307,
-0.046136245131492615,
-0.06918565183877945,
0.010453441180288792,
-0.07072113454341888,
-0.013302533887326717,
0.03500158339738846,
-0.009606212377548218,
-0.03844796121120453,
-0.01810322143137455,
-0.006134910508990288,
-0.04894082248210907,
0.07614147663116455,
0.059985529631376266,
0.0071364110335707664,
0.007103253155946732,
-0.04884997010231018,
-0.014953957870602608,
-0.033609747886657715,
-0.06692113727331161,
0.010520179755985737,
0.023293111473321915,
0.0032682146411389112,
-0.07367390394210815,
-0.03507361561059952,
-0.004235353786498308,
0.06741195917129517,
-0.019507020711898804,
0.00706825777888298,
0.070242740213871,
-0.0022522960789501667,
0.05883895605802536,
0.029802758246660233,
-0.015733780339360237,
0.008749615401029587,
-0.056887444108724594,
-0.03691071271896362,
-0.0406096950173378,
0.005275581032037735,
-0.023433171212673187,
0.028570804744958878,
-0.03201973810791969,
0.02288936637341976,
-0.033630963414907455,
-0.03483685106039047,
-0.04865557327866554,
0.04398050904273987,
-0.029668571427464485,
-0.02988126315176487,
0.03269205614924431,
-0.030905431136488914,
-0.0967220738530159,
0.006514161825180054,
0.0428353026509285,
0.02912166342139244,
-0.043016742914915085,
0.03779689595103264,
-0.0378112867474556,
0.012579487636685371,
0.01867552287876606,
0.00695514352992177,
0.08647210150957108,
-0.011218966916203499,
0.08414099365472794,
0.018100963905453682,
0.0461103655397892,
-0.020206522196531296,
0.03602457419037819,
0.043346233665943146,
-0.014318413101136684,
0.0017727728700265288,
0.05667616054415703,
-0.002617783844470978,
-0.016255440190434456,
0.09529712796211243,
0.04770319536328316,
-0.02626609429717064,
-0.0022224425338208675,
0.008984290063381195,
0.003875019261613488,
0.04713602364063263,
0.002657346660271287,
-0.008184066973626614,
0.024842793121933937,
-0.018610788509249687,
-0.017946815118193626,
0.014802277088165283,
-0.012753923423588276,
0.03566686809062958,
-0.06290395557880402,
0.004763149190694094,
-0.06140602380037308,
-0.01376606710255146,
0.08322639763355255,
-0.024900013580918312,
0.0021051838994026184,
-0.001961148576810956,
0.015918023884296417,
-0.05540700629353523,
-0.010012227110564709,
0.018719743937253952,
0.06973896920681,
-0.014508313499391079,
0.01142587698996067,
0.04335988685488701,
0.004057713318616152,
0.034172914922237396,
-0.05569061264395714,
-0.02114327810704708,
-0.032801833003759384,
-0.011338409036397934,
-0.01865629479289055,
-0.04173123836517334,
-0.046822428703308105,
0.024688243865966797,
0.056453362107276917,
-0.010381463915109634,
-0.0451253205537796,
-0.0007800757884979248,
0.0316796712577343,
-0.09965105354785919,
0.0005915297660976648,
-0.0014039665693417192,
0.01891203038394451,
-0.011180046945810318,
0.004447038285434246,
-0.03928634896874428,
0.03447290509939194,
-0.03238334134221077,
-0.06682714074850082,
0.035795293748378754,
-0.01843971759080887,
-0.006256662774831057,
-0.015225815586745739,
-0.027276519685983658,
0.00452452152967453,
-0.01926334574818611,
0.012206503190100193,
0.02492583356797695,
-0.023229382932186127,
0.003679575165733695,
-0.04043455794453621,
0.01583053357899189,
-0.00024056799884419888,
0.05878046900033951,
-0.05445248633623123,
-0.051749009639024734,
0.0492144450545311,
0.040019579231739044,
-0.09986267238855362,
-0.006773123051971197,
0.03465639427304268,
0.019338978454470634,
-0.004542942624539137,
-0.019565008580684662,
-0.004628515336662531,
-0.028859751299023628,
0.030379297211766243,
-0.02638751082122326,
0.003602995304390788,
-0.0009957054862752557,
0.000004316336799092824,
0.014526799321174622,
0.007096725516021252,
-0.004809078294783831,
-0.05041990801692009,
0.0015958407893776894,
0.023590324446558952,
0.019396401941776276,
-0.008138141594827175,
-0.051634736359119415,
-0.01482838299125433,
0.0224846750497818,
-0.02138591557741165,
0.044173289090394974,
0.012872133404016495,
0.0006020566215738654,
0.024637870490550995,
0.029027234762907028,
0.007955892011523247,
-0.039326246827840805,
0.0012999846367165446,
0.0649639144539833,
-0.02262810617685318,
0.041726768016815186,
-0.021137317642569542,
-0.033577434718608856,
0.07727286219596863,
-0.0495821051299572,
-0.013735376298427582,
-0.035752132534980774,
0.00222718040458858
] |
[
4.262228488922119,
4.764557838439941
] |
Numerical Analysis
|
Mathematics
|
math-NA
|
na
|
na
|
2007-03-31T11:42:13
|
The very nature of the solar chromosphere, its structuring and dynamics,
remains far from being properly understood, in spite of intensive research.
Here we point out the potential of chromospheric observations at millimeter
wavelengths to resolve this long-standing problem. Computations carried out
with a sophisticated dynamic model of the solar chromosphere due to Carlsson
and Stein demonstrate that millimeter emission is extremely sensitive to
dynamic processes in the chromosphere and the appropriate wavelengths to look
for dynamic signatures are in the range 0.8-5.0 mm. The model also suggests
that high resolution observations at mm wavelengths, as will be provided by
ALMA, will have the unique property of reacting to both the hot and the cool
gas, and thus will have the potential of distinguishing between rival models of
the solar atmosphere. Thus, initial results obtained from the observations of
the quiet Sun at 3.5 mm with the BIMA array (resolution of 12 arcsec) reveal
significant oscillations with amplitudes of 50-150 K and frequencies of 1.5-8
mHz with a tendency toward short-period oscillations in internetwork and longer
periods in network regions. However higher spatial resolution, such as that
provided by ALMA, is required for a clean separation between the features
within the solar atmosphere and for an adequate comparison with the output of
the comprehensive dynamic simulations.
|
ALMA as the ideal probe of the solar chromosphere
|
astro-ph
|
0704.0023
| 2,007
|
[
0.015156669542193413,
0.026736076921224594,
-0.006238467060029507,
-0.009443541057407856,
0.005167572759091854,
0.0035249670036137104,
0.050035469233989716,
-0.06247955560684204,
-0.019176455214619637,
0.0021993261761963367,
0.0076552401296794415,
0.08193137496709824,
0.04992525279521942,
-0.003703795373439789,
0.03887093439698219,
-0.05393533036112785,
0.014500083401799202,
-0.006730010733008385,
0.004107717424631119,
0.03469092771410942,
0.012452656403183937,
0.01687915250658989,
0.00919931661337614,
-0.07116986811161041,
0.0969548225402832,
0.07187726348638535,
-0.002176429610699415,
0.006416228134185076,
-0.017413916066288948,
0.030970746651291847,
0.09080562740564346,
-0.05770983546972275,
0.007612491492182016,
0.0036671236157417297,
0.003851168556138873,
-0.016185013577342033,
0.00792346615344286,
0.002924524713307619,
-0.04955798014998436,
0.047598306089639664,
0.04505697637796402,
-0.031930383294820786,
0.033819530159235,
0.010254944674670696,
0.058074455708265305,
0.002223727758973837,
-0.004477977752685547,
0.011691611260175705,
0.07807856798171997,
-0.018008451908826828,
0.02452278323471546,
0.005897438619285822,
0.004117118194699287,
-0.027326025068759918,
0.0017927814042195678,
0.040389224886894226,
0.05001650005578995,
-0.02256307192146778,
0.02785497158765793,
-0.0024900981225073338,
0.04721272364258766,
0.027287401258945465,
-0.028988124802708626,
-0.0062758056446909904,
-0.027045955881476402,
-0.05711403116583824,
-0.06324999779462814,
-0.03523418307304382,
-0.03702881187200546,
-0.07372899353504181,
0.05476560443639755,
-0.016581181436777115,
-0.012937949039041996,
0.04113522171974182,
-0.013485546223819256,
0.02854442596435547,
-0.006065142806619406,
-0.023967016488313675,
0.01714015193283558,
0.002140907570719719,
0.019235435873270035,
-0.01918635703623295,
0.0068048145622015,
-0.0018236124888062477,
0.017271263524889946,
-0.040840402245521545,
-0.020478811115026474,
0.022968867793679237,
-0.04477284103631973,
-0.023286446928977966,
0.056675370782613754,
-0.03914330154657364,
0.08545380085706711,
-0.0017319595208391547,
0.011224950663745403,
0.037021201103925705,
0.004252762999385595,
0.03904043510556221,
-0.03887375444173813,
-0.026907149702310562,
-0.019992422312498093,
0.04481768235564232,
0.013668223284184933,
0.05506472662091255,
0.056032296270132065,
-0.0007016357849352062,
-0.022827869281172752,
0.0016638939268887043,
0.01060602255165577,
-0.031422898173332214,
-0.05238163098692894,
-0.023036234080791473,
-0.008977790363132954,
0.001311835483647883,
-0.01880578137934208,
-0.04514797031879425,
0.023382294923067093,
-0.06373488157987595,
0.0076170144602656364,
0.08587571233510971,
-0.01797841303050518,
-0.006850181147456169,
0.0041816746816039085,
0.0023001169320195913,
0.026229366660118103,
0.011706850491464138,
-0.012396472506225109,
0.023554857820272446,
-0.006888886447995901,
-0.021807601675391197,
-0.034573666751384735,
0.029245903715491295,
-0.08542660623788834,
0.00029454976902343333,
0.060424309223890305,
-0.035693876445293427,
-0.008977818302810192,
-0.07624563574790955,
0.01328656543046236,
0.00234150979667902,
0.04246460273861885,
0.010964026674628258,
0.04061868041753769,
-0.030824029818177223,
-0.017270507290959358,
-0.03181140497326851,
0.022875577211380005,
-0.019228938966989517,
0.03419238701462746,
-0.038600239902734756,
0.028331656008958817,
0.08039630949497223,
0.02500384859740734,
0.0009998370660468936,
-0.06450370699167252,
-0.05630718171596527,
-0.044036392122507095,
-0.012845264747738838,
0.009931296110153198,
-0.0006795701920054853,
0.018799860030412674,
-0.03943007066845894,
-0.028377914801239967,
0.06818626075983047,
-0.041715674102306366,
-0.0031252519693225622,
0.018000002950429916,
0.007699447218328714,
0.017339203506708145,
0.04228080436587334,
-0.052821893244981766,
-0.0006269690929912031,
-0.05105588212609291,
-0.029375145211815834,
0.039700061082839966,
-0.0057548638433218,
0.04695245623588562,
-0.056149546056985855,
0.013163041323423386,
-0.004506499506533146,
0.018335269764065742,
-0.03796105831861496,
-0.0065246387384831905,
-0.010667418129742146,
0.02570214308798313,
0.00034234626218676567,
0.007622617296874523,
-0.06557230651378632,
-0.027976587414741516,
-0.026181107386946678,
0.023582149296998978,
0.032314885407686234,
-0.04861268401145935,
-0.06558816879987717,
0.0208955779671669,
-0.03747449442744255,
0.06324691325426102,
-0.02261100523173809,
-0.018668482080101967,
-0.01126573421061039,
-0.03371863439679146,
-0.005416400730609894,
-0.06773053109645844,
0.03227515518665314,
-0.008331887423992157,
0.05095670744776726,
0.014145826920866966,
0.007196299731731415,
0.024419639259576797,
0.002049778588116169,
0.0777452290058136,
-0.006289372686296701,
-0.0034786805044859648,
0.018498916178941727,
-0.03275680914521217,
-0.0036109406501054764,
-0.03810061886906624,
-0.02007981203496456,
-0.007741479203104973,
0.023316174745559692,
0.045453619211912155,
0.0021035573445260525,
0.026849649846553802,
-0.03732190653681755,
0.0016112804878503084,
0.005470121745020151,
-0.057325396686792374,
0.017376072704792023,
-0.02177656628191471,
-0.003620661562308669,
-0.012874607928097248,
-0.021828176453709602,
0.057843126356601715,
-0.009337155148386955,
-0.06804417073726654,
0.002947078552097082,
-0.010487139225006104,
0.02288270927965641,
0.028082754462957382,
0.04697562754154205,
0.0027230428531765938,
0.019984755665063858,
0.014855502173304558,
-0.017152393236756325,
-0.07187648117542267,
-0.009417965076863766,
-0.03693374618887901,
0.036406416445970535,
-0.022472301498055458,
-0.00990444514900446,
0.06731168180704117,
0.00352464965544641,
0.01250549592077732,
0.04952963814139366,
-0.017908375710248947,
-0.05687803030014038,
-0.03871779143810272,
0.007083967328071594,
-0.05172848328948021,
-0.029426269233226776,
-0.0037524262443184853,
-0.08300205320119858,
-0.013311967253684998,
-0.06208295375108719,
0.02835763990879059,
-0.04335525631904602,
-0.028658505529165268,
-0.015923546627163887,
-0.031092043966054916,
-0.04704385623335838,
0.034104760736227036,
0.001942915259860456,
0.0624680258333683,
0.011691528372466564,
-0.011189230717718601,
0.06752108037471771,
0.02002747915685177,
-0.015489238314330578,
-0.005455100908875465,
-0.04967179521918297,
-0.06631915271282196,
-0.002771953819319606,
-0.028034524992108345,
-0.07717227190732956,
-0.013469219207763672,
0.03962668776512146,
0.02201426960527897,
0.043100904673337936,
0.04537757486104965,
-0.009745845571160316,
0.0033011073246598244,
-0.04259666055440903,
0.04334999993443489,
0.103799007833004,
-0.02373952604830265,
0.027233032509684563,
0.10436634719371796,
0.004044297616928816,
-0.047006912529468536,
0.004159961827099323,
0.024236200377345085,
0.015361253172159195,
-0.03449481353163719,
-0.00010339009895687923,
-0.0012292165774852037,
-0.023499745875597,
-0.038547612726688385,
-0.021939966827630997,
0.03205889090895653,
-0.006107259541749954,
-0.0026017732452601194,
-0.01629067026078701,
-0.03431490436196327,
-0.029258517548441887,
-0.03086256794631481,
0.05067751184105873,
-0.037074971944093704,
0.014907676726579666,
0.08177513629198074,
0.05664030462503433,
0.0052209473215043545,
-0.030243806540966034,
0.01115466933697462,
-0.05797527730464935,
0.0070707350969314575,
0.010006395168602467,
0.0657920315861702,
-0.018062710762023926,
-0.07422897964715958,
0.029204944148659706,
-0.0305814016610384,
0.05588784068822861,
-0.06475459784269333,
0.0004529461730271578,
-0.0335422046482563,
0.04768174886703491,
0.002525061834603548,
0.03356778249144554,
0.009638876654207706,
0.0023962133564054966,
-0.006863406393676996,
-0.0006219412898644805,
-0.036455102264881134,
-0.10907553136348724,
-0.017339296638965607,
0.014839934185147285,
-0.06368252635002136,
-0.028036659583449364,
0.024956287816166878,
-0.0018695491598919034,
-0.029193000867962837,
-0.019036483019590378,
0.018190989270806313,
-0.03842909634113312,
-0.038893695920705795,
0.047792427241802216,
0.035096921026706696,
-0.019207576289772987,
0.06880322843790054,
0.020010368898510933,
0.018818434327840805,
-0.011966132558882236,
0.0342322513461113,
-0.002932770410552621,
0.00808748323470354,
0.03728513792157173,
-0.01596660166978836,
0.05091550201177597,
-0.0026114415377378464,
-0.04399900138378143,
-0.06093354523181915,
-0.009223024360835552,
0.004660550504922867,
0.07769607752561569,
0.020982449874281883,
-0.024841293692588806,
-0.03980936110019684,
0.00488907378166914,
0.017527209594845772,
0.03007822483778,
0.021606914699077606,
-0.012406077235937119,
0.02559957467019558,
0.008615948259830475,
0.05557116121053696,
0.023292988538742065,
-0.0258058849722147,
0.006045996677130461,
-0.047225452959537506,
-0.09004350751638412,
-0.003164160531014204,
-0.0545184351503849,
-0.05360059440135956,
0.04125117510557175,
0.019010858610272408,
-0.06384097039699554,
0.014506801031529903,
-0.01771552674472332,
0.058092180639505386,
0.0004908892442472279,
0.013645035214722157,
-0.03921252861618996,
0.016963638365268707,
-0.022463450208306313,
-0.0364188477396965,
0.004731799475848675,
-0.018399760127067566,
-0.056490205228328705,
0.05394984036684036,
0.028669903054833412,
-0.01826249063014984,
0.022910211235284805,
0.0007289890199899673,
-0.07418012619018555,
0.04428007826209068,
0.024385135620832443,
-0.01186125073581934,
-0.00018752648611553013,
0.0225233007222414,
-0.022738782688975334,
-0.015484882518649101,
0.07965466380119324,
-0.018608544021844864,
0.026610109955072403,
0.007835576310753822,
0.05209760740399361,
0.04112515598535538,
-0.027971426025032997,
-0.013426476158201694,
-0.0231943279504776,
0.045568954199552536,
-0.003473171265795827,
-0.006330318748950958,
0.04468340426683426,
-0.03205138444900513,
0.009157775901257992,
-0.019306642934679985,
-0.05702569708228111,
0.04297708719968796,
0.04842134192585945,
0.04036347195506096,
-0.04624795913696289,
0.00682023586705327,
-0.01667010597884655,
0.020850319415330887,
0.08768847584724426,
0.06994439661502838,
-0.04697596654295921,
-0.04569590464234352,
0.004422207362949848,
0.03580484539270401,
-0.014115779660642147,
-0.026670681312680244,
0.0461454913020134,
0.04303959012031555,
-0.022953519597649574,
-0.02992381900548935,
0.020697027444839478,
0.0717858225107193,
0.04018722102046013,
0.001531447866000235,
0.026987742632627487,
-0.03283084183931351,
0.02376360073685646,
0.05429995805025101,
-0.003602556651458144,
-0.03523900732398033,
0.004821405280381441,
-0.011044282466173172,
0.02107735350728035,
-0.013074137270450592,
0.004134390503168106,
0.019261537119746208,
-0.00017255006241612136,
-0.10625756531953812,
-0.0013675419613718987,
-0.009868021123111248,
-0.06357518583536148,
0.040878403931856155,
0.04373154416680336,
0.011054637841880322,
-0.01620575226843357,
-0.014425771310925484,
0.002923273481428623,
-0.005477436352521181,
0.0595628060400486,
-0.002759422641247511,
0.011025911197066307,
-0.003152326447889209,
0.02574853040277958,
0.002199773909524083,
0.009501801803708076,
0.0011251441901549697,
0.040483370423316956,
-0.04177612438797951,
-0.03742757812142372,
0.018811719492077827,
0.00442407326772809,
0.03813181445002556,
-0.05404212325811386,
-0.011846414767205715,
0.03289487957954407,
-0.035689521580934525,
0.00997945386916399,
0.04030930995941162,
0.009026692248880863,
0.0011080128606408834,
-0.025957182049751282,
0.05009493976831436,
0.020233744755387306,
-0.0230102501809597,
0.01516799721866846,
-0.01116221398115158,
0.07301050424575806,
0.061372507363557816,
-0.08120883256196976,
0.05148954689502716,
0.021663304418325424,
-0.021275322884321213,
-0.03862689808011055,
-0.02262786217033863,
-0.04489574953913689,
0.04886221885681152,
0.01666695810854435,
-0.02284650318324566,
0.023442342877388,
-0.03235669434070587,
-0.014692246913909912,
0.06382197886705399,
-0.06400064378976822,
0.002836812986060977,
0.057402148842811584,
-0.021035701036453247,
-0.02741362154483795,
0.05420204997062683,
-0.03513306751847267,
0.011741225607693195,
0.06921610981225967,
0.022338340058922768,
0.018818557262420654,
-0.03632776066660881,
-0.001298700226470828,
0.04457297548651695,
0.01194727048277855,
0.05960075929760933,
-0.027336208149790764,
-0.00858429167419672,
0.08510910719633102,
0.03076360747218132,
-0.029108794406056404,
0.02330746129155159,
-0.02611587382853031,
0.01600867323577404,
-0.07114269584417343,
-0.009805229492485523,
-0.04047612473368645,
-0.0005562022561207414,
-0.0050776656717062,
-0.03734489530324936,
0.003318269969895482,
0.014625982381403446,
0.03492562100291252,
0.09033938497304916,
-0.017446085810661316,
0.014718159101903439,
-0.083709217607975,
-0.028974460437893867,
-0.028634458780288696,
0.0400455966591835,
-0.0014787870459258556,
-0.011689754202961922,
-0.004777892958372831,
-0.010305814445018768,
0.057258639484643936,
0.04335639625787735,
-0.030585672706365585,
0.0543082095682621,
0.0587327778339386,
-0.07413271069526672,
-0.05119215324521065,
0.004199572838842869,
-0.035856712609529495,
-0.017675936222076416,
0.03977735713124275,
0.019847774878144264,
-0.04154449701309204,
-0.012125060893595219,
-0.015507139265537262,
0.0520554780960083,
-0.024598179385066032,
-0.01401459239423275,
-0.027026226744055748,
0.020946510136127472,
-0.018082180991768837,
-0.049394868314266205,
-0.05045020207762718,
0.010050448589026928,
-0.016154438257217407,
-0.03542129322886467,
-0.06534731388092041,
0.05972755700349808,
0.013812439516186714,
0.029677079990506172,
-0.029242977499961853,
0.020214837044477463,
0.036406029015779495,
0.014109249226748943,
0.029689911752939224,
0.05121653154492378,
-0.008838647045195103,
-0.03915992006659508,
0.038617126643657684,
0.0002322690561413765,
-0.06828618794679642,
-0.020274238660931587,
-0.023265162482857704,
0.05712417885661125,
-0.009855730459094048,
0.03533641993999481,
-0.03403962403535843,
-0.014262225478887558,
-0.015028632245957851,
0.02464386448264122,
-0.057765573263168335,
-0.0053419931791722775,
0.010961528867483139,
0.02551427111029625,
0.00012575603614095598,
-0.0117815425619483,
0.01922786422073841,
0.022960176691412926,
0.02155204303562641,
-0.03680522367358208,
-0.06029456853866577,
-0.017062261700630188,
-0.000011455933417892084,
0.009051987901329994,
-0.03723572567105293,
-0.01847863383591175,
0.010918790474534035,
0.028914451599121094,
-0.03706550970673561,
-0.005606546066701412,
0.009471846744418144,
0.08510532230138779,
0.02371354028582573,
-0.0033284290693700314,
0.017737576737999916,
0.020407836884260178,
0.02776861935853958,
0.033104028552770615,
-0.0210641510784626,
-0.014122657477855682,
0.024401124566793442,
0.047625891864299774,
0.03462201729416847,
-0.009189602918922901,
0.01885214075446129,
-0.03891383111476898,
-0.04000368341803551,
-0.014950942248106003,
-0.024241512641310692,
0.0021204559598118067,
-0.030689213424921036,
0.04144279286265373,
-0.037098392844200134,
0.008610259741544724,
-0.08168158680200577,
-0.03315019607543945,
0.02920592576265335,
-0.03887363523244858,
-0.006841380149126053,
0.010701633058488369,
-0.025271106511354446,
-0.05789799988269806,
0.011201945133507252,
-0.0024813786149024963,
-0.0036292197182774544,
-0.010402648709714413,
-0.028911646455526352,
0.034810785204172134,
-0.008926192298531532,
0.022023554891347885,
-0.010608085431158543,
0.022418254986405373,
-0.02590242400765419,
-0.03388623893260956,
-0.004387602210044861,
-0.0003540381439961493,
-0.049754299223423004,
-0.003972881007939577,
0.0522262267768383,
-0.00827424693852663,
-0.09491626918315887,
0.017904488369822502,
0.006307579576969147,
-0.07612423598766327,
-0.03367997705936432,
-0.006632554344832897,
0.03917645290493965,
-0.0015123210614547133,
0.027091365307569504,
-0.04071943461894989,
0.015093945898115635,
0.0005011457833461463,
0.013233193196356297,
0.05858427658677101,
0.04083288460969925,
0.024388154968619347,
0.00844541471451521,
-0.036551956087350845,
0.053780343383550644,
0.011752273887395859,
0.04755096510052681,
0.04171781241893768,
-0.02058510109782219,
-0.023854581639170647,
-0.06418628990650177,
-0.02234090119600296,
-0.01649485155940056,
-0.0078074513003230095,
-0.006751660723239183,
0.007837370969355106,
0.013106949627399445,
0.016384171321988106,
-0.055436041206121445,
0.02113107591867447,
-0.00497647887095809,
0.0748324990272522,
-0.040266383439302444,
0.025729594752192497,
-0.010057185776531696,
-0.017796531319618225,
-0.037061505019664764,
-0.05382337421178818,
0.0013273695949465036,
0.005017460789531469,
0.018359165638685226,
-0.045326486229896545,
-0.02686190791428089,
-0.016476869583129883,
-0.05364612862467766,
0.005999158136546612,
0.0008296733722090721,
0.035300113260746,
-0.046212729066610336,
-0.060748547315597534,
0.038607340306043625,
0.054065342992544174,
0.011400826275348663,
-0.02732762135565281,
0.0019135260954499245,
-0.03887461870908737,
0.010031200014054775,
0.01848873496055603,
0.06642460078001022,
0.022893434390425682,
-0.00027869053883478045,
0.043186359107494354,
-0.06620272248983383,
0.02804928831756115,
0.015232968144118786,
0.01882435940206051,
0.05684244632720947,
0.02094297856092453,
0.0023594526574015617,
-0.022860610857605934,
-0.012976775877177715
] |
[
12.233065605163574,
6.154007911682129
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
na
|
na
|
2007-03-31T11:44:22
|
The formation of quasi-2D spin-wave waveforms in longitudinally magnetized
stripes of ferrimagnetic film was observed by using time- and space-resolved
Brillouin light scattering technique. In the linear regime it was found that
the confinement decreases the amplitude of dynamic magnetization near the
lateral stripe edges. Thus, the so-called effective dipolar pinning of dynamic
magnetization takes place at the edges.
In the nonlinear regime a new stable spin wave packet propagating along a
waveguide structure, for which both transversal instability and interaction
with the side walls of the waveguide are important was observed. The
experiments and a numerical simulation of the pulse evolution show that the
shape of the formed waveforms and their behavior are strongly influenced by the
confinement.
|
Formation of quasi-solitons in transverse confined ferromagnetic film
media
|
nlin.PS
|
0704.0024
| 2,007
|
[
-0.03423914313316345,
0.04146849364042282,
-0.01369150634855032,
0.008144630119204521,
0.057987574487924576,
0.018218476325273514,
0.027083130553364754,
0.024066096171736717,
-0.04429302364587784,
-0.009462466463446617,
-0.08369927108287811,
0.04731743782758713,
0.012597490102052689,
-0.007536349352449179,
0.0071653937920928,
-0.049693427979946136,
0.0465058833360672,
-0.008459295146167278,
-0.017268363386392593,
-0.05123091861605644,
-0.035692453384399414,
-0.005827124696224928,
0.006951161194592714,
-0.0347595177590847,
0.11332565546035767,
0.05838354304432869,
0.013120442628860474,
-0.009515161626040936,
-0.010143973864614964,
0.032438602298498154,
0.041321996599435806,
-0.07387000322341919,
0.004145581275224686,
-0.009915121830999851,
0.006066682282835245,
-0.07034372538328171,
-0.017401792109012604,
0.002205881755799055,
-0.032433439046144485,
0.04207911342382431,
0.0316244475543499,
-0.04861542582511902,
0.003306798869743943,
-0.04528278484940529,
0.04503403604030609,
-0.005364545620977879,
0.009051885455846786,
-0.005974803119897842,
0.0195971317589283,
0.001595049281604588,
-0.04303215444087982,
0.0011336044408380985,
0.05896208807826042,
-0.04290524497628212,
0.046818021684885025,
0.016209987923502922,
-0.044680025428533554,
-0.013976349495351315,
0.06263609975576401,
0.018662601709365845,
0.016467465087771416,
0.03839189186692238,
-0.02557479217648506,
0.03153492510318756,
0.0026407011318951845,
-0.04484796151518822,
-0.032409511506557465,
-0.015588170848786831,
-0.015749024227261543,
-0.025916028767824173,
0.028194840997457504,
-0.027991337701678276,
-0.026066603139042854,
0.049098528921604156,
-0.011930874548852444,
0.08469858020544052,
0.010066124610602856,
-0.022888939827680588,
-0.08261413127183914,
0.02436540089547634,
-0.02233181893825531,
-0.024022508412599564,
-0.012185228057205677,
0.03142668306827545,
0.046381331980228424,
0.010419406928122044,
0.027700943872332573,
0.041229959577322006,
-0.07142382860183716,
0.08841275423765182,
0.03423056751489639,
-0.03865380212664604,
0.030130108818411827,
0.03281969577074051,
-0.027296746149659157,
0.030271044000983238,
-0.0044954740442335606,
0.03677571937441826,
-0.003902470925822854,
-0.020650863647460938,
-0.017640989273786545,
-0.02325381338596344,
0.007268131244927645,
0.011104225181043148,
0.024619434028863907,
0.050395797938108444,
0.02422863245010376,
0.015223361551761627,
-0.0038830675184726715,
-0.014660465531051159,
-0.013123800978064537,
0.013267996720969677,
0.034372612833976746,
0.025020703673362732,
-0.051100146025419235,
-0.026196729391813278,
0.008249009028077126,
-0.03855234012007713,
0.0046012611128389835,
0.07724659144878387,
0.057758964598178864,
-0.016979185864329338,
-0.011025299318134785,
0.054461654275655746,
0.07040778547525406,
0.055709123611450195,
-0.03528834879398346,
-0.020440436899662018,
0.054494019597768784,
0.0653594434261322,
-0.020016463473439217,
-0.037665028125047684,
-0.047987714409828186,
-0.017641879618167877,
0.02090536616742611,
0.029005559161305428,
-0.019915353506803513,
-0.04045918956398964,
-0.034992557018995285,
-0.04366558790206909,
0.030883613973855972,
-0.04339649900794029,
0.025339124724268913,
-0.03845178708434105,
-0.022877926006913185,
-0.11516661196947098,
0.035316117107868195,
-0.06894353032112122,
-0.008738730102777481,
-0.01564374752342701,
0.005537191405892372,
0.009979342110455036,
-0.029444677755236626,
-0.0008468635496683419,
-0.04896799102425575,
-0.0007479076739400625,
-0.013468378223478794,
-0.030393417924642563,
0.07958431541919708,
0.02959217131137848,
0.06361077725887299,
-0.019197499379515648,
-0.018555300310254097,
0.025330614298582077,
0.0009580268524587154,
0.039398908615112305,
0.07465093582868576,
0.05181853100657463,
0.029027815908193588,
0.058740634471178055,
-0.02494412660598755,
0.009315264411270618,
-0.028184296563267708,
0.036804672330617905,
0.05065326765179634,
0.06049150601029396,
0.010538152419030666,
-0.09352501481771469,
0.05707227438688278,
-0.0019722171127796173,
0.03984053060412407,
0.034355901181697845,
-0.022343307733535767,
-0.0009815102675929666,
0.04567321389913559,
0.040911559015512466,
0.017044179141521454,
-0.021259082481265068,
-0.0743681788444519,
-0.03860646113753319,
0.006474991329014301,
0.012827855534851551,
-0.020040102303028107,
-0.010378746315836906,
-0.04354029521346092,
-0.011130932718515396,
0.09460803866386414,
-0.02619902975857258,
-0.00816158764064312,
-0.03886474296450615,
-0.050019215792417526,
-0.0054363650269806385,
0.0124057587236166,
-0.022201724350452423,
-0.05274299904704094,
0.055547717958688736,
-0.034867286682128906,
0.02583872154355049,
0.038877736777067184,
-0.003505168715491891,
0.06699972599744797,
0.05963483825325966,
-0.03162166476249695,
0.02007998898625374,
-0.046324554830789566,
-0.03249965235590935,
0.0296332947909832,
-0.015446264296770096,
-0.029786745086312294,
0.0938534066081047,
0.015315125696361065,
0.013877562247216702,
-0.0235713142901659,
0.016146842390298843,
0.012015338987112045,
-0.03330293297767639,
-0.04210586100816727,
-0.0032555300276726484,
-0.042356327176094055,
-0.03180651739239693,
-0.018486371263861656,
-0.04629712924361229,
0.020140260457992554,
0.008067772723734379,
-0.010782917030155659,
0.005605048034340143,
-0.04456154257059097,
-0.0008523002034053206,
0.04456572234630585,
-0.011109688319265842,
0.009161845780909061,
0.02267792634665966,
0.007147725205868483,
0.00131101137958467,
-0.06282606720924377,
0.004928757436573505,
-0.0037301729898899794,
-0.01419757679104805,
-0.002008866984397173,
0.026518462225794792,
0.08678280562162399,
-0.07545804232358932,
0.029575290158391,
0.02557043544948101,
-0.011397541500627995,
-0.017573226243257523,
-0.03588547930121422,
0.05736403167247772,
-0.08771016448736191,
-0.038072146475315094,
0.01947498880326748,
-0.021577345207333565,
0.008079729974269867,
-0.06707996875047684,
0.025296583771705627,
0.0008712565759196877,
0.040653668344020844,
-0.010708254761993885,
-0.007821639999747276,
0.00018968753283843398,
-0.006887757685035467,
0.045953210443258286,
0.07335857301950455,
0.017541861161589622,
-0.023509254679083824,
-0.02365344949066639,
0.08344953507184982,
-0.00445421552285552,
0.009115629829466343,
-0.0319889672100544,
-0.0479578860104084,
0.008426828309893608,
-0.02393433265388012,
-0.052522700279951096,
-0.026032794266939163,
-0.009576528333127499,
0.06322422623634338,
-0.006424221675843,
-0.044035088270902634,
0.03623121976852417,
-0.08530749380588531,
-0.050209615379571915,
-0.0014733445132151246,
0.028391415253281593,
0.00380896357819438,
0.0339370034635067,
0.03145945444703102,
0.03163159266114235,
-0.033786553889513016,
0.013677841983735561,
0.002965075196698308,
0.041055694222450256,
0.002773764543235302,
-0.046462953090667725,
0.030665965750813484,
-0.029139449819922447,
-0.00486575486138463,
-0.009748753160238266,
0.05714525654911995,
0.027738071978092194,
-0.02176237665116787,
0.08387819677591324,
0.012775298207998276,
0.030171992257237434,
-0.015790602192282677,
0.04943416267633438,
0.03561853989958763,
-0.010981702245771885,
0.08672201633453369,
0.04484521970152855,
0.010854188352823257,
-0.013011475093662739,
-0.02370576560497284,
-0.030582090839743614,
0.027000565081834793,
-0.0032323524355888367,
0.053995531052351,
0.0007723410381004214,
-0.05617901682853699,
0.02383776567876339,
-0.002380118239670992,
0.0341484434902668,
0.007647253572940826,
-0.02797376736998558,
-0.004419054836034775,
0.011278469115495682,
-0.029832368716597557,
0.06626575440168381,
-0.02199454978108406,
0.04667729139328003,
-0.010369543917477131,
-0.05124703049659729,
-0.02265755832195282,
-0.04814959317445755,
-0.004274559207260609,
0.04646638035774231,
-0.0595521554350853,
-0.016499213874340057,
0.02305430918931961,
0.04221531003713608,
-0.06467263400554657,
-0.005907707381993532,
0.018765227869153023,
0.032812897115945816,
-0.07081513851881027,
0.04109909012913704,
0.056768275797367096,
0.0011024210834875703,
0.052929382771253586,
0.012878457084298134,
-0.021987460553646088,
-0.017840970307588577,
0.02426566556096077,
-0.015984492376446724,
0.02975708246231079,
0.03564594313502312,
0.018396694213151932,
0.01805899851024151,
0.006874279119074345,
-0.06435198336839676,
-0.035615671426057816,
-0.01956096850335598,
0.031769223511219025,
0.00036352264578454196,
-0.024990204721689224,
0.038427744060754776,
-0.10084798187017441,
0.002084696665406227,
-0.008369945921003819,
0.001982149900868535,
0.026402588933706284,
-0.03202636167407036,
0.03513796627521515,
0.013314778916537762,
-0.0027132767718285322,
0.006617198698222637,
-0.01491625513881445,
0.012148951180279255,
-0.03515659645199776,
0.0039332858286798,
-0.033345144242048264,
-0.019029101356863976,
-0.009708854369819164,
0.011034315451979637,
-0.034884389489889145,
-0.04833455756306648,
-0.004132086876779795,
-0.052034612745046616,
0.030152693390846252,
-0.013999898917973042,
-0.03907985985279083,
-0.00877546425908804,
-0.05214302986860275,
-0.04488444700837135,
-0.020803792402148247,
0.015613927505910397,
-0.007009265478700399,
-0.034487657248973846,
-0.002685169456526637,
0.0034885050263255835,
-0.0038778241723775864,
0.004647721070796251,
-0.04923008754849434,
-0.03348904475569725,
0.05772978067398071,
-0.0009153353748843074,
0.07097145915031433,
-0.0032300506718456745,
-0.01570182852447033,
-0.04437226057052612,
0.04110819846391678,
0.05855535715818405,
-0.001554100657813251,
0.036503829061985016,
-0.02706005983054638,
0.0015121273463591933,
-0.034295592457056046,
0.0069652763195335865,
0.002978600561618805,
-0.06078382954001427,
-0.030799025669693947,
-0.0022893021814525127,
0.02614886499941349,
0.03800714388489723,
-0.0379001647233963,
-0.030615640804171562,
-0.05323297902941704,
-0.04792580008506775,
0.053225044161081314,
0.06225864961743355,
0.020545026287436485,
-0.08001860231161118,
0.030449360609054565,
-0.06403321772813797,
0.05755353346467018,
0.0686439573764801,
0.0365510992705822,
-0.005658132489770651,
0.009783816523849964,
-0.015659678727388382,
0.007642474491149187,
0.01576562225818634,
0.0068640816025435925,
-0.028458891436457634,
0.09907059371471405,
-0.04349582642316818,
-0.031923770904541016,
-0.0027815874200314283,
0.05701703578233719,
0.02418988198041916,
0.022694464772939682,
0.04648621380329132,
-0.08130057156085968,
0.002189478138461709,
-0.004805934615433216,
-0.02876211702823639,
0.001240849494934082,
-0.04717246815562248,
0.02388075366616249,
-0.013521370477974415,
-0.019546683877706528,
-0.015699628740549088,
0.02474329061806202,
0.013295017182826996,
0.0006352034979499876,
0.057286255061626434,
0.008951288647949696,
-0.028629766777157784,
-0.00842426996678114,
-0.002624566201120615,
0.017198527231812477,
0.0008280986803583801,
0.0045621455647051334,
-0.05099305510520935,
-0.004530659876763821,
-0.00018913154781330377,
0.0026978556998074055,
0.061533551663160324,
0.007075809873640537,
0.004966598469763994,
-0.0020215166732668877,
-0.008128977380692959,
-0.04866178706288338,
0.0032135620713233948,
0.014631291851401329,
-0.05147666484117508,
0.03687838837504387,
-0.015009953640401363,
-0.015510458499193192,
-0.023851303383708,
-0.013591735623776913,
-0.00511679844930768,
0.012880959548056126,
-0.0018495810218155384,
-0.015851086005568504,
0.041420839726924896,
-0.006971145514398813,
-0.0335523895919323,
0.011791946366429329,
0.013158531859517097,
-0.05006980523467064,
-0.015047968365252018,
0.00965539924800396,
0.04794875532388687,
0.05130529776215553,
-0.08254684507846832,
0.06843356043100357,
0.012647151947021484,
-0.05438641831278801,
0.045720502734184265,
-0.04111037403345108,
-0.03842245787382126,
-0.020605016499757767,
-0.007214075420051813,
-0.04062281548976898,
0.0751965343952179,
-0.0526718944311142,
-0.03741193562746048,
0.045801613479852676,
-0.02782086841762066,
0.028277715668082237,
0.03441671282052994,
0.022146077826619148,
-0.01963927410542965,
0.025918036699295044,
-0.027953894808888435,
0.0488855242729187,
-0.013188189826905727,
-0.04415533319115639,
0.02268972061574459,
-0.009698002599179745,
-0.023756688460707664,
-0.015351350419223309,
0.016906123608350754,
0.0064566186629235744,
-0.05379414185881615,
-0.008299908600747585,
0.04341063275933266,
-0.027648858726024628,
-0.06167588755488396,
0.018663370981812477,
-0.06159196421504021,
0.014231878332793713,
-0.04318172112107277,
0.02869119495153427,
-0.025520887225866318,
0.013047156855463982,
-0.0751860961318016,
-0.005006866063922644,
-0.009883720427751541,
0.015398782677948475,
0.008526819758117199,
-0.01798527128994465,
-0.028947418555617332,
-0.03698021546006203,
-0.05250818654894829,
-0.01602284237742424,
-0.013189301826059818,
0.029677635058760643,
-0.007495696656405926,
0.007911731489002705,
-0.019874000921845436,
-0.052746307104825974,
0.04621707275509834,
-0.03605405241250992,
-0.03372775763273239,
0.0821480080485344,
0.018109548836946487,
-0.04587243124842644,
0.012131416238844395,
-0.06294694542884827,
-0.03977442905306816,
0.00859798863530159,
0.017089486122131348,
0.01565420627593994,
0.023722050711512566,
-0.02743835374712944,
-0.06350212544202805,
0.06515108048915863,
-0.042346060276031494,
0.006655444391071796,
0.022829921916127205,
0.001351771759800613,
-0.022382043302059174,
0.017552286386489868,
-0.007822133600711823,
-0.004723245278000832,
-0.022435516119003296,
-0.032253336161375046,
-0.001980195287615061,
-0.03573831170797348,
0.03257133066654205,
-0.01822681538760662,
0.01563671976327896,
0.03282085433602333,
0.004932592157274485,
-0.01697179488837719,
0.006119206082075834,
-0.007608987856656313,
0.03438592702150345,
0.05410739406943321,
0.033476170152425766,
-0.05132820084691048,
-0.03708929568529129,
-0.008699924685060978,
-0.07490623742341995,
0.032049428671598434,
-0.012907326221466064,
0.035089559853076935,
-0.019874032586812973,
-0.009149438701570034,
-0.05174562707543373,
0.012642311863601208,
-0.06707455962896347,
-0.011938931420445442,
0.0026313811540603638,
-0.010006677359342575,
-0.04045960679650307,
-0.017003493383526802,
0.03463251143693924,
0.013948333449661732,
-0.002164202043786645,
-0.07527796179056168,
-0.014356731437146664,
-0.033182598650455475,
-0.00006716643838444725,
0.012821630574762821,
-0.009004301391541958,
0.019938500598073006,
-0.002133064204826951,
0.06749976426362991,
0.0021435669623315334,
-0.008046683855354786,
0.002508260775357485,
0.03974117711186409,
0.07959524542093277,
-0.04516354575753212,
-0.0037059595342725515,
0.013383405283093452,
0.04004634916782379,
0.09119322896003723,
0.02142190933227539,
-0.029308652505278587,
0.031620658934116364,
0.012956284917891026,
0.033131640404462814,
0.03101392835378647,
-0.018277935683727264,
-0.06978841125965118,
-0.0008580444846302271,
-0.037885718047618866,
-0.00596507266163826,
-0.012547515332698822,
-0.03180744871497154,
0.05768504738807678,
0.005350296851247549,
-0.012606325559318066,
-0.022878281772136688,
0.009177998639643192,
0.04677196964621544,
-0.007951706647872925,
-0.008662298321723938,
-0.02992253005504608,
-0.007219836115837097,
-0.056279391050338745,
0.02630392648279667,
0.009376785717904568,
-0.02621716819703579,
0.019590133801102638,
-0.04629872739315033,
-0.02230924740433693,
-0.00032673071837052703,
0.027201713994145393,
-0.020060565322637558,
0.006654383148998022,
0.006207770202308893,
-0.020406225696206093,
-0.03418854624032974,
0.005642785225063562,
0.019889183342456818,
0.027032101526856422,
0.0447753369808197,
0.026055699214339256,
-0.01875261403620243,
-0.0012502026511356235,
-0.022604182362556458,
-0.029811222106218338,
0.03236236050724983,
-0.0062342118471860886,
0.022746093571186066,
0.02500990591943264,
0.07854112237691879,
-0.06222660467028618,
0.031607966870069504,
-0.028843536972999573,
-0.0011274805292487144,
-0.03980105742812157,
0.03221737965941429,
-0.006691586691886187,
-0.0012892575468868017,
0.005990919657051563,
0.02632489986717701,
0.07396281510591507,
0.005008062347769737,
0.058689240366220474,
0.021702924743294716,
-0.03263111039996147,
-0.008445206098258495,
0.004615051671862602,
0.01227073185145855,
0.0005345973186194897,
0.06283222138881683,
-0.04584672302007675,
0.0279212836176157,
0.01651729829609394,
-0.029913855716586113,
0.017268724739551544,
0.01955782063305378,
0.03784814104437828,
-0.018648281693458557,
0.010297122411429882,
-0.001432700315490365,
-0.05531298741698265,
0.0173373743891716,
-0.04319712892174721,
-0.014748758636415005,
-0.02139550819993019,
0.015446316450834274,
0.014305366203188896,
-0.049590688198804855,
0.0488460510969162,
-0.059936799108982086,
-0.011782683432102203,
-0.0034320626873522997,
-0.018590889871120453,
0.07186498492956161,
-0.0445888489484787,
0.03895801678299904,
0.04846462979912758,
0.011244154535233974,
-0.015288525260984898,
-0.030794085934758186,
0.0009675957262516022,
-0.0015988580416887999,
0.039522454142570496,
-0.04516619071364403,
-0.007814520969986916,
-0.006454126443713903,
0.09764399379491806,
0.01981368474662304,
-0.004476635251194239,
0.00761938001960516,
-0.013622486032545567,
0.04239398613572121,
0.011303387582302094,
0.04377822205424309,
-0.02082805149257183,
0.060992367565631866
] |
[
7.129979610443115,
-2.9083516597747803
] |
Pattern Formation and Solitons
|
Nonlinear Sciences
|
nlin-PS
|
na
|
na
|
2007-04-02T12:02:36
|
We present recent advances in understanding of the ground and excited states
of the electron-phonon coupled systems obtained by novel methods of
Diagrammatic Monte Carlo and Stochastic Optimization, which enable the
approximation-free calculation of Matsubara Green function in imaginary times
and perform unbiased analytic continuation to real frequencies. We present
exact numeric results on the ground state properties, Lehmann spectral function
and optical conductivity of different strongly correlated systems: Frohlich
polaron, Rashba-Pekar exciton-polaron, pseudo Jahn-Teller polaron, exciton, and
interacting with phonons hole in the t-J model.
|
Spectroscopic Properties of Polarons in Strongly Correlated Systems by
Exact Diagrammatic Monte Carlo Method
|
cond-mat.str-el cond-mat.stat-mech
|
0704.0025
| 2,007
|
[
-0.010951078496873379,
0.0072858864441514015,
0.0024451857898384333,
-0.03137722611427307,
0.020873507484793663,
0.010820669122040272,
0.00765681266784668,
0.008111509494483471,
0.014364532195031643,
0.029818395152688026,
-0.07623249292373657,
0.032047513872385025,
0.045204296708106995,
0.02443704754114151,
-0.013605772517621517,
-0.0020601546857506037,
0.036448609083890915,
0.013684229925274849,
-0.013552396558225155,
-0.03453540429472923,
-0.049746833741664886,
-0.001915617729537189,
-0.033167075365781784,
-0.018204646185040474,
0.07329443097114563,
-0.017939377576112747,
0.016939502209424973,
-0.007631879765540361,
-0.025292975828051567,
0.02395910955965519,
0.018800167366862297,
-0.05850830301642418,
0.0017144455341622233,
-0.03024367243051529,
-0.08250895142555237,
0.015151062980294228,
0.053462546318769455,
-0.03350759670138359,
0.020732441917061806,
0.07177356630563736,
0.05482833459973335,
-0.013134126551449299,
-0.0032492082100361586,
-0.057798076421022415,
0.006468469277024269,
0.010565599426627159,
0.018270354717969894,
-0.03900494799017906,
-0.0022659513633698225,
0.020138652995228767,
-0.030424853786826134,
0.053661465644836426,
0.0556359700858593,
-0.04693665727972984,
-0.022737467661499977,
0.011636076495051384,
0.007855604402720928,
-0.010491816326975822,
0.05689219757914543,
0.04443647712469101,
0.037464819848537445,
0.06497761607170105,
0.0010757193667814136,
0.0553104393184185,
0.035726889967918396,
-0.06589429080486298,
-0.01221491303294897,
-0.004843787755817175,
-0.033493220806121826,
-0.010095924139022827,
0.012489743530750275,
-0.05751624330878258,
0.005985603202134371,
0.026927681639790535,
0.0014869220321998,
-0.02490103803575039,
-0.00841898936778307,
-0.0224896389991045,
0.043013207614421844,
0.017486710101366043,
-0.005879077594727278,
-0.027667272835969925,
0.01632656157016754,
0.0020688825752586126,
0.07347521930932999,
-0.01737041585147381,
0.004942854400724173,
0.01901218667626381,
-0.06167522817850113,
0.04576243832707405,
0.04544060677289963,
0.001743755885399878,
0.026293104514479637,
0.03536181524395943,
0.0004464347439352423,
0.04907018318772316,
-0.04120631515979767,
0.05494978278875351,
-0.02499740943312645,
-0.03329432010650635,
-0.010918774642050266,
0.005170584190636873,
0.018639814108610153,
0.020238470286130905,
0.017158929258584976,
0.027775844559073448,
0.011347126215696335,
-0.043698377907276154,
0.013874264433979988,
0.010375152342021465,
-0.08891179412603378,
-0.004201071802526712,
0.036232635378837585,
-0.041579458862543106,
-0.025014767423272133,
-0.039294108748435974,
0.04682071879506111,
-0.08173895627260208,
0.01292720902711153,
0.059596605598926544,
0.017095088958740234,
0.017351876944303513,
0.019458984956145287,
0.021298205479979515,
-0.002408985747024417,
0.0397925041615963,
-0.042994383722543716,
-0.023945286870002747,
-0.047610167413949966,
-0.03083288110792637,
-0.028841393068432808,
0.017237287014722824,
-0.037792522460222244,
0.01638638973236084,
0.04200466722249985,
0.014256900176405907,
-0.015379729680716991,
-0.0407358780503273,
0.044747840613126755,
-0.029825719073414803,
0.04823508486151695,
-0.017778893932700157,
-0.012722505256533623,
-0.015630900859832764,
-0.05171177163720131,
-0.03907592222094536,
0.014563864096999168,
-0.054204538464546204,
-0.012801038101315498,
-0.0250637736171484,
0.03663771599531174,
0.022081945091485977,
0.03816186264157295,
0.06469064950942993,
-0.034443508833646774,
-0.0925988107919693,
0.001613373402506113,
-0.020754124969244003,
0.015224973671138287,
0.015077118761837482,
-0.018202457576990128,
0.0036491968203336,
-0.03649270534515381,
0.046044543385505676,
-0.021049024537205696,
-0.02676324173808098,
0.05523468554019928,
-0.004475991707295179,
0.03148920461535454,
0.02519966848194599,
-0.026994487270712852,
-0.008515609428286552,
-0.017654912546277046,
0.020120617002248764,
0.032523948699235916,
0.0005862853140570223,
-0.023238059133291245,
-0.029461033642292023,
0.035211414098739624,
0.017349258065223694,
0.0867840126156807,
-0.005278031341731548,
0.021259116008877754,
0.04663253203034401,
-0.03501445800065994,
0.014512990601360798,
-0.009616104885935783,
-0.014728656969964504,
-0.017557593062520027,
0.0003752121701836586,
0.022073477506637573,
0.03296872600913048,
-0.0872349739074707,
-0.055221643298864365,
0.005419643595814705,
-0.07003407180309296,
0.06286366283893585,
-0.03457086160778999,
-0.019517602398991585,
-0.06576620042324066,
-0.045762211084365845,
-0.016355566680431366,
-0.03676106780767441,
0.031152941286563873,
0.0029552485793828964,
0.037828970700502396,
0.030958665534853935,
-0.01888245902955532,
0.006834289059042931,
0.0027861150447279215,
0.04466114193201065,
0.017097266390919685,
-0.031272947788238525,
0.04086821898818016,
-0.036696068942546844,
-0.023277491331100464,
0.017573677003383636,
-0.04929431155323982,
-0.027651863172650337,
0.045429352670907974,
0.02361176162958145,
-0.01812540739774704,
0.03845890983939171,
0.02963998168706894,
0.06303077191114426,
-0.007087185513228178,
-0.030684931203722954,
0.030803527683019638,
-0.042508333921432495,
0.012924200855195522,
-0.04380813241004944,
-0.040947940200567245,
0.026768775656819344,
0.004257766529917717,
0.0018144964706152678,
0.036738816648721695,
-0.04497770592570305,
0.01214913371950388,
0.055652111768722534,
0.05911166965961456,
-0.004664488136768341,
0.02402612566947937,
0.031529784202575684,
-0.011209331452846527,
-0.04139396548271179,
0.010858157649636269,
0.009745554067194462,
0.003336831461638212,
-0.03488103672862053,
0.037138696759939194,
0.04344829171895981,
0.060208361595869064,
0.04107636213302612,
0.048798613250255585,
0.0206759013235569,
-0.007773120887577534,
-0.02139400690793991,
0.07305468618869781,
-0.0011504341382533312,
-0.06717701256275177,
0.016144931316375732,
-0.045728906989097595,
-0.010473780333995819,
-0.006211772561073303,
-0.0381382554769516,
0.009700926020741463,
0.026309147477149963,
-0.08203182369470596,
-0.0001768718211678788,
-0.09128330647945404,
-0.007130020763725042,
0.07745514065027237,
0.051722560077905655,
0.060415107756853104,
0.014017471112310886,
0.031042635440826416,
0.009759989567101002,
-0.040768396109342575,
0.020692020654678345,
-0.03358643501996994,
-0.047944966703653336,
-0.028889264911413193,
-0.013341536745429039,
-0.0029638807754963636,
-0.022043589502573013,
-0.031779441982507706,
0.0683739110827446,
-0.01952975057065487,
0.021544162184000015,
0.013405862264335155,
-0.010864312760531902,
-0.007548456080257893,
0.01157454028725624,
0.07430838793516159,
-0.013884946703910828,
0.0038139044772833586,
0.07578372210264206,
-0.03077561967074871,
0.015077859163284302,
0.053952936083078384,
0.03735165297985077,
0.025113483890891075,
-0.010915049351751804,
-0.00032972480403259397,
0.012363390997052193,
0.021324485540390015,
0.01909189112484455,
-0.01813947595655918,
0.025580383837223053,
0.028658946976065636,
-0.02414858341217041,
0.04643918573856354,
-0.025112155824899673,
-0.02184147760272026,
0.02442680299282074,
0.02170095406472683,
0.007274612318724394,
0.016088055446743965,
0.08176669478416443,
-0.03579818084836006,
0.004288610070943832,
0.01392708532512188,
0.012646648101508617,
-0.11389853805303574,
-0.015554127283394337,
0.028663281351327896,
-0.0407041497528553,
-0.018901178613305092,
0.00045227244845591486,
-0.02754870429635048,
-0.007918045856058598,
0.013893457129597664,
-0.02132115699350834,
-0.003726405091583729,
-0.046550288796424866,
-0.018159830942749977,
-0.030472731217741966,
0.059562716633081436,
-0.00579382898285985,
0.0015288774156942964,
-0.004933148622512817,
-0.08239194005727768,
-0.05715416744351387,
-0.04887467622756958,
-0.018657825887203217,
-0.009141153655946255,
-0.05105142667889595,
-0.025848256424069405,
0.03886391222476959,
-0.023961743339896202,
-0.051747534424066544,
-0.038869526237249374,
0.005207712762057781,
0.028801191598176956,
-0.026000216603279114,
0.02102559059858322,
0.011861955747008324,
0.005847515072673559,
0.05966504290699959,
0.047555532306432724,
0.04090864956378937,
-0.028799761086702347,
0.06269323080778122,
-0.008124144747853279,
0.008016800507903099,
-0.01406379509717226,
-0.002173517132177949,
0.03292182832956314,
0.029753534123301506,
-0.024756254628300667,
-0.026570163667201996,
-0.015106062404811382,
0.012209187261760235,
0.04879264906048775,
0.05996318161487579,
0.029682418331503868,
-0.10347107797861099,
-0.042953696101903915,
-0.053355757147073746,
-0.0045088198967278,
0.055259864777326584,
-0.019932666793465614,
0.026891499757766724,
0.044533658772706985,
0.07043787091970444,
-0.004031787160784006,
-0.053536556661129,
-0.02238791063427925,
-0.017187530174851418,
-0.009816287085413933,
-0.01682698354125023,
-0.04895685240626335,
-0.01147247850894928,
0.018338926136493683,
0.0004059020720887929,
-0.0674680694937706,
0.06457571685314178,
-0.021463235840201378,
0.034145671874284744,
-0.01774691417813301,
-0.07549917697906494,
-0.06767863780260086,
0.01343904621899128,
-0.041975900530815125,
-0.006871986668556929,
0.009494847618043423,
-0.04303056374192238,
-0.09086120873689651,
0.02477637492120266,
-0.04409071058034897,
-0.01106598973274231,
0.01912716217339039,
0.00408927770331502,
-0.058136049658060074,
0.023322345688939095,
-0.01213870756328106,
0.03528560325503349,
-0.03139106184244156,
0.008441274054348469,
-0.03141969069838524,
0.02874862030148506,
0.04806998744606972,
-0.02754632756114006,
-0.004540299065411091,
-0.02881588041782379,
-0.010339625179767609,
0.013453575782477856,
0.012534906156361103,
-0.013616342097520828,
-0.02921556681394577,
0.05097352713346481,
-0.0003169880947098136,
0.03369462117552757,
0.010609845630824566,
-0.07469560205936432,
0.06257784366607666,
-0.007582648191601038,
-0.008459778502583504,
0.023473374545574188,
0.059181392192840576,
0.05001882091164589,
-0.04432845860719681,
0.04373304545879364,
-0.01639007031917572,
0.04360869154334068,
0.03814771771430969,
-0.005684195552021265,
-0.04889423027634621,
0.022348245605826378,
-0.01980927214026451,
0.03215957060456276,
0.014169475063681602,
-0.046042654663324356,
0.02973145619034767,
0.06450242549180984,
-0.0497719943523407,
-0.010249685496091843,
0.04916735738515854,
0.03681551665067673,
0.05270547419786453,
-0.04422200098633766,
-0.0063542453572154045,
-0.027909649536013603,
0.008361078798770905,
0.009192252531647682,
0.027872387319803238,
-0.01886262372136116,
0.02491583861410618,
0.02837502211332321,
0.056057367473840714,
0.02329244278371334,
-0.002783243078738451,
0.09423645585775375,
0.02638246864080429,
-0.047419674694538116,
-0.016844095662236214,
0.003469350514933467,
-0.03419922664761543,
-0.008259549736976624,
0.014430162496864796,
0.013856635428965092,
-0.019862066954374313,
-0.023139899596571922,
-0.0531122125685215,
-0.04719112440943718,
0.02088167890906334,
-0.033528439700603485,
0.010515041649341583,
-0.05211402475833893,
-0.04318666085600853,
-0.04521681368350983,
0.0006558021996170282,
-0.01075354591012001,
0.0282996017485857,
0.0020282024051994085,
-0.02036605030298233,
-0.006620772648602724,
0.014989711344242096,
0.019826050847768784,
-0.00023598055122420192,
-0.019578788429498672,
-0.033751603215932846,
-0.005847386550158262,
-0.002835760125890374,
0.013040618970990181,
-0.018069323152303696,
-0.007195726502686739,
-0.09269716590642929,
-0.011827713809907436,
0.0005712111014872789,
0.0022050407715141773,
0.025980167090892792,
0.04731573536992073,
0.05772839114069939,
-0.03296584263443947,
-0.04836364835500717,
0.030589070171117783,
0.008649579249322414,
-0.08184456080198288,
-0.018181046470999718,
0.028979061171412468,
0.004664252046495676,
0.026458153501152992,
-0.025910936295986176,
-0.09013661742210388,
0.026308225467801094,
0.0007677134126424789,
-0.04956623166799545,
0.07546268403530121,
-0.019616713747382164,
-0.014125038869678974,
0.046500880271196365,
-0.015264837071299553,
0.03211073949933052,
0.027037296444177628,
-0.02097892016172409,
-0.029801739379763603,
-0.006648773793131113,
-0.01648065075278282,
0.018489189445972443,
0.024656832218170166,
0.011070235632359982,
0.05882114917039871,
0.016640977934002876,
0.026730038225650787,
-0.05158926546573639,
-0.041040193289518356,
0.03997278958559036,
-0.025323281064629555,
-0.026852840557694435,
-0.019682439044117928,
-0.029475761577486992,
-0.00201591569930315,
-0.104347825050354,
0.026750504970550537,
-0.01912456378340721,
0.009486071765422821,
-0.01724414713680744,
-0.049354325979948044,
0.030982138589024544,
0.01907445676624775,
-0.026263387873768806,
0.017850399017333984,
0.028431659564375877,
-0.02461887151002884,
-0.04071946442127228,
-0.04184110090136528,
0.0033989541698247194,
-0.0007938190246932209,
0.00975931528955698,
-0.005864221602678299,
-0.021054930984973907,
0.019004762172698975,
0.028545783832669258,
-0.02255423553287983,
-0.01236651185899973,
0.05059164762496948,
-0.019445741549134254,
-0.0014766876120120287,
-0.020169641822576523,
-0.03964952006936073,
-0.019263235852122307,
0.014402846805751324,
0.022872038185596466,
-0.04914086312055588,
0.04498670995235443,
-0.007783463224768639,
-0.043170757591724396,
0.07198796421289444,
-0.0008310728590004146,
-0.03236247971653938,
-0.05480392277240753,
-0.027214251458644867,
-0.06827586144208908,
0.005716650281101465,
0.0029143362771719694,
0.013171426020562649,
-0.00555181922391057,
-0.06290843337774277,
0.017082661390304565,
0.017126336693763733,
0.005031080450862646,
0.043190762400627136,
-0.029340289533138275,
0.0579533688724041,
0.024225695058703423,
0.006590462289750576,
0.057957034558057785,
-0.029975568875670433,
0.025090787559747696,
-0.008853983134031296,
-0.0105726458132267,
-0.02926091104745865,
-0.03623339533805847,
-0.0050904531963169575,
-0.019262051209807396,
0.08427213132381439,
0.027162835001945496,
0.030139893293380737,
0.0046800486743450165,
0.006636955309659243,
-0.06971365213394165,
0.015331785194575787,
-0.05976705625653267,
0.004146425519138575,
0.030257999897003174,
0.021791748702526093,
-0.07518546283245087,
0.007558995857834816,
0.013706852681934834,
0.009955232962965965,
0.008810926228761673,
-0.004292256664484739,
-0.02590871974825859,
0.004405919928103685,
0.05110296979546547,
-0.03394637256860733,
0.027126705273985863,
0.030815601348876953,
0.05328628793358803,
0.009981985203921795,
-0.0005635137786157429,
0.0015829016920179129,
0.026683693751692772,
0.023268479853868484,
0.04727921634912491,
0.007634584791958332,
-0.024100882932543755,
-0.022927064448595047,
0.006278512068092823,
0.10010983794927597,
0.03401515632867813,
-0.02547350339591503,
0.028142426162958145,
0.03028305433690548,
0.02222815342247486,
0.07914859056472778,
0.015814414247870445,
-0.02307313308119774,
0.005433296784758568,
-0.020007090643048286,
-0.01340020727366209,
-0.010526860132813454,
-0.05698015168309212,
0.07165729254484177,
0.005349114071577787,
-0.031402360647916794,
-0.06809381395578384,
-0.05967044085264206,
0.050564803183078766,
-0.011631397530436516,
-0.04673219472169876,
-0.06031041592359543,
-0.01892046444118023,
-0.05115378275513649,
-0.018255382776260376,
-0.01122178416699171,
0.038691453635692596,
-0.041381850838661194,
-0.025478443130850792,
0.018818654119968414,
0.01324670109897852,
0.045551665127277374,
-0.036560725420713425,
0.008548879064619541,
0.03607983514666557,
-0.05500037595629692,
-0.028992028906941414,
-0.03279266506433487,
0.008282072842121124,
0.04215395078063011,
0.05163169652223587,
-0.03881710767745972,
-0.06317371129989624,
0.031737469136714935,
0.031952302902936935,
-0.10168707370758057,
-0.027241958305239677,
0.0582558736205101,
0.034299418330192566,
0.014657690189778805,
0.057676706463098526,
-0.01914573833346367,
0.007008806336671114,
-0.021916834637522697,
0.013681420125067234,
0.02233264595270157,
-0.02073092944920063,
0.003774825716391206,
0.02233511209487915,
-0.004983488470315933,
0.037600938230752945,
0.026776084676384926,
0.05546053498983383,
0.000901286955922842,
0.01552736945450306,
-0.008117319084703922,
-0.04477471113204956,
-0.005879669450223446,
0.013573841191828251,
0.009779157117009163,
-0.017148735001683235,
-0.06038522720336914,
0.047321368008852005,
-0.004938388243317604,
-0.08017724007368088,
-0.017714226618409157,
0.029444102197885513,
0.09226439148187637,
0.028614135459065437,
-0.004444954451173544,
0.021352078765630722,
-0.04472988098859787,
0.019222373142838478,
-0.038568973541259766,
0.03827223181724548,
-0.02746523916721344,
-0.012232593260705471,
0.001380705856718123,
0.021076619625091553,
0.004184594377875328,
-0.08703635632991791,
0.03903594985604286,
-0.008482493460178375,
-0.0038700811564922333,
-0.015898490324616432,
-0.05853312090039253,
0.027745718136429787,
0.0784362331032753,
0.05114933103322983,
-0.025866037234663963,
-0.0242209043353796,
0.029437975957989693,
0.010618460364639759,
0.012906919233500957,
-0.015887871384620667,
-0.008385217748582363,
0.005135425832122564,
0.06158440187573433,
-0.012020417489111423,
0.019697273150086403,
0.009597843512892723,
0.004940719809383154,
0.03309397026896477,
0.04747869446873665,
0.004076655022799969,
-0.030483311042189598,
0.034660741686820984
] |
[
8.797758102416992,
-1.709244966506958
] |
Strongly Correlated Electrons
|
Condensed-Matter Physics
|
cond-mat-str-el
|
cond-mat-stat-mech
|
na
|
2007-03-31T12:24:06
|
Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from
N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent
singularities and, as N approaches infinite, fractals -- and thereby,scale-free
networks. Any integer greater than 8 and not a power of 2 generates a
meta-fractal or "Sky" when it is interpreted as the "strut constant" (S) of an
ensemble of octahedral vertex figures called "Box-Kites" (the fundamental
building blocks of ZDs). Remarkably simple bit-manipulation rules or "recipes"
provide tools for transforming one fractal genus into others within the context
of Wolfram's Class 4 complexity.
|
Placeholder Substructures II: Meta-Fractals, Made of Box-Kites, Fill
Infinite-Dimensional Skies
|
math.RA
|
0704.0026
| 2,007
|
[
-0.013368981890380383,
0.06667573750019073,
-0.029727306216955185,
-0.06860317289829254,
-0.00922247301787138,
0.00014627013297285885,
0.025815460830926895,
0.04602549970149994,
-0.029947372153401375,
-0.04441070929169655,
-0.05907432362437248,
0.01678631268441677,
0.07068870961666107,
0.026116520166397095,
0.016755633056163788,
-0.0053022573702037334,
0.0005501098348759115,
-0.026826296001672745,
-0.012067430652678013,
0.009336775168776512,
-0.025353163480758667,
-0.056137971580028534,
0.006857117637991905,
-0.03951654210686684,
0.05789656564593315,
0.0022690664045512676,
-0.004229915328323841,
-0.00811703409999609,
-0.06479708105325699,
-0.01515872124582529,
0.06806948035955429,
-0.037712324410676956,
0.032599516212940216,
-0.023431751877069473,
-0.059484709054231644,
-0.0018867990002036095,
0.07158006727695465,
-0.014222308062016964,
-0.014040255919098854,
0.023986823856830597,
-0.00846270564943552,
-0.046289168298244476,
0.006551867350935936,
-0.02846640534698963,
-0.05033252760767937,
0.018240446224808693,
0.0030545664485543966,
0.005104496609419584,
0.06479586660861969,
-0.0021369128953665495,
0.012101258151233196,
0.06418023258447647,
0.04642827436327934,
-0.025655921548604965,
-0.05001341179013252,
-0.022625554352998734,
0.04204638674855232,
-0.03760417923331261,
0.06568951904773712,
-0.0038682478480041027,
0.00808983389288187,
0.049818139523267746,
-0.015198125503957272,
0.03575371205806732,
0.025286469608545303,
-0.04048249498009682,
-0.03407147526741028,
0.028006555512547493,
0.0017225495539605618,
-0.03821725398302078,
0.055745210498571396,
-0.045696478337049484,
0.05255039408802986,
0.06984826177358627,
-0.020092470571398735,
0.015154781751334667,
0.018066611140966415,
0.002102483995258808,
-0.014732645824551582,
0.023503027856349945,
0.054566964507102966,
-0.024234838783740997,
0.03806617110967636,
-0.004818703047931194,
0.03879697620868683,
-0.020139919593930244,
-0.003270138753578067,
0.0038515885826200247,
-0.03808895871043205,
0.05172102898359299,
-0.01183138694614172,
-0.003041169373318553,
0.004043458960950375,
0.05352406948804855,
-0.015143048018217087,
0.029684247449040413,
0.003733809804543853,
0.010616001673042774,
-0.048838358372449875,
-0.04079287126660347,
0.012288488447666168,
0.05390752851963043,
0.00782238133251667,
0.030459310859441757,
0.026675237342715263,
0.0506514236330986,
0.021167725324630737,
-0.00662393169477582,
0.0609087236225605,
-0.022996658459305763,
-0.09207013994455338,
-0.031765542924404144,
-0.042657651007175446,
-0.01747458428144455,
-0.00981591921299696,
-0.003699624678120017,
0.044186048209667206,
-0.06997622549533844,
-0.035077136009931564,
0.059993598610162735,
0.05465221032500267,
-0.06661345809698105,
0.021083878353238106,
-0.0006064524641260505,
0.015406043268740177,
0.012113231234252453,
-0.022840213030576706,
-0.024199144914746284,
-0.018988894298672676,
-0.04997909441590309,
-0.010656389407813549,
0.017016464844346046,
-0.03544142469763756,
0.03303827345371246,
0.0029431134462356567,
0.05285918340086937,
-0.044541556388139725,
-0.07110892981290817,
0.054152656346559525,
-0.0008641462191008031,
-0.00736801465973258,
-0.03143273666501045,
-0.014620373025536537,
-0.040815290063619614,
0.0229610837996006,
-0.06195227801799774,
0.02348628081381321,
-0.055351417511701584,
-0.027923043817281723,
-0.026876742020249367,
0.00016052350110840052,
0.05974610894918442,
0.015459227375686169,
0.02194288931787014,
-0.011948127299547195,
-0.0003210207505617291,
0.046100497245788574,
0.029688652604818344,
0.019762372598052025,
0.0008321729255840182,
0.032520245760679245,
0.04173680394887924,
-0.0693482980132103,
0.0403447225689888,
-0.01972460001707077,
-0.021976681426167488,
0.010217186063528061,
0.021114399656653404,
-0.012133576907217503,
0.04929467290639877,
-0.06423059105873108,
-0.027412883937358856,
-0.024051986634731293,
-0.0007325353799387813,
0.018784422427415848,
-0.03878818824887276,
-0.01384457666426897,
-0.049295518547296524,
0.03802124783396721,
0.008692540228366852,
0.07255228608846664,
-0.010712502524256706,
-0.020984025672078133,
0.052973125129938126,
0.010829702019691467,
0.005322524346411228,
-0.002395716728642583,
0.01600000075995922,
0.009348323568701744,
-0.01710466295480728,
0.014073154889047146,
0.03947210684418678,
-0.0397871658205986,
-0.03702079877257347,
0.015336745418608189,
-0.005229560658335686,
0.04722752049565315,
-0.026842303574085236,
0.002875638660043478,
-0.06272247433662415,
0.01123120915144682,
-0.0076982020400464535,
-0.051112692803144455,
-0.013758322224020958,
-0.01407103706151247,
0.1320101022720337,
-0.03513875976204872,
0.04176769778132439,
0.01889960467815399,
0.008396695367991924,
0.06803087890148163,
0.0011804886162281036,
-0.0035223274026066065,
0.005366870667785406,
-0.012401971034705639,
-0.04548291116952896,
0.0030363742262125015,
-0.06480246037244797,
0.0042007737793028355,
0.0368049331009388,
0.03574468567967415,
0.002137827454134822,
-0.0023249026853591204,
0.0008341768407262862,
0.1006726622581482,
0.02463584765791893,
0.004633055999875069,
-0.034898530691862106,
-0.02150409296154976,
-0.025228256359696388,
-0.030585892498493195,
-0.0814230814576149,
0.05077569559216499,
-0.0027538181748241186,
-0.030753083527088165,
-0.00604505930095911,
-0.030515655875205994,
0.04115871340036392,
0.0561806783080101,
0.016447538509964943,
0.04748563468456268,
0.025940444320440292,
0.010444498620927334,
-0.05635732039809227,
-0.023734990507364273,
-0.04546617344021797,
0.0007683210424147546,
-0.017900563776493073,
-0.06293082237243652,
0.04728158563375473,
0.019582726061344147,
-0.002638964680954814,
0.03388488292694092,
0.07403496652841568,
-0.010821104981005192,
-0.011549847200512886,
-0.01638062857091427,
0.05507845804095268,
-0.016383720561861992,
-0.02010883018374443,
0.04269785061478615,
-0.04432199150323868,
-0.01385582983493805,
-0.03574569895863533,
-0.04777967184782028,
-0.052411485463380814,
-0.01228545606136322,
-0.02381310984492302,
0.015796856954693794,
-0.00505822291597724,
0.041216280311346054,
-0.025346314534544945,
0.0864097997546196,
0.03475034981966019,
-0.02461066283285618,
0.0010197842493653297,
0.04856272414326668,
-0.013944520615041256,
-0.061660319566726685,
0.04731615260243416,
-0.00038415947346948087,
-0.01881614699959755,
-0.037286948412656784,
0.021154312416911125,
-0.009643240831792355,
0.04457976296544075,
0.026808690279722214,
0.02630551904439926,
-0.026396753266453743,
0.02890942431986332,
-0.039451319724321365,
0.000388505810406059,
0.024428850039839745,
0.0024664353113621473,
0.041259992867708206,
0.05860023573040962,
0.03777579218149185,
-0.006856327410787344,
0.0007171148317866027,
-0.008295753039419651,
-0.002890174277126789,
0.039595019072294235,
0.02543863281607628,
-0.04495645686984062,
0.015198711305856705,
0.0005079617840237916,
0.04963328316807747,
0.007267700508236885,
-0.0010187312727794051,
0.0006139818578958511,
0.01176791824400425,
0.05697532743215561,
-0.017220662906765938,
-0.00244557554833591,
-0.04159892722964287,
0.0391874723136425,
0.028106532990932465,
-0.006776483729481697,
0.04946530982851982,
-0.02553148940205574,
0.020165475085377693,
-0.014795527793467045,
0.046223945915699005,
-0.05038931220769882,
0.011465129442512989,
0.07431037724018097,
-0.018075771629810333,
0.002162989927455783,
-0.031745631247758865,
-0.024381306022405624,
0.02430845983326435,
0.024422286078333855,
0.014457170851528645,
-0.02453828975558281,
-0.0048599885776638985,
-0.017050232738256454,
-0.039429549127817154,
0.006195122841745615,
-0.01731245405972004,
-0.004521706607192755,
-0.003985179588198662,
-0.014940516091883183,
-0.05012394115328789,
-0.046711646020412445,
0.0024586678482592106,
0.0180502962321043,
-0.02834692969918251,
0.014020116068422794,
0.030687440186738968,
-0.003999629057943821,
-0.03327879309654236,
-0.013112704269587994,
-0.013040680438280106,
-0.023373451083898544,
-0.0038796947337687016,
0.09674235433340073,
0.04173823818564415,
-0.04285106435418129,
0.07091216742992401,
0.05129987373948097,
0.04500289633870125,
-0.020822839811444283,
0.01431821659207344,
-0.016994228586554527,
0.02814803272485733,
0.06668266654014587,
0.016596077010035515,
0.04245644435286522,
-0.01320093497633934,
-0.004163752309978008,
-0.03954361379146576,
-0.04937438666820526,
0.007929231971502304,
0.03350415825843811,
0.03877508267760277,
-0.0030581876635551453,
-0.05418553203344345,
0.006787856109440327,
0.051336560398340225,
0.015188830904662609,
0.05235552787780762,
-0.0022924889344722033,
0.020835209637880325,
-0.03618729114532471,
-0.02366316318511963,
0.03703174367547035,
-0.0461660660803318,
-0.02006189338862896,
-0.03002999722957611,
0.01936158537864685,
-0.012385077774524689,
-0.031988371163606644,
0.022186869755387306,
-0.007940872572362423,
-0.023447604849934578,
-0.008916505612432957,
-0.008178888820111752,
-0.035900212824344635,
-0.03704151138663292,
0.009346531704068184,
-0.00840644259005785,
-0.02612335793673992,
-0.01420733705163002,
-0.017144903540611267,
0.028397010639309883,
0.011284144595265388,
-0.0115686459466815,
-0.058675751090049744,
0.08767861872911453,
-0.025376543402671814,
0.024319155141711235,
0.01617586240172386,
0.02997729741036892,
-0.11296239495277405,
0.07033578306436539,
-0.0015927067724987864,
0.07362054288387299,
-0.015963390469551086,
0.020297585055232048,
0.00020053682965226471,
-0.038990166038274765,
0.05866388604044914,
-0.03344237804412842,
-0.0079050837084651,
0.027894457802176476,
-0.02677314728498459,
-0.02410668320953846,
0.002645410830155015,
-0.020215319469571114,
-0.006610584445297718,
0.05429970845580101,
0.0042295693419873714,
-0.006525582633912563,
0.04997898265719414,
-0.08352258056402206,
-0.023360438644886017,
0.01858789101243019,
0.032142676413059235,
-0.02347288839519024,
0.024450616911053658,
0.06551502645015717,
-0.04417416825890541,
0.019711267203092575,
0.02288079634308815,
0.038231752812862396,
0.07219818979501724,
0.01513806264847517,
-0.032174814492464066,
-0.038562048226594925,
0.02992473542690277,
0.052010368555784225,
0.0027522589080035686,
0.004101298283785582,
0.010015849024057388,
0.07222995907068253,
-0.03161293640732765,
-0.019186237826943398,
-0.040476396679878235,
0.08008445054292679,
0.035740721970796585,
-0.003122533205896616,
-0.015504754148423672,
-0.03858960047364235,
0.06873857975006104,
-0.018997449427843094,
0.04182695969939232,
-0.049526844173669815,
-0.018695291131734848,
0.020860090851783752,
0.052976734936237335,
-0.008380889892578125,
0.0018292737659066916,
0.00036664234357886016,
-0.0026138657703995705,
-0.05018661171197891,
-0.019186336547136307,
0.031401410698890686,
-0.06753181666135788,
0.02838071808218956,
0.07239356637001038,
0.026376022025942802,
0.0029800154734402895,
-0.023961136117577553,
-0.0655587911605835,
0.0010509609710425138,
0.04265684261918068,
0.009918390773236752,
-0.04273141175508499,
-0.015582739375531673,
-0.03657679259777069,
-0.008370979689061642,
0.010256004519760609,
-0.023122137412428856,
0.02051791548728943,
-0.018919842317700386,
-0.055450137704610825,
0.0455559603869915,
0.011562268249690533,
0.061248816549777985,
0.014165614731609821,
0.010155143216252327,
0.03448307886719704,
0.018644381314516068,
0.011508211493492126,
-0.0015119216404855251,
0.024069620296359062,
0.05252191424369812,
-0.06925323605537415,
-0.03703334927558899,
0.028963342308998108,
-0.024276163429021835,
0.013322744518518448,
0.0509197823703289,
0.06920403987169266,
0.04904979467391968,
-0.012809386476874352,
0.0029783148784190416,
-0.04088408499956131,
-0.09711532294750214,
-0.0015342101687565446,
0.0016573314787819982,
-0.010539323091506958,
0.01593477837741375,
-0.008899195119738579,
-0.07247811555862427,
0.06925550848245621,
-0.04573650658130646,
-0.10570036619901657,
0.03333425149321556,
0.015547997318208218,
0.012857740744948387,
0.042746201157569885,
-0.03149764984846115,
-0.007842193357646465,
0.016676930710673332,
-0.05178293213248253,
-0.05782761052250862,
0.017873240634799004,
0.04232063889503479,
-0.007229618728160858,
0.047051601111888885,
0.03260645270347595,
0.029445331543684006,
0.02554936148226261,
-0.002258771099150181,
-0.07534602284431458,
-0.024159669876098633,
0.07653733342885971,
0.011785623617470264,
0.004349106922745705,
-0.03302447125315666,
-0.036389369517564774,
0.055036529898643494,
-0.03861108049750328,
-0.009375783614814281,
0.009170783683657646,
-0.017726261168718338,
-0.034137580543756485,
-0.06333834677934647,
-0.030701538547873497,
0.010488923639059067,
0.08156364411115646,
0.019145246595144272,
0.014173563569784164,
-0.022718220949172974,
-0.11731529235839844,
-0.03901220113039017,
-0.00036480443668551743,
0.033376824110746384,
0.000037819194403709844,
0.021545525640249252,
-0.01232926920056343,
0.029366385191679,
0.04222901165485382,
-0.030548138543963432,
-0.042265523225069046,
0.051253147423267365,
0.007489589508622885,
-0.013184097595512867,
-0.002996181370690465,
-0.016119524836540222,
-0.0038459887728095055,
0.02329406887292862,
-0.004484777804464102,
-0.029239680618047714,
0.05602264404296875,
-0.005368449725210667,
-0.031124362722039223,
0.02698392979800701,
0.001979266991838813,
0.02056923694908619,
-0.034773971885442734,
-0.03398466855287552,
-0.012415505014359951,
0.003431004472076893,
0.004696421325206757,
0.013043531216681004,
0.047531746327877045,
-0.028394095599651337,
-0.04319245368242264,
-0.024313949048519135,
0.009741030633449554,
0.06392485648393631,
-0.052170004695653915,
0.05884411931037903,
0.058157846331596375,
-0.010379660874605179,
-0.0042039440013468266,
-0.02659549005329609,
0.006870647892355919,
0.00803984422236681,
0.0013153433101251721,
-0.03327319025993347,
-0.01869799941778183,
-0.012069307267665863,
-0.0683465451002121,
0.08887945860624313,
-0.05058961361646652,
0.042573586106300354,
-0.08813111484050751,
0.006903631612658501,
-0.07336767762899399,
-0.009293047711253166,
-0.05905653536319733,
0.011600097641348839,
-0.02844790183007717,
0.010596644133329391,
-0.027653712779283524,
0.012496193870902061,
0.0809992328286171,
-0.03476066514849663,
-0.03228556364774704,
-0.016184883192181587,
0.008067372255027294,
-0.03069283254444599,
0.01009791623800993,
-0.042591966688632965,
0.02519148960709572,
-0.008783597499132156,
0.0222660880535841,
0.0032147082965821028,
0.012311200611293316,
-0.017039867118000984,
-0.02129504457116127,
0.06744586676359177,
-0.028283577412366867,
0.008498105220496655,
0.02463427372276783,
-0.008088850416243076,
-0.009328763000667095,
0.052497658878564835,
0.10737354308366776,
-0.03791242465376854,
0.06278221309185028,
-0.011371287517249584,
-0.02860710397362709,
-0.02677028439939022,
-0.03247388079762459,
-0.01173936016857624,
0.011019015684723854,
-0.02803140878677368,
0.026693733409047127,
0.0024569123052060604,
0.008656203746795654,
-0.0314275324344635,
-0.028238186612725258,
-0.005104363895952702,
0.00804930366575718,
-0.045136772096157074,
0.018913814797997475,
-0.01338972058147192,
0.0013413125416263938,
-0.02964000776410103,
-0.026837583631277084,
-0.023394761607050896,
-0.020761143416166306,
0.015757407993078232,
0.030900701880455017,
0.0030384708661586046,
-0.045293278992176056,
0.04130889102816582,
0.02595793455839157,
0.016665495932102203,
-0.04088975116610527,
-0.015472783707082272,
0.004888057708740234,
-0.016122641041874886,
-0.05456642061471939,
-0.04073738306760788,
-0.050154514610767365,
0.05763061344623566,
0.032789893448352814,
-0.012064856477081776,
-0.0512210913002491,
0.00477564986795187,
-0.0011917006922885776,
-0.019585438072681427,
-0.04088497906923294,
0.010933034121990204,
0.046838998794555664,
0.004285725299268961,
0.02066143974661827,
-0.0369761660695076,
0.02060077339410782,
-0.012215136550366879,
0.004515783861279488,
-0.003522445447742939,
0.02831702120602131,
-0.014763617888092995,
-0.05579590052366257,
0.0058500212617218494,
0.012308517470955849,
0.009329094551503658,
-0.006260606925934553,
0.011221627704799175,
-0.02043977566063404,
0.007543749641627073,
-0.06900926679372787,
0.011263852939009666,
0.028199447318911552,
-0.010651569813489914,
-0.026497701182961464,
-0.06874936074018478,
-0.017165934666991234,
-0.004448805004358292,
-0.04497721791267395,
-0.016714800149202347,
-0.057327378541231155,
0.020454052835702896,
0.017743773758411407,
-0.013226811774075031,
-0.002179507166147232,
-0.03323280066251755,
0.023068411275744438,
-0.04669634625315666,
-0.017053069546818733,
-0.02298141084611416,
-0.0022192494943737984,
-0.026929745450615883,
-0.03659490868449211,
-0.004717335104942322,
0.017986992374062538,
0.022199194878339767,
-0.002812630031257868,
-0.020381569862365723,
-0.03852221742272377,
-0.07979893684387207,
0.0352732390165329,
0.03552733734250069,
-0.011437734588980675,
-0.016507258638739586,
0.008061305619776249,
0.015062875114381313,
-0.04144461825489998,
-0.012362539768218994,
0.046249087899923325,
0.01537716668099165,
0.04164762422442436,
0.08182337880134583,
-0.03837459161877632,
0.018507273867726326,
-0.0060878111980855465,
0.014418913051486015,
0.057244673371315,
-0.02558864653110504,
-0.0026332924608141184,
0.01944177784025669,
0.04517247900366783
] |
[
1.2374937534332275,
3.874720573425293
] |
Rings and Algebras
|
Mathematics
|
math-RA
|
na
|
na
|
2007-04-02T19:17:14
|
We describe a peculiar fine structure acquired by the in-plane optical phonon
at the Gamma-point in graphene when it is brought into resonance with one of
the inter-Landau-level transitions in this material. The effect is most
pronounced when this lattice mode (associated with the G-band in graphene Raman
spectrum) is in resonance with inter-Landau-level transitions 0 -> (+,1) and
(-,1) -> 0, at a magnetic field B_0 ~ 30 T. It can be used to measure the
strength of the electron-phonon coupling directly, and its filling-factor
dependence can be used experimentally to detect circularly polarized lattice
modes.
|
Filling-Factor-Dependent Magnetophonon Resonance in Graphene
|
cond-mat.mes-hall
|
0704.0027
| 2,007
|
[
0.006308692507445812,
0.03945682570338249,
-0.006378369405865669,
-0.049497269093990326,
0.045862309634685516,
0.029740311205387115,
-0.013476892374455929,
-0.01161932572722435,
-0.022376252338290215,
0.02421519346535206,
-0.05849556252360344,
0.05409359559416771,
-0.0381295420229435,
-0.04534061625599861,
0.044295813888311386,
-0.03773423284292221,
0.03267694264650345,
-0.0002370307338424027,
0.018821626901626587,
0.019090980291366577,
-0.06316361576318741,
-0.013392649590969086,
-0.010428695939481258,
-0.01687970757484436,
0.08133750408887863,
0.04454942047595978,
0.036856357008218765,
-0.020728647708892822,
0.009670952335000038,
0.014402324333786964,
0.014157970435917377,
-0.030060769990086555,
0.006084141321480274,
-0.02093510888516903,
-0.029584327712655067,
-0.003881259122863412,
0.03116610273718834,
0.00845395214855671,
0.041758906096220016,
0.03652828186750412,
0.016320092603564262,
-0.047258589416742325,
-0.00003302990080555901,
-0.03219514712691307,
0.006138907745480537,
0.04246159642934799,
-0.033481087535619736,
-0.007080069277435541,
-0.019729290157556534,
0.013965096324682236,
-0.03735537454485893,
0.049893900752067566,
0.04140369966626167,
-0.05190723389387131,
-0.0025481332559138536,
0.010019738227128983,
0.019405191764235497,
-0.03589131683111191,
0.07414086163043976,
-0.008526233956217766,
0.005415433552116156,
0.06932856887578964,
-0.01582574099302292,
0.06248711422085762,
-0.00017825710528995842,
-0.033035919070243835,
-0.02438274212181568,
0.010539262555539608,
-0.05116555467247963,
-0.008853532373905182,
0.013085520826280117,
-0.05672638118267059,
-0.005368869751691818,
0.00691217090934515,
0.011529460549354553,
0.04046568274497986,
0.02543274126946926,
0.041936371475458145,
0.009948905557394028,
0.013452955521643162,
0.005467729177325964,
0.0054227858781814575,
-0.004834367893636227,
0.01986665651202202,
0.04245574027299881,
-0.01102507021278143,
0.008317767642438412,
0.0290396586060524,
-0.051747795194387436,
0.020239273086190224,
0.04274832457304001,
-0.04838427156209946,
0.013943661004304886,
0.01811159960925579,
-0.05941900610923767,
0.049330003559589386,
0.002360008889809251,
0.0009259029757231474,
-0.054781924933195114,
-0.014284651726484299,
-0.007294620852917433,
0.00009813808719627559,
-0.04448756203055382,
-0.031633492559194565,
0.01087640505284071,
0.05178220570087433,
-0.02755994349718094,
-0.057677142322063446,
0.012029742822051048,
-0.0057506440207362175,
-0.07295158505439758,
0.007084712851792574,
0.03509308397769928,
-0.0009961141040548682,
-0.038442909717559814,
-0.06741131842136383,
0.08441484719514847,
-0.05506156384944916,
0.02502530813217163,
0.039374787360429764,
0.03800329938530922,
-0.03640785813331604,
-0.018333332613110542,
0.019745714962482452,
-0.018147919327020645,
0.02457299269735813,
-0.022189561277627945,
0.021927140653133392,
0.01231514010578394,
0.00755264749750495,
0.0009980810573324561,
0.015961559489369392,
-0.01487142127007246,
0.014026313088834286,
0.046151772141456604,
0.028706321492791176,
-0.03713194653391838,
-0.009413646534085274,
0.012559483759105206,
-0.009472326375544071,
-0.024325605481863022,
-0.013947803527116776,
0.007291193585842848,
-0.09240101277828217,
0.0015021086437627673,
-0.018413212150335312,
0.02970612421631813,
-0.0728139653801918,
-0.009778487496078014,
0.029477687552571297,
0.032876450568437576,
0.021668007597327232,
0.03637843579053879,
0.03411311283707619,
-0.055618252605199814,
-0.03834965452551842,
0.03971372917294502,
-0.019288934767246246,
0.06426632404327393,
0.016578419134020805,
0.0036913673393428326,
0.008422112092375755,
-0.08030037581920624,
0.05436382442712784,
-0.0133428443223238,
-0.00980088859796524,
0.054591432213783264,
-0.026329083368182182,
-0.02783159166574478,
0.060281313955783844,
-0.048370394855737686,
-0.019461579620838165,
-0.020333420485258102,
0.007872172631323338,
0.0010709159541875124,
0.065976083278656,
0.008721559308469296,
-0.05899075046181679,
0.09173839539289474,
-0.0021338355727493763,
0.061784740537405014,
-0.005498894490301609,
0.03748740628361702,
-0.00475583178922534,
0.003479852108284831,
0.024415545165538788,
-0.03167976811528206,
-0.008876368403434753,
-0.03237777575850487,
0.0004579963569995016,
0.0015112238470464945,
0.005003806669265032,
-0.05362941697239876,
-0.09491415321826935,
0.025850938633084297,
-0.08492714911699295,
0.03867464140057564,
-0.013065324164927006,
-0.056057754904031754,
-0.028361421078443527,
-0.07288647443056107,
-0.04940411075949669,
0.03412455692887306,
-0.04345288500189781,
0.004576424136757851,
0.03611007332801819,
0.026197068393230438,
0.016538964584469795,
0.04132958501577377,
0.038131359964609146,
0.0972808375954628,
0.03926466405391693,
0.003958661109209061,
-0.0028326897881925106,
-0.03304382413625717,
-0.0008892114856280386,
0.005234162788838148,
-0.04325944185256958,
-0.010878942906856537,
0.056749094277620316,
0.010789439082145691,
0.037261851131916046,
0.04093492031097412,
-0.026362745091319084,
0.02227194793522358,
-0.03276895731687546,
-0.016518140211701393,
0.027036424726247787,
-0.004274703096598387,
-0.030633868649601936,
0.021222680807113647,
-0.011067156679928303,
0.00921869557350874,
-0.028778374195098877,
-0.006388209760189056,
-0.0046103461645543575,
-0.05722060054540634,
-0.0131764505058527,
-0.022217318415641785,
0.04762684553861618,
-0.009284992702305317,
0.018581587821245193,
-0.021044809371232986,
-0.04607343301177025,
-0.05931372940540314,
0.001049991580657661,
-0.0024753492325544357,
0.013827208429574966,
-0.0050301579758524895,
0.03223898634314537,
0.07079697400331497,
-0.022158240899443626,
0.05396763235330582,
0.06107335165143013,
0.037181682884693146,
0.027784274891018867,
-0.025182224810123444,
0.05519094318151474,
-0.06596863269805908,
-0.0576338917016983,
-0.004354425240308046,
-0.05083717033267021,
-0.019834036007523537,
-0.016802966594696045,
-0.03321067988872528,
-0.016962982714176178,
0.0514235757291317,
-0.016365882009267807,
-0.014420664869248867,
-0.03260239586234093,
-0.00894995778799057,
0.0649968758225441,
0.06912469863891602,
0.03567730262875557,
-0.006758429575711489,
0.006456817500293255,
0.05069909617304802,
-0.005366032477468252,
0.05194692686200142,
-0.043670956045389175,
-0.09117633104324341,
-0.018869444727897644,
-0.03540091589093208,
-0.03219841420650482,
-0.04014855623245239,
0.01620197296142578,
0.021523205563426018,
-0.0069795772433280945,
-0.008160069584846497,
0.07625389099121094,
-0.046478189527988434,
-0.039602067321538925,
-0.007169071119278669,
0.047929588705301285,
0.027477554976940155,
0.013136367313563824,
0.06287530809640884,
0.024843329563736916,
0.005890856962651014,
0.04630918800830841,
0.05440447852015495,
-0.030158143490552902,
-0.005847446154803038,
0.023102952167391777,
-0.039698146283626556,
0.0003242907114326954,
0.017905117943882942,
-0.023425249382853508,
-0.025929711759090424,
0.04111699387431145,
-0.011946126818656921,
0.028137769550085068,
0.026643473654985428,
-0.02218586578965187,
-0.001747796544805169,
0.06837422400712967,
0.002966783009469509,
-0.007013148628175259,
0.04493475332856178,
0.003811872098594904,
0.014606221579015255,
-0.019245639443397522,
0.018415307626128197,
-0.09755661338567734,
-0.06577521562576294,
0.020996563136577606,
-0.0071189203299582005,
0.033124327659606934,
-0.048902977257966995,
-0.02481354959309101,
-0.002283006440848112,
-0.011042830534279346,
-0.047576770186424255,
-0.018599700182676315,
0.033622730523347855,
0.019765987992286682,
-0.016619263216853142,
0.06898224353790283,
-0.03846871852874756,
0.0169350728392601,
0.00017414249305147678,
-0.05720549076795578,
0.004760331939905882,
-0.039148129522800446,
0.015281704254448414,
-0.002965083811432123,
-0.005292403511703014,
-0.004032623954117298,
0.022255200892686844,
-0.007052499335259199,
-0.06881982833147049,
0.010362274944782257,
0.0021473695524036884,
0.009072630666196346,
-0.0211726576089859,
-0.014108071103692055,
0.07960356026887894,
0.014719146303832531,
0.029845627024769783,
-0.002820195397362113,
0.03750481829047203,
-0.06228343024849892,
0.04380502551794052,
-0.049474529922008514,
-0.017031555995345116,
0.017033806070685387,
0.021466797217726707,
0.0657406747341156,
0.05335904657840729,
-0.020452041178941727,
-0.032782264053821564,
-0.056692104786634445,
0.0729779303073883,
-0.012743538245558739,
0.02334613725543022,
-0.06260866671800613,
-0.08300875872373581,
-0.05027010664343834,
-0.026271745562553406,
-0.030043216422200203,
-0.012994232587516308,
0.006911113858222961,
0.029180049896240234,
0.0262914951890707,
0.03468719497323036,
-0.04364243149757385,
-0.04874064028263092,
0.010649766772985458,
-0.037256885319948196,
-0.01586085744202137,
-0.036416925489902496,
-0.019734254106879234,
-0.010391144081950188,
0.03648825362324715,
-0.0033992892131209373,
-0.03592909127473831,
0.0055400775745511055,
-0.039561327546834946,
0.016767743974924088,
0.03999278321862221,
-0.01311628520488739,
-0.05268699303269386,
0.006521455477923155,
-0.00046446581836789846,
-0.019677255302667618,
-0.011272420175373554,
-0.03192466124892235,
-0.025355862453579903,
0.0356447733938694,
-0.03914608061313629,
-0.027349967509508133,
-0.03201897442340851,
-0.002804201329126954,
-0.05293949320912361,
0.03560072183609009,
0.031082918867468834,
0.03349282220005989,
-0.02842680551111698,
0.047839853912591934,
-0.04870029538869858,
0.03709680959582329,
0.0872097760438919,
-0.01661740057170391,
-0.0077699632383883,
-0.04295789822936058,
0.013142476789653301,
0.0035402255598455667,
-0.018976233899593353,
0.031176505610346794,
-0.044684186577796936,
0.06090467423200607,
0.02365335077047348,
0.016261881217360497,
0.026922747492790222,
-0.048248231410980225,
0.04079340770840645,
-0.01698782853782177,
-0.03680674731731415,
0.030879557132720947,
0.0627862960100174,
0.067245714366436,
-0.07206714153289795,
0.05565778911113739,
-0.009023923426866531,
0.024368494749069214,
0.002211981685832143,
-0.00020927039440721273,
-0.03598034381866455,
0.015947595238685608,
-0.014160466380417347,
0.013519811443984509,
-0.05659663677215576,
-0.01833518221974373,
-0.010889244265854359,
0.11375244706869125,
-0.05770852416753769,
-0.000036928613553754985,
0.018635811284184456,
0.06800031661987305,
0.009030265733599663,
0.017463842406868935,
-0.017189564183354378,
-0.07492498308420181,
0.03176785632967949,
-0.007683882489800453,
0.0657208263874054,
0.0066911447793245316,
-0.01379700843244791,
0.017865832895040512,
0.029371226206421852,
0.02659708261489868,
-0.008119039237499237,
0.04601740837097168,
0.01794533059000969,
-0.0219824630767107,
0.002894126810133457,
-0.01295862253755331,
-0.03555447608232498,
0.01770227961242199,
-0.027879750356078148,
0.03144421800971031,
0.004585170652717352,
0.03536491096019745,
-0.03521978482604027,
-0.00927721243351698,
-0.01119979191571474,
-0.006426061969250441,
0.04203999787569046,
-0.022097617387771606,
-0.04977076128125191,
0.004019619431346655,
0.013889801688492298,
-0.004418378695845604,
-0.002683326369151473,
0.03305460140109062,
-0.0351564846932888,
0.004404139705002308,
0.0028377159032970667,
0.010532556101679802,
-0.039378874003887177,
-0.03062634915113449,
0.03619705140590668,
-0.010839475318789482,
-0.04173458740115166,
-0.048829127103090286,
0.019720282405614853,
-0.04523124545812607,
-0.07192229479551315,
-0.010363157838582993,
0.004068356938660145,
-0.012952915392816067,
0.019567599520087242,
0.010562948882579803,
0.07999946177005768,
0.0580025389790535,
-0.06318946182727814,
0.04235689342021942,
-0.010562884621322155,
-0.05071019008755684,
-0.008199523203074932,
-0.014791483990848064,
0.030250994488596916,
-0.017181076109409332,
-0.048421166837215424,
-0.05318855866789818,
0.07131917774677277,
-0.04262375086545944,
-0.05548003688454628,
0.08115154504776001,
-0.002490035956725478,
0.034087587147951126,
0.007975411601364613,
0.028973711654543877,
0.011462965980172157,
0.03716210648417473,
-0.016489701345562935,
0.012441499158740044,
-0.0011574453674256802,
-0.03548102080821991,
0.0396677628159523,
0.011794713325798512,
-0.01283740159124136,
-0.0004139426746405661,
0.022781450301408768,
0.059224314987659454,
-0.014895619824528694,
-0.031540755182504654,
0.005360280629247427,
-0.05897736921906471,
-0.04833526164293289,
0.0020128474570810795,
-0.03148899972438812,
0.032624222338199615,
-0.01989520899951458,
-0.0025216792710125446,
-0.03061584010720253,
-0.021651899442076683,
-0.008292638696730137,
-0.06114860996603966,
0.03282421454787254,
0.02093994989991188,
-0.0023202227894216776,
0.023421574383974075,
-0.018616676330566406,
-0.013068723492324352,
-0.03052639588713646,
-0.027701271697878838,
-0.04836885258555412,
0.024395586922764778,
-0.05291502922773361,
-0.061643335968256,
-0.03393053263425827,
-0.013946904800832272,
0.03808861970901489,
-0.014909209683537483,
0.03127234801650047,
0.0518207773566246,
-0.010107859969139099,
-0.0257424209266901,
-0.022979790344834328,
0.006683948449790478,
0.014517299830913544,
0.01331342477351427,
0.03817731514573097,
-0.024159079417586327,
0.06331205368041992,
-0.023668725043535233,
-0.015910157933831215,
0.06806132197380066,
-0.0013802722096443176,
-0.024102292954921722,
-0.053243253380060196,
-0.06425826996564865,
0.0025629340671002865,
-0.01143938023597002,
0.002134348964318633,
-0.03635050356388092,
-0.03605552762746811,
0.0036677736788988113,
0.05254725366830826,
0.06297483295202255,
0.0032855095341801643,
0.01744496449828148,
-0.038730937987565994,
0.010462491773068905,
0.032534949481487274,
0.023966535925865173,
0.005102235823869705,
-0.061987414956092834,
0.005227844696491957,
0.02515038475394249,
0.012112485244870186,
0.009981593117117882,
-0.03192857280373573,
0.03969832509756088,
-0.05486834794282913,
0.03441532328724861,
-0.056763652712106705,
0.022631119936704636,
-0.02576957456767559,
-0.04586935043334961,
-0.07321809232234955,
0.0030306680127978325,
-0.07788581401109695,
0.02682129666209221,
-0.012906872667372227,
-0.03624145686626434,
-0.10190807282924652,
0.030149754136800766,
0.006700692232698202,
0.0029885077383369207,
0.02515619806945324,
-0.011236176826059818,
0.0031501969788223505,
0.04697326198220253,
0.025420265272259712,
0.012093687430024147,
-0.014216786250472069,
0.050155285745859146,
0.06224560737609863,
0.01608956605195999,
-0.01661766692996025,
-0.003809650195762515,
-0.036342181265354156,
0.07186385989189148,
0.0014260364696383476,
-0.030481992289423943,
-0.01038905419409275,
0.018182672560214996,
-0.006510845385491848,
0.06852956116199493,
0.0335790291428566,
0.005144954193383455,
0.0037272325716912746,
0.0056151822209358215,
0.02928038313984871,
0.059456318616867065,
0.008955040015280247,
0.003982689697295427,
0.014720520004630089,
-0.032435342669487,
-0.02181287854909897,
0.03751850873231888,
0.010517450049519539,
-0.022491753101348877,
-0.036180928349494934,
-0.07415157556533813,
-0.09643401950597763,
-0.019470645114779472,
-0.010382263921201229,
-0.04457097500562668,
-0.02774072252213955,
-0.0061251516453921795,
-0.011036548763513565,
-0.04599675536155701,
0.02040104568004608,
-0.04972148314118385,
0.01836363412439823,
-0.046911634504795074,
-0.01880793087184429,
-0.0346822515130043,
0.022907353937625885,
0.06016916409134865,
-0.058484505861997604,
0.02028474397957325,
-0.020627116784453392,
-0.0050093745812773705,
-0.0033597894944250584,
-0.004773916210979223,
-0.030726909637451172,
0.030865555629134178,
0.03356027975678444,
0.007940477691590786,
-0.04029079154133797,
0.004471899010241032,
0.028938964009284973,
-0.044602613896131516,
0.03439202159643173,
0.0053261942230165005,
0.02871236391365528,
-0.014550874009728432,
0.04481648653745651,
-0.046701643615961075,
0.004839406814426184,
0.012864873744547367,
-0.024059081450104713,
0.06693277508020401,
-0.012506692670285702,
-0.0013316409895196557,
0.0172764603048563,
0.0012800275580957532,
0.03762016072869301,
0.05268033221364021,
0.051235467195510864,
0.0889430046081543,
-0.0176613200455904,
0.004556485451757908,
-0.04285922273993492,
0.022342849522829056,
0.030133452266454697,
-0.026812653988599777,
0.01426071859896183,
-0.010952428914606571,
0.06407416611909866,
-0.001958176027983427,
-0.05341285094618797,
-0.02270178683102131,
-0.018168646842241287,
0.0877993181347847,
0.045333582907915115,
-0.0007885816739872098,
0.014328217133879662,
-0.03618605434894562,
0.017386119812726974,
-0.016914041712880135,
0.022432900965213776,
-0.023245414718985558,
-0.03314293175935745,
0.024163007736206055,
0.02066008560359478,
0.04917799308896065,
0.006838210858404636,
0.01839328370988369,
0.0009379631374031305,
0.011876224540174007,
0.0384134016931057,
-0.059857867658138275,
0.02865658700466156,
0.03819334879517555,
-0.014987291768193245,
-0.0344892293214798,
-0.024832047522068024,
0.01614639163017273,
-0.010801771655678749,
0.005443185102194548,
-0.012675369158387184,
-0.01119375042617321,
0.05461112782359123,
0.07514315098524094,
-0.02543301321566105,
0.04701656103134155,
0.017131416127085686,
-0.010828059166669846,
0.058904387056827545,
0.0030085581820458174,
0.08272074908018112,
-0.02482345700263977,
0.023149453103542328
] |
[
9.667925834655762,
-2.2629969120025635
] |
Mesoscale and Nanoscale Physics
|
Condensed-Matter Physics
|
cond-mat-mes-hall
|
na
|
na
|
2007-04-02T15:36:29
|
We prove pfaffian and hafnian versions of Lieb's inequalities on determinants
and permanents of positive semi-definite matrices. We use the hafnian
inequality to improve the lower bound of R\'ev\'esz and Sarantopoulos on the
norm of a product of linear functionals on a real Euclidean space (this subject
is sometimes called the `real linear polarization constant' problem).
|
Pfaffians, hafnians and products of real linear functionals
|
math.CA math.PR
|
0704.0028
| 2,007
|
[
-0.012024356052279472,
0.004880803637206554,
-0.01563846506178379,
-0.016118478029966354,
0.03765144944190979,
-0.007967870682477951,
0.04572436958551407,
0.030083104968070984,
-0.02747967094182968,
-0.0074378810822963715,
-0.07404947280883789,
-0.00016474789299536496,
-0.0007920264615677297,
-0.015416535548865795,
0.005714690312743187,
-0.0005820738151669502,
0.011289626359939575,
-0.01984819583594799,
-0.014417482540011406,
-0.007553366012871265,
-0.036070458590984344,
0.007267196197062731,
-0.02753380872309208,
-0.027673248201608658,
0.11832749098539352,
0.02166168764233589,
0.050238098949193954,
-0.01374723855406046,
0.0007005888619460166,
-0.017519066110253334,
0.032629139721393585,
-0.04112648963928223,
-0.028641145676374435,
-0.051300305873155594,
-0.0456630140542984,
-0.02419392764568329,
0.07670524716377258,
-0.014249847270548344,
0.03455597907304764,
0.022435862571001053,
0.059412285685539246,
0.002988508902490139,
-0.006691749207675457,
-0.05936688557267189,
0.017480570822954178,
-0.03922335058450699,
0.005129343364387751,
0.0010227184975519776,
0.04375860095024109,
-0.013973304070532322,
0.003561219200491905,
0.02119736187160015,
-0.011886431835591793,
-0.07461747527122498,
-0.00856730155646801,
0.043491896241903305,
0.05410536378622055,
-0.05057293549180031,
0.010087007656693459,
-0.00822928361594677,
0.004111192654818296,
0.057940177619457245,
-0.02473253570497036,
0.004771040286868811,
-0.005107690580189228,
-0.07680083066225052,
0.002837209030985832,
0.04384302720427513,
-0.05847068130970001,
0.029970476403832436,
-0.015471759252250195,
0.013702807947993279,
0.075253926217556,
-0.005295604467391968,
-0.029609709978103638,
0.007355801295489073,
0.0037175598554313183,
0.018963942304253578,
0.04098128899931908,
0.045867305248975754,
0.06996748596429825,
-0.012761018238961697,
0.05399923399090767,
0.04336320981383324,
0.04949088767170906,
0.02055400423705578,
0.058613117784261703,
0.0036499330308288336,
-0.01663943938910961,
0.00013837771257385612,
0.013402282260358334,
-0.0039028783794492483,
-0.0036758652422577143,
0.11545868217945099,
-0.030819706618785858,
0.029460182413458824,
-0.01520454790443182,
0.004096849821507931,
-0.037417780607938766,
-0.013015422970056534,
0.06272954493761063,
0.016317445784807205,
0.024889972060918808,
0.010744530707597733,
0.06979750096797943,
-0.004926781635731459,
0.04887878894805908,
0.005930535960942507,
-0.013304485939443111,
-0.016726616770029068,
-0.08733125776052475,
-0.007333636749535799,
-0.02248905785381794,
-0.04064667597413063,
-0.010792466811835766,
-0.00778633588925004,
0.05219171941280365,
-0.1094471886754036,
-0.04581313207745552,
0.08064987510442734,
0.0014141155406832695,
0.012814664281904697,
0.007931869477033615,
0.037443313747644424,
0.00004070544309797697,
0.01742664910852909,
-0.06718909740447998,
0.013086159713566303,
0.005683006253093481,
-0.024409940466284752,
0.00831490010023117,
0.0022299541160464287,
-0.023982707411050797,
-0.0035483480896800756,
0.022304091602563858,
0.07527696341276169,
-0.02694757841527462,
0.005804713349789381,
0.01556402537971735,
-0.04290572926402092,
0.022415317595005035,
-0.016204670071601868,
0.015256362035870552,
-0.027794837951660156,
-0.050552643835544586,
-0.05811019614338875,
0.04426674544811249,
-0.019528646022081375,
0.0030057034455239773,
-0.00475882925093174,
0.024187665432691574,
0.010845937766134739,
-0.023152245208621025,
0.0693177580833435,
-0.0284109003841877,
-0.036432065069675446,
-0.048993200063705444,
-0.005588584579527378,
0.05017692595720291,
0.027400024235248566,
0.0275771152228117,
-0.01984568126499653,
-0.07502348721027374,
0.0063959090039134026,
-0.055649787187576294,
0.056337691843509674,
-0.020491205155849457,
0.035948753356933594,
0.00029839854687452316,
0.017187071964144707,
-0.05499957129359245,
0.035372693091630936,
-0.038614142686128616,
-0.03446920961141586,
0.02061704359948635,
-0.023752229288220406,
-0.06036879122257233,
-0.035623081028461456,
0.030731262639164925,
0.01660951040685177,
0.05282754823565483,
-0.03139835223555565,
0.029115745797753334,
0.012660006061196327,
-0.01691455766558647,
0.025341179221868515,
0.011192910373210907,
-0.026367375627160072,
-0.11733123660087585,
0.00757525535300374,
0.0062933312729001045,
0.07114171981811523,
-0.07020097225904465,
-0.0640743225812912,
-0.03201780095696449,
-0.029177404940128326,
0.06294053792953491,
-0.05458937957882881,
0.030029011890292168,
-0.05820630118250847,
-0.026726143434643745,
0.0045587955974042416,
-0.007530017290264368,
-0.00036720657953992486,
-0.037808049470186234,
0.06210026890039444,
0.009146513417363167,
-0.027432512491941452,
0.049864962697029114,
-0.001212154165841639,
0.06843190640211105,
-0.023344367742538452,
0.005391544662415981,
-0.02891497127711773,
-0.027048911899328232,
-0.010966972447931767,
-0.0006243506213650107,
-0.015359833836555481,
-0.02010769583284855,
0.04453279450535774,
0.007493767887353897,
0.02783288061618805,
-0.0446847639977932,
0.062423594295978546,
0.004722018726170063,
0.017012903466820717,
-0.01693449169397354,
0.0008144797175191343,
-0.04334050789475441,
0.015047301538288593,
-0.028209909796714783,
-0.06931741535663605,
0.04533656686544418,
0.052384618669748306,
0.0055220904760062695,
-0.001120970817282796,
0.004081323277205229,
0.013227848336100578,
0.06934650242328644,
0.08457475900650024,
-0.00009619088814361021,
0.014733958058059216,
0.026524633169174194,
0.03962958976626396,
-0.02583087794482708,
-0.007005244493484497,
0.01158044021576643,
-0.029617058113217354,
-0.015684541314840317,
0.02145094983279705,
0.0015922064194455743,
0.036719366908073425,
0.09099011868238449,
0.021181277930736542,
0.002695726929232478,
-0.04042897745966911,
-0.037982277572155,
0.07125155627727509,
0.04264238476753235,
0.0010200373362749815,
0.01703420653939247,
-0.016450118273496628,
0.013429471291601658,
-0.046041347086429596,
-0.007803767919540405,
0.03136126324534416,
-0.005827704910188913,
-0.00487268902361393,
0.025169383734464645,
-0.027505410835146904,
0.009097051806747913,
0.029966507107019424,
0.056204903870821,
0.0794002041220665,
-0.029087213799357414,
-0.008666174486279488,
0.020738596096634865,
-0.08507809787988663,
-0.028173942118883133,
0.008366298861801624,
-0.049269866198301315,
0.02925608679652214,
-0.0425742007791996,
0.007321360986679792,
-0.04915561154484749,
0.002729070605710149,
0.02493925951421261,
-0.03346983715891838,
0.010113043710589409,
0.0276445671916008,
-0.04452534019947052,
-0.0073189265094697475,
-0.006664483807981014,
0.02029900625348091,
0.01714278757572174,
0.04559975489974022,
0.0476396307349205,
-0.022455384954810143,
-0.008514143526554108,
0.0076836454682052135,
-0.02066170610487461,
0.043732427060604095,
0.009580406360328197,
-0.028150025755167007,
0.0885554701089859,
0.0037266842555254698,
0.016444498673081398,
0.0008420121157541871,
0.026601208373904228,
0.052265916019678116,
-0.057315610349178314,
0.031340841203927994,
-0.051303304731845856,
0.0014858940849080682,
-0.0628919005393982,
0.03550843149423599,
0.06496933102607727,
0.03149624913930893,
0.07366025447845459,
0.012625643983483315,
0.04891546070575714,
-0.08797239512205124,
-0.016761664301156998,
-0.039922863245010376,
0.05088146775960922,
-0.02195892669260502,
0.02290084958076477,
0.05382464826107025,
-0.0033180667087435722,
-0.033656422048807144,
0.020069271326065063,
0.0572393499314785,
0.013246478512883186,
-0.036985743790864944,
0.010002132505178452,
0.018841486424207687,
-0.04458635300397873,
0.04326317086815834,
-0.01826070435345173,
-0.031534649431705475,
-0.009468738920986652,
-0.02672230824828148,
-0.06461158394813538,
-0.029621725901961327,
-0.003726829309016466,
0.01980649307370186,
-0.0516846738755703,
0.05261501297354698,
0.021048907190561295,
0.045334044843912125,
-0.05752809718251228,
-0.03862106800079346,
0.017456451430916786,
0.038303911685943604,
0.018674049526453018,
0.047870196402072906,
0.059431448578834534,
-0.051598142832517624,
0.05426926165819168,
0.01764087565243244,
0.04269416630268097,
-0.032790407538414,
-0.0049429722130298615,
0.0094833392649889,
0.014452533796429634,
0.034270163625478745,
0.032288808375597,
0.032598916441202164,
0.0032930634915828705,
-0.014106957241892815,
0.023510269820690155,
-0.025654064491391182,
0.03046550787985325,
0.04795149341225624,
0.0005863782134838402,
0.031343843787908554,
-0.06663994491100311,
-0.009809845127165318,
-0.024933697655797005,
-0.01716599613428116,
0.02984209917485714,
0.015754489228129387,
0.044585976749658585,
0.058212365955114365,
0.01590227335691452,
0.02562667988240719,
-0.04529199376702309,
0.025623485445976257,
0.033950015902519226,
0.01308718603104353,
-0.022606631740927696,
-0.03131703659892082,
0.008440414443612099,
0.03419532626867294,
-0.0019108869601041079,
-0.06768015027046204,
0.02995815873146057,
-0.01647879369556904,
0.03324970230460167,
-0.012065960094332695,
-0.06688147038221359,
-0.018273700028657913,
-0.007565109990537167,
-0.009669807739555836,
-0.033274710178375244,
0.02270038239657879,
-0.017926625907421112,
0.0005688287783414125,
0.04329243674874306,
-0.047219522297382355,
-0.039215538650751114,
0.00787363201379776,
-0.006497977301478386,
-0.04620448127388954,
0.03183913603425026,
0.02510281652212143,
0.003017556620761752,
-0.04493163898587227,
0.032842230051755905,
-0.06639764457941055,
0.001680455869063735,
0.04505043849349022,
-0.022969868034124374,
0.022023644298315048,
0.033594466745853424,
0.05297064408659935,
0.002700979821383953,
0.014792502857744694,
0.012767949141561985,
-0.05440231040120125,
-0.011188053525984287,
-0.01992080919444561,
0.021290868520736694,
0.03920237720012665,
-0.04960492253303528,
-0.032227929681539536,
-0.03768518194556236,
-0.03188518062233925,
0.0031789562199264765,
0.016201209276914597,
0.01562679000198841,
-0.015304031781852245,
0.015425506979227066,
-0.014919457957148552,
0.01991376094520092,
0.0430576354265213,
0.0033128682989627123,
-0.01956208050251007,
0.03728526830673218,
0.011696739122271538,
0.051217447966337204,
0.03328623250126839,
0.03917662799358368,
-0.018707821145653725,
0.06343503296375275,
-0.025189004838466644,
0.007806188892573118,
0.05310792848467827,
0.06424540281295776,
0.07754075527191162,
0.004478498827666044,
-0.004802934359759092,
-0.0613366961479187,
0.023042423650622368,
0.011852942407131195,
0.019511902704834938,
-0.01584276184439659,
0.0053011332638561726,
-0.03401999548077583,
0.08349060267210007,
-0.020687732845544815,
0.020758548751473427,
0.03237253054976463,
0.05141333490610123,
-0.07883378863334656,
-0.020904501900076866,
0.04518190771341324,
-0.0008798741619102657,
-0.045890189707279205,
0.020972903817892075,
-0.014092614874243736,
-0.034013308584690094,
-0.02816585637629032,
-0.0003641520452219993,
0.00044331487151794136,
0.04892066866159439,
-0.0052868034690618515,
-0.022371653467416763,
-0.026769118383526802,
-0.04708608612418175,
-0.020606689155101776,
0.015405834652483463,
0.006569563411176205,
0.011707938276231289,
-0.06766937673091888,
-0.00032000395003706217,
0.0010744179598987103,
-0.016641683876514435,
0.04552676901221275,
-0.0009242648375220597,
-0.003384144976735115,
-0.013941382989287376,
0.029533477500081062,
-0.03594372048974037,
0.02297711931169033,
0.001500423881225288,
-0.011139173991978168,
-0.07055024057626724,
-0.015393397770822048,
0.014982347376644611,
0.03391158580780029,
0.03311127424240112,
0.0644756630063057,
0.07662215828895569,
-0.006875602062791586,
-0.026905737817287445,
0.056113351136446,
0.02428445778787136,
-0.10286731272935867,
-0.010327373631298542,
-0.01331138052046299,
0.002789921360090375,
0.021684790030121803,
-0.02571186237037182,
0.007383469957858324,
-0.0011459151282906532,
0.008256899192929268,
-0.07546748220920563,
0.0395318903028965,
0.033036306500434875,
0.035495515912771225,
0.04550302028656006,
-0.035423651337623596,
-0.052746932953596115,
0.0009291978203691542,
-0.010765450075268745,
0.012574916705489159,
-0.0059157065115869045,
-0.023829946294426918,
0.05129120126366615,
-0.003677370958030224,
-0.005374317057430744,
0.02524123154580593,
0.06057877838611603,
0.017615575343370438,
-0.03050040267407894,
-0.03762145712971687,
-0.008795554749667645,
-0.002736239228397608,
-0.025610389187932014,
0.031951237469911575,
-0.017482765018939972,
-0.018987273797392845,
-0.0656651183962822,
0.06096712127327919,
-0.0034237494692206383,
-0.040360625833272934,
-0.028522547334432602,
-0.04307837039232254,
-0.009005199186503887,
0.06564994901418686,
-0.004804957192391157,
-0.008336691185832024,
-0.05653456971049309,
-0.029791809618473053,
-0.08384861797094345,
0.0013035987503826618,
0.0506262369453907,
0.0010111903538927436,
-0.001648860052227974,
0.008550404570996761,
-0.012743941508233547,
0.0026936582289636135,
0.026914432644844055,
0.005355563014745712,
-0.01827383041381836,
0.016628559678792953,
-0.029211338609457016,
-0.02605554647743702,
0.005753341130912304,
-0.05100535601377487,
-0.020469073206186295,
0.01453403290361166,
-0.015667233616113663,
-0.03756085783243179,
0.008800123818218708,
-0.023868033662438393,
-0.015152798034250736,
0.02651839517056942,
-0.03228925168514252,
0.03880823403596878,
-0.032437827438116074,
-0.04335265979170799,
-0.011826448142528534,
-0.04199032858014107,
-0.00865837000310421,
0.002601480344310403,
-0.03750938922166824,
-0.023814300075173378,
-0.03251759707927704,
0.044905390590429306,
0.015404201112687588,
0.08165720105171204,
-0.06815732270479202,
0.0468694269657135,
0.04050245136022568,
0.016073066741228104,
0.04783184453845024,
-0.023412691429257393,
0.018136117607355118,
-0.012626470066606998,
0.0007700813002884388,
-0.07874534279108047,
-0.036445099860429764,
0.04569870978593826,
-0.02967047318816185,
0.028216369450092316,
0.04326627403497696,
-0.015285319648683071,
-0.052083276212215424,
-0.0066091506741940975,
-0.08048347383737564,
-0.012290914542973042,
-0.015065687708556652,
0.030385155230760574,
0.02115200087428093,
0.0010101314401254058,
-0.05500338599085808,
0.0035151957999914885,
0.05673937499523163,
0.03620769828557968,
-0.014685345813632011,
-0.004868397954851389,
-0.03451332449913025,
-0.02175753377377987,
0.010229800827801228,
-0.04895136505365372,
-0.003916178364306688,
-0.0061875078827142715,
0.04535122215747833,
-0.007970660924911499,
-0.011245853267610073,
0.017213093116879463,
0.012529062107205391,
0.05928974226117134,
0.01886688731610775,
-0.04065854847431183,
-0.02120121754705906,
-0.03696032240986824,
-0.01785353757441044,
0.10958543419837952,
0.04977747052907944,
-0.023722536861896515,
0.007845777086913586,
-0.042288750410079956,
0.016108572483062744,
0.07233388721942902,
-0.038358330726623535,
-0.027546068653464317,
-0.0032476873602718115,
-0.009568235836923122,
-0.012342036701738834,
0.01934145949780941,
-0.02899731695652008,
0.00295459758490324,
-0.03842497617006302,
-0.023314382880926132,
-0.0424233116209507,
-0.03413100913167,
-0.008043574169278145,
-0.020903650671243668,
-0.04259142652153969,
0.019260749220848083,
-0.005470087751746178,
-0.05018338933587074,
0.05981585383415222,
0.00890839472413063,
0.019114907830953598,
-0.03487273305654526,
-0.0493200458586216,
-0.01786310039460659,
-0.03025876358151436,
-0.004923817235976458,
-0.040811412036418915,
-0.025452805683016777,
-0.025581954047083855,
-0.03048357181251049,
-0.04125864803791046,
0.025509022176265717,
-0.00883707869797945,
0.04459273815155029,
0.006010573357343674,
-0.008734459057450294,
-0.012782052159309387,
0.039633870124816895,
-0.020432718098163605,
-0.006428877357393503,
0.03906232863664627,
-0.014286239631474018,
0.01683203876018524,
-0.036640629172325134,
0.00400690920650959,
-0.0061256298795342445,
0.012192525900900364,
-0.019954854622483253,
0.003748839721083641,
-0.03163962438702583,
-0.013122436590492725,
-0.012655816972255707,
0.019322507083415985,
0.01786741241812706,
-0.005415357183665037,
-0.0071766311302781105,
-0.020300298929214478,
0.03264918550848961,
-0.013961844146251678,
-0.010317160747945309,
-0.05813106521964073,
0.01127798855304718,
-0.05601191148161888,
0.05928852781653404,
-0.017641833052039146,
-0.02453453280031681,
-0.016704469919204712,
-0.054697487503290176,
-0.03252459689974785,
-0.050677064806222916,
-0.07827766239643097,
0.06399223953485489,
0.01997462660074234,
0.009424152784049511,
0.013790871948003769,
-0.022863032296299934,
0.04769745096564293,
-0.05770396813750267,
-0.002848762320354581,
-0.029520360752940178,
0.005287188105285168,
-0.003226919798180461,
0.007578845135867596,
-0.011555282399058342,
-0.09887854754924774,
0.0016911220736801624,
0.02710956335067749,
-0.0032020036596804857,
-0.005218620412051678,
-0.01574496179819107,
0.010339967906475067,
0.037465900182724,
0.0049628932029008865,
-0.0961056649684906,
-0.023592831566929817,
-0.07009799033403397,
0.043270133435726166,
0.04188571870326996,
-0.009606443345546722,
-0.020642682909965515,
0.03189205750823021,
0.07208304852247238,
0.009478454478085041,
0.03691871091723442,
0.006254279520362616,
0.007170355878770351,
0.035771794617176056,
0.012468114495277405,
0.030387531965970993,
-0.007776195649057627,
-0.001551027991808951
] |
[
1.5797476768493652,
4.541884899139404
] |
Classical Analysis and ODEs
|
Mathematics
|
math-CA
|
math-PR
|
na
|
2007-03-31T14:10:06
|
In $\XQM$, a quark can emit Goldstone bosons. The flavor symmetry breaking in
the Goldstone boson emission process is used to intepret the nucleon
flavor-spin structure. In this paper, we study the inner structure of
constituent quarks implied in $\XQM$ caused by the Goldstone boson emission
process in nucleon. From a simplified model Hamiltonian derived from $\XQM$,
the intrinsic wave functions of constituent quarks are determined. Then the
obtained transition probabilities of the emission of Goldstone boson from a
quark can give a reasonable interpretation to the flavor symmetry breaking in
nucleon flavor-spin structure.
|
Understanding the Flavor Symmetry Breaking and Nucleon Flavor-Spin
Structure within Chiral Quark Model
|
hep-ph
|
0704.0029
| 2,007
|
[
-0.02339758537709713,
0.04287789389491081,
0.004383875988423824,
-0.07290752977132797,
0.053939979523420334,
0.023553142324090004,
0.02086377888917923,
0.02798011340200901,
-0.01793677918612957,
0.003224243177101016,
-0.08056555688381195,
0.08274929970502853,
-0.0012572648702189326,
-0.017634715884923935,
0.0355682447552681,
-0.02944868989288807,
0.009667032398283482,
0.02366333082318306,
0.05070843547582626,
-0.006083629559725523,
-0.036219075322151184,
-0.021919401362538338,
0.004559603054076433,
-0.06923046708106995,
0.042500291019678116,
-0.009282325394451618,
-0.004114520736038685,
0.05461537092924118,
-0.026538800448179245,
0.04178539291024208,
0.0425383485853672,
-0.03104587085545063,
-0.0014265287900343537,
-0.03509199619293213,
-0.05067150667309761,
-0.02058088593184948,
0.06235792115330696,
0.007596341427415609,
-0.012699461542069912,
0.022241704165935516,
0.013446674682199955,
-0.02901131473481655,
0.007335310336202383,
-0.06049515679478645,
0.005929650738835335,
0.05561638996005058,
0.03469768911600113,
0.019191088154911995,
-0.023658819496631622,
-0.007976701483130455,
-0.01365218497812748,
0.003203809494152665,
0.049256112426519394,
-0.010795455425977707,
-0.038840387016534805,
0.06654374301433563,
0.022491488605737686,
0.003910061903297901,
0.05828728526830673,
-0.010768341831862926,
0.020076414570212364,
0.05360811948776245,
-0.031080614775419235,
0.011944806203246117,
0.06886470317840576,
-0.06466545909643173,
-0.03732750564813614,
0.038269639015197754,
-0.01422912534326315,
0.005544223822653294,
0.024809282273054123,
-0.03638908639550209,
-0.046792641282081604,
0.04221068322658539,
-0.03138521686196327,
-0.000005488864189828746,
-0.007786903064697981,
0.016742320731282234,
-0.029282454401254654,
0.02005634643137455,
0.02294442243874073,
-0.02052960731089115,
0.04186243563890457,
0.03059707209467888,
0.04467281699180603,
0.014482689090073109,
-0.036172617226839066,
-0.007934978231787682,
-0.0525495745241642,
0.028311453759670258,
0.005382527131587267,
-0.010697177611291409,
0.026851439848542213,
0.06641120463609695,
-0.07001802325248718,
0.005505281500518322,
-0.0211139228194952,
0.06464531272649765,
-0.010899702087044716,
-0.014957986772060394,
-0.017539838328957558,
0.05256275087594986,
0.0619850717484951,
-0.019637003540992737,
0.048981618136167526,
-0.0004604535934049636,
0.011002978309988976,
0.020054278895258904,
-0.0006692623719573021,
0.01654321327805519,
-0.06769366562366486,
-0.018898002803325653,
-0.0058679538778960705,
0.019937679171562195,
-0.034759584814310074,
0.002394316019490361,
0.07918981462717056,
-0.07880491763353348,
0.004582895897328854,
0.05434969440102577,
-0.030407888814806938,
-0.03374457731842995,
0.005832974798977375,
0.0516180582344532,
0.021239660680294037,
0.007148022297769785,
-0.05717707425355911,
0.0022089381236582994,
0.016813743859529495,
-0.009783654473721981,
-0.0005942192510701716,
-0.02531038224697113,
-0.012120973318815231,
0.017947182059288025,
0.0936896800994873,
0.008122866973280907,
0.005161555018275976,
-0.011464888229966164,
0.03940567001700401,
-0.041500743478536606,
0.006153371650725603,
0.01882159151136875,
0.020443538203835487,
-0.004380721133202314,
0.017146868631243706,
-0.0461651012301445,
0.021639909595251083,
-0.07239167392253876,
-0.06047589331865311,
0.001461433945223689,
0.05810675024986267,
0.032664231956005096,
0.024150660261511803,
0.01812063157558441,
-0.03665482625365257,
-0.04469313099980354,
-0.019860271364450455,
-0.03238446265459061,
-0.02250431850552559,
-0.008602437563240528,
0.04382266476750374,
0.008215232752263546,
-0.014122437685728073,
0.06814445555210114,
-0.09453094750642776,
-0.01048662606626749,
0.053687214851379395,
0.000044149728637421504,
-0.016925115138292313,
0.02024107240140438,
-0.027787750586867332,
0.006642364431172609,
-0.07103078812360764,
0.0030954054091125727,
0.04465927556157112,
0.03306832164525986,
-0.02650022692978382,
-0.051507215946912766,
0.030195361003279686,
0.05205770209431648,
0.020650455728173256,
-0.005034515634179115,
0.01093037985265255,
0.03197643905878067,
-0.03353852778673172,
0.004819309804588556,
0.04395103082060814,
-0.0258623156696558,
0.010284757241606712,
-0.021187514066696167,
0.0020206777844578028,
0.004637144040316343,
-0.029936309903860092,
-0.040860824286937714,
0.0004668433975894004,
-0.03941649943590164,
0.010949031449854374,
-0.01258144062012434,
0.030520668253302574,
0.0021473809611052275,
-0.012158307246863842,
0.017598234117031097,
-0.058432307094335556,
-0.008746928535401821,
0.008862083777785301,
0.0076915849931538105,
0.02614757791161537,
0.03146004676818848,
0.04829452559351921,
-0.012044252827763557,
0.04608936235308647,
0.02958839200437069,
-0.06109939515590668,
0.03252739459276199,
-0.03444672003388405,
0.02456665225327015,
0.03482257202267647,
-0.015773341059684753,
-0.03233243525028229,
0.07518371939659119,
-0.01317110750824213,
-0.01740514114499092,
0.032358165830373764,
0.037741053849458694,
0.034905098378658295,
0.03780650720000267,
-0.03121039643883705,
-0.04370250180363655,
-0.028030650690197945,
-0.0339406318962574,
-0.05574125424027443,
-0.04223175346851349,
0.020823480561375618,
-0.031210340559482574,
0.013862176798284054,
-0.01482897624373436,
-0.019952531903982162,
0.026173856109380722,
0.0704626515507698,
0.01878923550248146,
0.0016881165793165565,
0.02413627691566944,
-0.01636393927037716,
-0.02903422713279724,
-0.057346463203430176,
0.0023814209271222353,
-0.021664058789610863,
-0.03116021119058132,
-0.02507767081260681,
0.013967476785182953,
0.05257729813456535,
0.0037046195939183235,
-0.031868886202573776,
-0.01170406211167574,
0.006949416361749172,
-0.0414176844060421,
-0.03736209124326706,
0.06957514584064484,
-0.05155685544013977,
-0.07694998383522034,
0.03555291146039963,
-0.07478343695402145,
-0.007167183794081211,
-0.05554978922009468,
-0.0217085313051939,
0.022430093958973885,
0.021030105650424957,
0.01580120250582695,
-0.027842020615935326,
0.02100461907684803,
-0.036898255348205566,
0.0648566409945488,
0.043721724301576614,
0.06168077513575554,
-0.017916709184646606,
-0.03187583014369011,
-0.016985924914479256,
-0.0014893225161358714,
-0.025109775364398956,
-0.03467254713177681,
-0.07374074310064316,
-0.041474394500255585,
-0.07190180569887161,
-0.004090421833097935,
-0.004968547262251377,
0.028063073754310608,
-0.015217012725770473,
-0.023616638034582138,
-0.004169896710664034,
0.020065564662218094,
-0.04482105001807213,
-0.007877519354224205,
0.04448889195919037,
0.08034097403287888,
0.006072705145925283,
0.050357989966869354,
0.06837398558855057,
0.018304336816072464,
0.014452335424721241,
0.001256301300600171,
-0.013886219821870327,
0.008698997087776661,
-0.031023457646369934,
-0.006136106792837381,
-0.05091230571269989,
0.022385545074939728,
-0.015585078857839108,
0.04820465296506882,
-0.00033485054154880345,
-0.027209028601646423,
-0.045684874057769775,
0.02612423337996006,
-0.0020272997207939625,
0.026368217542767525,
-0.011235847137868404,
0.00028498683241195977,
-0.050353772938251495,
0.036830879747867584,
0.0887579545378685,
-0.03036515600979328,
-0.03393654525279999,
-0.02692594565451145,
0.016329871490597725,
-0.07525563985109329,
0.0360390804708004,
0.03022952750325203,
0.021940840408205986,
0.059039391577243805,
-0.021048549562692642,
-0.08042019605636597,
-0.02380676008760929,
0.05853251367807388,
-0.022874966263771057,
0.0068568214774131775,
-0.017237018793821335,
-0.00897219404578209,
-0.04388820007443428,
0.04394618794322014,
-0.05241289362311363,
0.010210568085312843,
0.03836683928966522,
-0.04860334098339081,
-0.0033005154691636562,
-0.025918081402778625,
0.001433533150702715,
-0.03798915445804596,
-0.09171898663043976,
-0.016050228849053383,
0.0523814857006073,
0.026023568585515022,
-0.07689560949802399,
0.040364187210798264,
0.016285289078950882,
0.007683089468628168,
-0.02298235148191452,
-0.009263266809284687,
0.056151121854782104,
0.008443444035947323,
0.0697483941912651,
0.017077302560210228,
0.04605620354413986,
-0.0746924951672554,
0.07532524317502975,
-0.026581399142742157,
0.004058815538883209,
0.04116268828511238,
0.02202104963362217,
0.0077210357412695885,
0.07387133687734604,
-0.012020404450595379,
-0.014636789448559284,
-0.016909485682845116,
0.030421478673815727,
-0.011754082515835762,
0.046079494059085846,
-0.00877299439162016,
-0.04678497835993767,
0.03910791873931885,
-0.04067666456103325,
-0.00962828379124403,
0.05774947255849838,
0.047036174684762955,
0.03592401370406151,
-0.024633318185806274,
0.020183691754937172,
0.015139392577111721,
-0.039437130093574524,
-0.06293050944805145,
-0.025312546640634537,
-0.030262408778071404,
0.003708175616338849,
-0.042697105556726456,
-0.009929738007485867,
0.004812479019165039,
-0.012326080352067947,
-0.05080417916178703,
0.01647191122174263,
0.01517675630748272,
0.03054976649582386,
0.021937383338809013,
-0.07095243781805038,
-0.09047863632440567,
-0.03007625974714756,
-0.026545092463493347,
0.005252194125205278,
0.03524141013622284,
-0.022616706788539886,
-0.07987179607152939,
0.042025089263916016,
-0.010933754965662956,
-0.001651862869039178,
0.0676618367433548,
-0.013583874329924583,
-0.015087919309735298,
0.021898115053772926,
0.0059924041852355,
0.02786753699183464,
0.01353495754301548,
-0.02198573760688305,
-0.03479340672492981,
0.0480068102478981,
0.018977224826812744,
-0.017593832686543465,
0.05555500462651253,
-0.011220346204936504,
-0.05523260682821274,
0.012801612727344036,
0.027786627411842346,
0.023457404226064682,
-0.054961636662483215,
0.01434444822371006,
0.00040361436549574137,
-0.011846322566270828,
0.039763323962688446,
-0.05432794243097305,
-0.0005990643985569477,
-0.024482639506459236,
0.01886032521724701,
-0.056581299751996994,
0.059294648468494415,
0.04426664486527443,
-0.04976855590939522,
0.015072622336447239,
0.035548727959394455,
0.08308718353509903,
0.05969996750354767,
0.07576967775821686,
-0.0543643981218338,
-0.031873010098934174,
-0.03809485584497452,
0.04643137753009796,
-0.007092251908034086,
-0.029202092438936234,
0.0013240179978311062,
0.08506400883197784,
-0.04806558042764664,
-0.005404347088187933,
0.027614891529083252,
0.019023098051548004,
0.04221881926059723,
-0.048367008566856384,
-0.004346039611846209,
-0.01900455355644226,
-0.017077459022402763,
0.015703696757555008,
-0.014018591493368149,
-0.03741857782006264,
0.023441972211003304,
0.02329174615442753,
0.0500577948987484,
0.0030254055745899677,
-0.019136331975460052,
0.040202490985393524,
0.017789442092180252,
0.0025807900819927454,
-0.0015104466583579779,
0.02104320377111435,
-0.049851443618535995,
0.003748107235878706,
0.02715463377535343,
0.039703451097011566,
-0.012119477614760399,
-0.0009252470335923135,
-0.04216207563877106,
-0.005596015136688948,
-0.0010483256774023175,
0.0007630203035660088,
0.0013291954528540373,
0.0020908445585519075,
0.009651181288063526,
0.003661436727270484,
0.02861333079636097,
0.039147548377513885,
-0.040897537022829056,
-0.021056778728961945,
-0.013623747043311596,
-0.002111342502757907,
-0.005126620642840862,
0.001590921776369214,
-0.006624463014304638,
-0.01750325597822666,
0.008972210809588432,
0.03124423325061798,
0.005015580914914608,
0.028481679037213326,
0.02770678699016571,
-0.009108648635447025,
-0.05096171051263809,
-0.0152268772944808,
0.003398063825443387,
0.0354301854968071,
0.0234233345836401,
0.051450036466121674,
0.01942255347967148,
0.024015052244067192,
0.0016818258445709944,
0.02743350714445114,
-0.013614751398563385,
-0.01818101666867733,
0.01235409639775753,
-0.019943295046687126,
-0.005048488732427359,
0.0025412016548216343,
-0.011867616325616837,
-0.03515143692493439,
0.056127071380615234,
-0.021512052044272423,
-0.07791189849376678,
0.040244005620479584,
-0.020955592393875122,
0.004825783893465996,
-0.003761405125260353,
0.07639957964420319,
0.04603969678282738,
0.05640161782503128,
-0.07977093756198883,
0.013306453824043274,
0.03551206737756729,
-0.04589185491204262,
0.06819359213113785,
0.012644610367715359,
-0.006202091462910175,
0.027759969234466553,
-0.022618860006332397,
-0.012144295498728752,
-0.01557815819978714,
-0.07771987468004227,
0.0034041637554764748,
-0.050364941358566284,
-0.0714554563164711,
0.05105727165937424,
0.0034795179963111877,
0.05500257387757301,
-0.12101082503795624,
0.04211647808551788,
0.0004554926126729697,
-0.007939934730529785,
-0.024701880291104317,
-0.08236537128686905,
-0.018341364338994026,
-0.007718229666352272,
-0.030584637075662613,
0.0317816361784935,
-0.019355084747076035,
0.04797470569610596,
-0.03205622732639313,
-0.036404192447662354,
-0.03358430787920952,
0.01828945428133011,
0.009084733203053474,
0.027998600155115128,
0.002392831491306424,
-0.03373100608587265,
0.02700721099972725,
-0.017551708966493607,
-0.02169696055352688,
0.03826801851391792,
-0.04220766946673393,
-0.024872075766324997,
-0.010608748532831669,
-0.005713524762541056,
-0.011718115769326687,
0.0007883298676460981,
-0.010587567463517189,
0.004324981942772865,
0.04686964675784111,
-0.047811783850193024,
-0.027343513444066048,
0.05650715529918671,
-0.0032355180010199547,
-0.02991747483611107,
-0.028580186888575554,
-0.03136418014764786,
0.014919095672667027,
0.0037743356078863144,
0.05075778067111969,
-0.002502311021089554,
-0.060482386499643326,
0.01518616545945406,
-0.06435301899909973,
0.04189840704202652,
-0.010689263232052326,
0.04489472508430481,
-0.009839944541454315,
0.040898509323596954,
0.01806339994072914,
0.0037247170694172382,
0.02575654722750187,
-0.009018413722515106,
0.028393376618623734,
0.026063572615385056,
0.02112993597984314,
-0.013712110929191113,
-0.06963897496461868,
0.010525193065404892,
-0.053969401866197586,
0.07303599268198013,
-0.005679402966052294,
0.019006384536623955,
0.000011679306226142216,
-0.0003314864297863096,
-0.02402908354997635,
0.05014204978942871,
-0.04237114265561104,
0.012534006498754025,
0.042700137943029404,
-0.02577938139438629,
-0.010115128010511398,
0.0360075868666172,
0.03508305177092552,
-0.0008417733479291201,
-0.011198494583368301,
-0.02478681690990925,
-0.06928537786006927,
-0.056584447622299194,
0.029515326023101807,
-0.00843854621052742,
-0.002572969999164343,
0.002438254887238145,
0.06847219914197922,
0.027433492243289948,
-0.05911547318100929,
-0.0029117725789546967,
-0.00013213715283200145,
-0.021819792687892914,
0.03784232214093208,
0.016146713867783546,
-0.00290279439650476,
0.010974712669849396,
0.0010833845008164644,
0.09109106659889221,
0.07339312881231308,
0.03059796243906021,
0.032459061592817307,
0.015884531661868095,
-0.04925093427300453,
0.049170080572366714,
-0.024756278842687607,
-0.028357574716210365,
-0.04227159917354584,
-0.0034892642870545387,
-0.03256892412900925,
-0.003924820106476545,
-0.01682804897427559,
0.038021933287382126,
-0.005022195167839527,
-0.005167752504348755,
-0.005050293635576963,
0.013917232863605022,
0.026313958689570427,
-0.06280069053173065,
-0.007566277403384447,
-0.022474756464362144,
-0.05917850881814957,
-0.04772331938147545,
-0.033050209283828735,
-0.014921976253390312,
0.0273610670119524,
0.0037869263906031847,
-0.03845977783203125,
0.01845572143793106,
0.0013545016990974545,
-0.0158466137945652,
0.014997873455286026,
-0.005952418781816959,
-0.02293667569756508,
-0.013070100918412209,
-0.03225575014948845,
-0.02052922174334526,
-0.01432587020099163,
-0.022564712911844254,
0.009534940123558044,
0.020276829600334167,
-0.07660634815692902,
0.052253514528274536,
0.01444427203387022,
-0.030156761407852173,
0.04379403963685036,
0.02564757503569126,
0.06864576786756516,
0.046392641961574554,
0.030844487249851227,
-0.0053975703194737434,
0.027669470757246017,
-0.010292795486748219,
0.004197373986244202,
-0.012656849808990955,
-0.006730344612151384,
-0.03306225314736366,
-0.029381589964032173,
-0.040828410536050797,
-0.005921351257711649,
0.12293101102113724,
0.06069096550345421,
0.06511055678129196,
-0.006332560442388058,
0.003709611017256975,
-0.019582366570830345,
0.04214055463671684,
0.017635563388466835,
-0.021091021597385406,
0.0067660268396139145,
-0.0392950065433979,
0.04642622545361519,
-0.01851511187851429,
-0.059651363641023636,
-0.004417347721755505,
-0.03344530984759331,
0.02569236047565937,
0.0072683352045714855,
-0.01398689579218626,
0.023593349382281303,
-0.03939034417271614,
0.021855881437659264,
-0.01023419201374054,
-0.02417406626045704,
-0.03510647267103195,
0.01816619373857975,
-0.021418288350105286,
0.005669667851179838,
-0.0077340626157820225,
-0.01562429778277874,
0.015841176733374596,
0.012511147186160088,
-0.06965672224760056,
-0.045708104968070984,
-0.06146145612001419,
0.02896219864487648,
0.040574777871370316,
0.0002281112247146666,
-0.04961862787604332,
-0.017109300941228867,
0.028047624975442886,
0.014687297865748405,
0.010011847130954266,
0.0030738026835024357,
-0.053689874708652496,
0.06196717917919159,
0.02070910669863224,
-0.04614229500293732,
0.02171906642615795,
0.017022714018821716,
0.0035351074766367674,
0.06352975964546204,
-0.02379491738975048,
0.026536734774708748,
-0.023134823888540268,
0.048789191991090775
] |
[
15.113271713256836,
-2.2357282638549805
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
na
|
na
|
2007-03-31T14:14:18
|
We investigate the effect of tuning the phonon energy on the correlation
effects in models of electron-phonon interactions using DMFT. In the regime
where itinerant electrons, instantaneous electron-phonon driven correlations
and static distortions compete on similar energy scales, we find several
interesting results including (1) A crossover from band to Mott behavior in the
spectral function, leading to hybrid band/Mott features in the spectral
function for phonon frequencies slightly larger than the band width. (2) Since
the optical conductivity depends sensitively on the form of the spectral
function, we show that such a regime should be observable through the low
frequency form of the optical conductivity. (3) The resistivity has a double
kondo peak arrangement
|
Tuning correlation effects with electron-phonon interactions
|
cond-mat.str-el
|
0704.0030
| 2,007
|
[
-0.01393038034439087,
0.03356045112013817,
0.005519408266991377,
-0.017250079661607742,
0.03095100075006485,
0.018262682482600212,
0.003697808366268873,
0.01128578931093216,
0.0017234495608136058,
-0.019060535356402397,
-0.05285957083106041,
0.04908575862646103,
-0.004364855587482452,
-0.018857154995203018,
-0.021353689953684807,
-0.020028825849294662,
0.034863751381635666,
0.038696855306625366,
-0.007561905775219202,
-0.0005423190305009484,
-0.049764152616262436,
-0.030623313039541245,
-0.04743306338787079,
-0.037867121398448944,
0.06715128570795059,
0.03174081817269325,
0.013329902663826942,
-0.02997284196317196,
-0.027396993711590767,
0.04136229306459427,
0.054238904267549515,
-0.015126504004001617,
0.01871315948665142,
-0.024405136704444885,
-0.04950346425175667,
-0.015909675508737564,
0.05913790315389633,
-0.01733686774969101,
0.008053665049374104,
0.05116621032357216,
0.004364727530628443,
-0.03202976658940315,
-0.012327003292739391,
-0.026252062991261482,
-0.005000288598239422,
-0.008793164975941181,
0.004603500012308359,
0.00611661933362484,
-0.04542267322540283,
-0.006088900379836559,
0.0125152338296175,
0.04044220224022865,
0.03205619379878044,
-0.04844433069229126,
0.020392339676618576,
-0.01965716853737831,
-0.007879537530243397,
-0.010729131288826466,
0.08160212635993958,
0.007228660862892866,
0.0142177389934659,
0.03639918193221092,
-0.005190528929233551,
0.057033006101846695,
0.0385296605527401,
-0.06345944851636887,
0.00286745629273355,
-0.016324570402503014,
0.008294207975268364,
-0.04269284009933472,
0.01938435435295105,
-0.02426278404891491,
-0.0054060774855315685,
0.04984423890709877,
0.006910615134984255,
0.009727907367050648,
-0.012091600336134434,
-0.04149557650089264,
-0.005310900509357452,
-0.006027381867170334,
-0.009397383779287338,
-0.023018091917037964,
0.017857549712061882,
0.04047952592372894,
0.035199329257011414,
-0.029943756759166718,
0.027078263461589813,
0.05024197697639465,
-0.07159208506345749,
0.033053163439035416,
0.012306920252740383,
-0.02685830369591713,
0.03870292007923126,
-0.018740607425570488,
-0.04276132583618164,
0.0690174326300621,
-0.03744225203990936,
0.08907174319028854,
0.01300457026809454,
-0.04173548147082329,
-0.012170568108558655,
0.03260626643896103,
0.05466088280081749,
0.0632229745388031,
0.0015427522594109178,
0.029095225036144257,
-0.007703421637415886,
-0.005953902844339609,
0.023623954504728317,
-0.020244449377059937,
-0.10766974091529846,
-0.03760829195380211,
-0.002203236799687147,
-0.014705280773341656,
-0.03988106921315193,
-0.03079395554959774,
0.01728305220603943,
-0.07919032126665115,
-0.007275966927409172,
0.050798818469047546,
0.0007319353753700852,
-0.0401177704334259,
0.025558648630976677,
0.04175662621855736,
0.005767027381807566,
0.0433519072830677,
-0.05403244122862816,
-0.023181837052106857,
-0.0015373923815786839,
-0.029693851247429848,
0.005615131463855505,
0.022749977186322212,
-0.03875479847192764,
0.004539498593658209,
0.03248254209756851,
0.02944069914519787,
0.024752680212259293,
-0.056535255163908005,
0.044568631798028946,
-0.020903296768665314,
-0.00042359609506092966,
-0.020724110305309296,
0.011895359493792057,
-0.02856406569480896,
0.004636702593415976,
-0.059114135801792145,
0.037558384239673615,
-0.03468186780810356,
0.013389693573117256,
-0.002273418940603733,
0.04166041687130928,
0.024230942130088806,
-0.0018760631792247295,
0.038396671414375305,
-0.008696266449987888,
-0.07403144985437393,
-0.0262277964502573,
-0.028178786858916283,
0.04655197262763977,
-0.008994165807962418,
-0.016352467238903046,
0.01905355416238308,
-0.019002772867679596,
0.026427844539284706,
-0.0033945853356271982,
-0.011045289225876331,
0.055154792964458466,
0.04497261345386505,
-0.006156268995255232,
0.03240923210978508,
-0.02555478736758232,
-0.04142538085579872,
-0.03568379208445549,
-0.012421000748872757,
0.015014494769275188,
0.026850562542676926,
0.0138856777921319,
-0.03793427348136902,
0.042477916926145554,
-0.0025032104458659887,
0.0538763664662838,
-0.0249641016125679,
0.006783739663660526,
0.029770269989967346,
0.043974269181489944,
0.03530354052782059,
-0.020687371492385864,
-0.018939699977636337,
-0.035279326140880585,
-0.014131760224699974,
0.02016683667898178,
-0.01929953135550022,
-0.06457914412021637,
-0.05877958983182907,
-0.023691978305578232,
-0.07586369663476944,
0.0562608502805233,
-0.014365806244313717,
-0.022398274391889572,
-0.11600691080093384,
-0.035664815455675125,
-0.026922935619950294,
-0.00781401339918375,
-0.0021060453727841377,
0.029077034443616867,
0.03203709051012993,
-0.000611756753642112,
0.003315602196380496,
0.013722642324864864,
-0.027203282341361046,
0.05779565870761871,
0.004289111588150263,
-0.021121583878993988,
0.02056327648460865,
-0.03251627832651138,
0.008106060326099396,
0.016592202708125114,
-0.03747980669140816,
-0.037684448063373566,
0.07906164973974228,
0.009567431174218655,
-0.01685597375035286,
0.020426912233233452,
0.00048360059736296535,
-0.0017638973658904433,
-0.01684206910431385,
-0.0030808181036263704,
-0.020971478894352913,
-0.07056578248739243,
-0.010327707976102829,
0.006346398964524269,
0.006250189151614904,
0.04382594674825668,
0.004991940222680569,
0.017189225181937218,
0.0023582971189171076,
-0.02200867235660553,
0.0019867869559675455,
0.023244772106409073,
0.03956072777509689,
0.03865422308444977,
0.007677331101149321,
0.006581906694918871,
-0.030631287023425102,
-0.07168075442314148,
-0.027756182476878166,
0.019198214635252953,
0.013976283371448517,
-0.023746145889163017,
0.021618273109197617,
0.03406146541237831,
0.03838854655623436,
0.04097195714712143,
0.02405872568488121,
0.03337594494223595,
-0.03332885354757309,
-0.06070408970117569,
0.06628644466400146,
-0.048241451382637024,
-0.015000386163592339,
0.06570567190647125,
-0.024954235181212425,
0.000016589912775089033,
-0.06696107983589172,
-0.048379670828580856,
-0.01496207807213068,
0.06200851872563362,
-0.04881589487195015,
-0.05276907980442047,
-0.05926259979605675,
-0.0070458659902215,
0.06597334891557693,
0.05419197306036949,
0.03292112052440643,
-0.009430124424397945,
0.02071707881987095,
0.026049787178635597,
-0.06460119783878326,
0.03696560114622116,
-0.009918511845171452,
-0.07065655291080475,
-0.02915036678314209,
-0.03971336409449577,
-0.04322422295808792,
0.0005855736671946943,
-0.0030777286738157272,
0.039367057383060455,
-0.023577045649290085,
-0.005312799476087093,
0.04128659516572952,
-0.03538595139980316,
-0.007591548375785351,
-0.018094146624207497,
0.09378252178430557,
0.019881896674633026,
0.01654781587421894,
0.06746011227369308,
-0.0338527113199234,
-0.023446697741746902,
0.06103748828172684,
-0.006147182080894709,
-0.010342706926167011,
0.00850958563387394,
0.035965096205472946,
0.01710020937025547,
0.027224646881222725,
0.033054839819669724,
0.003040828974917531,
-0.019024740904569626,
0.002143329009413719,
-0.028737587854266167,
0.04439937695860863,
-0.030370282009243965,
-0.01999402977526188,
-0.01691979356110096,
0.03007253259420395,
0.02440013736486435,
0.030835939571261406,
0.041333697736263275,
-0.01923765428364277,
0.047596536576747894,
0.012521144933998585,
0.004994300194084644,
-0.10839662700891495,
-0.03873559832572937,
0.05888095125555992,
-0.002523317001760006,
0.025852393358945847,
0.006181197706609964,
0.024231303483247757,
-0.016291216015815735,
0.025857260450720787,
-0.051227424293756485,
-0.024011872708797455,
-0.02838284522294998,
0.02469039149582386,
-0.0079297861084342,
0.06827190518379211,
-0.02276580035686493,
0.046789005398750305,
-0.005107000935822725,
-0.04254143685102463,
-0.053474053740501404,
-0.04052135348320007,
-0.01738850586116314,
0.030400706455111504,
-0.045657556504011154,
0.005382840987294912,
0.058198846876621246,
-0.002700591227039695,
-0.06282395124435425,
-0.03775377571582794,
0.007393525447696447,
0.0044806343503296375,
0.004870099946856499,
0.01058020070195198,
0.05085625499486923,
-0.004391205497086048,
0.038972314447164536,
-0.004048846662044525,
0.04214001074433327,
-0.03385213389992714,
0.051975317299366,
-0.006751564331352711,
-0.015003222040832043,
0.012074708938598633,
0.0006147569511085749,
0.04269735887646675,
0.04039480537176132,
-0.028456320986151695,
-0.05732163414359093,
-0.03569451719522476,
0.0420893169939518,
0.03757784143090248,
0.04547828435897827,
0.022107478231191635,
-0.039198823273181915,
-0.008987652137875557,
-0.010953235439956188,
0.005864537321031094,
0.0428515262901783,
0.04852164536714554,
0.02886558696627617,
0.05202346295118332,
0.06736230105161667,
-0.044468969106674194,
-0.06440674513578415,
-0.01672033593058586,
-0.01235273852944374,
0.011516544967889786,
-0.010699800215661526,
-0.012879783287644386,
-0.02360033430159092,
-0.008295855484902859,
0.02354377508163452,
-0.07810396701097488,
0.08678443729877472,
-0.03293579816818237,
0.05372242629528046,
-0.005491967312991619,
-0.0689074844121933,
-0.0536152720451355,
0.011782446876168251,
-0.03402849659323692,
-0.055770717561244965,
-0.001268144347704947,
-0.01904413476586342,
-0.05640481412410736,
0.011624475009739399,
-0.0626269057393074,
-0.03293239325284958,
0.005877768620848656,
-0.03621668368577957,
-0.0756860002875328,
0.005051007028669119,
-0.00024104716430883855,
0.020281095057725906,
-0.033559247851371765,
0.06109421327710152,
-0.027544498443603516,
-0.012170054018497467,
0.08412424474954605,
-0.003851416287943721,
0.011752971448004246,
-0.03513287752866745,
0.011356680653989315,
0.022973906248807907,
-0.03528749197721481,
-0.0034834828693419695,
-0.05648573115468025,
0.049283843487501144,
0.006911893375217915,
0.011063837446272373,
0.03478551656007767,
-0.07065051794052124,
0.03044710122048855,
0.029809681698679924,
-0.0060431682504713535,
0.008718781173229218,
0.027647558599710464,
0.041422486305236816,
-0.06263770163059235,
-0.008081169798970222,
0.02580530196428299,
0.027668869122862816,
0.07894738763570786,
0.03172949701547623,
-0.024397024884819984,
-0.030538206920027733,
0.0071310605853796005,
0.006878967396914959,
0.003925460856407881,
-0.022347019985318184,
0.019401762634515762,
0.07526858896017075,
-0.06800349801778793,
0.0011110929772257805,
0.0022968167904764414,
0.06560251861810684,
0.049443699419498444,
-0.016544442623853683,
0.037269145250320435,
-0.03225424140691757,
0.01670488715171814,
0.00773985730484128,
0.036446619778871536,
0.00710839219391346,
-0.017171025276184082,
-0.019939761608839035,
0.0006967543158680201,
0.017413558438420296,
-0.02015908993780613,
0.04831951856613159,
0.04832376539707184,
0.0003277584328316152,
-0.022489504888653755,
0.026950877159833908,
-0.05807773023843765,
0.011941174045205116,
-0.008999855257570744,
0.02280276268720627,
0.002954200841486454,
0.017370106652379036,
0.025823529809713364,
-0.026290971785783768,
-0.013588566333055496,
0.009956090711057186,
0.007628235500305891,
0.02183575928211212,
-0.017517289146780968,
0.0602945014834404,
0.020288126543164253,
-0.004614807665348053,
0.014761158265173435,
-0.026373177766799927,
0.062158312648534775,
-0.00636815931648016,
0.04646782949566841,
0.03076459839940071,
-0.05241304636001587,
0.005961945280432701,
-0.01130678877234459,
0.004013466648757458,
-0.03966659680008888,
-0.00970500335097313,
0.008869148790836334,
0.017266815528273582,
-0.06373309344053268,
-0.025806255638599396,
0.004497641697525978,
-0.01849297061562538,
0.06703661382198334,
0.02611350826919079,
0.07904695719480515,
0.005558687727898359,
-0.05431009456515312,
-0.021415594965219498,
-0.01351228728890419,
-0.08189301937818527,
-0.01890828087925911,
-0.0005217212019488215,
0.02153255045413971,
-0.03266835957765579,
-0.02991216629743576,
-0.06190994381904602,
0.0535091757774353,
-0.015478171408176422,
-0.033014073967933655,
0.07786688208580017,
-0.018548350781202316,
0.0013815067941322923,
0.04225543513894081,
0.022393997758626938,
0.02055576629936695,
0.03846319392323494,
0.021191418170928955,
0.021349387243390083,
0.034686390310525894,
-0.03893376514315605,
0.09904976934194565,
-0.011419377289712429,
0.004076614044606686,
0.051538508385419846,
-0.009954073466360569,
0.05373271927237511,
-0.0389077365398407,
-0.031644102185964584,
0.04371843859553337,
-0.03978250175714493,
-0.022434193640947342,
0.05110914260149002,
-0.03522393852472305,
-0.01600712165236473,
-0.06463265419006348,
0.007508148439228535,
-0.04276976361870766,
0.02027958817780018,
-0.04545329138636589,
-0.04893818125128746,
0.02090870402753353,
0.03441651910543442,
-0.0017908490262925625,
0.01726413145661354,
0.013051614165306091,
0.05052905157208443,
-0.07621347904205322,
-0.027255918830633163,
-0.0016827002400532365,
0.025274936109781265,
-0.03376709669828415,
-0.01268124021589756,
-0.039998698979616165,
-0.003225624794140458,
-0.03256770223379135,
-0.07567808032035828,
-0.00334146898239851,
0.0031706884037703276,
-0.05143589898943901,
-0.047137387096881866,
-0.011403224430978298,
-0.03376700356602669,
-0.021148132160305977,
-0.012726781889796257,
0.008813858032226562,
-0.058269914239645004,
0.039019741117954254,
0.030970143154263496,
-0.013515622355043888,
0.07089152187108994,
-0.019221529364585876,
-0.04270990937948227,
-0.04601706191897392,
-0.018211809918284416,
-0.003579729702323675,
-0.025527633726596832,
-0.004656130913645029,
0.010618145577609539,
-0.010643620043992996,
-0.07114611566066742,
0.04513171687722206,
0.035053182393312454,
0.005235177930444479,
0.09660613536834717,
-0.022302713245153427,
0.06252129375934601,
0.023654257878661156,
0.03458547592163086,
0.056754935532808304,
-0.059786099940538406,
0.009842130355536938,
-0.02880617044866085,
0.002003934234380722,
0.022792760282754898,
-0.029043657705187798,
-0.018665142357349396,
-0.037745483219623566,
0.047368068248033524,
0.0291157066822052,
-0.016168775036931038,
-0.007284683175384998,
-0.01037711650133133,
-0.06833714991807938,
-0.006355172488838434,
-0.09064968675374985,
0.011908476240932941,
0.021817361935973167,
-0.015765512362122536,
-0.08651455491781235,
0.03642117977142334,
-0.036043256521224976,
-0.005315924063324928,
0.004945624154061079,
-0.025413082912564278,
-0.004403730854392052,
0.009957930073142052,
0.0010084669338539243,
-0.022040357813239098,
-0.011246904730796814,
0.02750050649046898,
0.06425228714942932,
0.036633625626564026,
0.011742469854652882,
0.003967890050262213,
0.022488005459308624,
0.03224828839302063,
0.0339784137904644,
0.021635057404637337,
0.022534886375069618,
0.011509914882481098,
-0.052914056926965714,
0.11628876626491547,
0.040480367839336395,
-0.01351632084697485,
0.030876465141773224,
0.014840836636722088,
0.012127085588872433,
0.042759526520967484,
0.015901697799563408,
-0.018641483038663864,
-0.02047061175107956,
-0.037063293159008026,
-0.034844402223825455,
-0.04488270357251167,
0.0013430111575871706,
0.017164837568998337,
-0.019018035382032394,
0.0037516921292990446,
-0.12986108660697937,
-0.026938002556562424,
0.04516524076461792,
-0.0271600354462862,
-0.03473759442567825,
-0.013411538675427437,
-0.01641080528497696,
-0.026913665235042572,
-0.032297637313604355,
-0.057617977261543274,
0.03080080635845661,
-0.0074205463752150536,
-0.024865251034498215,
0.0028601689264178276,
-0.01771838404238224,
0.08753207325935364,
-0.0457470566034317,
-0.04085274040699005,
0.011546710506081581,
-0.03345735743641853,
-0.030387090519070625,
-0.0550125427544117,
0.00006074787233956158,
0.03992513194680214,
0.008902118541300297,
-0.023116931319236755,
-0.02933952771127224,
-0.027046551927924156,
0.029559116810560226,
-0.025948282331228256,
0.007315925322473049,
0.017884831875562668,
0.07572659850120544,
0.03237113356590271,
0.029297152534127235,
-0.03873680159449577,
0.012983513064682484,
0.01531237456947565,
0.00987018458545208,
0.051273833960294724,
-0.02358776330947876,
-0.026807544752955437,
0.020584406331181526,
0.02523186057806015,
-0.0002565835020504892,
0.04292663559317589,
0.06557914614677429,
0.025890465825796127,
-0.003956501372158527,
0.004074529744684696,
-0.05672598257660866,
-0.003751390380784869,
0.010602300055325031,
0.019659338518977165,
-0.004923135042190552,
-0.0042202649638056755,
0.03837282583117485,
0.017460905015468597,
-0.05551324784755707,
0.004150232765823603,
0.0006865797913633287,
0.06460830569267273,
0.03633415699005127,
0.001888094819150865,
-0.004687828477472067,
-0.046511661261320114,
-0.03922620415687561,
-0.027767077088356018,
0.0328875333070755,
0.019781876355409622,
0.06954888254404068,
-0.007313558831810951,
0.011803653091192245,
0.00008741544297663495,
-0.05555105209350586,
0.001708359457552433,
0.011610335670411587,
-0.02603059634566307,
-0.03424885869026184,
-0.037135329097509384,
-0.023739615455269814,
0.035920049995183945,
-0.013992460444569588,
-0.0417732298374176,
-0.015728456899523735,
-0.02122727781534195,
0.01417311280965805,
0.038217201828956604,
0.014861617237329483,
-0.013483541086316109,
-0.013081163167953491,
0.059115707874298096,
-0.013709542341530323,
0.0477975495159626,
0.014475833624601364,
-0.015628738328814507,
0.06242963299155235,
0.021679123863577843,
0.0562041699886322,
-0.024788692593574524,
0.038064777851104736
] |
[
8.56911563873291,
-2.423844814300537
] |
Strongly Correlated Electrons
|
Condensed-Matter Physics
|
cond-mat-str-el
|
na
|
na
|
2007-03-31T14:14:46
|
We show that crystal can trap a broad (x, x', y, y', E) distribution of
particles and channel it preserved with a high precision. This sampled-and-hold
distribution can be steered by a bent crystal for analysis downstream. In
simulations for the 7 TeV Large Hadron Collider, a crystal adapted to the
accelerator lattice traps 90% of diffractively scattered protons emerging from
the interaction point with a divergence 100 times the critical angle. We set
the criterion for crystal adaptation improving efficiency ~100-fold. Proton
angles are preserved in crystal transmission with accuracy down to 0.1
microrad. This makes feasible a crystal application for measuring very forward
protons at the LHC.
|
Crystal channeling of LHC forward protons with preserved distribution in
phase space
|
hep-ph
|
0704.0031
| 2,007
|
[
0.01566479541361332,
0.055711887776851654,
-0.009947497397661209,
-0.06312266737222672,
0.03022310510277748,
-0.016223959624767303,
-0.009620383381843567,
0.06678757071495056,
-0.02983253076672554,
-0.00024634270812384784,
-0.046909742057323456,
0.07644524425268173,
-0.028296388685703278,
-0.017971936613321304,
-0.0051391758024692535,
0.01960148476064205,
0.036373525857925415,
-0.02850978821516037,
-0.04755718261003494,
0.028935659676790237,
0.02089281566441059,
0.0032663217280060053,
-0.03624701127409935,
-0.03920084610581398,
0.03953419625759125,
-0.015499291941523552,
0.014817527495324612,
-0.00968190748244524,
-0.08614976704120636,
0.015439125709235668,
0.062174536287784576,
-0.07772351056337357,
-0.0014934417558833957,
-0.019665999338030815,
-0.036293935030698776,
-0.03305894136428833,
0.040217526257038116,
-0.029989449307322502,
0.036757390946149826,
0.004830934107303619,
0.045989878475666046,
-0.019011177122592926,
-0.017774976789951324,
-0.023174235597252846,
0.05682740733027458,
0.007066093850880861,
0.00870390422642231,
-0.02565397508442402,
0.022584129124879837,
-0.024088017642498016,
-0.026083918288350105,
0.042182836681604385,
-0.00046146594104357064,
-0.030207283794879913,
0.007188834715634584,
0.04328730329871178,
-0.01865687035024166,
0.013772755861282349,
0.11306057870388031,
-0.044500358402729034,
0.007373906206339598,
0.02692781202495098,
-0.07969364523887634,
0.008471967652440071,
0.00037522768252529204,
-0.01971191167831421,
-0.04981968179345131,
0.015764988958835602,
-0.021072836592793465,
-0.05978376045823097,
0.03678751736879349,
0.0009038144489750266,
0.008757032454013824,
0.013671518303453922,
-0.02758067101240158,
0.020184949040412903,
0.0262201689183712,
-0.00038553893682546914,
-0.004526371601969004,
-0.005862067453563213,
-0.04551059380173683,
-0.030550260096788406,
0.0040334672667086124,
0.01189509965479374,
0.10088273882865906,
0.05772711709141731,
-0.004264510702341795,
0.04754628986120224,
-0.057420387864112854,
0.02757049910724163,
0.01472056470811367,
0.01153051108121872,
0.009331691078841686,
0.0352468378841877,
-0.04472171515226364,
0.05062593147158623,
-0.00040761727723293006,
0.02998213656246662,
-0.01230887696146965,
-0.013915219344198704,
0.033142782747745514,
0.015473512932658195,
-0.008847658522427082,
0.03961097449064255,
0.05892312526702881,
0.019879134371876717,
0.012671930715441704,
-0.010753672569990158,
0.0467950813472271,
-0.004348806571215391,
-0.06308533996343613,
-0.0751870796084404,
0.011961030773818493,
0.03910868987441063,
-0.03310127928853035,
-0.023995213210582733,
0.08426468819379807,
-0.014316840097308159,
-0.03414444252848625,
0.04057569056749344,
0.019964784383773804,
-0.002646873239427805,
-0.023742731660604477,
0.07708011567592621,
0.015222322195768356,
0.051810432225465775,
-0.045188240706920624,
-0.000963826896622777,
0.008123871870338917,
0.028315654024481773,
-0.03292985260486603,
0.00028867018409073353,
-0.05361606553196907,
-0.005797416903078556,
0.017347974702715874,
0.014514799229800701,
-0.004566890187561512,
-0.011501121334731579,
0.043302152305841446,
0.005861279089003801,
0.006696778349578381,
-0.003903019707649946,
0.03353271633386612,
-0.02155572548508644,
0.021600907668471336,
-0.03245921432971954,
-0.016565589234232903,
-0.04143524914979935,
-0.03460643067955971,
0.022956838831305504,
-0.02678506262600422,
0.06892476975917816,
0.06022310629487038,
0.07591380178928375,
-0.029675783589482307,
-0.07174985110759735,
-0.006161130499094725,
0.0028621761593967676,
0.006794517859816551,
0.013498540036380291,
0.026706213131546974,
0.024621278047561646,
-0.1072060689330101,
0.05315253138542175,
-0.03867918998003006,
-0.023919526487588882,
0.03140009939670563,
-0.008242420852184296,
0.05775371566414833,
0.045129355043172836,
-0.03818579018115997,
-0.03286220505833626,
-0.012516023591160774,
-0.02647644281387329,
0.013742255046963692,
0.015261339955031872,
0.042696528136730194,
-0.053797703236341476,
0.03472656384110451,
0.03501514717936516,
0.03712661936879158,
-0.03596721589565277,
0.020080439746379852,
-0.006309133023023605,
0.004013080149888992,
0.0037750410847365856,
0.019647717475891113,
-0.03412565588951111,
0.0487091988325119,
-0.037687260657548904,
0.04202859103679657,
-0.0051857889629900455,
-0.0858689546585083,
-0.05086343735456467,
0.01711508259177208,
-0.09341547638177872,
0.0754295215010643,
-0.061618462204933167,
-0.006012724246829748,
-0.004011192824691534,
-0.06405314803123474,
-0.03230256214737892,
0.011704572476446629,
0.03363639488816261,
0.007280332967638969,
0.024319585412740707,
-0.029981398954987526,
0.005046708509325981,
0.013284160755574703,
-0.004006184171885252,
0.04299692064523697,
0.0596780963242054,
-0.03415694460272789,
-0.004945249762386084,
0.0024371834006160498,
-0.008032253943383694,
0.02947332337498665,
-0.04635608568787575,
-0.03785131126642227,
0.04780200123786926,
0.02554086595773697,
-0.030986232683062553,
0.008798697032034397,
-0.012469314970076084,
0.042229387909173965,
0.022636588662862778,
0.018360568210482597,
-0.0011470114113762975,
-0.05342504754662514,
-0.010030406527221203,
-0.035029537975788116,
-0.01669076457619667,
0.024693375453352928,
0.017054829746484756,
0.017956465482711792,
-0.05037800222635269,
-0.05951407924294472,
0.021220633760094643,
0.012041122652590275,
0.03367024287581444,
0.008663506247103214,
-0.045079994946718216,
-0.0447331927716732,
-0.07950092107057571,
-0.07807811349630356,
0.016413558274507523,
0.02172965183854103,
-0.0033572728279978037,
-0.01976771466434002,
0.004299719352275133,
0.03462596237659454,
-0.010266720317304134,
0.031683485954999924,
0.005739759653806686,
0.021701762452721596,
-0.01596171222627163,
-0.026852793991565704,
0.03000861220061779,
-0.061215586960315704,
-0.0799408033490181,
0.040534310042858124,
-0.06932397931814194,
0.01617956906557083,
-0.06884724646806717,
-0.01757650449872017,
0.0161533672362566,
0.05075422301888466,
-0.01710587367415428,
0.01990676485002041,
-0.024645933881402016,
0.0075916419737041,
0.019003083929419518,
0.11698424071073532,
0.03774024173617363,
-0.018528806045651436,
0.02835441567003727,
0.02102820761501789,
-0.05151922628283501,
-0.008502478711307049,
-0.00928996317088604,
-0.07200631499290466,
-0.014508289285004139,
-0.007994871586561203,
-0.03373512253165245,
-0.04975404962897301,
0.07787100225687027,
0.04496416822075844,
-0.05479278787970543,
-0.03512093797326088,
0.0036011547781527042,
-0.031168663874268532,
-0.023484572768211365,
0.048263173550367355,
0.024395834654569626,
0.00929450523108244,
0.02334483526647091,
0.09384558349847794,
0.02696496993303299,
-0.022161182016134262,
0.05555082485079765,
0.006274175364524126,
0.011549767106771469,
0.005598621908575296,
0.002150728600099683,
0.0001605723227839917,
0.04742547497153282,
0.008580068126320839,
0.0006853333325125277,
0.05606621876358986,
-0.010000650770962238,
0.01862761750817299,
0.056235216557979584,
-0.0041192639619112015,
0.050206512212753296,
-0.054174769669771194,
-0.03687286376953125,
0.06964890658855438,
0.022579284384846687,
0.06091122329235077,
0.008684767410159111,
0.05031464993953705,
0.046149905771017075,
0.03105541691184044,
-0.06135982275009155,
0.03445800766348839,
0.03868003189563751,
0.01847660355269909,
0.056453946977853775,
-0.027623375877738,
-0.022826965898275375,
-0.0015529398806393147,
0.041979093104600906,
0.015032824128866196,
0.031222201883792877,
-0.020284973084926605,
0.013597206212580204,
-0.01546851173043251,
0.028441447764635086,
0.020857805386185646,
-0.05914890021085739,
-0.006840240675956011,
-0.05919550731778145,
-0.03702873736619949,
-0.01554801780730486,
0.040754981338977814,
-0.017135493457317352,
-0.041274312883615494,
-0.010831613093614578,
0.052749793976545334,
0.019406555220484734,
-0.024808788672089577,
0.01670745015144348,
-0.004177557770162821,
-0.016627907752990723,
0.007353784516453743,
0.013231620192527771,
0.023747039958834648,
-0.04938097298145294,
0.08878401666879654,
0.017509466037154198,
0.014154288917779922,
-0.04067632555961609,
0.031032288447022438,
-0.006372193340212107,
-0.023003770038485527,
0.034086234867572784,
-0.01011315081268549,
0.03930087015032768,
0.002465673955157399,
-0.013485681265592575,
-0.015498136170208454,
-0.07802893221378326,
0.01379472017288208,
0.024521417915821075,
0.02859240025281906,
0.006843840703368187,
-0.0613841786980629,
0.015309889800846577,
-0.014366170391440392,
-0.007611124310642481,
0.04750630632042885,
0.03193848580121994,
0.03693228214979172,
-0.029250172898173332,
-0.026976339519023895,
-0.01308723259717226,
-0.04966742917895317,
-0.009418823756277561,
-0.025538578629493713,
0.03764818236231804,
0.006302727852016687,
-0.013768283650279045,
-0.014134065248072147,
-0.004374440759420395,
-0.005325607489794493,
-0.0359363779425621,
0.029414821416139603,
0.01855503022670746,
-0.03625298663973808,
0.0004902384825982153,
-0.029608584940433502,
-0.04536993056535721,
0.04652974754571915,
-0.03717060014605522,
-0.00734113622456789,
0.009870539419353008,
-0.030415276065468788,
-0.038194142282009125,
0.03186473622918129,
0.03211483731865883,
0.014550366438925266,
0.0027653358411043882,
-0.015398358926177025,
-0.051355037838220596,
0.0323651097714901,
-0.01756437122821808,
0.02314908429980278,
-0.021536845713853836,
0.05314333364367485,
-0.02675011195242405,
0.026825176551938057,
0.04943471774458885,
-0.008201008662581444,
-0.007177857216447592,
0.03310971334576607,
0.0014533024514093995,
-0.015919040888547897,
0.006066491827368736,
-0.012433147057890892,
-0.004472126718610525,
0.037904638797044754,
0.011097045615315437,
0.025241250172257423,
-0.001594948465935886,
-0.0040499665774405,
-0.021396610885858536,
0.023851851001381874,
-0.04929720610380173,
-0.01919235661625862,
0.059650860726833344,
0.05948067456483841,
-0.050762150436639786,
0.016078252345323563,
-0.000878489576280117,
0.0014315810985863209,
0.04360423609614372,
0.02410198003053665,
0.005796981509774923,
0.008645904250442982,
0.027152463793754578,
0.03046324849128723,
0.004475420340895653,
-0.021746046841144562,
0.024670671671628952,
0.08354690670967102,
0.0009413048392161727,
0.032841265201568604,
-0.02336660586297512,
0.0939982607960701,
0.056771405041217804,
-0.003769972361624241,
0.04052744805812836,
-0.009503327310085297,
0.005000631790608168,
-0.0142799261957407,
0.01024311501532793,
-0.010187575593590736,
-0.055875930935144424,
0.01133307907730341,
0.027327345684170723,
-0.04576852545142174,
-0.03051532804965973,
0.040002405643463135,
0.004331438336521387,
-0.023184090852737427,
-0.03903069347143173,
-0.04509343206882477,
-0.032823968678712845,
0.001420649467036128,
0.07183370739221573,
-0.0028569733258336782,
0.012214453890919685,
0.02972777560353279,
-0.047471657395362854,
-0.043533939868211746,
0.03362760692834854,
-0.050086818635463715,
0.002938056131824851,
-0.017033349722623825,
0.006545436568558216,
-0.022635644301772118,
0.041768137365579605,
0.02758403867483139,
0.03658413141965866,
-0.019311049953103065,
-0.06235635653138161,
0.02093096449971199,
0.03642464801669121,
-0.006655809935182333,
0.018123645335435867,
0.01733088679611683,
-0.036334529519081116,
-0.007339840289205313,
-0.03254565969109535,
-0.027212100103497505,
0.015286342240869999,
-0.003575690556317568,
-0.05247695744037628,
-0.04439332336187363,
-0.021389242261648178,
0.03977850452065468,
0.035227492451667786,
0.04645046219229698,
0.039549291133880615,
0.061833303421735764,
-0.043771084398031235,
0.017513256520032883,
0.03068041428923607,
-0.0938202366232872,
-0.007113353814929724,
-0.027457235381007195,
0.013593868352472782,
0.0016774097457528114,
-0.002604251727461815,
-0.12184590101242065,
-0.02063833922147751,
-0.038880862295627594,
-0.0699092373251915,
0.0076128458604216576,
-0.04464596509933472,
0.015909625217318535,
0.06706004589796066,
-0.0020361675415188074,
0.011715526692569256,
0.03346000239253044,
-0.028511108830571175,
-0.03657320514321327,
0.02327927201986313,
-0.03439342603087425,
-0.007353827822953463,
0.007454350590705872,
0.018710510805249214,
0.0502266101539135,
0.07724178582429886,
0.0246744304895401,
-0.03770923614501953,
-0.05042589455842972,
-0.003246024250984192,
-0.010103600099682808,
-0.07890018075704575,
-0.007974790409207344,
0.003579461947083473,
0.053588539361953735,
-0.0638548955321312,
-0.0004511021834332496,
-0.0032947424333542585,
0.004934495314955711,
-0.07081595808267593,
0.01634323224425316,
-0.052322715520858765,
-0.062479112297296524,
0.0119820237159729,
0.010734552517533302,
-0.033677540719509125,
0.025832517072558403,
-0.05380506068468094,
-0.0376429446041584,
0.00849977508187294,
0.020065905526280403,
-0.023118125274777412,
-0.004085477441549301,
-0.048201922327280045,
-0.03547879680991173,
0.0284161027520895,
0.01936090737581253,
0.01724262163043022,
0.019997593015432358,
0.008334575220942497,
-0.000885779329109937,
0.004835457541048527,
-0.013454745523631573,
0.0009331161854788661,
0.019643157720565796,
0.003986515570431948,
-0.04717260226607323,
0.007631636690348387,
-0.026979463174939156,
-0.031061939895153046,
0.0683332085609436,
-0.030598824843764305,
0.023473836481571198,
-0.02746475115418434,
-0.019975339993834496,
-0.02509000152349472,
-0.062034253031015396,
0.0011495756916701794,
-0.01719883643090725,
-0.01788303256034851,
-0.032268226146698,
-0.001121548586525023,
-0.023238981142640114,
0.03760256990790367,
0.026962194591760635,
0.004913262091577053,
0.029294101521372795,
0.003704564180225134,
0.02107783406972885,
0.045389968901872635,
0.0011021767277270555,
0.017916442826390266,
-0.010152825154364109,
-0.0008020920213311911,
-0.002499180845916271,
-0.08181780576705933,
-0.02810942754149437,
-0.05374491959810257,
0.08136802911758423,
-0.021322963759303093,
0.009048623964190483,
-0.041576799005270004,
-0.0271828081458807,
0.015149176120758057,
-0.03894679620862007,
-0.055134162306785583,
-0.012839709408581257,
0.013632280752062798,
-0.007102955132722855,
-0.0041384208016097546,
-0.011195672675967216,
0.03551812842488289,
0.01790999062359333,
-0.04207364469766617,
-0.01986071467399597,
-0.023440809920430183,
-0.014837492257356644,
0.05602283030748367,
-0.035115376114845276,
0.06970410794019699,
0.036063820123672485,
0.05915607139468193,
0.024334365501999855,
0.013816522434353828,
-0.021356690675020218,
0.006115482654422522,
-0.02029360830783844,
0.00947791151702404,
-0.013970490545034409,
0.05807267129421234,
-0.036364588886499405,
-0.025763312354683876,
0.05107089504599571,
0.0963376984000206,
0.003027169266715646,
-0.004539721645414829,
0.02746245078742504,
0.009641330689191818,
0.04989580065011978,
0.04140741378068924,
-0.023961141705513,
-0.05858960747718811,
-0.061135195195674896,
-0.03800198435783386,
0.04547799006104469,
-0.02922520786523819,
0.01881542056798935,
-0.0522257499396801,
-0.04879402369260788,
-0.07045039534568787,
-0.020883778110146523,
0.0054948232136666775,
-0.07060283422470093,
-0.018294181674718857,
-0.04274657368659973,
-0.014305575750768185,
-0.05287694185972214,
-0.03215691074728966,
0.01729913055896759,
0.015364617109298706,
0.0018104229820892215,
0.038464777171611786,
0.05341019108891487,
0.006386163644492626,
0.02051824890077114,
0.0008516241796314716,
0.004233726765960455,
-0.037871360778808594,
-0.03775014728307724,
-0.009902726858854294,
-0.04375642538070679,
-0.053124990314245224,
0.013914206065237522,
0.009405354969203472,
0.011574759148061275,
-0.07548867911100388,
0.006277102045714855,
0.03559949994087219,
-0.01667170412838459,
0.02579188533127308,
-0.004377561621367931,
-0.010351643897593021,
0.008319743908941746,
0.039625316858291626,
0.0083375358954072,
0.09410224854946136,
0.042534250766038895,
-0.013232657685875893,
0.016877207905054092,
0.04092856124043465,
0.03272603079676628,
-0.027135610580444336,
-0.022727834060788155,
0.002028401242569089,
0.07135618478059769,
0.030229417607188225,
0.07972652465105057,
0.01736234314739704,
0.0013524338137358427,
-0.028756652027368546,
0.02246425487101078,
-0.007578546181321144,
0.003582707839086652,
-0.02123665064573288,
-0.026696063578128815,
0.010497206822037697,
0.02427668124437332,
-0.0754198506474495,
-0.023389585316181183,
-0.0033017226960510015,
0.03441735357046127,
0.023867089301347733,
0.031106987968087196,
-0.005358785390853882,
-0.03590124845504761,
0.0306292362511158,
-0.012416746467351913,
0.0005075474618934095,
-0.019282525405287743,
0.0017889906885102391,
-0.0751761943101883,
0.0014221217716112733,
0.005605596583336592,
-0.017410224303603172,
-0.026075972244143486,
-0.03650614246726036,
-0.021973613649606705,
0.004747461527585983,
-0.03941166028380394,
0.04043745622038841,
0.05866869539022446,
0.01143480185419321,
-0.007742314599454403,
-0.033928848803043365,
0.0031566352117806673,
0.005979133304208517,
-0.014295988716185093,
0.012645985931158066,
0.04048175737261772,
0.03117806650698185,
0.03732382506132126,
-0.06684858351945877,
0.02234782464802265,
-0.02343708463013172,
0.058989960700273514,
0.037732768803834915,
0.00003363143696333282,
0.035416990518569946,
-0.042639221996068954,
-0.02445727214217186
] |
[
10.218371391296387,
2.1989235877990723
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
na
|
na
|
2007-04-02T18:35:33
|
We analyze the possibility of probing non-standard neutrino interactions
(NSI, for short) through the detection of neutrinos produced in a future
galactic supernova (SN).We consider the effect of NSI on the neutrino
propagation through the SN envelope within a three-neutrino framework, paying
special attention to the inclusion of NSI-induced resonant conversions, which
may take place in the most deleptonised inner layers. We study the possibility
of detecting NSI effects in a Megaton water Cherenkov detector, either through
modulation effects in the $\bar\nu_e$ spectrum due to (i) the passage of shock
waves through the SN envelope, (ii) the time dependence of the electron
fraction and (iii) the Earth matter effects; or, finally, through the possible
detectability of the neutronization $\nu_e$ burst. We find that the $\bar\nu_e$
spectrum can exhibit dramatic features due to the internal NSI-induced resonant
conversion. This occurs for non-universal NSI strengths of a few %, and for
very small flavor-changing NSI above a few$\times 10^{-5}$.
|
Probing non-standard neutrino interactions with supernova neutrinos
|
hep-ph
|
0704.0032
| 2,007
|
[
-0.020445937290787697,
0.07478374242782593,
0.0097128264605999,
-0.009979765862226486,
0.00732149463146925,
0.031002050265669823,
-0.02948799915611744,
0.027613282203674316,
-0.0055526793003082275,
-0.03507688269019127,
-0.06645374000072479,
0.04037398844957352,
-0.00347424135543406,
0.01611700840294361,
0.010024990886449814,
-0.04967315122485161,
0.05039208009839058,
0.0005957572138868272,
0.0011963347205892205,
0.017211267724633217,
-0.03177473321557045,
-0.024607978761196136,
-0.0050735133700072765,
-0.0708710178732872,
0.09975790232419968,
0.0022536669857800007,
0.05373925343155861,
0.022508561611175537,
-0.05783282592892647,
0.028463440015912056,
0.050277210772037506,
-0.07031786441802979,
-0.009504579938948154,
-0.05254020541906357,
-0.06534279137849808,
-0.054295141249895096,
0.04907739907503128,
-0.009068097919225693,
0.00935693271458149,
0.05954303592443466,
0.023425282910466194,
0.004015389364212751,
-0.0391496941447258,
-0.044067010283470154,
0.03208133205771446,
0.026700859889388084,
0.020511336624622345,
-0.02054060436785221,
0.03731768578290939,
-0.018659893423318863,
-0.033685483038425446,
-0.010610624216496944,
0.013958792202174664,
0.0044543626718223095,
0.012887160293757915,
-0.002621021354570985,
0.04808785021305084,
-0.021883537992835045,
0.07263191044330597,
-0.04644548147916794,
0.007816328667104244,
0.014652409590780735,
-0.02204924076795578,
-0.003922723699361086,
0.012974885292351246,
-0.028593353927135468,
-0.05007774010300636,
0.040871601551771164,
-0.009508602321147919,
-0.015746217221021652,
0.041584957391023636,
-0.0005285522202029824,
-0.030517421662807465,
0.05734151974320412,
0.029144039377570152,
0.015697672963142395,
-0.025208236649632454,
0.0034735219087451696,
-0.0233172457665205,
0.04446270689368248,
0.028928080573678017,
-0.03895599767565727,
0.02631445787847042,
0.0077604372054338455,
0.0549754835665226,
0.018317880108952522,
0.005218670703470707,
0.00996375922113657,
-0.03946933522820473,
0.009607721120119095,
0.028646888211369514,
-0.02374536171555519,
0.013417392037808895,
0.012219651602208614,
-0.020445117726922035,
-0.005264234263449907,
0.046759508550167084,
0.07594030350446701,
-0.013740959577262402,
-0.0281522236764431,
-0.02190631628036499,
0.055054258555173874,
0.015288698486983776,
-0.0073927524499595165,
0.0528792068362236,
0.04967308044433594,
0.044834524393081665,
0.009286080487072468,
0.018177134916186333,
-0.06391699612140656,
-0.06636868417263031,
-0.08382125198841095,
0.056507907807826996,
0.016863740980625153,
-0.024258717894554138,
-0.0384196899831295,
-0.015510660596191883,
-0.06806863844394684,
-0.019993828609585762,
0.09383215010166168,
0.00009230310388375074,
0.02093522436916828,
-0.023956870660185814,
0.07061143964529037,
-0.02760336361825466,
0.022048475220799446,
-0.02256123162806034,
0.025617776438593864,
0.041583459824323654,
-0.02156047523021698,
-0.02105441503226757,
-0.015026746317744255,
-0.028428837656974792,
0.026625709608197212,
0.07559682428836823,
0.06280438601970673,
-0.015147857367992401,
-0.06786742806434631,
0.02203276753425598,
-0.02715723030269146,
-0.004966667387634516,
0.013316776603460312,
0.017330391332507133,
0.010013782419264317,
0.015840956941246986,
-0.06288817524909973,
-0.01973714306950569,
0.0050011929124593735,
-0.0951148197054863,
0.01083532813936472,
0.020466431975364685,
0.012169827707111835,
0.015829376876354218,
0.027215266600251198,
-0.01577802561223507,
-0.002567568328231573,
-0.05562597140669823,
0.005231679882854223,
0.014206520281732082,
0.01394210197031498,
0.02928854711353779,
-0.019635992124676704,
-0.04127153009176254,
0.04243087023496628,
-0.05730129033327103,
0.0356503464281559,
0.030202742666006088,
0.009843834675848484,
0.015576963312923908,
0.025830473750829697,
-0.07717543095350266,
-0.00973994005471468,
-0.026287056505680084,
-0.0007898189360275865,
-0.02280215546488762,
0.044067416340112686,
0.005009918939322233,
-0.07090701162815094,
-0.0004954430623911321,
0.009754311293363571,
0.004396991338580847,
-0.03319812938570976,
-0.0005069260369054973,
0.0174587182700634,
-0.009221117943525314,
0.062038201838731766,
0.03933758661150932,
-0.018905840814113617,
0.02201743610203266,
-0.0028713035862892866,
0.015314517542719841,
0.00890517421066761,
-0.0030675253365188837,
-0.03301038220524788,
0.006560734938830137,
-0.013444328680634499,
0.016956878826022148,
-0.01482795737683773,
-0.012878221459686756,
-0.04797159135341644,
-0.05664131045341492,
-0.01571308821439743,
-0.0449262335896492,
-0.05409777909517288,
0.03992999717593193,
0.005256284959614277,
-0.002030777744948864,
0.021493079140782356,
0.019351700320839882,
-0.018939124420285225,
0.07741762697696686,
-0.0007568032015115023,
-0.02778855711221695,
-0.027738971635699272,
-0.0324104018509388,
0.03390006348490715,
0.011218699626624584,
-0.021590838208794594,
-0.019299859181046486,
0.08046123385429382,
0.0034390888176858425,
-0.0026311944238841534,
-0.00018172581621911377,
-0.03895583003759384,
-0.009887215681374073,
0.0160516444593668,
-0.009589388966560364,
-0.015208101831376553,
-0.00825639721006155,
-0.029512306675314903,
-0.006337921600788832,
0.0011058301897719502,
0.04902368783950806,
0.015267605893313885,
-0.037947770208120346,
0.009149478748440742,
0.023442568257451057,
-0.0062861633487045765,
0.018945837393403053,
0.010419247671961784,
0.0033750932198017836,
-0.018380185589194298,
-0.0343988798558712,
0.003507825080305338,
0.002496421569958329,
-0.038093093782663345,
-0.009517943486571312,
-0.008503608405590057,
-0.03243033587932587,
0.014636908657848835,
-0.000045530334318755195,
0.014146420173346996,
0.02785058319568634,
0.06608965247869492,
0.036900594830513,
0.0033379988744854927,
-0.021293696016073227,
0.05432268604636192,
-0.08650816231966019,
-0.030621541664004326,
0.02708698809146881,
-0.04218913987278938,
-0.019612137228250504,
-0.041731975972652435,
0.022367754951119423,
-0.02050667069852352,
0.007439938373863697,
-0.00513959676027298,
-0.05111861228942871,
-0.0006675219046883285,
-0.0007436664309352636,
0.007132458500564098,
0.06161767989397049,
0.02606712281703949,
0.005694831255823374,
0.0349583700299263,
0.025318510830402374,
0.03494401276111603,
-0.023702016100287437,
-0.04375317320227623,
-0.08234482258558273,
0.05009423941373825,
-0.05286003649234772,
-0.04490434378385544,
-0.0014184161555022001,
0.054432712495326996,
0.0051286546513438225,
-0.021419784054160118,
0.009056854993104935,
0.04427238926291466,
0.0007244484731927514,
-0.04999741539359093,
0.0019409526139497757,
0.06000925227999687,
0.03440730273723602,
0.0034482441842556,
0.11475770175457001,
0.043601736426353455,
0.008321240544319153,
0.011915692128241062,
0.04856245219707489,
-0.03296038880944252,
-0.020894933491945267,
0.006429229862987995,
-0.0013100231299176812,
-0.028458021581172943,
-0.02523922733962536,
-0.007057346869260073,
0.07429178059101105,
0.01153587456792593,
-0.02773194946348667,
0.026005852967500687,
0.006275685969740152,
0.016749482601881027,
-0.012350838631391525,
0.07476424425840378,
-0.01383562758564949,
0.005549141205847263,
0.0959547609090805,
0.029667304828763008,
0.023658590391278267,
-0.06828698515892029,
0.029044397175312042,
-0.03951316699385643,
0.009011013433337212,
0.06996750086545944,
0.03317645937204361,
0.058110643178224564,
-0.06867928057909012,
-0.012751178815960884,
-0.012356055900454521,
0.03244035691022873,
-0.007555190473794937,
-0.025067290291190147,
-0.042614005506038666,
0.05753416195511818,
0.010476808995008469,
0.09059276431798935,
0.002780476352199912,
0.051273856312036514,
0.007605781778693199,
-0.09204592555761337,
-0.030356114730238914,
-0.060991764068603516,
-0.023966867476701736,
-0.006898373831063509,
-0.06546888500452042,
-0.01946333236992359,
-0.003636830486357212,
-0.008020268753170967,
-0.027712658047676086,
-0.0017649471992626786,
0.006433618254959583,
-0.008357423357665539,
0.0028270352631807327,
0.00660711107775569,
0.03287462890148163,
-0.03659868240356445,
0.03045930527150631,
0.020405402407050133,
0.025852836668491364,
-0.05641230568289757,
0.018555987626314163,
0.029310720041394234,
0.010915894992649555,
0.05878591910004616,
0.030905837193131447,
0.00811068806797266,
0.029449257999658585,
-0.04945971444249153,
-0.04922596365213394,
-0.010184873826801777,
0.01890737935900688,
0.019074518233537674,
0.04899996891617775,
-0.005624495446681976,
-0.047448206692934036,
0.029470939189195633,
0.005160357803106308,
0.020927095785737038,
0.042082883417606354,
-0.02946295402944088,
0.027176257222890854,
-0.03217628225684166,
0.05627329275012016,
0.020799832418560982,
-0.04680703207850456,
-0.01375742070376873,
-0.036143332719802856,
-0.044432632625103,
-0.032806396484375,
-0.06452266871929169,
-0.022418342530727386,
0.01878509484231472,
-0.007175569888204336,
-0.052236855030059814,
0.044942520558834076,
-0.04174114391207695,
0.0015318323858082294,
0.0031709710601717234,
-0.05407164990901947,
-0.08169825375080109,
-0.010937651619315147,
-0.06423216313123703,
-0.03995600342750549,
0.025217095389962196,
-0.02186422049999237,
-0.0520336888730526,
0.01701417565345764,
-0.03545186668634415,
0.016537480056285858,
0.01520498562604189,
-0.02045886591076851,
-0.07995513081550598,
0.00441753538325429,
-0.05234355106949806,
0.07860353589057922,
-0.0011184903560206294,
-0.014290450140833855,
-0.024907955899834633,
0.017515365034341812,
0.053570110350847244,
-0.027422798797488213,
0.010983839631080627,
-0.0025502159260213375,
0.01996903494000435,
-0.010635500773787498,
-0.012356660328805447,
0.016778862103819847,
-0.02374984696507454,
0.035473376512527466,
-0.004979670513421297,
-0.003977165557444096,
0.061762817203998566,
-0.06591108441352844,
0.011599511839449406,
-0.0009117514709942043,
-0.025989210233092308,
-0.00024132344697136432,
0.01335932407528162,
0.06593343615531921,
-0.06254064291715622,
0.002343152416869998,
-0.028542151674628258,
0.05135984718799591,
0.10535503923892975,
0.004965583328157663,
-0.0075351782143116,
-0.03633732348680496,
-0.003259244840592146,
0.025640331208705902,
-0.05974654480814934,
-0.005838161334395409,
0.0398562066257,
0.08375824987888336,
-0.03858280926942825,
0.004716615192592144,
-0.0010942032095044851,
0.03087812103331089,
0.04309682920575142,
0.020296035334467888,
0.054306212812662125,
-0.02749827317893505,
0.008840742520987988,
0.031039975583553314,
-0.017348358407616615,
0.004091592039912939,
-0.01367549691349268,
0.03817213326692581,
0.0328865610063076,
0.043735578656196594,
-0.02140728197991848,
0.06518156081438065,
0.03544041886925697,
-0.024325624108314514,
-0.041174210608005524,
0.03554421290755272,
-0.048361122608184814,
0.027072636410593987,
0.022270146757364273,
0.03668728470802307,
-0.025820063427090645,
-0.05033570155501366,
-0.006971265655010939,
-0.050425201654434204,
0.04745585098862648,
-0.05865819379687309,
0.0182754285633564,
0.0064911022782325745,
-0.013139289803802967,
0.011573830619454384,
-0.001428955583833158,
0.04588688164949417,
-0.020466195419430733,
-0.02683098614215851,
-0.004997274372726679,
0.04400987923145294,
-0.010111385025084019,
0.014629850164055824,
-0.026993822306394577,
-0.034242261201143265,
-0.010966903530061245,
0.003972817212343216,
0.01084032841026783,
0.016254253685474396,
-0.0013581867096945643,
-0.04332933947443962,
-0.0663212239742279,
-0.002752631204202771,
-0.012083570472896099,
-0.002992410911247134,
0.02279839478433132,
0.01984473690390587,
0.029959602281451225,
0.0227914210408926,
-0.04052212834358215,
0.0023089630994945765,
-0.022799458354711533,
-0.028982115909457207,
0.027309568598866463,
-0.01694287545979023,
0.01238627266138792,
0.020393626764416695,
0.018055938184261322,
-0.02660653181374073,
0.006931928917765617,
0.0029185006860643625,
-0.06002278998494148,
0.08108900487422943,
-0.03881188854575157,
0.013462998904287815,
0.011215933598577976,
0.056708309799432755,
-0.004642074927687645,
0.051642607897520065,
-0.04630087688565254,
-0.006737458519637585,
0.0277990885078907,
0.0015477458946406841,
0.006384100299328566,
0.009750716388225555,
0.00419230991974473,
0.0412629097700119,
0.010469812899827957,
-0.027301520109176636,
-0.03079206496477127,
-0.05587601661682129,
0.05658610165119171,
-0.050516895949840546,
-0.023803096264600754,
0.030859163030982018,
-0.027676627039909363,
0.023927051573991776,
-0.10211397707462311,
0.03711856156587601,
-0.02316012792289257,
0.06084004417061806,
-0.04446076601743698,
-0.05391162261366844,
-0.03833317384123802,
0.005963247735053301,
-0.030106283724308014,
0.04412120208144188,
0.05075940489768982,
0.010914376936852932,
-0.06615718454122543,
-0.046756647527217865,
0.0012144973734393716,
0.03496689349412918,
-0.012108171358704567,
0.0002058833051705733,
0.00955689325928688,
-0.033327359706163406,
-0.033426422625780106,
-0.005903483368456364,
-0.06832510977983475,
0.06055464968085289,
0.012608038261532784,
-0.043092384934425354,
-0.023971697315573692,
-0.034376733005046844,
-0.023417942225933075,
0.01009522844105959,
0.040784500539302826,
0.00119808001909405,
0.027574829757213593,
0.021662341430783272,
0.0031250780448317528,
0.03205399215221405,
-0.018449701368808746,
0.029542025178670883,
-0.07411772757768631,
0.021326901391148567,
-0.003923499025404453,
-0.048486825078725815,
0.0022721863351762295,
0.000907657784409821,
-0.042863599956035614,
-0.04638155922293663,
0.07003886997699738,
-0.025337697938084602,
0.022104766219854355,
0.061616428196430206,
-0.012456964701414108,
0.036413755267858505,
0.007198827341198921,
-0.012523635290563107,
0.025029130280017853,
0.019266504794359207,
-0.016430901363492012,
0.03238171339035034,
0.008806377649307251,
-0.0016695564845576882,
-0.09343260526657104,
-0.04194103926420212,
-0.08770368993282318,
0.05669083446264267,
-0.0795014277100563,
0.030884090811014175,
0.004380733240395784,
0.009691359475255013,
-0.020423244684934616,
0.05745207890868187,
-0.022420765832066536,
-0.00013888282410334796,
0.005976892076432705,
-0.06437940895557404,
-0.0905158743262291,
0.016659609973430634,
0.04434802755713463,
-0.006950596813112497,
0.02837938629090786,
-0.0015431997599080205,
0.005521057173609734,
-0.04804500192403793,
-0.013766510412096977,
0.04862116277217865,
0.025736358016729355,
0.006875792518258095,
0.02532428503036499,
0.021729858592152596,
-0.03613259270787239,
0.03583800047636032,
0.007607882376760244,
0.03291430324316025,
0.05227363109588623,
0.006793210748583078,
0.044034115970134735,
-0.0002755021268967539,
-0.013365820981562138,
0.09640754014253616,
0.020631058141589165,
-0.013135087676346302,
0.03689245879650116,
-0.020355800166726112,
0.013367596082389355,
0.025246446952223778,
-0.03559466451406479,
-0.025857040658593178,
-0.011993897147476673,
-0.05761721730232239,
-0.044568438082933426,
0.0244040135294199,
0.015913084149360657,
0.04738203063607216,
-0.017774054780602455,
0.013110998086631298,
-0.08152236044406891,
0.010795913636684418,
0.05379417538642883,
-0.015687210485339165,
-0.04219900444149971,
-0.030035879462957382,
-0.014371685683727264,
-0.09638825058937073,
-0.05845816805958748,
-0.016232233494520187,
-0.03010687418282032,
0.02606467343866825,
-0.013431726023554802,
0.06583022326231003,
0.010321926325559616,
0.03351675719022751,
0.0024074665270745754,
-0.02682502381503582,
0.006567686330527067,
-0.03319808840751648,
-0.013810678385198116,
0.018428374081850052,
0.0006207780679687858,
0.030209483578801155,
0.04780251905322075,
0.0500895194709301,
-0.029945215210318565,
-0.008731670677661896,
-0.012068016454577446,
-0.07569937407970428,
0.038791265338659286,
0.014506123960018158,
0.014566579833626747,
-0.027591248974204063,
0.06722839921712875,
-0.015461532399058342,
-0.009483153000473976,
-0.05733179301023483,
-0.016671035438776016,
0.019529983401298523,
-0.008727391250431538,
0.012399686500430107,
0.0091177336871624,
-0.007566517684608698,
0.021399151533842087,
0.08828861266374588,
0.024267883971333504,
0.01321391947567463,
-0.004174595698714256,
0.013620407320559025,
-0.04225197806954384,
0.030762162059545517,
0.0065989987924695015,
-0.013455838896334171,
0.008761043660342693,
-0.04694652929902077,
0.06494364142417908,
0.014466354623436928,
-0.06051898002624512,
-0.010143082588911057,
0.03659983351826668,
0.015740538015961647,
-0.0026447847485542297,
-0.01755373552441597,
-0.01809416338801384,
-0.047908879816532135,
-0.024869652464985847,
-0.04743541032075882,
-0.007477325852960348,
-0.023162109777331352,
-0.012045266106724739,
-0.051038987934589386,
-0.012670747935771942,
0.03821664676070213,
-0.044954556971788406,
0.02300531417131424,
0.01313758920878172,
-0.02450246550142765,
-0.014197158627212048,
-0.037367045879364014,
0.03395839035511017,
-0.02582736127078533,
-0.022328926250338554,
0.03702457621693611,
-0.036145176738500595,
0.023216530680656433,
0.05211079493165016,
0.03285592421889305,
0.0204030629247427,
-0.042288653552532196,
0.012911316938698292,
0.025308221578598022,
-0.030614202842116356,
0.042818184942007065,
0.027923595160245895,
0.008291278034448624,
0.0453677773475647,
0.006395952310413122,
0.0006744699785485864,
-0.015256664715707302,
0.04530021548271179
] |
[
16.293807983398438,
2.1458678245544434
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
na
|
na
|
2007-03-31T15:34:25
|
We performed a rigorous theoretical convergence analysis of the discrete
dipole approximation (DDA). We prove that errors in any measured quantity are
bounded by a sum of a linear and quadratic term in the size of a dipole d, when
the latter is in the range of DDA applicability. Moreover, the linear term is
significantly smaller for cubically than for non-cubically shaped scatterers.
Therefore, for small d errors for cubically shaped particles are much smaller
than for non-cubically shaped. The relative importance of the linear term
decreases with increasing size, hence convergence of DDA for large enough
scatterers is quadratic in the common range of d. Extensive numerical
simulations were carried out for a wide range of d. Finally we discuss a number
of new developments in DDA and their consequences for convergence.
|
Convergence of the discrete dipole approximation. I. Theoretical
analysis
|
physics.optics physics.comp-ph
|
0704.0033
| 2,007
|
[
0.016483139246702194,
0.03245043754577637,
-0.0034515690058469772,
-0.03778185322880745,
0.0005971138016320765,
0.00720186298713088,
0.04758090525865555,
-0.01014017779380083,
-0.04874558746814728,
-0.040231797844171524,
-0.07404391467571259,
0.004904342349618673,
0.03896311670541763,
-0.0008651395328342915,
0.010375726968050003,
-0.060094475746154785,
0.005140861961990595,
-0.02618401125073433,
-0.019148437306284904,
0.04184948652982712,
0.013257060199975967,
0.002956392941996455,
-0.04095825180411339,
-0.087337926030159,
0.04366891831159592,
-0.016662416979670525,
0.0011459332890808582,
0.03365826979279518,
-0.056352026760578156,
0.026109451428055763,
0.02767549268901348,
-0.06279297918081284,
0.019030116498470306,
-0.01752203330397606,
-0.003336477791890502,
-0.029825372621417046,
0.016393600031733513,
-0.011868352070450783,
0.04179548844695091,
0.018631840124726295,
0.039022862911224365,
-0.037112049758434296,
-0.03235249221324921,
-0.011549989692866802,
-0.003138297237455845,
-0.014201835729181767,
0.023212211206555367,
0.0009639596682973206,
0.06155604124069214,
0.02270404063165188,
-0.027026381343603134,
0.03803344815969467,
0.06343588978052139,
-0.04110245779156685,
-0.021463800221681595,
0.01455469150096178,
0.006651703733950853,
-0.03507464379072189,
0.04448593035340309,
-0.013475870713591576,
0.008823471143841743,
0.06149638444185257,
-0.0824475809931755,
0.023863930255174637,
0.04546532779932022,
-0.04478568956255913,
-0.050276823341846466,
-0.014344535768032074,
0.019242549315094948,
-0.035477492958307266,
0.06329964846372604,
-0.07914921641349792,
0.04016680642962456,
0.013632780872285366,
-0.005572689231485128,
0.007721571251749992,
-0.021101471036672592,
-0.010844238102436066,
-0.01158361230045557,
-0.031443219631910324,
-0.039095669984817505,
-0.05071735009551048,
0.055123746395111084,
0.05018530413508415,
0.071162648499012,
0.045902326703071594,
-0.0023338408209383488,
0.0037504490464925766,
-0.011640850454568863,
0.015127504244446754,
-0.0006188173429109156,
-0.03534018248319626,
0.0034438453149050474,
0.04817057028412819,
-0.027483556419610977,
0.011375158093869686,
-0.026802990585565567,
0.04350937157869339,
0.06422112137079239,
0.007912800647318363,
0.022200290113687515,
0.04450450837612152,
0.019477708265185356,
0.0432007759809494,
0.03995361924171448,
0.027018552646040916,
-0.008493115194141865,
-0.03152609243988991,
0.0367216132581234,
-0.0016224250430241227,
-0.08447400480508804,
-0.04230119660496712,
-0.003948735073208809,
-0.021110493689775467,
-0.01416425034403801,
-0.003147362731397152,
0.052443716675043106,
-0.10704294592142105,
0.0013840080937370658,
0.04230321943759918,
0.021858874708414078,
-0.008555062115192413,
0.023792387917637825,
0.06976650655269623,
0.029260795563459396,
0.0026179193519055843,
-0.032308463007211685,
-0.002193205524235964,
0.042276155203580856,
-0.023916173726320267,
-0.025754529982805252,
-0.007986737415194511,
-0.044122856110334396,
0.0007441505440510809,
0.0381765216588974,
0.020516246557235718,
-0.015525490045547485,
-0.0656137466430664,
0.0016272973734885454,
0.005646429490298033,
0.01119795348495245,
0.003529924200847745,
0.05794006958603859,
-0.023472849279642105,
0.041161052882671356,
-0.04088454321026802,
-0.05036512762308121,
-0.067377470433712,
-0.036754753440618515,
-0.01793437823653221,
0.025510229170322418,
0.027745485305786133,
0.05495044216513634,
0.017655255272984505,
-0.05282995477318764,
0.002832731232047081,
0.0018310758750885725,
0.0024618126917630434,
0.06346481293439865,
-0.013538829982280731,
-0.02722238190472126,
0.01701066456735134,
-0.11879044026136398,
0.04519536718726158,
-0.0036225863732397556,
0.038118135184049606,
0.061181046068668365,
0.01565389893949032,
0.010764717124402523,
0.012120882980525494,
-0.01291351206600666,
-0.01028701476752758,
-0.002010104013606906,
-0.02885240875184536,
-0.030268192291259766,
0.031164683401584625,
0.011437132954597473,
-0.04691162705421448,
0.0010009236866608262,
0.01193670742213726,
0.039712198078632355,
-0.0027539299335330725,
-0.027893345803022385,
0.05303656682372093,
0.06332714110612869,
0.04334229603409767,
0.026280663907527924,
-0.03857220336794853,
-0.009484526701271534,
-0.019691532477736473,
0.007761285174638033,
-0.014326515607535839,
-0.0007608553860336542,
-0.013330011628568172,
-0.0037446299102157354,
-0.022698186337947845,
0.07681136578321457,
-0.06246427074074745,
0.024674709886312485,
-0.029697144404053688,
-0.04853099584579468,
0.018095996230840683,
0.042899034917354584,
0.015071296133100986,
0.014870475977659225,
0.02923509106040001,
-0.016444476321339607,
0.03289256989955902,
0.028951989486813545,
0.0002237755252281204,
0.06603962928056717,
-0.003489644266664982,
-0.0497799888253212,
0.023164814338088036,
-0.014262131415307522,
0.0120189618319273,
-0.02420331910252571,
-0.03855610638856888,
-0.047726109623909,
0.05795710161328316,
-0.012219076044857502,
-0.05116311460733414,
0.029771434143185616,
0.036312974989414215,
-0.0014497771626338363,
0.023671315982937813,
-0.016041399911046028,
0.005323268938809633,
-0.0013387094950303435,
-0.02770736627280712,
-0.0647040456533432,
-0.07723729312419891,
0.005693880375474691,
-0.028961267322301865,
-0.006274772342294455,
0.009369710460305214,
-0.04360060766339302,
-0.0019200340611860156,
0.05954904481768608,
0.038622431457042694,
0.01912725530564785,
0.020115207880735397,
0.01861337199807167,
-0.014474094845354557,
-0.08341861516237259,
0.01246058288961649,
-0.023722782731056213,
0.026016298681497574,
-0.05762430280447006,
0.044687073677778244,
0.021303510293364525,
0.0217369943857193,
0.042560283094644547,
0.059388309717178345,
0.019063159823417664,
-0.03914296254515648,
-0.048946209251880646,
0.02303784340620041,
0.026946136727929115,
-0.03228665515780449,
0.010038964450359344,
-0.021754706278443336,
-0.02480936422944069,
-0.05926349759101868,
-0.026204749941825867,
0.03571970760822296,
0.009585353545844555,
-0.030709456652402878,
0.0015886402688920498,
-0.019253108650445938,
-0.04983827471733093,
0.01452071126550436,
0.09111233800649643,
0.05507814139127731,
0.029503947123885155,
-0.000007439524779329076,
0.03995878994464874,
-0.028953639790415764,
0.04698733612895012,
0.0056295376271009445,
-0.058773357421159744,
-0.0035423198714852333,
-0.02771691232919693,
-0.02283937856554985,
0.03662431985139847,
0.008430118672549725,
-0.012276898138225079,
-0.08258667588233948,
-0.005074921529740095,
0.017208032310009003,
-0.042759958654642105,
0.03658592328429222,
0.004949451424181461,
0.022150475531816483,
-0.022488348186016083,
0.05843229591846466,
0.09965500980615616,
-0.005970466881990433,
-0.00475702527910471,
0.03046153485774994,
0.01996227353811264,
0.036382004618644714,
0.000542813737411052,
-0.0256629791110754,
0.030625667423009872,
0.08425106853246689,
-0.01752370595932007,
-0.037842731922864914,
0.020060256123542786,
-0.018401896581053734,
0.02539047971367836,
0.06847728788852692,
-0.013085223734378815,
-0.05039045214653015,
-0.011515600606799126,
-0.03800659626722336,
0.09237971901893616,
0.030384378507733345,
0.06470920145511627,
0.033221591264009476,
0.05535009503364563,
-0.0488438755273819,
-0.038254477083683014,
-0.009878108277916908,
-0.003337226575240493,
0.02688242681324482,
0.02702195756137371,
0.03621955215930939,
0.001812751404941082,
0.02289772592484951,
0.047476958483457565,
0.008574137464165688,
-0.05772174149751663,
-0.026964114978909492,
-0.05131237208843231,
-0.07059462368488312,
-0.024986734613776207,
0.011285170912742615,
-0.005539147648960352,
0.019100571051239967,
-0.0012455438263714314,
-0.04409600421786308,
-0.08460689336061478,
-0.060536883771419525,
0.0026174739468842745,
0.03746703639626503,
-0.009773324243724346,
0.010335348546504974,
0.0027932983357459307,
0.008068164810538292,
0.008394005708396435,
-0.01620221510529518,
-0.0022259156685322523,
0.027167508378624916,
-0.03171944618225098,
0.0368252694606781,
0.06423357129096985,
-0.025359923020005226,
0.039201945066452026,
0.02032337710261345,
0.03241882473230362,
-0.0035661037545651197,
0.013589361682534218,
0.004325335379689932,
0.022824537009000778,
0.040227849036455154,
-0.016709724441170692,
0.03095216117799282,
-0.003372946521267295,
-0.05453919991850853,
-0.09376052021980286,
-0.0045965202152729034,
0.022170424461364746,
0.022390738129615784,
0.014204544015228748,
-0.010092802345752716,
-0.04376143217086792,
0.010543565265834332,
-0.00969272293150425,
0.0014129442861303687,
0.025272388011217117,
0.03164023160934448,
0.025323016569018364,
-0.014721719548106194,
-0.0034145787358283997,
-0.005735241342335939,
-0.029728081077337265,
-0.01670312136411667,
-0.0605289489030838,
0.011217571794986725,
-0.0070411209017038345,
-0.0771627277135849,
-0.002138060051947832,
0.04747452586889267,
-0.013666431419551373,
-0.01384985912591219,
0.01810169592499733,
0.04846212640404701,
-0.013695214875042439,
0.017036085948348045,
-0.015401937067508698,
-0.06932863593101501,
0.026478685438632965,
-0.052711859345436096,
0.00634442875161767,
0.007154491264373064,
-0.04053789749741554,
-0.0035584326833486557,
0.018291015177965164,
-0.017593296244740486,
-0.04290570318698883,
0.013949757441878319,
-0.047754187136888504,
-0.03192772716283798,
0.04568624123930931,
0.006237769033759832,
0.016990622505545616,
-0.03193921968340874,
0.015545068308711052,
0.011853436008095741,
0.026991523802280426,
0.030937453731894493,
-0.07154154777526855,
-0.021434186026453972,
-0.022636819630861282,
0.01689787767827511,
-0.014368034899234772,
0.07718566060066223,
-0.0009261355735361576,
-0.08372750878334045,
0.01203196495771408,
-0.0011417183559387922,
-0.007504289038479328,
0.05997633561491966,
-0.02443103678524494,
-0.01859758421778679,
0.02904161997139454,
0.028539644554257393,
-0.008289511315524578,
0.022027580067515373,
0.04914957284927368,
-0.009533433243632317,
0.017009802162647247,
0.009792661294341087,
0.06373167037963867,
0.09140635281801224,
0.006898175925016403,
-0.02109082229435444,
0.006881941109895706,
0.036169905215501785,
0.05515620484948158,
-0.003233459545299411,
0.013558117672801018,
-0.0004324877227190882,
0.05892167612910271,
-0.04052503779530525,
-0.006731726229190826,
-0.013510191813111305,
0.06862803548574448,
0.08611173927783966,
0.05508582293987274,
0.03322799131274223,
-0.06560125946998596,
0.01722257398068905,
-0.015958677977323532,
-0.008955958299338818,
0.01929907500743866,
-0.03608729690313339,
-0.05047329515218735,
0.019355881959199905,
-0.04176849499344826,
0.03285551071166992,
0.013698563911020756,
-0.005826770793646574,
-0.042302705347537994,
-0.03713164106011391,
-0.033198244869709015,
-0.011068344116210938,
-0.002167396480217576,
0.023461319506168365,
0.023790420964360237,
-0.05710747838020325,
-0.033631738275289536,
0.06182483211159706,
-0.016543153673410416,
0.025554439052939415,
0.02979886718094349,
-0.043355438858270645,
0.039991527795791626,
-0.016939550638198853,
0.04160372167825699,
-0.01979057677090168,
0.029475277289748192,
-0.045006584376096725,
-0.049039728939533234,
0.0012999660102650523,
-0.00863544549793005,
0.03810632973909378,
-0.012292777188122272,
0.01942037232220173,
-0.03489157184958458,
-0.032877400517463684,
-0.008286526426672935,
-0.022030550986528397,
0.028977587819099426,
0.049637675285339355,
0.043175432831048965,
-0.0867927223443985,
0.024856118485331535,
0.001221474609337747,
0.024829141795635223,
0.04033733159303665,
0.08466895669698715,
0.0644734725356102,
-0.004585381597280502,
-0.03398193046450615,
0.026736434549093246,
0.022362247109413147,
-0.09067684412002563,
0.002981460653245449,
0.0012643737718462944,
-0.0038425319362431765,
-0.04702701047062874,
-0.0005653758998960257,
-0.06685908138751984,
0.011317436583340168,
-0.05303967371582985,
-0.07584282755851746,
0.030210118740797043,
-0.026799947023391724,
0.02751133032143116,
0.06513143330812454,
-0.006849536672234535,
-0.025941230356693268,
-0.03267623111605644,
0.02644416131079197,
-0.012234185822308064,
-0.009336528368294239,
0.014291476458311081,
0.02145668864250183,
-0.028911923989653587,
0.04124340042471886,
0.03516703099012375,
0.041367802768945694,
0.052826713770627975,
-0.046207915991544724,
0.016438215970993042,
0.041832517832517624,
-0.017586639150977135,
-0.043399859219789505,
0.01738893613219261,
-0.026704108342528343,
0.004634164273738861,
-0.03806032985448837,
0.02555541694164276,
-0.016107546165585518,
-0.0027838030364364386,
-0.025211181491613388,
-0.031338732689619064,
-0.0113481804728508,
-0.007658701390028,
0.01308413315564394,
-0.031927723437547684,
-0.0443912111222744,
0.032632242888212204,
-0.08808543533086777,
-0.015432983636856079,
0.020432494580745697,
0.00046387792099267244,
-0.005278966389596462,
-0.03621366620063782,
-0.06220996379852295,
-0.0012901736190542579,
0.04944562911987305,
-0.005383152514696121,
-0.04038724675774574,
0.07153775542974472,
-0.036911740899086,
-0.027792664244771004,
-0.01945699006319046,
0.0041477191261947155,
0.007724639493972063,
0.011047225445508957,
-0.01188373751938343,
-0.0026065639685839415,
0.03568897396326065,
-0.0746341347694397,
-0.0013539012288674712,
0.034914351999759674,
-0.028930779546499252,
-0.010864511132240295,
-0.04266129434108734,
0.018053194507956505,
-0.0721646323800087,
-0.07436899095773697,
-0.05700187385082245,
0.002866452094167471,
0.008317765779793262,
-0.04433850571513176,
0.002234797924757004,
0.004638774320483208,
0.02864537015557289,
0.008604981936514378,
-0.0179729126393795,
0.03100275620818138,
-0.010670765303075314,
-0.018044831231236458,
-0.0025806704070419073,
0.011081642471253872,
-0.014950249344110489,
0.041615091264247894,
0.03462393954396248,
0.01810004934668541,
-0.03380291908979416,
0.01755472645163536,
-0.0704398900270462,
0.025501800701022148,
-0.010401248931884766,
0.02454182505607605,
-0.05212441831827164,
-0.023614276200532913,
-0.05341586470603943,
0.005019871983677149,
-0.09653910249471664,
-0.10352825373411179,
0.007953256368637085,
-0.013715415261685848,
-0.002683772938326001,
0.039598558098077774,
0.05953218415379524,
0.012107259593904018,
0.019693531095981598,
-0.009417375549674034,
-0.015250318683683872,
0.016751360148191452,
0.058180030435323715,
-0.01459420658648014,
0.016622938215732574,
0.010693652555346489,
0.06828473508358002,
0.025774134323000908,
-0.008107304573059082,
0.0008000071393325925,
-0.03463134169578552,
-0.010442893952131271,
0.03874783217906952,
0.007850692607462406,
0.05452658236026764,
-0.011565469205379486,
0.003415179206058383,
0.07070726156234741,
0.06129191070795059,
0.007618388161063194,
0.031262077391147614,
0.013077533803880215,
0.019920820370316505,
0.029663503170013428,
0.03529379144310951,
0.001421034219674766,
-0.0044392189010977745,
0.004331791307777166,
-0.005681359674781561,
0.03534654527902603,
-0.019761811941862106,
0.02273288182914257,
-0.04809717833995819,
-0.004301958251744509,
-0.06204119324684143,
-0.0374688059091568,
0.0015644499799236655,
0.0467916838824749,
-0.008578093722462654,
-0.049824297428131104,
-0.0038432637229561806,
-0.009861939586699009,
0.03654013201594353,
-0.044330496340990067,
0.01389056071639061,
0.0012314587365835905,
0.013734996318817139,
0.0491972453892231,
-0.05254490673542023,
0.005729896482080221,
0.0021336940117180347,
-0.04382183402776718,
-0.011414874345064163,
-0.0034052571281790733,
-0.030148101970553398,
-0.012486354447901249,
-0.03594047948718071,
0.008052277378737926,
-0.0045295641757547855,
0.03736533224582672,
-0.07706036418676376,
-0.012582925148308277,
0.08711163699626923,
-0.020618708804249763,
-0.014827356673777103,
0.03856508433818817,
0.015077357180416584,
-0.05371776595711708,
-0.013398894108831882,
0.008135629817843437,
0.02618708461523056,
0.016691653057932854,
-0.030857577919960022,
0.0019938594195991755,
0.02581624500453472,
-0.022956224158406258,
-0.0061318217776715755,
0.028619470074772835,
-0.017736995592713356,
0.040441811084747314,
-0.0016474085859954357,
0.033268146216869354,
0.005272585432976484,
-0.00012368460011202842,
-0.025496406480669975,
0.027131615206599236,
-0.028791502118110657,
0.05089796334505081,
0.007000458426773548,
-0.028963247314095497,
0.012911989353597164,
0.0072303651832044125,
-0.08230143785476685,
-0.028664780780673027,
-0.02564600482583046,
0.045911457389593124,
0.02822761982679367,
-0.02100248448550701,
0.056156545877456665,
-0.04038165882229805,
-0.012418914586305618,
-0.05071687325835228,
0.03751072287559509,
-0.00029066306888125837,
0.02703121490776539,
-0.05125545710325241,
-0.0230573657900095,
-0.02307395450770855,
-0.03604705631732941,
-0.002884412882849574,
0.01770743727684021,
-0.010253463871777058,
-0.057744890451431274,
-0.033861082047224045,
0.015838943421840668,
0.0872400626540184,
0.0008960693376138806,
-0.03596465662121773,
-0.0034182805102318525,
-0.03803946450352669,
0.017056668177247047,
0.028730235993862152,
0.029166696593165398,
-0.011802095919847488,
0.08119702339172363,
0.033969566226005554,
-0.028125682845711708,
0.034513041377067566,
-0.014969758689403534,
0.00936162006109953,
0.047473564743995667,
0.012394378893077374,
-0.009964312426745892,
-0.05106145143508911,
-0.015117018483579159
] |
[
9.38244342803955,
1.664518117904663
] |
Optics
|
General Physics
|
physics-optics
|
physics-comp-ph
|
na
|
2007-03-31T15:36:48
|
This is a supplement to the paper arXiv:q-bio/0701050, containing the text of
correspondence sent to Nature in 1990.
|
Origin of adaptive mutants: a quantum measurement?
|
q-bio.PE q-bio.CB quant-ph
|
0704.0034
| 2,007
|
[
0.004162312019616365,
-0.00011367184924893081,
0.004144415725022554,
-0.03838055580854416,
0.02423013746738434,
0.03235223516821861,
0.014353984035551548,
0.03866993263363838,
0.008347615599632263,
-0.0031704155262559652,
-0.08695629984140396,
0.06366030871868134,
0.040803421288728714,
0.06399781256914139,
-0.009530266746878624,
-0.05760641396045685,
0.06686976552009583,
-0.04644005000591278,
0.027858244255185127,
-0.006375174969434738,
0.0024047689512372017,
-0.025894595310091972,
-0.027801839634776115,
-0.021449757739901543,
0.0965387374162674,
-0.011093403212726116,
-0.00862234178930521,
0.01444184873253107,
-0.01596958376467228,
0.0255258958786726,
0.036366406828165054,
-0.036490172147750854,
0.022065702825784683,
-0.036246221512556076,
-0.006849873811006546,
-0.014634344726800919,
0.04349875822663307,
-0.013616468757390976,
-0.0014629893703386188,
0.05615054443478584,
-0.027318857610225677,
-0.015659045428037643,
-0.018634192645549774,
-0.022414563223719597,
0.04429195448756218,
0.03214048221707344,
0.06313368678092957,
0.007161463610827923,
0.01184818148612976,
-0.00968874990940094,
-0.007042278535664082,
0.0037851198576390743,
0.018966346979141235,
0.008194967173039913,
0.04237757623195648,
0.018900729715824127,
-0.007162187714129686,
-0.038922131061553955,
0.05211053043603897,
0.0013478173641487956,
0.026006394997239113,
0.03434809669852257,
-0.03961216285824776,
-0.02134380117058754,
0.08633903414011002,
-0.044139474630355835,
0.0022278691176325083,
-0.003994881175458431,
-0.03836129233241081,
-0.028694886714220047,
0.05438549071550369,
-0.029526902362704277,
-0.025524411350488663,
0.06695429235696793,
0.048146240413188934,
0.039798296988010406,
0.013063727878034115,
0.0009199618361890316,
-0.01720915362238884,
0.017330298200249672,
0.0025228268932551146,
-0.033563923090696335,
0.06183001399040222,
0.009397076442837715,
0.09458974748849869,
-0.010995457880198956,
0.009706549346446991,
0.005050609353929758,
-0.04827876016497612,
0.05403467267751694,
0.03269043192267418,
0.02204182930290699,
0.0966835618019104,
0.019464729353785515,
-0.07674463093280792,
0.010026424191892147,
-0.026137370616197586,
-0.03648191690444946,
-0.04001234471797943,
0.027426203712821007,
-0.010649824514985085,
0.031243469566106796,
0.04279320687055588,
-0.018837429583072662,
0.0166016798466444,
0.03710540011525154,
0.020847484469413757,
-0.0447479672729969,
-0.035518549382686615,
-0.01818995736539364,
-0.13562017679214478,
-0.011843196116387844,
-0.008775190450251102,
-0.062364716082811356,
-0.045663993805646896,
-0.047544632107019424,
0.037074435502290726,
-0.04735908284783363,
-0.01979636959731579,
0.04560518264770508,
-0.03246547654271126,
0.03287642076611519,
0.00577306654304266,
0.03550836071372032,
-0.012145797722041607,
0.0408635176718235,
-0.05257754400372505,
-0.054302286356687546,
0.023348208516836166,
0.027273908257484436,
0.00959064345806837,
0.05252440646290779,
-0.05512498691678047,
0.01022618543356657,
0.045777615159749985,
0.03743424639105797,
0.00011355458991602063,
-0.027629083022475243,
0.05522232875227928,
-0.01374463364481926,
-0.01382057461887598,
-0.04097430408000946,
0.038116540759801865,
0.006333556026220322,
0.030043799430131912,
-0.08002849668264389,
0.04405684769153595,
-0.008679074235260487,
-0.07747037708759308,
-0.028669245541095734,
0.006871464662253857,
0.01611916534602642,
-0.0036995140835642815,
0.009381670504808426,
-0.01368480734527111,
-0.034925900399684906,
-0.01648980751633644,
0.029010415077209473,
-0.0010712121147662401,
0.024743227288126945,
0.04119054228067398,
0.03368375822901726,
-0.07834514230489731,
0.058970849961042404,
-0.02014302834868431,
0.016133394092321396,
0.00854776706546545,
0.004706661682575941,
0.007029026281088591,
0.057589706033468246,
-0.02005802094936371,
-0.04228454455733299,
0.002100653015077114,
-0.04692848026752472,
-0.020483657717704773,
0.04943139851093292,
0.04522703215479851,
-0.03599947318434715,
0.012701800093054771,
-0.035477157682180405,
0.06330373883247375,
-0.02914557419717312,
0.003843336133286357,
0.03745722770690918,
0.011091894470155239,
-0.040440287441015244,
0.033290717750787735,
-0.016886884346604347,
-0.03928246721625328,
-0.07792027294635773,
0.01199574489146471,
-0.013885716907680035,
-0.035442352294921875,
-0.07257349789142609,
-0.015124935656785965,
-0.07121475785970688,
0.030774354934692383,
-0.038638483732938766,
0.021343562752008438,
-0.03459274768829346,
-0.003075256710872054,
0.009591199457645416,
-0.061659324914216995,
-0.016034197062253952,
-0.009990345686674118,
0.0006512574036605656,
0.005974820349365473,
-0.004093842580914497,
0.0536082461476326,
-0.014476259239017963,
0.08240460604429245,
0.08319048583507538,
-0.019199684262275696,
-0.019253363832831383,
-0.04081285744905472,
-0.012009432539343834,
0.03706923872232437,
-0.038381583988666534,
0.009362658485770226,
0.017685523256659508,
0.03129781782627106,
-0.010389601811766624,
-0.0007370967068709433,
0.028526434674859047,
0.006308285985141993,
0.05128759518265724,
-0.03996695205569267,
-0.06557885557413101,
-0.04522797465324402,
-0.016461791470646858,
-0.04565947875380516,
-0.038314200937747955,
0.03670385852456093,
0.01296332385390997,
-0.01511492021381855,
0.06206488981842995,
-0.00811305083334446,
0.05237689986824989,
0.03185460716485977,
0.02786833792924881,
0.04823126643896103,
0.018482379615306854,
0.009973167441785336,
0.017840664833784103,
-0.04377315938472748,
0.011668261140584946,
0.017099866643548012,
-0.03305540233850479,
-0.06653765588998795,
0.0004174450587015599,
0.008834454230964184,
-0.028030982241034508,
0.03252992406487465,
-0.002033533761277795,
0.0025790769141167402,
0.008264623582363129,
-0.01570262387394905,
-0.0011153199011459947,
-0.0278118047863245,
-0.011997288092970848,
0.04628065228462219,
-0.037657324224710464,
0.003926136996597052,
-0.028953175991773605,
-0.04212675988674164,
-0.011290660127997398,
0.04310793802142143,
-0.04101463034749031,
-0.05521195009350777,
-0.05006438493728638,
-0.041962746530771255,
0.04848392680287361,
0.050410591065883636,
0.014390094205737114,
-0.01657710410654545,
-0.03952739015221596,
-0.04241608455777168,
0.027675358578562737,
-0.012724332511425018,
-0.028925634920597076,
-0.050990939140319824,
0.01875876821577549,
-0.07050374895334244,
0.0003045329649467021,
-0.0074819037690758705,
0.045643728226423264,
0.047015007585287094,
-0.021003061905503273,
-0.047463465481996536,
-0.01914001815021038,
-0.030563456937670708,
-0.07384377717971802,
-0.02276267111301422,
0.07186970114707947,
-0.00031317080720327795,
0.049664631485939026,
0.060637228190898895,
0.0031465080101042986,
-0.01181003451347351,
0.007948018610477448,
-0.0013235146179795265,
0.009807107970118523,
0.004670469090342522,
-0.0035343340132385492,
0.013400916941463947,
0.0004083101521246135,
0.005764485336840153,
-0.011086294427514076,
0.020021751523017883,
0.005208059214055538,
-0.036921560764312744,
0.004226066637784243,
-0.044432662427425385,
-0.01890437863767147,
-0.02227933518588543,
0.02215934731066227,
0.0051691969856619835,
0.026209698989987373,
0.06109161674976349,
-0.035141754895448685,
-0.014679834246635437,
-0.07010316103696823,
0.030397824943065643,
-0.044975608587265015,
0.06738735735416412,
0.04392203688621521,
-0.014896254055202007,
0.03675612807273865,
0.02441059798002243,
-0.0073975929990410805,
0.058158520609140396,
0.03374385088682175,
-0.050123874098062515,
-0.04582228884100914,
-0.0649196207523346,
-0.004962909501045942,
-0.0008055904763750732,
0.04558359459042549,
-0.013924294151365757,
0.0011710172984749079,
0.05848390609025955,
-0.01201079972088337,
0.003906359896063805,
0.010991568677127361,
0.005376086570322514,
-0.010744930244982243,
-0.007409901823848486,
0.010264539159834385,
0.04870809242129326,
0.017448699101805687,
-0.048398323357105255,
0.000057102453865809366,
0.0171901173889637,
0.007696390617638826,
-0.029450247064232826,
0.05387413501739502,
0.043367184698581696,
-0.027706285938620567,
0.07729169726371765,
0.021210188046097755,
-0.003470685798674822,
-0.015592258423566818,
0.04757773503661156,
0.018523389473557472,
0.005006974563002586,
0.014959623105823994,
0.01573401689529419,
0.020177248865365982,
0.012319711036980152,
-0.02584794908761978,
-0.0645919218659401,
-0.030819866806268692,
0.0019294230733066797,
0.01862448826432228,
0.020336352288722992,
0.0071140252985060215,
-0.07561323046684265,
0.011600137688219547,
-0.03811025992035866,
-0.016456469893455505,
0.06307997554540634,
0.007181210909038782,
0.0636478066444397,
-0.021571064367890358,
0.047525834292173386,
0.03965155780315399,
-0.06802362203598022,
-0.03380657732486725,
0.013646249659359455,
0.029195183888077736,
-0.028095396235585213,
0.01611645705997944,
-0.042537566274404526,
-0.001375530264340341,
0.02600327879190445,
0.08030229061841965,
0.040456853806972504,
-0.00629342719912529,
0.0038253229577094316,
0.018128197640180588,
-0.03324926644563675,
-0.04477376490831375,
0.021105699241161346,
0.01817716658115387,
-0.02214185893535614,
0.020061982795596123,
0.03628496080636978,
0.034116480499506,
0.02060222439467907,
0.015699710696935654,
-0.004534462932497263,
0.05953826755285263,
-0.035954155027866364,
-0.0814225897192955,
-0.011083152145147324,
0.03644619882106781,
0.05013600364327431,
-0.038721684366464615,
-0.01776471920311451,
0.0030865217559039593,
-0.02712082862854004,
0.025566227734088898,
-0.009174132719635963,
0.017428509891033173,
0.00042695962474681437,
-0.002566780662164092,
-0.032553479075431824,
0.036067087203264236,
0.011392283253371716,
-0.03424223139882088,
0.0164381992071867,
0.0005046380683779716,
0.020061606541275978,
0.01316493097692728,
-0.023039808496832848,
-0.0205617006868124,
0.0316365510225296,
-0.0012587910750880837,
0.07876615971326828,
0.0009158578468486667,
0.10130421072244644,
-0.02159019187092781,
0.005529291927814484,
-0.0236042533069849,
-0.007915342226624489,
0.051705602556467056,
0.041744254529476166,
0.0014933961210772395,
-0.028698058798909187,
-0.03101140819489956,
0.07388921082019806,
-0.00733176851645112,
0.038840971887111664,
0.01847328245639801,
0.04802795127034187,
-0.007349720224738121,
-0.0005859718658030033,
0.006193163339048624,
0.0741892084479332,
0.05377091467380524,
-0.005616887006908655,
0.011360391043126583,
-0.032206859439611435,
0.04453621059656143,
-0.018478864803910255,
0.02771897055208683,
-0.02009366638958454,
0.03516940027475357,
-0.024794340133666992,
0.018454864621162415,
-0.02374209091067314,
-0.03606187924742699,
0.03613559156656265,
0.05419248342514038,
-0.0183422714471817,
-0.07230797410011292,
0.033526115119457245,
-0.04468466714024544,
0.04202001169323921,
0.055707573890686035,
0.03648234158754349,
-0.03272351995110512,
-0.03661811351776123,
-0.053546786308288574,
-0.0007978888461366296,
0.023570116609334946,
-0.031117618083953857,
0.003673653118312359,
0.020656391978263855,
-0.02269122190773487,
0.03853670507669449,
0.05477955937385559,
0.027948355302214622,
-0.0006335111684165895,
-0.026002179831266403,
-0.03412812948226929,
-0.0062608965672552586,
-0.020711330696940422,
0.07651417702436447,
-0.026235265657305717,
0.00758821377530694,
0.05468805134296417,
-0.006258218549191952,
0.0004176175280008465,
0.010152246803045273,
0.044104259461164474,
-0.004379366524517536,
-0.06198956444859505,
-0.0043833255767822266,
0.000702941557392478,
-0.002188071608543396,
0.02667813003063202,
0.05656784027814865,
0.03076217882335186,
0.050526347011327744,
-0.008260775357484818,
0.03432328626513481,
-0.02268890105187893,
-0.03723156079649925,
-0.01488402858376503,
0.019736550748348236,
-0.011086291633546352,
0.0004884441732428968,
0.007158663589507341,
-0.06222596764564514,
0.03127934783697128,
-0.0694403275847435,
-0.05340519919991493,
0.055233582854270935,
0.012155376374721527,
0.020465146750211716,
0.05799920856952667,
0.002188481390476227,
0.0032585763838142157,
0.00047559893573634326,
-0.038029685616493225,
-0.003584388643503189,
-0.016858244314789772,
0.02658119425177574,
0.015987742692232132,
-0.017160195857286453,
0.008391128852963448,
0.038403019309043884,
0.03505372628569603,
0.045781854540109634,
-0.03147130459547043,
-0.07602330297231674,
-0.007042387500405312,
0.01715584099292755,
-0.05157438665628433,
-0.006180392578244209,
-0.005623651668429375,
0.003053562715649605,
-0.03620096668601036,
0.026649953797459602,
-0.0443311482667923,
-0.00818646140396595,
-0.04430614784359932,
-0.03590729460120201,
-0.02744649536907673,
0.011822252534329891,
0.012523708865046501,
0.009069074876606464,
0.006207882426679134,
-0.020239679142832756,
-0.07825849205255508,
-0.0438556894659996,
-0.0016053796280175447,
0.034503478556871414,
0.06003512442111969,
-0.00309418304823339,
-0.0227249413728714,
-0.014308315701782703,
0.018068943172693253,
0.012799730524420738,
-0.02604304999113083,
-0.002853827318176627,
-0.011827785521745682,
-0.07654012739658356,
-0.07230128347873688,
-0.016787735745310783,
0.00353494961746037,
-0.029486875981092453,
-0.04292166605591774,
-0.057643961161375046,
0.02632811665534973,
-0.031833454966545105,
0.003495795652270317,
0.08289641886949539,
0.018866151571273804,
-0.027835853397846222,
-0.02640625275671482,
-0.03647328540682793,
-0.009301832877099514,
-0.038230542093515396,
-0.026506414636969566,
-0.00007679678674321622,
-0.0037812429945915937,
-0.018774745985865593,
-0.03161858767271042,
-0.014990023337304592,
-0.050373878329992294,
0.04694046452641487,
-0.03198845311999321,
0.031987499445676804,
0.0637374296784401,
0.01763744279742241,
0.03998831287026405,
0.02041051723062992,
0.004836938809603453,
-0.029777394607663155,
-0.0020126409363001585,
-0.016603460535407066,
-0.0030191040132194757,
-0.01128477044403553,
-0.0651489645242691,
0.05024096369743347,
-0.00598530238494277,
-0.055374424904584885,
-0.02697797864675522,
0.004881515633314848,
-0.02784518338739872,
0.02771822176873684,
-0.08847849816083908,
0.0001731395022943616,
0.016139883548021317,
0.0015933517133817077,
-0.017879705876111984,
0.04238278046250343,
0.06015077605843544,
-0.0762062817811966,
-0.009754215367138386,
-0.014121398329734802,
-0.016858279705047607,
-0.033168163150548935,
0.012692350894212723,
-0.06798892468214035,
0.01345516461879015,
0.02648109383881092,
0.049635399132966995,
0.016041796654462814,
-0.026793912053108215,
-0.044035203754901886,
-0.042925477027893066,
-0.00614506658166647,
0.05706017464399338,
0.029503798112273216,
0.044565800577402115,
-0.030458424240350723,
-0.004181312397122383,
0.10311612486839294,
0.04267006367444992,
-0.048117052763700485,
0.03714778646826744,
0.003472809446975589,
0.05152222514152527,
0.04411326348781586,
-0.023469876497983932,
-0.02721807174384594,
-0.053641531616449356,
-0.029390031471848488,
-0.07011592388153076,
0.020938344299793243,
0.029506245627999306,
0.022362252697348595,
-0.03284284099936485,
0.025730499997735023,
-0.0493425615131855,
-0.027684396132826805,
-0.010892108082771301,
-0.011004644446074963,
-0.009121394716203213,
-0.012919222936034203,
-0.05150574818253517,
-0.07125010341405869,
-0.0315069854259491,
0.017537878826260567,
0.02303176186978817,
-0.0005547291366383433,
-0.020227493718266487,
0.02238526940345764,
0.008177246898412704,
0.010878578759729862,
0.003539750585332513,
-0.047311779111623764,
-0.062420982867479324,
-0.03348711133003235,
-0.040824852883815765,
-0.00965148489922285,
-0.02396046370267868,
-0.020390493795275688,
-0.022616175934672356,
0.0026178108528256416,
-0.06198548898100853,
0.007083225063979626,
0.0037580919452011585,
-0.006794721819460392,
0.04077370837330818,
0.019034037366509438,
0.02471042238175869,
0.016341689974069595,
0.0065361023880541325,
-0.04898471385240555,
0.020377574488520622,
-0.012833031825721264,
-0.0004680368583649397,
0.05172695592045784,
0.03128728270530701,
0.010794843547046185,
-0.02786678820848465,
-0.023175787180662155,
-0.0016479556215927005,
0.05699266865849495,
0.06163514032959938,
0.03029279224574566,
-0.0008253577398136258,
0.03569331765174866,
-0.01245894655585289,
0.016392884775996208,
-0.008425150066614151,
0.02862747572362423,
-0.009144115261733532,
-0.07941766828298569,
-0.006106162443757057,
-0.03267606720328331,
-0.04969087988138199,
0.01120700128376484,
0.009292885661125183,
0.04902517423033714,
0.022678328678011894,
0.03960220515727997,
-0.06575579941272736,
-0.05179086700081825,
0.02926836535334587,
-0.014503161422908306,
0.003484520595520735,
-0.0527738593518734,
-0.004978690296411514,
-0.0634961947798729,
0.014389525167644024,
-0.004324602894484997,
0.00002067563582386356,
0.05054890736937523,
0.008230279199779034,
-0.023562965914607048,
-0.11224687099456787,
-0.05608350783586502,
0.03396637737751007,
0.03565511852502823,
-0.008165121078491211,
0.0003825895255431533,
-0.035868823528289795,
-0.0342312790453434,
0.02828333154320717,
0.026086140424013138,
0.005080459173768759,
-0.002690393477678299,
0.025714896619319916,
0.06584357470273972,
-0.05103054270148277,
0.04157187044620514,
-0.0008616890991106629,
0.028250722214579582,
0.041800662875175476,
-0.0006344110006466508,
0.040433987975120544,
-0.008733678609132767,
-0.015348164364695549
] |
[
6.946381092071533,
1.1304469108581543
] |
Populations and Evolution
|
Quantitative Biology
|
q-bio-PE
|
q-bio-CB
|
quant-ph
|
2007-03-31T15:52:56
|
We propose an extrapolation technique that allows accuracy improvement of the
discrete dipole approximation computations. The performance of this technique
was studied empirically based on extensive simulations for 5 test cases using
many different discretizations. The quality of the extrapolation improves with
refining discretization reaching extraordinary performance especially for
cubically shaped particles. A two order of magnitude decrease of error was
demonstrated. We also propose estimates of the extrapolation error, which were
proven to be reliable. Finally we propose a simple method to directly separate
shape and discretization errors and illustrated this for one test case.
|
Convergence of the discrete dipole approximation. II. An extrapolation
technique to increase the accuracy
|
physics.optics physics.comp-ph
|
0704.0035
| 2,007
|
[
0.01193658821284771,
0.007185809314250946,
0.005500128027051687,
-0.04938603565096855,
0.020086325705051422,
0.003462923225015402,
0.029406793415546417,
0.02964753471314907,
-0.054255690425634384,
-0.013510188087821007,
-0.08320625871419907,
0.017617151141166687,
0.027474943548440933,
0.017887845635414124,
-0.0045344168320298195,
-0.03527199104428291,
0.017075292766094208,
-0.01579214632511139,
-0.025444190949201584,
0.008897497318685055,
0.017950113862752914,
-0.011337042786180973,
-0.0032990763429552317,
-0.07969237118959427,
0.04008570685982704,
-0.009362447075545788,
-0.01551854982972145,
0.013448226265609264,
-0.09605878591537476,
0.04860401898622513,
0.02442704327404499,
-0.08054091781377792,
0.02836436964571476,
-0.027811555191874504,
-0.01737382262945175,
-0.014638214372098446,
0.0402715839445591,
-0.008542440831661224,
0.03774058446288109,
0.03729017823934555,
0.02117154374718666,
-0.03668361157178879,
-0.003484153188765049,
0.04360015690326691,
0.014994696713984013,
-0.039197612553834915,
0.045150287449359894,
-0.024720054119825363,
0.03018375113606453,
0.03746090456843376,
-0.030875694006681442,
0.044226404279470444,
0.05191248282790184,
-0.011944378726184368,
-0.007125575095415115,
0.012825701385736465,
0.018697168678045273,
-0.022602705284953117,
0.09422947466373444,
0.005951079539954662,
0.0009759161039255559,
0.03330693766474724,
-0.04970962554216385,
0.01947954297065735,
-0.010870952159166336,
-0.05991661548614502,
-0.041930023580789566,
-0.00581179978325963,
-0.01621486060321331,
-0.03758339211344719,
0.02331598475575447,
-0.033366940915584564,
0.0035781506448984146,
0.0016729020280763507,
-0.02984597161412239,
0.008022991009056568,
-0.013908445835113525,
0.0017714439891278744,
-0.02537887543439865,
-0.008488694205880165,
-0.03187410533428192,
-0.059786565601825714,
0.013709496706724167,
0.013652442023158073,
0.05421336367726326,
0.011538609862327576,
-0.024962641298770905,
0.020924929529428482,
0.002911476418375969,
0.005265761632472277,
0.015739761292934418,
-0.006219882518053055,
0.021272672340273857,
0.06170127913355827,
-0.034203533083200455,
0.0019195708446204662,
-0.002627760637551546,
0.030515361577272415,
0.05710313096642494,
-0.01305459439754486,
0.02239401452243328,
0.03198078274726868,
0.028350358828902245,
0.030219437554478645,
0.01709078438580036,
0.034337520599365234,
-0.013734770007431507,
-0.011997409164905548,
0.03560326620936394,
0.015645142644643784,
-0.09198298305273056,
-0.05311095714569092,
0.021876245737075806,
-0.039038144052028656,
-0.03583117946982384,
-0.006882086396217346,
0.04920068010687828,
-0.11834874749183655,
-0.010084927082061768,
0.027150558307766914,
0.02929634042084217,
-0.014287889003753662,
0.004587237723171711,
0.03745635971426964,
0.037415970116853714,
-0.0027614273130893707,
-0.030398916453123093,
-0.03370042145252228,
0.015470528975129128,
-0.034158386290073395,
-0.0441572442650795,
-0.035311903804540634,
-0.031189825385808945,
0.011059077456593513,
0.011435828171670437,
0.003616365371271968,
-0.006718541961163282,
-0.060281768441200256,
0.014203169383108616,
0.03760409355163574,
0.01569105125963688,
-0.01505038607865572,
0.05409010127186775,
-0.0006984152714721859,
0.020826809108257294,
-0.041634704917669296,
-0.06335415691137314,
-0.04814787954092026,
-0.038018759340047836,
-0.0189015232026577,
0.027127927169203758,
-0.006163083016872406,
0.06742611527442932,
0.05110959708690643,
-0.02841963991522789,
-0.01019350253045559,
0.013724743388593197,
0.000745483092032373,
0.04631611332297325,
0.00575612299144268,
0.00756091857329011,
0.0017906115390360355,
-0.08966794610023499,
0.04062813147902489,
0.02408878691494465,
0.047036003321409225,
0.06317945569753647,
0.03442754969000816,
0.0027911891229450703,
0.003950378857553005,
-0.02553880214691162,
-0.04479403793811798,
-0.024086453020572662,
-0.0046888599172234535,
-0.006221924442797899,
0.0026796567253768444,
0.006714795250445604,
-0.04856937751173973,
0.007669617421925068,
0.012684752233326435,
0.049642663449048996,
0.007545589003711939,
-0.017173955217003822,
0.08502873033285141,
0.04396144300699234,
0.055295076221227646,
0.004464338067919016,
-0.046004511415958405,
-0.02487746626138687,
-0.019154079258441925,
0.018182942643761635,
0.0009524599881842732,
-0.006077684462070465,
-0.01574491336941719,
-0.020839523524045944,
-0.006838440429419279,
0.10908222198486328,
-0.03284085914492607,
-0.010199828073382378,
-0.017176352441310883,
-0.03813902661204338,
0.012337775900959969,
0.04570306837558746,
0.00559116480872035,
0.02750902622938156,
0.02315998636186123,
-0.0032890706788748503,
-0.013490868732333183,
0.0349600575864315,
0.014493508264422417,
0.0596434660255909,
0.06817533075809479,
-0.04492434114217758,
0.007149686571210623,
-0.017126111313700676,
0.0016010593390092254,
-0.017287330701947212,
-0.028451621532440186,
-0.0526464581489563,
0.030877327546477318,
-0.009197192266583443,
-0.03844317048788071,
0.03120918571949005,
0.04677614942193031,
0.0005544909508898854,
-0.01691075600683689,
0.000987647334113717,
0.027242381125688553,
-0.005543663166463375,
0.010266506113111973,
-0.03885833919048309,
-0.10945190489292145,
0.03662890940904617,
-0.03794172406196594,
0.015164025127887726,
-0.007922486402094364,
-0.05964973196387291,
0.021371159702539444,
0.05041561275720596,
0.05839977785944939,
0.04028667137026787,
0.030157506465911865,
0.028602639213204384,
-0.05452769249677658,
-0.07956907153129578,
0.01892150565981865,
-0.0035459212958812714,
0.013198879547417164,
-0.06857246905565262,
0.019260136410593987,
0.029981745406985283,
0.051840413361787796,
0.03030848316848278,
0.052274055778980255,
0.048885904252529144,
0.007932435721158981,
-0.03669866546988487,
0.037559762597084045,
0.022944793105125427,
-0.03189717233181,
0.015029698610305786,
-0.030086416751146317,
0.007898390293121338,
-0.04768279567360878,
-0.016400989145040512,
0.04758608341217041,
0.02166721597313881,
-0.048780202865600586,
0.013890287838876247,
-0.04414421319961548,
-0.02728806436061859,
0.0007605204591527581,
0.058622896671295166,
0.0443975068628788,
-0.005312928929924965,
0.0037025015335530043,
0.07519646733999252,
0.004869864322245121,
0.024809183552861214,
0.028280101716518402,
-0.05938112735748291,
-0.019525844603776932,
-0.020985981449484825,
0.012496301904320717,
0.018605252727866173,
0.005322599317878485,
-0.03105589747428894,
-0.054203588515520096,
-0.026104308664798737,
-0.03197440505027771,
-0.046149034053087234,
-0.0024134782142937183,
0.010871289297938347,
0.030607661232352257,
-0.0031738998368382454,
0.06857345253229141,
0.09618547558784485,
-0.03597985580563545,
-0.0009050951921381056,
0.021475398913025856,
0.0002244167699245736,
0.032080650329589844,
-0.021319665014743805,
0.014181671664118767,
0.00566224567592144,
0.06217123195528984,
0.003907760139554739,
-0.025246404111385345,
0.027543799951672554,
-0.031511563807725906,
-0.010593822225928307,
0.060716792941093445,
-0.049585603177547455,
0.006925801746547222,
-0.006829463876783848,
-0.017238151282072067,
0.04422224685549736,
0.018568366765975952,
0.05416536331176758,
0.040467407554388046,
0.03736085072159767,
-0.03740396723151207,
-0.00045567136839963496,
-0.023843158036470413,
0.023685304448008537,
0.05899546295404434,
-0.004448592662811279,
0.024255072697997093,
0.02744678594172001,
-0.01021189521998167,
0.039388589560985565,
0.036057282239198685,
-0.05774426460266113,
-0.021817611530423164,
-0.06900503486394882,
-0.06222774088382721,
-0.015946120023727417,
0.011879856698215008,
-0.012062650173902512,
0.00781349278986454,
-0.007524259388446808,
-0.03692561760544777,
-0.060307640582323074,
-0.034441735595464706,
-0.010771000757813454,
0.01307770051062107,
0.004853159189224243,
-0.01983456499874592,
0.0037460944149643183,
0.0036613745614886284,
-0.001042887568473816,
-0.01739044114947319,
-0.009404158219695091,
0.04174172133207321,
-0.005128159653395414,
0.02501707151532173,
0.058580685406923294,
-0.03739407658576965,
0.019930288195610046,
0.05063536390662193,
0.05065228044986725,
-0.01957673765718937,
0.034948188811540604,
0.0020060862880200148,
0.017507240176200867,
0.05100313574075699,
0.00774607015773654,
0.04740734025835991,
-0.02498243935406208,
-0.04454172030091286,
-0.0669708326458931,
0.018225986510515213,
0.025036541745066643,
0.02316463738679886,
-0.008442784659564495,
-0.006283029913902283,
-0.022324204444885254,
0.0032769932877272367,
0.02310916595160961,
-0.01351570338010788,
0.023975268006324768,
0.024408532306551933,
0.007687277160584927,
0.015494205988943577,
-0.01887512393295765,
-0.022428033873438835,
-0.03329610824584961,
-0.02215960994362831,
-0.026738202199339867,
0.003984490875154734,
-0.02641974575817585,
-0.060202643275260925,
-0.0035884964745491743,
0.0430547334253788,
0.002196958754211664,
-0.0028797294944524765,
0.04035542905330658,
0.01970769837498665,
0.013024631887674332,
0.020094912499189377,
-0.04054524749517441,
-0.08032312989234924,
0.031435780227184296,
-0.010491225868463516,
-0.03953050449490547,
-0.0030151531100273132,
-0.03804072365164757,
-0.0006239881622605026,
0.023497644811868668,
-0.013059526681900024,
-0.03296838700771332,
0.03028276190161705,
-0.007129071280360222,
-0.03865378350019455,
0.06472849100828171,
-0.0023933746851980686,
0.050819769501686096,
-0.008389437571167946,
0.021220030263066292,
0.03655518963932991,
0.012472308240830898,
0.06633715331554413,
-0.07174542546272278,
0.013735703192651272,
-0.012148101814091206,
0.00859781913459301,
-0.009042966179549694,
0.0032103268895298243,
0.02904403768479824,
-0.08143240213394165,
0.021612683311104774,
0.006325939204543829,
-0.0012168408138677478,
0.05169397220015526,
-0.06528721004724503,
-0.020221900194883347,
0.04500621184706688,
0.0028230815660208464,
0.010524360463023186,
-0.0014107093447819352,
0.034770719707012177,
-0.03382822498679161,
0.027846289798617363,
-0.016537010669708252,
0.06405194103717804,
0.08995424211025238,
0.014816369861364365,
-0.023924145847558975,
0.039676617830991745,
0.02691943570971489,
0.021477699279785156,
-0.008698150515556335,
0.0007391941617242992,
0.029041893780231476,
0.05355190485715866,
-0.0543321818113327,
-0.0007588014705106616,
-0.023706434294581413,
0.050864387303590775,
0.09403230249881744,
0.0409894660115242,
0.0720311626791954,
-0.07255343347787857,
0.01110687293112278,
-0.028333188965916634,
0.004932085983455181,
0.005335547495633364,
-0.042877260595560074,
0.006969676818698645,
0.02157163806259632,
-0.06583184003829956,
0.028666922822594643,
0.04604872316122055,
-0.02217256836593151,
-0.005891357082873583,
-0.019371196627616882,
-0.02621370553970337,
0.008381427265703678,
0.018652837723493576,
0.03444535657763481,
0.014348149299621582,
-0.04812663048505783,
-0.020698625594377518,
0.016169410198926926,
-0.042155470699071884,
0.023492274805903435,
0.00319813285022974,
-0.03173248469829559,
0.028864437714219093,
-0.0034824293106794357,
0.03440336883068085,
0.0031090639531612396,
0.023855241015553474,
-0.056123290210962296,
-0.0181099995970726,
-0.01921582594513893,
0.015258342027664185,
0.03515898436307907,
0.0024235087912529707,
-0.003341403789818287,
-0.03351332247257233,
0.011823086999356747,
-0.0232736524194479,
-0.037141624838113785,
0.009347795508801937,
0.04719681292772293,
0.015385614708065987,
-0.07617774605751038,
-0.021082982420921326,
-0.015823302790522575,
-0.006474996451288462,
0.04321855679154396,
0.06921805441379547,
0.02266579121351242,
0.013829005882143974,
-0.022563260048627853,
0.05016699060797691,
0.03619229048490524,
-0.08141625672578812,
-0.039618998765945435,
0.062253065407276154,
0.022101256996393204,
-0.049445465207099915,
0.0023773321881890297,
-0.07685437053442001,
0.026315633207559586,
-0.049310989677906036,
-0.08015669137239456,
0.029209543019533157,
-0.029625974595546722,
0.014175808988511562,
0.014782796613872051,
-0.038181327283382416,
-0.0013108098646625876,
-0.04731250926852226,
-0.006462928839027882,
-0.04308966547250748,
-0.05276314914226532,
0.02068580500781536,
0.038943156599998474,
-0.03220777213573456,
0.054234299808740616,
0.06041611358523369,
0.056112438440322876,
0.035947296768426895,
-0.03967706486582756,
0.004885221365839243,
0.0468827560544014,
-0.00048211083048954606,
-0.045026663690805435,
0.016023220494389534,
-0.026505030691623688,
0.012573541142046452,
-0.04511342570185661,
0.016624728217720985,
-0.010290158912539482,
0.01522536389529705,
-0.053998738527297974,
0.00009072807733900845,
-0.007081538904458284,
-0.05403205007314682,
-0.04713693633675575,
0.0017943060956895351,
-0.0034477298613637686,
0.03181925415992737,
-0.12403424084186554,
-0.03952436149120331,
0.02466311864554882,
-0.020165294408798218,
-0.0481022372841835,
-0.026166491210460663,
-0.0767265260219574,
-0.009496350772678852,
0.0661105215549469,
-0.00859613437205553,
-0.023618681356310844,
0.08526265621185303,
-0.024169491603970528,
0.008590534329414368,
0.0030887583270668983,
-0.02153719589114189,
-0.001475103897973895,
0.016246745362877846,
0.0008339365012943745,
-0.011630148626863956,
0.0792594775557518,
-0.046647679060697556,
0.023965010419487953,
0.024968784302473068,
-0.05948933586478233,
-0.007860774174332619,
-0.05714704096317291,
0.014722625724971294,
-0.08284930139780045,
-0.03365771472454071,
-0.052297286689281464,
-0.013179927133023739,
0.023566097021102905,
-0.022770611569285393,
-0.004206252750009298,
0.03618856146931648,
-0.0018395434599369764,
0.02546476572751999,
-0.03390263766050339,
0.03873096778988838,
0.00026956122019328177,
-0.022724278271198273,
0.015902310609817505,
-0.015567474067211151,
-0.034044310450553894,
0.03630220517516136,
0.013035716488957405,
-0.032000619918107986,
-0.027333661913871765,
0.015237976796925068,
-0.06156385317444801,
0.030691049993038177,
-0.0232327152043581,
0.041448190808296204,
-0.05839678272604942,
0.0026656086556613445,
-0.04557004198431969,
0.012101097963750362,
-0.11235716193914413,
-0.07711604982614517,
0.017979897558689117,
-0.013226283714175224,
-0.012682766653597355,
0.05437738448381424,
0.00544737046584487,
0.0017950955079868436,
-0.009257405996322632,
0.0016081423964351416,
-0.011892211623489857,
-0.019267629832029343,
0.05384359508752823,
0.001795504824258387,
0.04202966392040253,
0.005480904132127762,
0.09614326804876328,
0.008285189978778362,
-0.0041028656996786594,
0.008749356493353844,
-0.029602617025375366,
-0.006017955951392651,
0.004234627354890108,
0.05478609725832939,
0.06403762102127075,
0.009700721129775047,
0.020155062898993492,
0.08325446397066116,
0.04310452565550804,
0.00048765676910988986,
0.04443882033228874,
0.04401089996099472,
0.015447722747921944,
0.01258722972124815,
0.009971818886697292,
-0.017789512872695923,
-0.007044702302664518,
-0.016805162653326988,
-0.019128022715449333,
0.02954053319990635,
-0.03308751806616783,
0.04956774041056633,
-0.06006048247218132,
-0.03517931327223778,
-0.0771305114030838,
-0.04962256923317909,
0.008514594286680222,
-0.00025535502936691046,
-0.040190890431404114,
-0.05704091861844063,
-0.0028702006675302982,
0.006811575032770634,
0.012216303497552872,
-0.03572502359747887,
0.044514432549476624,
-0.04715792462229729,
-0.023677289485931396,
0.018325310200452805,
-0.010417151264846325,
0.0006719407392665744,
0.0033516534604132175,
-0.06415458768606186,
0.0009823751170188189,
-0.0121848713606596,
-0.042007140815258026,
-0.043575648218393326,
-0.0324372835457325,
0.0016444731736555696,
0.03398244455456734,
-0.0032843868248164654,
-0.03936761990189552,
-0.0430014543235302,
0.05191807821393013,
-0.027975358068943024,
-0.03225509077310562,
0.08089388161897659,
0.019440945237874985,
-0.013831140473484993,
0.008767806924879551,
0.00036736048059538007,
-0.004467244725674391,
0.007327163591980934,
-0.04127201810479164,
-0.0264075119048357,
0.034232575446367264,
-0.03480604290962219,
0.02141863852739334,
0.06026753783226013,
-0.0010021290509030223,
0.03977262228727341,
-0.0003784341679420322,
0.01872306317090988,
-0.0039091575890779495,
0.004462430253624916,
-0.013643587939441204,
0.010510164313018322,
0.011742991395294666,
0.01797238551080227,
0.0049605099484324455,
-0.03777826949954033,
0.027675466611981392,
0.01371594239026308,
-0.08095023781061172,
-0.042527951300144196,
-0.004331562202423811,
0.04107926785945892,
0.02961977943778038,
0.021638136357069016,
0.03837117180228233,
-0.07137046754360199,
0.011926522478461266,
-0.04562600702047348,
0.020048612728714943,
-0.009380326606333256,
0.030248969793319702,
-0.06873226165771484,
-0.026557639241218567,
-0.012378648854792118,
-0.05888088047504425,
0.023486953228712082,
-0.006027938332408667,
-0.005583317019045353,
-0.035698894411325455,
-0.018658749759197235,
0.05910959839820862,
0.06789721548557281,
0.062195200473070145,
-0.04335860535502434,
0.0020195588003844023,
-0.024259325116872787,
-0.02408844232559204,
0.027501344680786133,
0.01718994788825512,
-0.026600027456879616,
0.051826126873493195,
0.05493556335568428,
-0.022383451461791992,
0.004628745838999748,
-0.004597090650349855,
0.031623292714357376,
0.05117851868271828,
0.020553505048155785,
0.04143458977341652,
-0.0432853139936924,
-0.008838661946356297
] |
[
9.395772933959961,
1.658486247062683
] |
Optics
|
General Physics
|
physics-optics
|
physics-comp-ph
|
na
|
2007-03-31T15:55:50
|
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly
used in cell signaling. This motif itself can generate a variety of dynamic
behaviors like bistability and ultrasensitivity without direct positive
feedbacks. In this paper, we study the number of positive steady states of a
general multisite phosphorylation-dephosphorylation cycle, and how the number
of positive steady states varies by changing the biological parameters. We show
analytically that (1) for some parameter ranges, there are at least n+1 (if n
is even) or n (if n is odd) steady states; (2) there never are more than 2n-1
steady states (in particular, this implies that for n=2, including single
levels of MAPK cascades, there are at most three steady states); (3) for
parameters near the standard Michaelis-Menten quasi-steady state conditions,
there are at most n+1 steady states; and (4) for parameters far from the
standard Michaelis-Menten quasi-steady state conditions, there is at most one
steady state.
|
A remark on the number of steady states in a multiple futile cycle
|
q-bio.QM q-bio.MN
|
0704.0036
| 2,007
|
[
-0.034483056515455246,
0.07049181312322617,
-0.02012510597705841,
-0.009502805769443512,
0.024837631732225418,
-0.023172803223133087,
0.05748731270432472,
0.012092448770999908,
-0.0367124006152153,
0.01348248403519392,
-0.12748555839061737,
0.02830667234957218,
0.04460219293832779,
0.010379918850958347,
0.0032691045198589563,
-0.03669752553105354,
0.04123638942837715,
0.011506221257150173,
0.02035587839782238,
0.00885810423642397,
-0.03334267437458038,
0.006502192001789808,
-0.05680545046925545,
-0.045187488198280334,
0.0904274433851242,
0.05528707802295685,
0.02302396111190319,
0.01844542659819126,
-0.06193632632493973,
0.029511932283639908,
0.01775265671312809,
-0.05434258282184601,
-0.03466438874602318,
-0.016524435952305794,
-0.02369765192270279,
-0.012989587150514126,
0.007772216107696295,
-0.0014747361419722438,
0.008741196244955063,
0.019193265587091446,
0.062429603189229965,
0.033380042761564255,
0.0009446005569770932,
-0.020654786378145218,
-0.016313103958964348,
0.008470783941447735,
-0.021526047959923744,
-0.00205420795828104,
0.03666408732533455,
-0.03419224172830582,
-0.00836100708693266,
0.044175855815410614,
0.03763724863529205,
-0.047879964113235474,
0.01733526587486267,
0.00928217638283968,
-0.009318082593381405,
-0.024924898520112038,
-0.00542929582297802,
0.03778963163495064,
0.030381174758076668,
0.030098743736743927,
-0.013563642278313637,
0.014325353316962719,
0.05039064213633537,
-0.06233804300427437,
-0.03890090808272362,
-0.003651029895991087,
-0.0018153935670852661,
-0.013245219364762306,
0.009863598272204399,
-0.057078614830970764,
-0.03230622410774231,
0.038155313581228256,
-0.0020015439949929714,
0.025437692180275917,
-0.0011978070251643658,
-0.004464815836399794,
0.020378774031996727,
0.0076675754971802235,
-0.01977858506143093,
-0.03795970603823662,
0.06068684160709381,
0.03524347022175789,
0.04609747603535652,
0.012414398603141308,
0.0046849679201841354,
-0.00000870388339535566,
-0.08603732287883759,
0.04347515106201172,
0.015929225832223892,
0.041509583592414856,
0.041253626346588135,
0.058295294642448425,
-0.08766662329435349,
0.025504088029265404,
-0.007791451644152403,
0.06640259176492691,
-0.04819077253341675,
-0.023397399112582207,
0.005821696016937494,
0.023831766098737717,
-0.012022047303617,
-0.026112128049135208,
0.03321585804224014,
0.004603484179824591,
-0.011815885081887245,
-0.034944552928209305,
0.014299014583230019,
-0.0448492094874382,
-0.026025420054793358,
-0.002444511977955699,
-0.0023042340762913227,
-0.017658885568380356,
-0.058504801243543625,
-0.023539789021015167,
0.0640539675951004,
-0.07116013765335083,
-0.02702980861067772,
0.044183868914842606,
0.02354337088763714,
-0.022520029917359352,
-0.022674372419714928,
0.021096503362059593,
0.022844307124614716,
0.014167210087180138,
-0.04857252165675163,
0.0011155790416523814,
0.00032504289993084967,
0.023555973544716835,
0.02709304168820381,
-0.018518764525651932,
-0.060562025755643845,
0.003354809945449233,
0.02862370014190674,
0.05537935346364975,
-0.012138646095991135,
-0.05054091289639473,
0.0065615796484053135,
-0.028729286044836044,
-0.02033507637679577,
-0.02971387468278408,
-0.003074668115004897,
-0.039433129131793976,
-0.016718290746212006,
-0.024526488035917282,
0.01595958322286606,
-0.01916801556944847,
0.04152066633105278,
-0.00981029961258173,
0.014380388893187046,
0.05415676534175873,
0.020917393267154694,
0.05533948168158531,
-0.026478059589862823,
-0.04825486242771149,
-0.016582446172833443,
0.03353334963321686,
0.026293853297829628,
0.048341795802116394,
0.018908271566033363,
0.012134172953665257,
-0.06512241065502167,
0.029366711154580116,
-0.058242317289114,
0.006454954389482737,
0.04890678450465202,
0.024495650082826614,
-0.023389391601085663,
0.06499210000038147,
-0.009029868990182877,
-0.00803484208881855,
0.005610194057226181,
-0.016262739896774292,
0.041024189442396164,
-0.04813672602176666,
-0.004776734858751297,
0.0015260545769706368,
-0.0036779872607439756,
-0.02813809923827648,
0.038812074810266495,
0.004958190489560366,
-0.014837795868515968,
0.018005892634391785,
0.00031766341999173164,
0.015627404674887657,
-0.04788794368505478,
-0.05246074125170708,
-0.03091789409518242,
-0.05610234662890434,
0.013262126594781876,
0.054707083851099014,
-0.05376554653048515,
-0.0425490103662014,
-0.022054573521018028,
-0.0022559945937246084,
0.07056661695241928,
-0.06072106957435608,
0.06891205906867981,
-0.03176623210310936,
-0.01280415989458561,
-0.008438515476882458,
-0.018410734832286835,
0.009985457174479961,
-0.04617462307214737,
0.03178173303604126,
0.0032523993868380785,
0.03296259418129921,
-0.002537955529987812,
0.009557926096022129,
0.07585078477859497,
0.010053180158138275,
-0.06553784757852554,
0.04704045504331589,
-0.006270498037338257,
-0.02808104269206524,
0.01714417338371277,
-0.06375233829021454,
0.016348887234926224,
-0.004443701822310686,
0.041366443037986755,
0.000861985026858747,
-0.042486269026994705,
0.040316738188266754,
0.05066137760877609,
0.03917763754725456,
-0.044238731265068054,
-0.01694907434284687,
-0.013168109580874443,
-0.01254365872591734,
-0.07006262987852097,
-0.04564828425645828,
0.04185100644826889,
-0.042763978242874146,
-0.04396903142333031,
-0.017705023288726807,
-0.0009108941303566098,
0.04244808107614517,
-0.01290783379226923,
0.027497297152876854,
0.04438149183988571,
-0.011928372085094452,
-0.013500338420271873,
0.014511560089886189,
-0.10604187101125717,
-0.009235153906047344,
-0.026346774771809578,
-0.01861029863357544,
0.016475535929203033,
0.024170802906155586,
0.0042170751839876175,
0.010474846698343754,
0.0433705598115921,
0.06926999241113663,
0.023354817181825638,
-0.04037097096443176,
-0.013890842907130718,
0.06033238768577576,
-0.011059229262173176,
-0.0012851505307480693,
0.04661979898810387,
-0.034585632383823395,
0.012523885816335678,
-0.05218880623579025,
-0.05154426023364067,
-0.0006861704168841243,
0.006072812248021364,
-0.02517879195511341,
-0.0083325719460845,
0.002289506606757641,
0.013853338547050953,
-0.012079023756086826,
0.03866509720683098,
0.07391095906496048,
-0.027070624753832817,
0.033019501715898514,
0.026509331539273262,
-0.017366735264658928,
-0.007285008206963539,
-0.059741463512182236,
-0.057851642370224,
-0.005604627542197704,
-0.010190594010055065,
-0.029462983831763268,
0.012612853199243546,
0.03234196454286575,
0.03014102578163147,
-0.0008596202824264765,
-0.025255531072616577,
0.08842694014310837,
-0.007596948184072971,
-0.03790510073304176,
0.04428010433912277,
0.03395593538880348,
-0.05377562716603279,
0.0211175624281168,
0.011696877889335155,
-0.07158054411411285,
0.026806147769093513,
0.06458462029695511,
0.050383780151605606,
0.042135316878557205,
0.026351407170295715,
-0.023582812398672104,
0.04664888605475426,
-0.009769303724169731,
-0.01538789737969637,
0.008457900956273079,
0.025632208213210106,
0.03425063565373421,
-0.027971941977739334,
0.04909559339284897,
-0.04436352476477623,
-0.0008826290140859783,
-0.07216177135705948,
0.05378161743283272,
0.026946906000375748,
0.016007432714104652,
0.10737505555152893,
-0.02908453904092312,
0.023616749793291092,
-0.04336873069405556,
0.01575397700071335,
-0.06549380719661713,
0.02686452865600586,
0.024608619511127472,
-0.01659412495791912,
0.02543206699192524,
-0.052135877311229706,
-0.01571398414671421,
0.04200023040175438,
0.037046004086732864,
-0.02061634510755539,
-0.012805111706256866,
-0.01876356452703476,
-0.02725507691502571,
-0.031068654730916023,
0.01195831410586834,
0.028667015954852104,
0.009419605135917664,
-0.012026340700685978,
0.005567413289099932,
-0.02294447459280491,
-0.06397692859172821,
0.00787767767906189,
0.017284419387578964,
-0.05587909743189812,
-0.009752410463988781,
0.030246807262301445,
-0.017226101830601692,
0.0005069550825282931,
0.0074820066802203655,
-0.018464595079421997,
-0.011313223280012608,
-0.03011932037770748,
-0.03284154832363129,
-0.015413107350468636,
-0.019285429269075394,
0.013129380531609058,
0.0513448491692543,
0.034388355910778046,
-0.03661103919148445,
0.022458672523498535,
0.023434091359376907,
0.050963666290044785,
0.04528318718075752,
-0.00012591069389600307,
0.048634909093379974,
0.03581371158361435,
-0.06761596351861954,
-0.049373578280210495,
-0.044150400906801224,
-0.004198792390525341,
0.028197890147566795,
0.04445130378007889,
0.0022039986215531826,
-0.053578391671180725,
0.030180668458342552,
-0.046004749834537506,
0.03123733401298523,
0.0636533871293068,
-0.035055965185165405,
0.035984430462121964,
-0.02478634938597679,
0.009837757796049118,
0.027554785832762718,
-0.021951034665107727,
0.03776369243860245,
-0.049643464386463165,
0.03904527425765991,
0.0257189329713583,
-0.018151529133319855,
-0.027603773400187492,
0.05305119976401329,
0.005852620583027601,
-0.023706482723355293,
0.04759810492396355,
0.0017261956818401814,
0.04293058440089226,
0.024159925058484077,
0.01468972209841013,
-0.08454073220491409,
-0.017712222412228584,
-0.028306975960731506,
-0.011993237771093845,
0.033523596823215485,
-0.01737266220152378,
-0.021218249574303627,
0.029173435643315315,
-0.007604147773236036,
0.012435132637619972,
0.01165181677788496,
0.011808863840997219,
-0.05037058889865875,
0.020929038524627686,
0.01519357692450285,
0.0256044864654541,
-0.04235239326953888,
0.03910699114203453,
0.0070969173684716225,
0.02087564766407013,
0.061022039502859116,
-0.061139509081840515,
-0.024261074140667915,
0.00911301001906395,
0.0018985598580911756,
-0.011908236891031265,
0.03024872951209545,
-0.010059941560029984,
-0.06362999230623245,
0.060430653393268585,
0.01722870022058487,
0.011418276466429234,
0.043284229934215546,
-0.050349652767181396,
0.02998124621808529,
0.007882021367549896,
-0.005800751503556967,
-0.014327599667012691,
0.05140237882733345,
0.06383047997951508,
-0.04114419221878052,
0.02196698822081089,
-0.006413729395717382,
0.036709897220134735,
0.05884569510817528,
0.017618317157030106,
-0.02683112770318985,
-0.02218993566930294,
-0.008358405902981758,
0.046870119869709015,
0.004571991506963968,
-0.012244069017469883,
0.023134969174861908,
0.05219859257340431,
-0.03182830289006233,
-0.011985693126916885,
0.028202956542372704,
0.0089579988270998,
0.1167885810136795,
0.04281243681907654,
0.039450328797101974,
-0.011353530921041965,
0.0065979124046862125,
-0.03726186975836754,
-0.007156468462198973,
0.009063555859029293,
0.039901744574308395,
0.012701122090220451,
0.04552004486322403,
-0.004172415938228369,
0.01310680340975523,
-0.002808698918670416,
0.0600941963493824,
-0.023004526272416115,
-0.07597135752439499,
0.03349394351243973,
-0.02710600011050701,
0.003921331837773323,
0.06310081481933594,
0.05092831328511238,
-0.031400468200445175,
-0.035033125430345535,
-0.01437363401055336,
-0.02085394784808159,
-0.010732702910900116,
0.017116572707891464,
-0.0353403314948082,
-0.029101546853780746,
-0.0000769117395975627,
-0.0006013361853547394,
0.03598858043551445,
0.04788626357913017,
0.001861907890997827,
-0.02201216295361519,
-0.06933411210775375,
0.0023780984338372946,
-0.0032614145893603563,
-0.033013179898262024,
-0.01129001472145319,
-0.03160087764263153,
-0.037272874265909195,
0.025211865082383156,
0.01481292862445116,
0.002585776848718524,
0.008799407631158829,
-0.009954031556844711,
-0.11688857525587082,
0.028201017528772354,
0.021671755239367485,
0.02361958660185337,
0.03042903169989586,
0.033198483288288116,
0.07474885135889053,
-0.001232786220498383,
-0.028454644605517387,
0.010801344178617,
0.011571046896278858,
-0.08397355675697327,
-0.0043934546411037445,
0.02301124855875969,
-0.016205351799726486,
0.035797249525785446,
-0.012775026261806488,
-0.037761956453323364,
0.022647006437182426,
-0.08182170987129211,
-0.03827641159296036,
0.018111923709511757,
0.023581866174936295,
0.030117126181721687,
-0.0014463310362771153,
-0.004992325324565172,
0.011814993806183338,
0.02961246855556965,
-0.016619157046079636,
-0.01276608370244503,
0.021494125947356224,
0.016927208751440048,
0.03198883682489395,
0.015658356249332428,
0.00153670075815171,
0.021499240770936012,
0.05177988484501839,
0.019578665494918823,
-0.05776692181825638,
-0.0910063236951828,
0.016282591968774796,
-0.0521080307662487,
-0.058472469449043274,
0.010921449400484562,
-0.028760774061083794,
0.0018192969728261232,
-0.07669708132743835,
-0.015103892423212528,
0.005826882552355528,
0.0251162126660347,
-0.021332768723368645,
-0.017564106732606888,
-0.016604574397206306,
-0.04203987494111061,
0.04479265213012695,
0.02828705683350563,
0.014164046384394169,
0.05400897189974785,
-0.06901537626981735,
-0.06473647803068161,
0.014934387058019638,
0.02622518688440323,
0.05751056596636772,
0.0681380033493042,
-0.012570134364068508,
0.0015704070683568716,
0.045739367604255676,
0.011799131520092487,
0.0022411837708204985,
-0.017446530982851982,
0.06614905595779419,
-0.03960287943482399,
-0.013999832794070244,
-0.06451781094074249,
-0.024955134838819504,
0.0004953709430992603,
-0.01153897400945425,
-0.020019108429551125,
0.025168420746922493,
-0.019724024459719658,
-0.015308680012822151,
0.04455278068780899,
0.02799028344452381,
0.017274441197514534,
-0.012467176653444767,
-0.04840439558029175,
-0.06713907420635223,
-0.004795119632035494,
0.0048852767795324326,
-0.01666511595249176,
-0.05538500100374222,
-0.027591392397880554,
-0.05785653740167618,
0.030268551781773567,
0.013170880265533924,
0.062700055539608,
-0.07577309012413025,
-0.005080500151962042,
0.06439229100942612,
-0.01569501683115959,
0.028267785906791687,
-0.0347561351954937,
0.045430608093738556,
0.025039296597242355,
-0.03871799260377884,
-0.01797996275126934,
-0.06234360113739967,
0.007817212492227554,
-0.05804944783449173,
0.0670769214630127,
0.02480124682188034,
-0.0002916634257417172,
-0.01886909082531929,
-0.017984390258789062,
-0.049153201282024384,
0.012795321643352509,
-0.06820615381002426,
0.029124101623892784,
0.026673056185245514,
-0.0001115442646550946,
-0.04183299094438553,
-0.00006272186146816239,
0.03702311962842941,
0.017887664958834648,
-0.04792475327849388,
-0.08336888998746872,
0.010838373564183712,
-0.018360676243901253,
-0.0057465494610369205,
-0.050559669733047485,
0.0013232515193521976,
0.01651502400636673,
0.002738979645073414,
0.042098090052604675,
-0.026052990928292274,
0.03254498541355133,
0.0049992711283266544,
0.05080908536911011,
-0.0016822183970361948,
0.030402425676584244,
0.015341396443545818,
0.026287736371159554,
0.019110143184661865,
0.06845156848430634,
0.021608449518680573,
-0.04270550236105919,
0.0470433384180069,
-0.006300941109657288,
0.032326340675354004,
0.05789867788553238,
-0.008458506315946579,
-0.021208176389336586,
-0.019257210195064545,
0.01143948920071125,
-0.037764858454465866,
0.0063253347761929035,
0.03699825704097748,
0.03867766633629799,
-0.006574499420821667,
0.013482733629643917,
-0.025468334555625916,
-0.001321059069596231,
-0.00500405253842473,
-0.0008472276967950165,
0.011592952534556389,
-0.05345742404460907,
0.03362170234322548,
-0.051145073026418686,
0.010207118466496468,
0.01614534668624401,
-0.00026800352497957647,
0.03962406888604164,
-0.03253551945090294,
0.04360771179199219,
-0.03354281187057495,
-0.0027612722478806973,
-0.020567769184708595,
-0.035157397389411926,
0.03825296089053154,
-0.03324781730771065,
-0.021006951108574867,
-0.05134127289056778,
-0.03525464981794357,
0.04936886578798294,
0.0025270851328969,
0.01837005838751793,
-0.08352208882570267,
-0.023906316608190536,
0.01848311349749565,
-0.06201324239373207,
-0.0036074980162084103,
0.02174380049109459,
-0.00007184885180322453,
0.006297276355326176,
0.031038368120789528,
-0.05367061123251915,
0.07020299881696701,
0.011216478422284126,
0.008154529146850109,
-0.03675144538283348,
0.01217375323176384,
0.04688376560807228,
-0.0027737622149288654,
-0.006000719498842955,
0.020575597882270813,
-0.031008146703243256,
-0.01999986357986927,
-0.00811129342764616,
-0.013816718012094498,
-0.007002395577728748,
-0.071110300719738,
0.030258608981966972,
0.01013182196766138,
-0.03611190989613533,
-0.033008184283971786,
-0.09838061779737473,
0.04549479857087135,
0.007800769992172718,
-0.03573116287589073,
0.0544339157640934,
-0.04201203212141991,
0.03132107853889465,
0.04690036550164223,
-0.017433444038033485,
-0.027051279321312904,
-0.04122762009501457,
0.02335333824157715,
-0.03356832638382912,
-0.008114256896078587,
-0.0006010957295075059,
0.026175053790211678,
-0.09460782259702682,
-0.02601456828415394,
-0.012266022153198719,
-0.04844419285655022,
0.004573605488985777,
0.021477941423654556,
0.03350725769996643,
0.0578170008957386,
-0.07914146035909653,
0.04989471659064293,
0.08263107389211655,
-0.0047981021925807,
-0.045599471777677536,
0.001189043396152556,
0.007700116839259863,
0.029907070100307465,
0.050053711980581284,
-0.00143937929533422,
0.019742438569664955,
0.02859983779489994,
0.046079058200120926,
-0.036008186638355255,
0.015568756498396397,
0.00353427417576313,
-0.012610611505806446,
0.005431259982287884,
-0.022530362010002136,
-0.014894996769726276,
-0.02482004277408123,
-0.0061984858475625515
] |
[
5.997396469116211,
5.84290885925293
] |
Quantitative Methods
|
Quantitative Biology
|
q-bio-QM
|
q-bio-MN
|
na
|
2007-03-31T16:06:05
|
In this manuscript we investigate the capabilities of the Discrete Dipole
Approximation (DDA) to simulate scattering from particles that are much larger
than the wavelength of the incident light, and describe an optimized publicly
available DDA computer program that processes the large number of dipoles
required for such simulations. Numerical simulations of light scattering by
spheres with size parameters x up to 160 and 40 for refractive index m=1.05 and
2 respectively are presented and compared with exact results of the Mie theory.
Errors of both integral and angle-resolved scattering quantities generally
increase with m and show no systematic dependence on x. Computational times
increase steeply with both x and m, reaching values of more than 2 weeks on a
cluster of 64 processors. The main distinctive feature of the computer program
is the ability to parallelize a single DDA simulation over a cluster of
computers, which allows it to simulate light scattering by very large
particles, like the ones that are considered in this manuscript. Current
limitations and possible ways for improvement are discussed.
|
The discrete dipole approximation for simulation of light scattering by
particles much larger than the wavelength
|
physics.optics physics.comp-ph
|
0704.0037
| 2,007
|
[
-0.033631034195423126,
0.05319737643003464,
-0.0023365698289126158,
-0.07169346511363983,
-0.02367982640862465,
-0.012237511575222015,
0.03335895016789436,
0.005728905089199543,
-0.02091503143310547,
-0.011897712014615536,
-0.024557562544941902,
0.027265502139925957,
0.03987535834312439,
-0.003683066926896572,
-0.005588748026639223,
-0.02904939465224743,
0.03891145810484886,
-0.013625695370137691,
-0.0397937074303627,
0.019067544490098953,
0.018073730170726776,
-0.03577622398734093,
-0.028046727180480957,
-0.08280321955680847,
0.05181896314024925,
0.02980726584792137,
-0.006030266173183918,
0.013751291669905186,
-0.04132632538676262,
0.060795173048973083,
0.007367304526269436,
-0.08778957277536392,
0.01045228261500597,
-0.013167209923267365,
-0.02369074337184429,
-0.002675106981769204,
0.017767585813999176,
0.00047778268344700336,
-0.014426321722567081,
0.022924020886421204,
0.0381951704621315,
-0.029657261446118355,
-0.007969146594405174,
-0.020630111917853355,
0.016174191609025,
0.016527246683835983,
0.05515014007687569,
0.009370498359203339,
0.013809921219944954,
0.0023702960461378098,
0.005325836129486561,
0.022001713514328003,
0.02404213882982731,
-0.04859045892953873,
-0.019258227199316025,
0.0447058230638504,
-0.0031390893273055553,
-0.018486320972442627,
0.07734539359807968,
0.029446415603160858,
0.05080476030707359,
0.06494689732789993,
-0.08308803290128708,
0.00835616048425436,
0.0027454160153865814,
-0.07547414302825928,
-0.044282473623752594,
-0.03508506715297699,
-0.019922450184822083,
-0.0785536989569664,
0.02357148379087448,
-0.06418795138597488,
0.014854378998279572,
-0.0068048639222979546,
-0.01796375773847103,
-0.018749207258224487,
-0.01979883573949337,
0.005965059623122215,
-0.041978619992733,
0.022510811686515808,
0.005944343749433756,
-0.044123560190200806,
0.03064390830695629,
0.004656286910176277,
-0.0035821886267513037,
0.011885052546858788,
-0.018735628575086594,
-0.010918778367340565,
-0.028577199205756187,
0.015469546429812908,
0.056358326226472855,
-0.0015526089118793607,
0.05127231031656265,
0.054013121873140335,
-0.004483650904148817,
0.050502147525548935,
-0.03971197456121445,
0.07902606576681137,
-0.01732560060918331,
-0.03686955198645592,
0.04465686157345772,
0.05124755576252937,
0.030610477551817894,
0.040489789098501205,
0.05192871764302254,
0.014208987355232239,
0.006537220440804958,
0.01902332715690136,
0.022564008831977844,
0.029570093378424644,
-0.08943790197372437,
-0.05603046715259552,
-0.01811157912015915,
-0.01716447062790394,
-0.05430396646261215,
-0.03269312158226967,
0.06412240862846375,
-0.09057611972093582,
0.022749897092580795,
0.08164288103580475,
0.026227343827486038,
-0.01875852793455124,
0.015166055411100388,
0.03950080648064613,
0.06558608263731003,
0.0022752496879547834,
-0.02191586047410965,
0.022756699472665787,
0.01967616379261017,
-0.02276206761598587,
-0.03201744705438614,
-0.0322459451854229,
-0.07429236173629761,
0.010102852247655392,
0.030433181673288345,
0.03818024322390556,
-0.003264870960265398,
-0.05032344162464142,
0.007023693062365055,
0.014721332117915154,
0.041299041360616684,
0.028316877782344818,
0.01347268745303154,
-0.011264429427683353,
0.006886715069413185,
-0.03173605352640152,
-0.05023062229156494,
-0.058143552392721176,
-0.029218852519989014,
-0.04781220480799675,
0.011915373615920544,
0.012518106959760189,
0.06341056525707245,
0.009962846525013447,
-0.05640888214111328,
-0.00798864383250475,
-0.012949613854289055,
-0.027299782261252403,
0.023486968129873276,
0.008113873191177845,
-0.020214717835187912,
-0.007999273017048836,
-0.08413054794073105,
0.04520723596215248,
-0.016123929992318153,
0.03147510066628456,
0.059073325246572495,
0.01661520078778267,
0.005194284487515688,
-0.03256779909133911,
-0.0361412912607193,
-0.00712716206908226,
0.02366730011999607,
-0.015169464983046055,
-0.0230408925563097,
0.02123887836933136,
-0.003451933851465583,
-0.030293667688965797,
-0.015793439000844955,
0.018263254314661026,
0.031938064843416214,
-0.038244280964136124,
-0.023361166939139366,
0.04644892364740372,
0.05482868105173111,
0.01776012033224106,
0.02774166129529476,
-0.033950742334127426,
-0.022395558655261993,
-0.028812257573008537,
0.0011013108305633068,
0.013950326479971409,
0.005901154596358538,
-0.04063323140144348,
0.02302173152565956,
-0.02551354095339775,
0.09430420398712158,
-0.032166678458452225,
-0.0012704281834885478,
0.015301230363547802,
-0.03227109834551811,
0.04235919192433357,
0.019259635359048843,
0.03623413294553757,
0.0233010146766901,
0.018547914922237396,
-0.001707452698610723,
0.026362989097833633,
0.010732676833868027,
-0.02069474756717682,
0.09826880693435669,
0.0287616103887558,
-0.02945028245449066,
0.02457328885793686,
-0.04510226100683212,
0.015089054591953754,
-0.043437160551548004,
-0.03020222671329975,
-0.021930532529950142,
0.07110554724931717,
0.0068677449598908424,
-0.028926720842719078,
0.016081735491752625,
0.018672849982976913,
0.014534346759319305,
0.004768968094140291,
-0.025048892945051193,
0.04191901162266731,
0.021209003403782845,
0.01448602881282568,
-0.05511888861656189,
-0.0412926971912384,
0.02796950191259384,
-0.021507585421204567,
-0.003339446149766445,
0.02381070703268051,
-0.08793406933546066,
0.021429352462291718,
0.05082659050822258,
0.04766267538070679,
0.046224530786275864,
0.025681300088763237,
0.03275725990533829,
-0.026179946959018707,
-0.10636165738105774,
0.0242098867893219,
-0.01010025292634964,
0.020222129300236702,
-0.03519628569483757,
0.03695371374487877,
0.00919940136373043,
0.005697970744222403,
0.04008970037102699,
0.031566061079502106,
-0.011036507785320282,
-0.025191348046064377,
-0.0518825389444828,
0.054337840527296066,
-0.005713724531233311,
-0.013015848584473133,
0.014171863906085491,
-0.03991437703371048,
0.013626974076032639,
-0.06520631909370422,
-0.029496287927031517,
0.06755975633859634,
0.03513531759381294,
-0.0071256086230278015,
-0.008610524237155914,
-0.008291000500321388,
-0.019271589815616608,
0.028204450383782387,
0.08964341133832932,
0.026601893827319145,
0.009225128218531609,
0.006385740824043751,
0.06790553778409958,
-0.009890543296933174,
0.02794232778251171,
0.01508187036961317,
-0.07568207383155823,
-0.01394820585846901,
-0.02548256702721119,
-0.02141137421131134,
0.041788697242736816,
-0.04882553592324257,
-0.017235560342669487,
-0.02265586331486702,
-0.001264719059690833,
-0.025097403675317764,
-0.009303386323153973,
0.024538369849324226,
0.04194164276123047,
0.03314346820116043,
-0.015054767951369286,
0.04961608722805977,
0.08135558664798737,
0.017344212159514427,
-0.015542260371148586,
0.032975196838378906,
-0.025633351877331734,
0.03200133517384529,
0.002707108622416854,
0.010754991322755814,
0.03870338574051857,
0.057810645550489426,
-0.041765909641981125,
-0.020710136741399765,
0.0037547287065535784,
-0.01272048894315958,
0.04252779856324196,
0.0861329734325409,
-0.02482173591852188,
0.005532089155167341,
-0.012233731336891651,
0.006470234598964453,
0.04919669032096863,
-0.0007728060591034591,
0.04929094761610031,
0.02263089455664158,
0.056465547531843185,
-0.00542061310261488,
0.001625651610083878,
-0.026093287393450737,
-0.005637087859213352,
0.036084000021219254,
-0.010793541558086872,
0.039203595370054245,
-0.032779499888420105,
-0.01260343100875616,
0.02982124127447605,
0.005230002570897341,
-0.07282282412052155,
0.0036551919765770435,
-0.06329914927482605,
-0.05526454746723175,
-0.04650406539440155,
-0.004459891933947802,
0.02922859601676464,
-0.03540822118520737,
-0.01505536399781704,
-0.04875120520591736,
-0.09935053437948227,
-0.05609285086393356,
0.0026976699009537697,
0.019465114921331406,
-0.016671197488904,
-0.024706333875656128,
0.04607003554701805,
-0.0032786107622087,
0.018550410866737366,
0.017503706738352776,
0.001144884037785232,
0.019576163962483406,
-0.045028507709503174,
-0.00452798418700695,
0.041390836238861084,
-0.010188339278101921,
0.05117277055978775,
0.02414320781826973,
0.03135582432150841,
0.0023217415437102318,
0.023199299350380898,
-0.026838459074497223,
0.029537050053477287,
0.03779126703739166,
0.0046630920842289925,
0.02253866195678711,
0.0022070596460253,
-0.026508690789341927,
-0.06692814081907272,
-0.010078455321490765,
0.01969534158706665,
0.03239249810576439,
0.001015765592455864,
-0.006621001288294792,
-0.06235091760754585,
-0.0008898683590814471,
0.024079980328679085,
-0.012938984669744968,
0.027355466037988663,
0.04542674869298935,
0.04834730178117752,
0.009842431172728539,
-0.0020680264569818974,
0.011936391703784466,
-0.031891390681266785,
-0.03158068656921387,
-0.03021140769124031,
-0.028149262070655823,
0.029576390981674194,
-0.11425497382879257,
-0.04375715181231499,
0.04309313744306564,
-0.0007418605964630842,
-0.00442317221313715,
0.004122369922697544,
-0.01913469284772873,
0.016760557889938354,
-0.015269468538463116,
-0.018685422837734222,
-0.05592598021030426,
0.018757810816168785,
-0.01347463857382536,
-0.007486548740416765,
0.0008171624504029751,
-0.053076907992362976,
-0.0432594008743763,
-0.005145912989974022,
0.016771161928772926,
-0.0019190108869224787,
0.012315129861235619,
-0.04482269659638405,
-0.08597756177186966,
0.01561124436557293,
0.008461507968604565,
0.03559704124927521,
-0.003913199529051781,
0.002674860181286931,
0.013765815645456314,
-0.003273762995377183,
0.013192490674555302,
-0.049285758286714554,
-0.016044994816184044,
-0.0033992149401456118,
-0.01583259552717209,
-0.02297174744307995,
0.011922730132937431,
-0.0064771706238389015,
-0.08179354667663574,
0.02028816007077694,
0.0124064851552248,
-0.004908889997750521,
0.0501469261944294,
-0.013863279484212399,
0.032830290496349335,
0.030486591160297394,
-0.023171769455075264,
0.009036453440785408,
0.006322240456938744,
0.05862506479024887,
-0.025955555960536003,
0.0564730204641819,
-0.015948308631777763,
0.07086358219385147,
0.0931989997625351,
0.005096204578876495,
-0.02374543994665146,
-0.040245335549116135,
0.017903603613376617,
0.0681615099310875,
-0.013784891925752163,
-0.02573259361088276,
-0.01975218579173088,
0.046917594969272614,
-0.038119807839393616,
-0.027733460068702698,
0.00034725162549875677,
0.05802685767412186,
0.07002381235361099,
-0.013468455523252487,
0.06813130527734756,
-0.06296837329864502,
0.012541605159640312,
0.0051834722980856895,
0.0021888415794819593,
0.010857295244932175,
-0.0394156239926815,
-0.028036978095769882,
0.03473838046193123,
-0.05046593397855759,
-0.017083000391721725,
0.028076207265257835,
-0.012017258442938328,
-0.008271191269159317,
-0.038846440613269806,
-0.04814576730132103,
-0.039205972105264664,
0.008168013766407967,
0.059968989342451096,
0.008252308703958988,
-0.03508125618100166,
-0.01454426534473896,
0.0065958499908447266,
0.0017127664759755135,
0.026800990104675293,
0.006004462018609047,
0.049113500863313675,
0.006993240211158991,
-0.024946777150034904,
-0.0140696931630373,
-0.06714925169944763,
-0.024277331307530403,
-0.03129696100950241,
0.0011757115134969354,
-0.013465525582432747,
0.02610829286277294,
0.029214775189757347,
0.007939107716083527,
0.02440844476222992,
0.01548016257584095,
-0.04281902685761452,
0.008374733850359917,
-0.017641697078943253,
0.0028866189531981945,
0.060314200818538666,
0.016573140397667885,
-0.04278033971786499,
0.0034760143607854843,
0.025575166568160057,
0.02106633596122265,
0.055413998663425446,
0.1031857579946518,
0.05571816489100456,
-0.0035319144371896982,
-0.03472619503736496,
0.02925368957221508,
0.020113522186875343,
-0.08075141906738281,
-0.004132052417844534,
0.004151455592364073,
-0.025278693065047264,
0.00004357790021458641,
0.004711846821010113,
-0.06867998838424683,
0.05827578529715538,
-0.0312512069940567,
-0.06851832568645477,
0.011072619818150997,
-0.04044365882873535,
0.024167288094758987,
0.026685399934649467,
-0.041973911225795746,
-0.029170749709010124,
-0.013621928170323372,
-0.00552263343706727,
-0.02013198845088482,
-0.012528489343822002,
0.01373887900263071,
0.007062631659209728,
-0.003246597247198224,
0.04068806767463684,
0.061388056725263596,
0.022206107154488564,
0.000521883019246161,
-0.03212829679250717,
0.013252769596874714,
0.03722533583641052,
-0.009087618440389633,
-0.02014780230820179,
0.03980185464024544,
-0.020301062613725662,
0.06921589374542236,
-0.03592615947127342,
0.04484982788562775,
-0.02208518236875534,
0.004490839783102274,
-0.04584329575300217,
-0.022109583020210266,
0.013472553342580795,
-0.017306307330727577,
-0.02403441071510315,
0.005471315700560808,
-0.05310855805873871,
-0.002931940834969282,
-0.07689722627401352,
-0.025674061849713326,
-0.004967416170984507,
0.02640875056385994,
0.00663389777764678,
-0.03413950651884079,
-0.061337340623140335,
-0.020525401458144188,
0.04569109156727791,
0.021855143830180168,
-0.03729299455881119,
0.07411186397075653,
-0.009006069041788578,
-0.030681688338518143,
0.0031142262741923332,
0.02869470976293087,
-0.014664986170828342,
0.0013050491688773036,
0.011950844898819923,
-0.019898025318980217,
-0.0027739936485886574,
-0.0655585452914238,
0.0006477691349573433,
0.04611640423536301,
-0.06602484732866287,
-0.02150149829685688,
-0.02764481119811535,
-0.010064270347356796,
-0.09232158213853836,
-0.0539507195353508,
-0.06264689564704895,
0.023140257224440575,
0.013822023756802082,
-0.032579291611909866,
-0.005749115254729986,
0.020741889253258705,
0.022410884499549866,
0.030376862734556198,
-0.03181002661585808,
0.024473024532198906,
0.010995646007359028,
-0.046104542911052704,
0.0007347477367147803,
0.02748331055045128,
0.006818179041147232,
0.06640615314245224,
0.027805645018815994,
-0.019171424210071564,
-0.02662302926182747,
-0.009531250223517418,
-0.07626480609178543,
0.05822601541876793,
-0.03883267194032669,
0.037037257105112076,
-0.051495470106601715,
-0.027693405747413635,
-0.07041169703006744,
0.023122942075133324,
-0.09981836378574371,
-0.07346083968877792,
0.019538037478923798,
-0.026521921157836914,
-0.019722914323210716,
0.026421982795000076,
0.06422159075737,
0.053886182606220245,
-0.022761572152376175,
0.006310123018920422,
0.002254949416965246,
0.02487018331885338,
0.02820296213030815,
-0.04854188114404678,
0.046064719557762146,
-0.018756788223981857,
0.07981037348508835,
0.03710639476776123,
-0.022668007761240005,
-0.013150861486792564,
0.007967708632349968,
0.035963013768196106,
0.004476497415453196,
0.03770153224468231,
0.049508824944496155,
0.025302086025476456,
-0.017915861681103706,
0.06454900652170181,
0.048957448452711105,
-0.004804100841283798,
0.0036890844348818064,
0.02840656042098999,
-0.03149507939815521,
0.014428391121327877,
0.045072589069604874,
-0.06711850315332413,
-0.005312612745910883,
-0.02864181064069271,
-0.014947931282222271,
-0.00792624056339264,
-0.03170651197433472,
0.0023195967078208923,
-0.02016369253396988,
-0.02429433912038803,
-0.025801295414566994,
-0.014346667565405369,
0.051321059465408325,
-0.014655699022114277,
0.003983905538916588,
-0.056652601808309555,
-0.0069266436621546745,
-0.03003823384642601,
-0.003487412817776203,
-0.04170163720846176,
0.00846632570028305,
-0.008509986102581024,
-0.005545441061258316,
0.060437045991420746,
-0.010039971210062504,
0.024264024570584297,
-0.00021205413213465363,
-0.014800500124692917,
-0.024896875023841858,
-0.03536943718791008,
0.009958704933524132,
-0.013568402267992496,
-0.0351986326277256,
0.0012782418634742498,
0.00797369983047247,
0.005222524981945753,
-0.06536424905061722,
-0.001022997428663075,
0.03176560252904892,
-0.010708934627473354,
-0.026437481865286827,
0.0932309553027153,
0.005904788617044687,
-0.04339561611413956,
0.0018572069238871336,
0.027933483943343163,
0.0018087514908984303,
-0.0066019268706440926,
0.011147747747600079,
-0.014699704945087433,
0.05668930336833,
0.015093371272087097,
-0.035817984491586685,
0.059454821050167084,
-0.008982432074844837,
0.013734347186982632,
0.021524228155612946,
-0.024247314780950546,
-0.005144324619323015,
0.004077463876456022,
-0.006561333779245615,
-0.024099228903651237,
-0.0050224014557898045,
0.07348695397377014,
-0.0017232507234439254,
-0.027684172615408897,
0.046892691403627396,
0.03732794150710106,
-0.10889502614736557,
-0.011701023206114769,
0.027767695486545563,
0.047894153743982315,
0.032895009964704514,
0.03615085408091545,
-0.006288581993430853,
-0.060671694576740265,
-0.010554899461567402,
-0.03154755383729935,
0.01944904401898384,
-0.030523313209414482,
-0.029231766238808632,
-0.036524634808301926,
0.02928944118320942,
0.008331258781254292,
-0.06910552829504013,
-0.00459019560366869,
0.006916593294590712,
-0.000418115290813148,
-0.017237544059753418,
-0.04652121663093567,
0.026990719139575958,
0.10487339645624161,
0.041012972593307495,
-0.021941110491752625,
-0.008801637217402458,
-0.006607084069401026,
0.012767795473337173,
0.03182892128825188,
-0.0031636443454772234,
0.026348592713475227,
0.045812513679265976,
0.02490483596920967,
-0.06372030079364777,
0.023472676053643227,
-0.004963940475136042,
0.026585055515170097,
0.055485136806964874,
0.03127660974860191,
-0.014463537372648716,
-0.04468916729092598,
0.018518883734941483
] |
[
9.28438949584961,
1.6524735689163208
] |
Optics
|
General Physics
|
physics-optics
|
physics-comp-ph
|
na
|
2007-03-31T16:25:01
|
We present a review of the discrete dipole approximation (DDA), which is a
general method to simulate light scattering by arbitrarily shaped particles. We
put the method in historical context and discuss recent developments, taking
the viewpoint of a general framework based on the integral equations for the
electric field. We review both the theory of the DDA and its numerical aspects,
the latter being of critical importance for any practical application of the
method. Finally, the position of the DDA among other methods of light
scattering simulation is shown and possible future developments are discussed.
|
The discrete dipole approximation: an overview and recent developments
|
physics.optics physics.comp-ph
|
0704.0038
| 2,007
|
[
-0.026012323796749115,
0.03592129796743393,
-0.010558119975030422,
-0.07583124190568924,
0.0059091439470648766,
0.0043253470212221146,
0.021264877170324326,
-0.0006005105096846819,
-0.023317351937294006,
-0.027249183505773544,
-0.010454043745994568,
0.0009848136687651277,
0.0374346598982811,
-0.019580919295549393,
0.016765883192420006,
-0.042159583419561386,
0.022984595969319344,
-0.007846795953810215,
-0.0140951843932271,
-0.01218983344733715,
0.014668270014226437,
0.0033566502388566732,
-0.00615363335236907,
-0.0676635280251503,
0.08490346372127533,
0.005127938464283943,
-0.012256019748747349,
-0.0020928673911839724,
-0.021770557388663292,
0.023386884480714798,
0.018440192565321922,
-0.066379614174366,
0.03540807589888573,
-0.0023647432681173086,
-0.022542934864759445,
-0.024656623601913452,
0.026175500825047493,
0.010284622199833393,
-0.012110436335206032,
0.0325627364218235,
0.04727679118514061,
0.025961898267269135,
-0.01444037165492773,
-0.006844707299023867,
0.04366432502865791,
0.010013731196522713,
0.013123235665261745,
-0.020609399303793907,
0.0036324630491435528,
0.02694694884121418,
-0.006318027153611183,
0.01903419941663742,
0.024468624964356422,
-0.06587523967027664,
-0.010386716574430466,
0.002092719543725252,
0.020305616781115532,
-0.029290728271007538,
0.0644335001707077,
0.021872561424970627,
0.016298821195960045,
0.06778471171855927,
-0.05732402577996254,
-0.005186018999665976,
0.009653366170823574,
-0.078229159116745,
-0.042536661028862,
-0.04467754438519478,
0.007992262952029705,
-0.07715099304914474,
0.02244468964636326,
-0.06157948821783066,
0.01208129059523344,
-0.014166630804538727,
0.016789281740784645,
-0.03582378104329109,
-0.03262518346309662,
0.010011360049247742,
-0.006791774649173021,
-0.031248729676008224,
-0.002028612419962883,
-0.047007545828819275,
0.034595880657434464,
0.027223452925682068,
0.019010474905371666,
0.008647213689982891,
0.012174485251307487,
0.022436894476413727,
-0.013341091573238373,
-0.013915630988776684,
0.015478219836950302,
-0.015429490245878696,
0.049488238990306854,
0.014602858573198318,
-0.03371889889240265,
0.01541969645768404,
-0.010522538796067238,
0.0503702349960804,
0.005826442968100309,
-0.0235071312636137,
0.034952037036418915,
0.05792434886097908,
0.030924741178750992,
0.045362286269664764,
0.02467299997806549,
0.01889936439692974,
-0.016040006652474403,
-0.002159252529963851,
0.036363307386636734,
0.0067370119504630566,
-0.10683601349592209,
-0.036267828196287155,
0.0076317437924444675,
-0.014810380525887012,
-0.04806755483150482,
-0.02544088289141655,
0.07588377594947815,
-0.12306074798107147,
0.039390210062265396,
0.039383821189403534,
0.019741088151931763,
0.015160458162426949,
0.018231766298413277,
0.04960660636425018,
0.04345399886369705,
-0.0039343214593827724,
-0.044479094445705414,
-0.002255226718261838,
0.010043547488749027,
-0.03592110052704811,
-0.006718529853969812,
-0.0010860215406864882,
-0.06871870905160904,
0.00351230357773602,
0.03983832150697708,
0.024278484284877777,
0.006327283568680286,
-0.0659562423825264,
0.024074165150523186,
0.009086104109883308,
0.06070632115006447,
-0.0024266079999506474,
0.022306527942419052,
-0.01777239888906479,
0.046344008296728134,
-0.03127213940024376,
-0.04485940933227539,
-0.07716773450374603,
-0.03862403333187103,
-0.024333493784070015,
0.03432675823569298,
-0.007286319509148598,
0.06058233603835106,
-0.01434553787112236,
-0.054185256361961365,
-0.011087104678153992,
-0.01845027320086956,
-0.013430980034172535,
0.033418167382478714,
0.010400187224149704,
-0.01558666117489338,
0.022111373022198677,
-0.0874210074543953,
0.019277187064290047,
0.010396670550107956,
0.03135555610060692,
0.06854099780321121,
0.024046070873737335,
0.012172188609838486,
-0.029018254950642586,
0.006411884445697069,
-0.01665971241891384,
-0.004086857661604881,
-0.00014755719166714698,
-0.032358672469854355,
0.010059566237032413,
0.012155196629464626,
-0.04860614612698555,
-0.020568419247865677,
0.005718715488910675,
0.005556337535381317,
-0.04737119376659393,
-0.03067481704056263,
0.06201748922467232,
0.02875787764787674,
0.024621007964015007,
0.005630159750580788,
-0.020741604268550873,
-0.028752021491527557,
-0.048793599009513855,
-0.001228139502927661,
0.018275050446391106,
0.014662932604551315,
-0.024653123691678047,
0.01566074788570404,
-0.011696990579366684,
0.10519766062498093,
-0.016732366755604744,
0.04958277568221092,
-0.0143052339553833,
-0.057188231498003006,
0.04622476175427437,
0.030646586790680885,
0.04453784599900246,
0.02555730566382408,
0.02613714337348938,
0.013019653968513012,
0.03265624865889549,
0.02935861237347126,
-0.022294556722044945,
0.07206553220748901,
0.012671155855059624,
-0.009052019566297531,
0.020591484382748604,
-0.0487755611538887,
-0.011501218192279339,
-0.0347944051027298,
-0.01975766383111477,
-0.04101806879043579,
0.053458187729120255,
-0.014338182285428047,
-0.028594769537448883,
-0.0009171972633339465,
0.033506736159324646,
0.01292449701577425,
0.0037179021164774895,
0.001359156216494739,
0.04097709432244301,
-0.0040497686713933945,
0.007626615464687347,
-0.09824735671281815,
-0.07032182812690735,
-0.0034658173099160194,
-0.028919003903865814,
-0.00505198584869504,
-0.0029047641437500715,
-0.08926312625408173,
0.0076011898927390575,
0.07091521471738815,
0.0405389629304409,
0.03357607498764992,
0.015459319576621056,
0.054112762212753296,
-0.00034248922020196915,
-0.07256952673196793,
0.032641615718603134,
0.013150450773537159,
0.02704184502363205,
-0.05911143124103546,
0.0012178802862763405,
0.002668683882802725,
0.017738772556185722,
0.017597300931811333,
0.03225548192858696,
0.013580329716205597,
-0.042002737522125244,
-0.05855072662234306,
0.03673139587044716,
0.003194940509274602,
-0.021808911114931107,
0.03374109044671059,
-0.03963081166148186,
-0.024481264874339104,
-0.059691641479730606,
-0.038084570318460464,
0.051289357244968414,
0.049981869757175446,
-0.03177293762564659,
0.003474883735179901,
-0.06279899924993515,
-0.047514695674180984,
0.030528005212545395,
0.07699097692966461,
0.02026531472802162,
0.017077626660466194,
-0.030417058616876602,
0.05028168484568596,
-0.04419828578829765,
0.019051527604460716,
0.008476709015667439,
-0.03983745351433754,
-0.03987601771950722,
-0.02739899419248104,
-0.04177171736955643,
0.0198680367320776,
-0.00924680009484291,
-0.00032156091765500605,
-0.06062609702348709,
-0.027397863566875458,
-0.03841415420174599,
-0.013402792625129223,
0.031214194372296333,
0.002170167863368988,
0.005517064593732357,
-0.0403938926756382,
0.08243663609027863,
0.09789308905601501,
-0.0033024682197719812,
-0.010143307037651539,
0.04436202347278595,
-0.00449047377333045,
0.021068328991532326,
-0.014041141606867313,
-0.001859390176832676,
0.06151400879025459,
0.0583215169608593,
-0.0120347049087286,
-0.03661820665001869,
0.039125967770814896,
0.032331544905900955,
0.017753787338733673,
0.08707817643880844,
-0.040918316692113876,
0.002566912677139044,
-0.023321975022554398,
-0.024938834831118584,
0.06568986922502518,
0.008457346819341183,
0.07837223261594772,
0.035984113812446594,
0.06196462735533714,
0.0009894802933558822,
0.0062578702345490456,
-0.0339573472738266,
0.003264673985540867,
0.04246513545513153,
0.015584993176162243,
0.060228317975997925,
-0.03498641029000282,
-0.0060143726877868176,
0.030771655961871147,
0.006068846210837364,
-0.07510694861412048,
-0.01657736860215664,
-0.045949533581733704,
-0.05145448446273804,
-0.052341245114803314,
0.001141380169428885,
0.009264334104955196,
-0.012976421043276787,
0.027254413813352585,
-0.08574365079402924,
-0.08955194056034088,
-0.05153980106115341,
0.015915093943476677,
0.007971826009452343,
-0.008226235397160053,
-0.009081436321139336,
0.029935220256447792,
0.015240943990647793,
-0.0026253280229866505,
0.03931595757603645,
-0.008114390075206757,
0.04978211596608162,
-0.03003530763089657,
0.02609246037900448,
0.03474375978112221,
0.006427715998142958,
0.06608163565397263,
0.04880299046635628,
0.030064713209867477,
-0.009961237199604511,
0.047243162989616394,
-0.03642628341913223,
0.03188442438840866,
0.028925172984600067,
-0.007479020394384861,
0.012044534087181091,
-0.02011977881193161,
-0.05371357128024101,
-0.08357291668653488,
0.012705490924417973,
0.00854528322815895,
0.009250381961464882,
-0.01985940709710121,
-0.012720385566353798,
-0.05481548234820366,
0.005927185993641615,
-0.007366981357336044,
-0.008599531836807728,
0.006846834439784288,
0.04276493564248085,
0.07091689854860306,
0.05196480453014374,
0.014271281659603119,
0.02485014870762825,
-0.04461836814880371,
-0.003777127480134368,
-0.03897222504019737,
-0.0282621830701828,
0.0010730905923992395,
-0.07662764936685562,
-0.026890479028224945,
0.036309026181697845,
-0.0063412864692509174,
0.027367014437913895,
0.03439043462276459,
0.008645102381706238,
-0.011912559159100056,
-0.006695867516100407,
-0.005315450485795736,
-0.08973632752895355,
0.006255543790757656,
-0.03127623721957207,
0.021552903577685356,
0.028569120913743973,
-0.0468243807554245,
-0.05818339064717293,
0.022961510345339775,
-0.006534740328788757,
-0.02703855000436306,
0.03231896087527275,
-0.046213217079639435,
-0.020114794373512268,
0.059140678495168686,
0.009825333021581173,
0.03556438907980919,
-0.018943851813673973,
0.007014407776296139,
0.0352071113884449,
0.02887018211185932,
0.0300384983420372,
-0.08250349014997482,
-0.028542570769786835,
-0.045718614012002945,
0.007207544520497322,
-0.00994460191577673,
0.04285626485943794,
0.01302857231348753,
-0.06927292793989182,
0.02545812353491783,
0.033972688019275665,
-0.004111167974770069,
0.03144459426403046,
-0.04868851974606514,
0.02036755159497261,
-0.013698849827051163,
-0.007111719809472561,
-0.003219240577891469,
0.019949590787291527,
0.07295561581850052,
-0.02866748906672001,
0.059670478105545044,
0.027240300551056862,
0.07276756316423416,
0.08105401694774628,
-0.0073758759535849094,
-0.03041243366897106,
-0.006262640934437513,
0.0023913411423563957,
0.03488010913133621,
0.023441635072231293,
0.004079572856426239,
-0.024577923119068146,
0.03436774015426636,
-0.020810626447200775,
-0.004353638738393784,
-0.03346898406744003,
0.060640621930360794,
0.10406673699617386,
-0.0026574628427624702,
0.036452244967222214,
-0.05640759319067001,
0.012110359966754913,
0.000007023501439107349,
-0.020263727754354477,
-0.013069406151771545,
-0.028459668159484863,
-0.023468559607863426,
-0.004975652322173119,
-0.03311094641685486,
0.01334083080291748,
0.0008800645591691136,
-0.04223501309752464,
-0.020021941512823105,
-0.03906267136335373,
-0.032537732273340225,
-0.015381556004285812,
-0.00834350660443306,
0.042106591165065765,
0.020848935469985008,
-0.05773201584815979,
-0.045104652643203735,
0.019273120909929276,
-0.01887679658830166,
0.011272908188402653,
0.03905491530895233,
0.025208136066794395,
0.021687787026166916,
-0.01287967897951603,
0.0026426250115036964,
-0.0396256223320961,
0.006871185731142759,
-0.056799016892910004,
0.010789048857986927,
-0.0021794692147523165,
-0.012728829868137836,
0.049030523747205734,
-0.02724018506705761,
0.012764849700033665,
-0.040781911462545395,
-0.009621819481253624,
-0.007559867110103369,
-0.021234573796391487,
0.031600020825862885,
0.031242506578564644,
0.010547113604843616,
-0.08755302429199219,
-0.014884588308632374,
-0.004314021207392216,
0.03568899258971214,
0.03924689441919327,
0.09019508212804794,
0.06646526604890823,
-0.01285763643682003,
-0.053040746599435806,
-0.00026239859289489686,
0.005424950737506151,
-0.06390709429979324,
-0.015708258375525475,
-0.007307468447834253,
-0.01026337780058384,
-0.03647240623831749,
0.004191284533590078,
-0.049888744950294495,
0.05076751857995987,
-0.054965171962976456,
-0.07713223993778229,
0.03385768085718155,
-0.02326549030840397,
-0.004018746316432953,
0.015203083865344524,
-0.005240095313638449,
-0.008823608048260212,
-0.04430951550602913,
-0.02792133390903473,
-0.020357385277748108,
0.0010779184522107244,
0.02235504426062107,
0.014887639321386814,
-0.006367559544742107,
0.031050199642777443,
0.0427272692322731,
0.011667530983686447,
0.041066985577344894,
-0.013195856474339962,
0.008917035534977913,
0.02235948108136654,
-0.033984992653131485,
-0.016314756125211716,
0.0469965860247612,
-0.02507128193974495,
0.04058549925684929,
-0.023036502301692963,
0.04094322398304939,
-0.045361846685409546,
-0.010851467028260231,
-0.03815876320004463,
-0.01738124154508114,
0.009075957350432873,
-0.004099502693861723,
-0.006789718754589558,
0.005666519980877638,
-0.05089844390749931,
0.030389776453375816,
-0.06806882470846176,
0.0002966976317111403,
-0.00544489361345768,
-0.011727030389010906,
0.01785123348236084,
-0.004312048200517893,
-0.05887434631586075,
0.005049438681453466,
0.05293598398566246,
-0.023961592465639114,
-0.044387660920619965,
0.041763290762901306,
-0.037384871393442154,
-0.054446034133434296,
0.01617233268916607,
0.033527761697769165,
0.007677251007407904,
0.012412603944540024,
-0.03223701938986778,
-0.016768086701631546,
0.042361922562122345,
-0.06488080322742462,
-0.022884689271450043,
0.03206891939043999,
-0.061941780149936676,
-0.013256749138236046,
-0.023893242701888084,
-0.009877991862595081,
-0.09042283147573471,
-0.05513991042971611,
-0.016396721825003624,
0.02874610386788845,
0.012959135696291924,
-0.004294971469789743,
0.004299158696085215,
0.001936423941515386,
-0.0035026762634515762,
0.0008317229221574962,
-0.023851903155446053,
0.06375280767679214,
0.02219109795987606,
-0.02275664545595646,
0.02098957449197769,
0.02649909257888794,
-0.017990905791521072,
0.05142085254192352,
0.021268486976623535,
-0.03280257806181908,
-0.034205362200737,
0.033507686108350754,
-0.07567256689071655,
0.03374747559428215,
-0.02346212789416313,
0.05837215855717659,
-0.02280355431139469,
-0.04419805109500885,
-0.061131127178668976,
0.021568825468420982,
-0.08825943619012833,
-0.057134658098220825,
0.059169817715883255,
-0.042653605341911316,
-0.0424245186150074,
-0.011936761438846588,
0.039346374571323395,
0.027518494054675102,
-0.02478293515741825,
-0.020209262147545815,
0.014927510172128677,
0.024060426279902458,
0.04413972422480583,
-0.000008682459338160697,
0.05245254933834076,
0.01413244940340519,
0.06170501559972763,
0.012664384208619595,
-0.001895889756269753,
0.025096524506807327,
0.003338972805067897,
0.026333855465054512,
0.009047693572938442,
0.024724876508116722,
0.03321120887994766,
0.017590004950761795,
0.013447210192680359,
0.06555180996656418,
0.05111343041062355,
0.015023025684058666,
0.02680131047964096,
0.04209783673286438,
-0.012550070881843567,
0.03444213047623634,
0.017651569098234177,
-0.04926683008670807,
0.0002963643055409193,
-0.0008963535074144602,
-0.007521364372223616,
-0.00039380189264193177,
-0.0355936698615551,
0.019643552601337433,
-0.02715463936328888,
0.01035131886601448,
-0.03495701774954796,
0.0017440889496356249,
0.056764066219329834,
0.003934146370738745,
-0.04605166241526604,
-0.024531273171305656,
-0.011073149740695953,
-0.02236340008676052,
0.034422919154167175,
-0.0255141519010067,
0.03721630573272705,
0.00527034280821681,
-0.008730122819542885,
0.04413725808262825,
0.008361224085092545,
-0.00645841471850872,
-0.02082316018640995,
-0.024635808542370796,
-0.02235710807144642,
0.0010857114102691412,
-0.02121444046497345,
-0.04231741651892662,
-0.029423177242279053,
-0.008900173008441925,
0.01353831123560667,
0.007799239829182625,
-0.07464995980262756,
0.02393496036529541,
0.04186972603201866,
-0.011500162072479725,
-0.0022422478068619967,
0.05213948339223862,
0.014754509553313255,
-0.05795009061694145,
-0.0038115782663226128,
0.018150456249713898,
0.014347834512591362,
-0.006847001612186432,
-0.03888225555419922,
-0.012857640162110329,
0.028512654826045036,
-0.0219463761895895,
-0.014532573521137238,
0.05785493552684784,
-0.020673388615250587,
0.05629502236843109,
0.0022855480201542377,
-0.027160292491316795,
0.02268003672361374,
0.029911024495959282,
0.010815317742526531,
-0.02097906917333603,
-0.014011758379638195,
0.08619209378957748,
-0.012533665634691715,
-0.04255371540784836,
0.07493375241756439,
0.04295119643211365,
-0.07173135876655579,
-0.03621809184551239,
0.014830570667982101,
0.0886596143245697,
0.025611938908696175,
0.048610538244247437,
-0.002422530436888337,
-0.04238365218043327,
-0.023407544940710068,
-0.03746502101421356,
0.053484801203012466,
-0.006060140207409859,
-0.013717295601963997,
-0.0035126374568790197,
0.006038436200469732,
0.002877015620470047,
-0.07219240814447403,
0.0029536825604736805,
0.02793070115149021,
-0.013745978474617004,
-0.04976852610707283,
-0.057511307299137115,
0.02996964193880558,
0.07330185920000076,
0.03674827888607979,
-0.03417814150452614,
0.007577204145491123,
-0.028511377051472664,
0.01062737312167883,
0.06211019679903984,
-0.011898873373866081,
0.02447223663330078,
0.03638853505253792,
0.030683394521474838,
-0.019473958760499954,
0.005208614747971296,
-0.013315806165337563,
0.032920148223638535,
0.056911226361989975,
-0.004004493355751038,
-0.0035568219609558582,
-0.05319591984152794,
-0.013264971785247326
] |
[
9.345623016357422,
1.675376534461975
] |
Optics
|
General Physics
|
physics-optics
|
physics-comp-ph
|
na
|
2007-03-31T17:06:06
|
The quadratic pion scalar radius, \la r^2\ra^\pi_s, plays an important role
for present precise determinations of \pi\pi scattering. Recently, Yndur\'ain,
using an Omn\`es representation of the null isospin(I) non-strange pion scalar
form factor, obtains \la r^2\ra^\pi_s=0.75\pm 0.07 fm^2. This value is larger
than the one calculated by solving the corresponding Muskhelishvili-Omn\`es
equations, \la r^2\ra^\pi_s=0.61\pm 0.04 fm^2. A large discrepancy between both
values, given the precision, then results. We reanalyze Yndur\'ain's method and
show that by imposing continuity of the resulting pion scalar form factor under
tiny changes in the input \pi\pi phase shifts, a zero in the form factor for
some S-wave I=0 T-matrices is then required. Once this is accounted for, the
resulting value is \la r^2\ra_s^\pi=0.65\pm 0.05 fm^2. The main source of error
in our determination is present experimental uncertainties in low energy S-wave
I=0 \pi\pi phase shifts. Another important contribution to our error is the not
yet settled asymptotic behaviour of the phase of the scalar form factor from
QCD.
|
Scalar radius of the pion and zeros in the form factor
|
hep-ph hep-lat nucl-th
|
0704.0039
| 2,007
|
[
-0.00789655651897192,
0.015053103677928448,
-0.0039177630096673965,
-0.046994902193546295,
0.06972130388021469,
0.002305910922586918,
-0.004758469294756651,
0.019810866564512253,
-0.009758617728948593,
-0.005608565639704466,
-0.08733115345239639,
0.042633943259716034,
0.014187745749950409,
-0.008483889512717724,
0.02726086974143982,
-0.022984309121966362,
0.042273588478565216,
-0.021750308573246002,
-0.002539027249440551,
0.03500554710626602,
-0.05955148860812187,
-0.04503829404711723,
-0.006860258057713509,
-0.04747811332345009,
0.07881331443786621,
-0.020187584683299065,
-0.021575864404439926,
-0.006805042736232281,
-0.05026203766465187,
-0.0022530772257596254,
0.051373835653066635,
-0.00193809496704489,
0.007280950900167227,
-0.07944933325052261,
-0.04029497131705284,
-0.0512094646692276,
0.06328459084033966,
-0.005086545832455158,
-0.002713517053052783,
0.0611642450094223,
0.016384677961468697,
-0.06471695005893707,
-0.008582979440689087,
-0.003944595344364643,
0.032714273780584335,
0.005751581396907568,
-0.014102847315371037,
0.0076212044805288315,
0.007737488020211458,
0.018775319680571556,
-0.014752473682165146,
0.02598974108695984,
0.0430416613817215,
-0.0327187106013298,
-0.04402453824877739,
0.015521496534347534,
0.022269295528531075,
0.011602051556110382,
0.06569406390190125,
0.051458071917295456,
-0.006886339280754328,
0.06366806477308273,
-0.02952372282743454,
0.0321236215531826,
0.048087574541568756,
-0.026380442082881927,
-0.04296994209289551,
-0.002497231587767601,
-0.02375800535082817,
-0.021447647362947464,
0.012408822774887085,
-0.050984349101781845,
0.007954753004014492,
0.03043910302221775,
-0.043253399431705475,
0.015475526452064514,
0.010721664875745773,
0.01748190075159073,
-0.025583529844880104,
0.03731928765773773,
-0.006581965833902359,
-0.07263998687267303,
0.008406723849475384,
0.03408671170473099,
0.04647865891456604,
0.00847673136740923,
0.051723215728998184,
0.03808389976620674,
-0.013574635609984398,
0.05497802421450615,
-0.00681568868458271,
0.013486618176102638,
0.04600174352526665,
0.007648380007594824,
0.008060218766331673,
0.01649448461830616,
-0.025579897686839104,
0.040618907660245895,
-0.007169794291257858,
0.0055730389431118965,
-0.01886614039540291,
0.0515340231359005,
0.00492821354418993,
0.015181124210357666,
0.0709100067615509,
0.03759098798036575,
0.002347127068787813,
-0.00451022619381547,
0.03859040141105652,
-0.04004509374499321,
-0.07770383358001709,
0.0007296384428627789,
0.05415748059749603,
-0.035042084753513336,
-0.02825636975467205,
-0.07397875189781189,
0.0748291090130806,
-0.0618223138153553,
0.02279563993215561,
0.061464130878448486,
-0.015360185876488686,
-0.04071515426039696,
0.0668511688709259,
0.04844409599900246,
0.025996079668402672,
-0.034519653767347336,
-0.012616591528058052,
0.017759015783667564,
0.05795473977923393,
-0.015572509728372097,
0.003038679016754031,
-0.004831076133996248,
-0.09185469895601273,
-0.007287485059350729,
0.039650216698646545,
0.012604756280779839,
-0.05917704850435257,
-0.04632415995001793,
-0.020665276795625687,
-0.03431346267461777,
0.003277281764894724,
0.031477827578783035,
0.026230614632368088,
-0.05071985349059105,
0.00960979051887989,
-0.056761354207992554,
-0.0019486119272187352,
-0.04708855226635933,
0.004994409158825874,
-0.012097295373678207,
0.05080942064523697,
-0.0016621863469481468,
-0.004461080767214298,
0.06027425825595856,
-0.024126345291733742,
-0.03377342224121094,
-0.012498384341597557,
0.003320105141028762,
0.035626545548439026,
0.01205736305564642,
0.022678058594465256,
0.028884653002023697,
-0.08284232020378113,
0.00794539786875248,
-0.08986988663673401,
0.03111705370247364,
0.030202217400074005,
0.015964986756443977,
-0.030420871451497078,
0.04213372617959976,
-0.017699452117085457,
-0.018574869260191917,
-0.0005546556785702705,
-0.05383216589689255,
-0.017662126570940018,
0.01340043731033802,
-0.01930370181798935,
-0.03843073174357414,
0.08642767369747162,
0.06474203616380692,
0.04323196038603783,
-0.008380722254514694,
0.007608781568706036,
0.02879674918949604,
0.006840088404715061,
0.03116600587964058,
0.05826166644692421,
0.030300697311758995,
-0.02438165433704853,
-0.019190873950719833,
-0.010940794833004475,
0.04338338226079941,
-0.023984244093298912,
-0.026999128982424736,
-0.020462919026613235,
0.030428143218159676,
0.04436761885881424,
-0.032556552439928055,
-0.032797712832689285,
-0.0036806385032832623,
-0.01897449977695942,
0.00979322474449873,
-0.04055577144026756,
0.0027251422870904207,
0.007887264713644981,
0.03216741979122162,
0.001665344345383346,
-0.012108290567994118,
0.049222271889448166,
-0.016046062111854553,
0.04123356565833092,
0.01816171407699585,
-0.01525343582034111,
0.031274233013391495,
-0.01999439112842083,
-0.00035658254637382925,
0.020134638994932175,
-0.01921427808701992,
-0.03554459288716316,
0.05986276641488075,
0.005289984866976738,
-0.021110698580741882,
0.039319463074207306,
0.011216704733669758,
0.026306472718715668,
0.04428120329976082,
-0.04543987661600113,
-0.02425955981016159,
0.00877318810671568,
-0.010618147440254688,
-0.0424308106303215,
-0.024376172572374344,
-0.04167969152331352,
0.05617762729525566,
-0.03401715308427811,
-0.02417648211121559,
-0.028559932485222816,
0.009996662847697735,
0.05294838175177574,
0.07269745320081711,
0.013313434086740017,
0.03435736522078514,
-0.035413116216659546,
-0.004326585214585066,
-0.0642191469669342,
-0.01974845677614212,
0.019745197147130966,
-0.04155808687210083,
-0.053328368812799454,
-0.01177533995360136,
-0.0114403972402215,
0.023636220023036003,
0.01891096867620945,
0.019100835546851158,
-0.04255273565649986,
-0.057757239788770676,
0.013751927763223648,
0.05181485787034035,
-0.024323195219039917,
-0.08325307816267014,
0.004245819989591837,
-0.008101172745227814,
0.0025317270774394274,
0.0006059535080567002,
-0.04801575094461441,
0.03831905499100685,
-0.02022453583776951,
0.02988736517727375,
-0.014764929190278053,
-0.04112141579389572,
0.020574497058987617,
0.033847626298666,
0.0732022374868393,
0.025300106033682823,
-0.017884163185954094,
-0.03152436017990112,
0.027069000527262688,
-0.04574524238705635,
0.034009311348199844,
0.020812001079320908,
-0.0432015024125576,
-0.020143715664744377,
0.0016162426909431815,
-0.02505282498896122,
-0.024093318730592728,
-0.03716433420777321,
-0.025298994034528732,
-0.02725270204246044,
-0.011317616328597069,
0.007345994468778372,
-0.0598689541220665,
0.03834478184580803,
-0.006428197957575321,
0.028694158419966698,
0.008272155188024044,
0.10105135291814804,
0.06587611138820648,
-0.020893393084406853,
0.015299131162464619,
-0.002576147671788931,
0.017730625346302986,
0.034306664019823074,
-0.019262131303548813,
-0.013479387387633324,
-0.019262636080384254,
-0.005073683802038431,
0.034707821905612946,
-0.0007212865748442709,
-0.001128606148995459,
-0.0005055249202996492,
-0.05017181485891342,
0.055365364998579025,
-0.012837986461818218,
-0.014617804437875748,
-0.05967320129275322,
0.003991610836237669,
0.037107955664396286,
0.01552935503423214,
0.0748642086982727,
0.06938347220420837,
0.03402547910809517,
-0.058677058666944504,
0.02548537589609623,
-0.03928280994296074,
-0.003346063196659088,
0.06211626157164574,
-0.005870089866220951,
0.02442535012960434,
-0.05027598515152931,
-0.026463525369763374,
0.0026106927543878555,
0.058031972497701645,
-0.00455942889675498,
-0.03776033595204353,
-0.02942207083106041,
0.021769728511571884,
-0.02067676931619644,
0.024420680478215218,
0.010911602526903152,
0.03035869263112545,
0.05167795345187187,
-0.03162234276533127,
-0.06846360117197037,
0.024885451421141624,
0.01723194494843483,
0.011951711028814316,
-0.026875047013163567,
-0.022618120536208153,
0.014840031042695045,
-0.038111280649900436,
-0.029173878952860832,
0.020952600985765457,
-0.01548085268586874,
-0.024693282321095467,
0.01329958625137806,
0.06550222635269165,
0.023279793560504913,
-0.00022438446467276663,
0.03359506279230118,
0.014043280854821205,
0.04416636377573013,
-0.09020598232746124,
0.05351532995700836,
0.015567350201308727,
0.045089032500982285,
0.03380579128861427,
-0.0009659688803367317,
0.0015400322154164314,
0.0021007743198424578,
-0.043205875903367996,
-0.015698855742812157,
-0.03113611415028572,
0.052686698734760284,
0.012882919050753117,
0.009743512608110905,
-0.01690821722149849,
-0.06826794147491455,
-0.01186529640108347,
-0.010865937918424606,
0.016211874783039093,
0.037095293402671814,
-0.017784185707569122,
-0.0068496535532176495,
-0.06122010201215744,
-0.005796907003968954,
-0.03549150004982948,
-0.054532792419195175,
-0.03961329534649849,
-0.01484766323119402,
-0.03672517091035843,
-0.003022535238415003,
-0.016679666936397552,
-0.012228183448314667,
0.00335882231593132,
-0.0031929146498441696,
-0.024898843839764595,
0.07371554523706436,
-0.03383879363536835,
-0.036967743188142776,
0.05208749324083328,
-0.06062199920415878,
-0.06492438912391663,
0.059966299682855606,
-0.01700558327138424,
-0.017986077815294266,
0.025513386353850365,
-0.009005468338727951,
-0.025498265400528908,
0.07664817571640015,
-0.036194656044244766,
-0.03703617677092552,
0.026932979002594948,
-0.011994274333119392,
-0.04754282906651497,
0.012629532255232334,
-0.0041083525866270065,
0.0528157502412796,
-0.04267583787441254,
0.002644050633534789,
-0.030465107411146164,
0.01020455826073885,
0.05880090221762657,
-0.026943545788526535,
-0.009075263515114784,
0.027709312736988068,
-0.013342575170099735,
0.0047766659408807755,
0.03611506149172783,
0.032458774745464325,
-0.029520606622099876,
0.022614264860749245,
0.03377315774559975,
0.013572180643677711,
0.04786873236298561,
-0.09042920172214508,
0.021390844136476517,
0.012192322872579098,
-0.03000500611960888,
0.017454756423830986,
0.05079477280378342,
0.007841981947422028,
-0.042578089982271194,
0.01415254082530737,
0.029326699674129486,
0.024454034864902496,
0.04859413206577301,
0.05511380359530449,
-0.05448115989565849,
0.026287663727998734,
0.01769903674721718,
0.026766858994960785,
-0.012852098792791367,
0.05137186497449875,
-0.010597437620162964,
0.059663232415914536,
-0.01981453225016594,
-0.024366874247789383,
0.030375327914953232,
0.03965853154659271,
0.038070257753133774,
0.01731926202774048,
0.03381373733282089,
-0.04204287379980087,
0.03017829731106758,
0.017276106402277946,
0.002510893391445279,
0.0028653391636908054,
0.023342834785580635,
-0.016109256073832512,
0.03293326497077942,
-0.0020744353532791138,
-0.008449853397905827,
0.03090856783092022,
0.031034300103783607,
0.007925990968942642,
-0.014848004095256329,
-0.002173712709918618,
-0.03421260043978691,
-0.008655420504510403,
0.054927513003349304,
0.007494703400880098,
-0.03418787941336632,
-0.046256452798843384,
-0.012626232579350471,
0.04248642176389694,
0.06309709697961807,
-0.00966620072722435,
0.00046238029608502984,
0.006809738930314779,
-0.03762756660580635,
0.025255786255002022,
0.08328329026699066,
0.0102027403190732,
-0.01826794072985649,
-0.0024764989502727985,
0.050721846520900726,
-0.010070795193314552,
-0.0047767674550414085,
0.007808542810380459,
0.03209804370999336,
-0.042828820645809174,
0.0372173935174942,
-0.008485423400998116,
0.030617373064160347,
-0.05822324752807617,
0.021408138796687126,
-0.05632290244102478,
-0.02949596382677555,
-0.029394013807177544,
-0.011724106967449188,
0.057918235659599304,
0.036704324185848236,
0.05768807232379913,
0.0276096910238266,
0.0067771729081869125,
-0.08716729283332825,
0.011708784848451614,
0.06030093505978584,
-0.07673802226781845,
0.02782118134200573,
0.028999891132116318,
-0.03087107464671135,
-0.000360440812073648,
-0.06394116580486298,
-0.06758236140012741,
0.028319688513875008,
-0.0020978592801839113,
-0.049993861466646194,
0.04376176744699478,
-0.004399359226226807,
0.01709752343595028,
0.008769601583480835,
0.0329868383705616,
-0.02044668421149254,
0.0158788301050663,
-0.0148563701659441,
-0.00941008236259222,
0.0074428473599255085,
-0.002242926973849535,
-0.010851842351257801,
-0.022829214110970497,
0.0008293171413242817,
-0.0032614138908684254,
0.03691012039780617,
0.008460198529064655,
-0.0471663661301136,
-0.008293546736240387,
0.003067830577492714,
-0.028407223522663116,
-0.06945233047008514,
0.04540209844708443,
-0.014462151564657688,
-0.0032792154233902693,
-0.006369727198034525,
0.01619596779346466,
-0.038560669869184494,
0.0244525745511055,
-0.03128283843398094,
-0.05861746892333031,
-0.02517492137849331,
0.02599882334470749,
-0.0005530442576855421,
-0.03434833511710167,
-0.009189536795020103,
-0.008440451696515083,
-0.12536637485027313,
0.005994235165417194,
-0.020741961896419525,
0.003425540402531624,
-0.01079685240983963,
0.018996702507138252,
-0.06000767648220062,
-0.0009260819060727954,
0.010003694333136082,
0.003216763259842992,
-0.029588302597403526,
0.03291502222418785,
-0.01647692732512951,
-0.014374869875609875,
0.014764782972633839,
-0.04926278814673424,
0.0042234850116074085,
-0.011386515572667122,
-0.045727264136075974,
-0.030222168192267418,
0.0642525851726532,
-0.014971552416682243,
-0.014177612029016018,
0.07939688861370087,
0.007328038569539785,
0.006356595084071159,
-0.040107518434524536,
-0.07376305758953094,
-0.03664515167474747,
-0.03772769123315811,
0.007073673885315657,
-0.037136707454919815,
-0.0012150249676778913,
-0.013677749782800674,
0.01563635841012001,
0.03623410686850548,
0.04896457865834236,
0.043227218091487885,
-0.031353458762168884,
0.024832164868712425,
0.013498763553798199,
-0.0019877434242516756,
0.07525811344385147,
0.0023878535721451044,
0.018686562776565552,
0.0008857796201482415,
0.05098733678460121,
-0.05970461294054985,
-0.0571514368057251,
0.017573805525898933,
-0.05976501852273941,
0.07547181844711304,
-0.004814486484974623,
-0.03308378905057907,
-0.06637885421514511,
-0.0023671940434724092,
-0.020702240988612175,
-0.002574712270870805,
-0.07478728890419006,
0.019181011244654655,
0.012565676122903824,
0.005665249191224575,
0.0026244353502988815,
0.016443202272057533,
0.005031723063439131,
0.016632389277219772,
-0.000034481938200769946,
0.04333001747727394,
-0.0021709611173719168,
0.010667038150131702,
-0.006506199948489666,
-0.05576527863740921,
0.0034557997714728117,
0.008958491496741772,
0.1047763079404831,
0.07852686196565628,
-0.02742883190512657,
0.01774526573717594,
-0.05914805829524994,
-0.040896251797676086,
0.07149161398410797,
-0.0527951642870903,
0.035161763429641724,
-0.04092027246952057,
-0.0008937788661569357,
0.07982391119003296,
0.027486499398946762,
0.01899695210158825,
0.021164055913686752,
0.04106390103697777,
-0.00382982543669641,
0.004581329878419638,
0.028651628643274307,
-0.042125921696424484,
-0.03388143330812454,
0.022528156638145447,
-0.02870241180062294,
0.04496191814541817,
0.02438163198530674,
-0.02072245068848133,
0.0036738954950124025,
-0.06544645875692368,
-0.06446241587400436,
-0.008169973269104958,
-0.00010420465696370229,
-0.01551886647939682,
-0.061998263001441956,
-0.06589938700199127,
-0.05740170180797577,
0.01060787495225668,
0.01233032438904047,
-0.0020355102606117725,
0.01771528273820877,
0.010095400735735893,
0.027956055477261543,
0.050270773470401764,
-0.0008261706097982824,
-0.006117672193795443,
0.012887906283140182,
-0.008715002797544003,
0.021104106679558754,
-0.0056852116249501705,
-0.04852184280753136,
-0.06581716984510422,
-0.00013058667536824942,
0.028142284601926804,
0.04991547390818596,
-0.03757535666227341,
-0.058902569115161896,
0.011011461727321148,
-0.02382563427090645,
-0.025019360706210136,
0.056291718035936356,
0.0006350549519993365,
0.01694508269429207,
0.012806268408894539,
-0.02822256274521351,
-0.0031854906119406223,
0.035369277000427246,
0.04286682978272438,
-0.010441225953400135,
0.03741346299648285,
0.04072345420718193,
-0.04982307180762291,
0.005256142932921648,
-0.022544899955391884,
0.017983999103307724,
0.018458083271980286,
0.032141149044036865,
0.08027061074972153,
0.039054445922374725,
-0.025298841297626495,
-0.0675935447216034,
0.006365386303514242,
-0.014552942477166653,
0.022059984505176544,
-0.020747343078255653,
-0.06389978528022766,
-0.010247303172945976,
-0.01322196051478386,
-0.07226204872131348,
-0.026039613410830498,
-0.01240770798176527,
0.06130962073802948,
0.018841667100787163,
0.0007127628778107464,
0.05825016275048256,
-0.040681079030036926,
-0.006121810059994459,
-0.028809040784835815,
-0.006570274010300636,
-0.012651561759412289,
0.0005700936308130622,
-0.026736371219158173,
-0.0137741444632411,
0.049800049513578415,
-0.025674838572740555,
0.013606843538582325,
0.017938049510121346,
-0.008838013745844364,
-0.05435267463326454,
-0.05822151526808739,
0.012582872062921524,
0.04664743319153786,
-0.019517607986927032,
-0.06654265522956848,
0.01706128939986229,
-0.03227739781141281,
0.05938134714961052,
0.008881918154656887,
-0.02871738187968731,
-0.06328969448804855,
0.018223904073238373,
0.016819041222333908,
-0.059770844876766205,
0.0672558918595314,
-0.02069547399878502,
0.013356050476431847,
0.07051414251327515,
-0.008955530822277069,
0.010303291492164135,
-0.020066216588020325,
0.04775216802954674
] |
[
14.706847190856934,
-2.3584606647491455
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
hep-lat
|
nucl-th
|
2007-03-31T17:05:04
|
As in the cases of freeness and monotonic independence, the notion of
conditional freeness is meaningful when complex-valued states are replaced by
positive conditional expectations. In this framework, the paper presents
several positivity results, a version of the central limit theorem and an
analogue of the conditionally free R-transform constructed by means of
multilinear function series.
|
Multilinear function series in conditionally free probability with
amalgamation
|
math.OA math.FA
|
0704.0040
| 2,007
|
[
0.0016719842096790671,
0.04445264860987663,
-0.011808107607066631,
-0.030932333320379257,
-0.04413791373372078,
-0.019530460238456726,
0.0033927562180906534,
0.028952008113265038,
-0.026196882128715515,
-0.022588612511754036,
-0.09661377221345901,
0.0020550203043967485,
0.06841625273227692,
-0.02561004087328911,
-0.004949786700308323,
0.001357618602924049,
0.0033189274836331606,
0.042951468378305435,
-0.002789213554933667,
0.016709627583622932,
-0.0031608943827450275,
0.0008306056261062622,
-0.01895502395927906,
-0.03355835750699043,
0.13336242735385895,
-0.002176716225221753,
0.031126221641898155,
0.0050365314818918705,
-0.030080102384090424,
0.0027909292839467525,
0.02987903356552124,
-0.016553690657019615,
0.00956946611404419,
-0.06426329165697098,
-0.04723610728979111,
-0.015756232663989067,
0.07622067630290985,
-0.011771990917623043,
0.024362212046980858,
-0.021969223394989967,
0.03905530273914337,
0.03726585581898689,
0.018536826595664024,
-0.032286595553159714,
-0.004023359622806311,
0.047184284776449203,
0.041750408709049225,
-0.010337959975004196,
0.035519830882549286,
-0.01156909205019474,
-0.031067878007888794,
0.042364463210105896,
-0.026478879153728485,
-0.056589461863040924,
-0.04246083274483681,
0.030668167397379875,
0.045867543667554855,
-0.02911894954741001,
-0.006072164047509432,
-0.001945414231158793,
0.009696787223219872,
0.021408218890428543,
-0.03783942013978958,
0.021183058619499207,
0.06780097633600235,
-0.05347886309027672,
0.002708020620048046,
0.012775355949997902,
0.007459522690623999,
0.006550623569637537,
0.0603710301220417,
-0.014300663955509663,
0.02343386597931385,
0.04462812840938568,
-0.04800126701593399,
-0.010287405923008919,
-0.0034337746910750866,
0.01637803576886654,
0.018825223669409752,
-0.01337427832186222,
0.01875665970146656,
-0.05901442468166351,
0.03067881613969803,
0.02444913238286972,
0.03807508572936058,
-0.026601705700159073,
0.08974280208349228,
-0.012931021861732006,
-0.0481858067214489,
0.051809899508953094,
0.03627070412039757,
-0.004505340475589037,
0.030735565349459648,
0.05448028817772865,
-0.07521269470453262,
0.014654936268925667,
-0.02811454050242901,
0.025883588939905167,
-0.020289752632379532,
-0.06144517660140991,
-0.000980026787146926,
0.06670311838388443,
0.03032904677093029,
-0.037388723343610764,
0.055076226592063904,
0.035979289561510086,
0.003386755706742406,
0.007622300647199154,
-0.040696725249290466,
-0.05054933950304985,
-0.050942834466695786,
0.03191859647631645,
0.015819553285837173,
-0.016881393268704414,
-0.003968625795096159,
-0.021261611953377724,
0.03986417502164841,
-0.09162634611129761,
0.031493041664361954,
0.043541938066482544,
0.021204281598329544,
-0.013202372938394547,
0.011939149349927902,
0.016919950023293495,
-0.03254632279276848,
0.014941714704036713,
-0.08539135009050369,
0.021460486575961113,
0.04063913971185684,
-0.024424413219094276,
0.05670333281159401,
0.00795238371938467,
-0.010294720530509949,
0.005943158641457558,
0.029136907309293747,
0.05654146149754524,
-0.027510225772857666,
-0.04745754227042198,
0.025130903348326683,
-0.026337511837482452,
0.007381117437034845,
0.0010448141256347299,
-0.005227024666965008,
0.02409392036497593,
0.08424034714698792,
-0.07630334794521332,
0.017375022172927856,
-0.03205948695540428,
-0.02520078420639038,
0.01854095607995987,
0.017251448705792427,
0.022409727796912193,
-0.017288926988840103,
0.049189116805791855,
-0.03928737714886665,
-0.008327895775437355,
-0.0028178105130791664,
-0.02866717241704464,
0.007919944822788239,
-0.04888777434825897,
0.0016312595689669251,
0.04226640984416008,
-0.03920937702059746,
0.03458833321928978,
-0.02763328328728676,
0.003109219716861844,
0.03929165005683899,
-0.00033611245453357697,
0.007300817407667637,
0.044039804488420486,
0.003724467009305954,
0.016096530482172966,
-0.02683253586292267,
-0.03293867036700249,
0.0379570834338665,
-0.05696214735507965,
-0.035060517489910126,
-0.014239849522709846,
0.01101707573980093,
-0.006606471259146929,
-0.018399082124233246,
0.004750153515487909,
0.002617527963593602,
-0.006112553179264069,
0.008978302590548992,
-0.007865619845688343,
0.040878307074308395,
0.03905165567994118,
-0.04551105201244354,
0.026788298040628433,
-0.015581822022795677,
0.005509290844202042,
-0.07715971022844315,
-0.0152399567887187,
-0.0294968131929636,
-0.02559913881123066,
0.06514807045459747,
-0.012142141349613667,
0.036380328238010406,
-0.02733754925429821,
0.006412919145077467,
-0.005325633566826582,
-0.030799852684140205,
0.004018981009721756,
-0.03591180220246315,
0.03845898061990738,
-0.021069305017590523,
0.010546517558395863,
-0.004374952986836433,
-0.01524296309798956,
0.0229733195155859,
-0.048600245267152786,
-0.006597616244107485,
0.06345777213573456,
0.0457109697163105,
-0.027123915031552315,
0.0023283171467483044,
-0.029310578480362892,
-0.04968857765197754,
-0.008542148396372795,
0.02920342981815338,
-0.03723882511258125,
0.004689888097345829,
0.01789581961929798,
0.014066365547478199,
0.06789517402648926,
0.009533700533211231,
-0.01748650148510933,
-0.05848748981952667,
-0.03201470896601677,
-0.030849717557430267,
-0.020998839288949966,
0.03827624395489693,
0.04147898405790329,
0.006630741525441408,
0.04208454117178917,
0.02205987647175789,
0.06288374960422516,
0.018535804003477097,
0.08512476831674576,
0.0092917550355196,
0.023039814084768295,
-0.013315505348145962,
0.01257364358752966,
-0.06967748701572418,
0.0026081607211381197,
0.005886872764676809,
0.008451131172478199,
-0.015443899668753147,
0.007316442206501961,
-0.0281587615609169,
0.010633133351802826,
0.03168869763612747,
0.044947221875190735,
0.022298645228147507,
-0.02611398510634899,
-0.07035846263170242,
0.012203004211187363,
-0.024900361895561218,
-0.032377976924180984,
0.07709191739559174,
-0.02457658387720585,
-0.010074179619550705,
-0.061601266264915466,
-0.0782601460814476,
0.012682531960308552,
-0.01615220308303833,
-0.06569724529981613,
-0.028046738356351852,
0.029641708359122276,
-0.005252084694802761,
0.02872755005955696,
0.09408117085695267,
0.0913882851600647,
-0.0021255516912788153,
0.00002956779280793853,
0.04353915899991989,
-0.04214642941951752,
0.0017159233102574944,
0.017490195110440254,
-0.03923173248767853,
-0.04664573818445206,
-0.017726652324199677,
-0.002733539557084441,
-0.03687956929206848,
0.014472546987235546,
0.06577660888433456,
-0.00656809750944376,
0.00033336415071971714,
0.060902487486600876,
-0.006763265933841467,
0.004260862246155739,
-0.0010901252971962094,
0.028941374272108078,
-0.013407332822680473,
0.03486248105764389,
0.03873821720480919,
-0.04692772030830383,
0.0189202930778265,
-0.0023444441612809896,
-0.01812874898314476,
-0.025030765682458878,
0.022507278248667717,
0.010365706868469715,
-0.0038135957438498735,
-0.004751432221382856,
-0.01311088353395462,
0.030220791697502136,
0.031086748465895653,
-0.02328416332602501,
-0.01670382358133793,
-0.005632906686514616,
-0.047057799994945526,
-0.0025671743787825108,
-0.058057691901922226,
0.033801764249801636,
0.07334279268980026,
0.03620181232690811,
0.0989171639084816,
-0.053763292729854584,
0.018642131239175797,
-0.05179707333445549,
0.023448282852768898,
-0.03155723959207535,
0.026788676157593727,
-0.018360920250415802,
-0.012170891277492046,
-0.01843036338686943,
-0.01599102094769478,
0.0035615868400782347,
0.006798576097935438,
0.08608409017324448,
0.033735308796167374,
-0.010561213828623295,
-0.039465002715587616,
0.007157071493566036,
0.0035072413738816977,
0.008278890512883663,
0.0010797909926623106,
0.021212080493569374,
0.03053942881524563,
-0.03818159177899361,
-0.03727128729224205,
-0.017389042302966118,
-0.03743431717157364,
-0.008236989378929138,
-0.0132747245952487,
0.03025636449456215,
0.12570872902870178,
0.038609132170677185,
-0.08149787038564682,
0.021418409422039986,
0.03140568360686302,
-0.016667168587446213,
0.049130626022815704,
0.05876755341887474,
0.05646873265504837,
-0.031596872955560684,
0.028156492859125137,
0.037262529134750366,
0.03261909261345863,
-0.03486661985516548,
-0.0335286445915699,
0.01559706311672926,
-0.0000018672062651603483,
0.020277446135878563,
0.040996626019477844,
0.04097799211740494,
0.011689447797834873,
-0.03405653312802315,
-0.02907693386077881,
-0.01329949963837862,
0.08298805356025696,
0.0284583643078804,
0.008591784164309502,
0.011145870201289654,
-0.020775334909558296,
0.06487993150949478,
-0.022665873169898987,
0.01638719066977501,
0.08567814528942108,
-0.013217960484325886,
0.02579435333609581,
0.016578417271375656,
0.0221421979367733,
0.006272388622164726,
-0.03952701762318611,
0.036597274243831635,
-0.025162218138575554,
0.022882094606757164,
0.04361652210354805,
-0.010315285064280033,
-0.028686117380857468,
0.04103289917111397,
0.037505924701690674,
-0.02700722962617874,
0.049929503351449966,
-0.034408438950777054,
0.008306090719997883,
-0.0054208808578550816,
-0.02847817726433277,
-0.09152805060148239,
0.006485393736511469,
-0.023702777922153473,
-0.024275219067931175,
0.023606766015291214,
-0.0015491531230509281,
-0.02902287058532238,
0.06429125368595123,
-0.060495972633361816,
-0.00869404524564743,
0.0008372457232326269,
-0.023684773594141006,
-0.06618830561637878,
0.04528138414025307,
0.02404399774968624,
0.07610389590263367,
-0.02759549207985401,
0.021207749843597412,
0.005091780796647072,
-0.00214229803532362,
0.051611315459012985,
-0.00933921430259943,
0.0009848627960309386,
-0.03054078482091427,
0.0037878016009926796,
0.025895612314343452,
0.009282990358769894,
0.011151262558996677,
-0.061114612966775894,
0.011533256620168686,
0.028082679957151413,
0.03234626725316048,
0.0015241875080391765,
-0.06272315979003906,
-0.012889242731034756,
-0.006842448376119137,
-0.019444433972239494,
-0.05253398418426514,
0.00021771648607682437,
-0.011621554382145405,
-0.026908185333013535,
-0.020893404260277748,
-0.016056401655077934,
0.014156687073409557,
0.04999920353293419,
0.07060425728559494,
-0.043506428599357605,
-0.009706203825771809,
-0.019765710458159447,
0.027120763435959816,
0.044364672154188156,
-0.023392802104353905,
0.012373934499919415,
0.035609323531389236,
-0.024373967200517654,
-0.04104841873049736,
-0.008814983069896698,
0.07066339254379272,
0.05931774899363518,
0.04202299937605858,
0.007223268039524555,
-0.01606198400259018,
-0.022908290848135948,
0.01951960287988186,
0.015544562600553036,
-0.035973526537418365,
0.011067722924053669,
0.009767570532858372,
0.06775125116109848,
-0.036316126585006714,
0.046889614313840866,
0.031523171812295914,
-0.02122909389436245,
-0.05992639437317848,
0.003922941628843546,
0.03173932433128357,
-0.0356019027531147,
0.01243214588612318,
0.06273265182971954,
0.010093716904520988,
-0.001963129034265876,
-0.0552067793905735,
-0.04043043404817581,
-0.03825995326042175,
0.031401149928569794,
0.06586285680532455,
-0.03652840107679367,
-0.004284720402210951,
-0.043666381388902664,
0.018656568601727486,
0.049572817981243134,
0.0613248236477375,
0.00293847918510437,
-0.01674870029091835,
-0.041792355477809906,
-0.03359285742044449,
-0.01973871886730194,
0.006021591834723949,
-0.04710240289568901,
-0.05900256335735321,
-0.022981753572821617,
0.031072305515408516,
0.03400494530797005,
-0.010623227804899216,
0.04503066465258598,
-0.059141259640455246,
-0.03780269995331764,
-0.015474927611649036,
0.034435201436281204,
0.0448547899723053,
-0.017845461145043373,
0.0007239755359478295,
-0.00009287085413234308,
-0.009761718101799488,
-0.050930775701999664,
-0.01543741300702095,
-0.030386660248041153,
-0.07028920203447342,
0.05406854301691055,
0.04901643097400665,
0.001908948295749724,
0.03139624744653702,
-0.010259013622999191,
-0.06313556432723999,
0.0264811422675848,
-0.05936915799975395,
-0.04327499866485596,
0.04078051447868347,
-0.057413626462221146,
0.014806252904236317,
0.006106835789978504,
0.041759688407182693,
-0.04701493680477142,
-0.012311442755162716,
-0.046105850487947464,
-0.035637401044368744,
0.011797197163105011,
0.03658054396510124,
0.01095204520970583,
-0.005490817595273256,
0.0035552438348531723,
0.009737805463373661,
0.0077667501755058765,
-0.01852038875222206,
0.021058151498436928,
-0.09611254930496216,
0.02780279330909252,
-0.0037634079344570637,
-0.03264857828617096,
0.049844034016132355,
-0.07065993547439575,
-0.019162220880389214,
-0.07808820903301239,
0.06259355694055557,
0.02449091151356697,
0.000859306484926492,
-0.03222727030515671,
-0.04927550256252289,
0.030849438160657883,
-0.015227229334414005,
-0.028217047452926636,
0.027151571586728096,
0.018840519711375237,
0.04030066728591919,
-0.07409889996051788,
0.0364447720348835,
0.05550878494977951,
-0.010927315801382065,
0.019785882905125618,
0.009791640564799309,
-0.0221556443721056,
-0.04407087340950966,
0.024706389755010605,
0.004155136179178953,
-0.06998633593320847,
0.042271360754966736,
0.0006732350448146462,
-0.029680045321583748,
-0.02341131865978241,
-0.0452163927257061,
-0.05415773019194603,
0.025896532461047173,
-0.01507884357124567,
-0.0710093080997467,
0.030582135543227196,
-0.01826864667236805,
-0.04056931287050247,
-0.014351283200085163,
-0.014224993996322155,
-0.027717482298612595,
-0.023945456370711327,
0.00087875867029652,
-0.0408555269241333,
0.01512349396944046,
-0.024717306718230247,
-0.01268863771110773,
-0.032543789595365524,
-0.04749275743961334,
-0.08752381801605225,
-0.020592059940099716,
0.06473493576049805,
0.08972593396902084,
-0.059974394738674164,
0.04088761657476425,
0.044887132942676544,
0.02320922166109085,
-0.003425545757636428,
-0.029718780890107155,
-0.005373538471758366,
0.008314884267747402,
-0.00175675714854151,
0.01615091972053051,
-0.011379222385585308,
0.015293474309146404,
-0.029060501605272293,
0.09059025347232819,
-0.008577786386013031,
-0.007810892537236214,
-0.07008719444274902,
-0.003132791956886649,
-0.02607579156756401,
0.017087463289499283,
-0.03676818683743477,
0.030546346679329872,
0.001862921635620296,
0.0023588244803249836,
-0.06050961837172508,
0.009238173253834248,
0.05810215324163437,
-0.02784024365246296,
-0.022774774581193924,
-0.033198822289705276,
-0.023847244679927826,
-0.04319501668214798,
-0.0001276357361348346,
-0.050138380378484726,
0.02800712361931801,
0.021919528022408485,
0.03702869266271591,
-0.025540875270962715,
0.010648434050381184,
0.015611083246767521,
-0.025178400799632072,
0.02816532365977764,
0.0206356942653656,
0.0220892746001482,
-0.03980877622961998,
-0.02581619843840599,
0.015438862144947052,
0.053299590945243835,
0.06979908794164658,
0.009265085682272911,
0.011927301995456219,
-0.032775867730379105,
-0.00430263439193368,
0.04375668987631798,
0.04059240594506264,
-0.007091904990375042,
-0.011146096512675285,
-0.03853780776262283,
-0.02913769707083702,
-0.02881546877324581,
0.002237828681245446,
0.03699974715709686,
-0.014409070834517479,
0.05020624026656151,
-0.05302520841360092,
-0.02736414223909378,
-0.018811579793691635,
0.0010327543132007122,
-0.012820263393223286,
-0.03251693770289421,
0.025468681007623672,
-0.0022510592825710773,
-0.025738554075360298,
-0.04506198316812515,
0.04984381049871445,
-0.021029410883784294,
0.030280359089374542,
-0.06666363030672073,
0.008156456984579563,
0.022966919466853142,
0.021137148141860962,
0.004535255953669548,
0.03649469465017319,
0.029871180653572083,
0.027274440973997116,
-0.007973207160830498,
-0.07529091835021973,
-0.000180416478542611,
-0.002767855767160654,
0.07187382131814957,
-0.0510876290500164,
0.0028683708515018225,
-0.00323092145845294,
-0.039641570299863815,
0.012843864969909191,
0.00314651383087039,
0.035624854266643524,
-0.047208022326231,
0.018602855503559113,
-0.04237084463238716,
-0.008307211101055145,
0.03794919326901436,
-0.04937244579195976,
-0.0009384179720655084,
-0.013424089178442955,
-0.01646602712571621,
-0.01874731108546257,
-0.025707272812724113,
0.0010591716272756457,
0.009647930972278118,
0.008993906900286674,
0.0009525215136818588,
-0.019694454967975616,
0.010753657668828964,
-0.012404241599142551,
0.015104325488209724,
-0.0033370701130479574,
0.04657511040568352,
-0.042594872415065765,
-0.07472354918718338,
0.05996658280491829,
-0.027372125536203384,
0.0036615384742617607,
-0.046965308487415314,
-0.07170750200748444,
-0.022004852071404457,
-0.005989504046738148,
0.02204255759716034,
-0.022310718894004822,
-0.04947526380419731,
0.054860468953847885,
0.004506187979131937,
0.0016093660378828645,
-0.036270033568143845,
0.026889285072684288,
-0.011308198794722557,
-0.008393500931560993,
-0.01725398190319538,
-0.02761242538690567,
0.06199348717927933,
0.02685147151350975,
-0.04774586856365204,
0.015788258984684944,
-0.06408414989709854,
0.051733847707509995,
0.03596024587750435,
-0.00712266331538558,
-0.04851146414875984,
0.014858566224575043,
0.004523697309195995,
-0.0027040259446948767,
0.03384939208626747,
0.01960933208465576,
-0.004237547982484102,
0.0049175540916621685,
0.07385963201522827,
-0.009405290707945824,
0.06136853247880936,
-0.007811123039573431,
-0.00408715708181262,
0.037076663225889206,
-0.022556189447641373,
-0.0039000753313302994,
-0.019860101863741875,
0.014627676457166672
] |
[
2.829765796661377,
4.554051399230957
] |
Operator Algebras
|
Mathematics
|
math-OA
|
math-FA
|
na
|
2007-03-31T21:04:54
|
We formulate a quantum generalization of the notion of the group of
Riemannian isometries for a compact Riemannian manifold, by introducing a
natural notion of smooth and isometric action by a compact quantum group on a
classical or noncommutative manifold described by spectral triples, and then
proving the existence of a universal object (called the quantum isometry group)
in the category of compact quantum groups acting smoothly and isometrically on
a given (possibly noncommutative) manifold satisfying certain regularity
assumptions. In fact, we identify the quantum isometry group with the universal
object in a bigger category, namely the category of `quantum families of smooth
isometries', defined along the line of Woronowicz and Soltan. We also construct
a spectral triple on the Hilbert space of forms on a noncommutative manifold
which is equivariant with respect to a natural unitary representation of the
quantum isometry group. We give explicit description of quantum isometry groups
of commutative and noncommutative tori, and in this context, obtain the quantum
double torus defined in \cite{hajac} as the universal quantum group of
holomorphic isometries of the noncommutative torus.
|
Quantum Group of Isometries in Classical and Noncommutative Geometry
|
math.QA math-ph math.MP
|
0704.0041
| 2,007
|
[
-0.023741796612739563,
0.037505459040403366,
-0.01756550371646881,
-0.035776861011981964,
0.01819937862455845,
0.005760247819125652,
0.04290254786610603,
0.025644289329648018,
-0.025783585384488106,
0.00753386877477169,
-0.0335223488509655,
0.016543809324502945,
0.010688717477023602,
0.008643028326332569,
-0.04317492991685867,
-0.024930700659751892,
0.007731342688202858,
0.008085484616458416,
0.027876267209649086,
0.02607756108045578,
-0.02303331345319748,
-0.028044288977980614,
0.00408271374180913,
-0.019526325166225433,
0.1008111760020256,
-0.0012952120741829276,
0.07356654852628708,
-0.01586800441145897,
-0.008287318982183933,
0.013618954457342625,
0.07074980437755585,
-0.009949460625648499,
0.038265302777290344,
-0.03993041440844536,
-0.023335246369242668,
-0.058258235454559326,
0.08079835027456284,
-0.01123039796948433,
-0.0034861876629292965,
0.022440651431679726,
0.047813791781663895,
-0.04184931889176369,
0.02347519062459469,
-0.007037696894258261,
0.02746814675629139,
-0.01311305072158575,
0.08202411234378815,
0.016819573938846588,
0.05488840863108635,
-0.007670764345675707,
0.00830541830509901,
0.010508062317967415,
0.018549298867583275,
-0.03369399160146713,
-0.02380095236003399,
-0.011865249834954739,
0.019860055297613144,
-0.020553795620799065,
0.04471876099705696,
0.01174674741923809,
-0.019450630992650986,
0.029412707313895226,
-0.03889317810535431,
0.03498018532991409,
0.04333075135946274,
-0.04465216398239136,
-0.012722763232886791,
0.01423958595842123,
-0.023404018953442574,
-0.01744435355067253,
-0.00019226945005357265,
-0.0032492622267454863,
0.07838340103626251,
0.03136250004172325,
-0.007826634682714939,
0.0034966219682246447,
0.03146854043006897,
-0.021491507068276405,
-0.00935493502765894,
0.006285354029387236,
0.024856286123394966,
-0.037330836057662964,
0.03488506004214287,
0.028210710734128952,
0.07424566894769669,
0.018450438976287842,
0.01961194910109043,
0.02288786694407463,
-0.045877717435359955,
0.037437599152326584,
0.06426235288381577,
-0.019167037680745125,
0.061034396290779114,
0.046537309885025024,
-0.017270855605602264,
-0.0028889691457152367,
-0.04263541102409363,
0.02722940780222416,
-0.04669338837265968,
0.009155940264463425,
0.0032359587494283915,
0.004851360805332661,
0.03230702877044678,
-0.0015116599388420582,
0.09196121245622635,
0.01772012747824192,
0.014246735721826553,
0.025631505995988846,
-0.00534723699092865,
0.023684469982981682,
-0.07341153174638748,
0.013723830692470074,
0.046406593173742294,
-0.035425297915935516,
-0.024214383214712143,
0.019454462453722954,
0.051007259637117386,
-0.09167210757732391,
0.016883574426174164,
0.06420459598302841,
0.03855089843273163,
-0.015753190964460373,
0.02569967694580555,
0.06975702196359634,
-0.020542241632938385,
0.016187814995646477,
-0.03341156989336014,
-0.012110227718949318,
0.04374032840132713,
-0.03362823650240898,
0.012429981492459774,
0.035598427057266235,
-0.03250879794359207,
0.026813684031367302,
0.001340056536719203,
0.0716954842209816,
-0.019035739824175835,
-0.01885266974568367,
0.07544191926717758,
-0.01530435774475336,
0.027813782915472984,
-0.01327106636017561,
-0.019678428769111633,
-0.009963305667042732,
0.044465452432632446,
-0.09564542770385742,
-0.007878663018345833,
-0.0895097628235817,
-0.003237655386328697,
-0.01247220579534769,
0.04366826266050339,
0.040847163647413254,
0.02910490334033966,
0.026711739599704742,
-0.010146031156182289,
-0.029647039249539375,
0.004532358609139919,
0.03970173001289368,
0.04931486025452614,
0.016651980578899384,
0.019473327323794365,
0.014984220266342163,
0.006343387998640537,
0.015183654613792896,
-0.02067885734140873,
0.011405878700315952,
0.04761631041765213,
0.005818404722958803,
0.055817972868680954,
0.018724841997027397,
-0.054749492555856705,
0.009477893821895123,
-0.037943605333566666,
-0.06416848301887512,
0.028866445645689964,
0.0021162477787584066,
-0.02513258531689644,
-0.023812105879187584,
-0.008651480078697205,
-0.00607829075306654,
0.0073467520996928215,
-0.03397632762789726,
0.016081003472208977,
0.008082910440862179,
-0.034198369830846786,
0.05205049738287926,
-0.010518282651901245,
-0.02473912201821804,
-0.038003794848918915,
-0.021240418776869774,
-0.005429954268038273,
0.023076938465237617,
-0.0023471666499972343,
-0.06348765641450882,
-0.00009998137102229521,
-0.00431031221523881,
0.05220077931880951,
0.005588911939412355,
0.0003921165189240128,
-0.035787809640169144,
0.018338007852435112,
0.01670680195093155,
-0.061402834951877594,
0.0039942627772688866,
0.0005421904497779906,
0.09756449609994888,
0.046320341527462006,
-0.031427089124917984,
0.042811255902051926,
-0.016882237046957016,
0.0733475387096405,
0.047182969748973846,
0.028654932975769043,
0.007838445715606213,
0.013471376150846481,
0.019292140379548073,
0.014904535375535488,
-0.09779123216867447,
-0.026402531191706657,
0.004878513514995575,
0.029924694448709488,
-0.000498832028824836,
0.0188917089253664,
0.020210525020956993,
0.037136759608983994,
0.014327053911983967,
-0.06558678299188614,
-0.027676217257976532,
-0.00420191278681159,
-0.005358018446713686,
-0.006797025911509991,
-0.06877201050519943,
0.06168808043003082,
-0.0038211222272366285,
-0.006576600484549999,
0.008654994890093803,
-0.009426933713257313,
0.045947954058647156,
0.05732410401105881,
0.06085545942187309,
0.0535682737827301,
0.005945408716797829,
-0.0004354348639026284,
-0.023144736886024475,
-0.05510702356696129,
0.0033649280667304993,
-0.050911612808704376,
-0.03896130993962288,
-0.0607486367225647,
0.03666649013757706,
-0.02286062389612198,
-0.027827508747577667,
-0.016702160239219666,
-0.025865843519568443,
0.008673072792589664,
0.008034835569560528,
-0.024429339915513992,
0.014473618008196354,
-0.020354172214865685,
-0.06617708504199982,
-0.0025357333943247795,
-0.03054482489824295,
0.038610681891441345,
-0.025558626279234886,
-0.036800406873226166,
0.014742784202098846,
0.07104355096817017,
0.0007890741107985377,
0.0025373785756528378,
-0.023030802607536316,
0.04698638990521431,
-0.00835480447858572,
0.038643766194581985,
0.030881108716130257,
-0.03622303530573845,
-0.018844448029994965,
-0.026083698496222496,
-0.03267132490873337,
-0.035437047481536865,
-0.013854198157787323,
-0.07247353345155716,
0.013638931326568127,
-0.03988223150372505,
0.00014481504331342876,
-0.005881024524569511,
0.031090358272194862,
0.029451023787260056,
0.024512195959687233,
-0.02299647033214569,
0.0587271973490715,
-0.010533472523093224,
0.018251901492476463,
0.036416999995708466,
0.04969096928834915,
-0.015270954929292202,
0.06392145156860352,
0.02839823253452778,
-0.011533482931554317,
-0.0240919329226017,
0.03756159543991089,
-0.04099075868725777,
0.005669123493134975,
0.020146869122982025,
-0.018320593982934952,
0.033698663115501404,
-0.031612105667591095,
-0.005139033310115337,
-0.03697178140282631,
0.07113207876682281,
0.006188395898789167,
-0.07342898845672607,
0.042006805539131165,
-0.021114986389875412,
0.0010556711349636316,
-0.040985919535160065,
0.008538265712559223,
-0.009323734790086746,
-0.024769769981503487,
0.06255782395601273,
-0.018186436966061592,
-0.03073454461991787,
-0.06480729579925537,
0.03880447894334793,
-0.02751930058002472,
0.008774705231189728,
0.041705358773469925,
-0.024248311296105385,
0.011001847684383392,
0.008609977550804615,
-0.05070970579981804,
-0.008337714709341526,
0.057963717728853226,
0.006526927929371595,
0.006438006181269884,
-0.05837784707546234,
0.00584264425560832,
-0.013031280599534512,
-0.0030277103651314974,
-0.017531460151076317,
-0.058930654078722,
0.006528938189148903,
-0.041344065219163895,
-0.012561406940221786,
-0.016798410564661026,
-0.03988395631313324,
0.00810466893017292,
-0.02406548708677292,
0.0012406465830281377,
0.0326332189142704,
0.010774263180792332,
-0.06973616778850555,
-0.01589825376868248,
0.004628858529031277,
-0.013366658240556717,
-0.0025647119618952274,
0.06436232477426529,
0.03277379274368286,
0.026884619146585464,
0.05310098081827164,
-0.028565533459186554,
0.019482897594571114,
-0.031849171966314316,
0.02563401125371456,
0.009819328784942627,
0.028340265154838562,
0.03887694701552391,
0.03802156820893288,
0.026067428290843964,
0.006157618947327137,
0.02850445918738842,
-0.044568903744220734,
-0.0778648778796196,
0.0047786785289645195,
0.04603404924273491,
0.004196763504296541,
0.028578944504261017,
-0.027366237714886665,
-0.030585400760173798,
-0.03791196644306183,
-0.05215898156166077,
0.04000553488731384,
-0.013770729303359985,
0.053680676966905594,
0.0036902183201164007,
0.02814185619354248,
0.054598987102508545,
-0.02071218378841877,
-0.0018088124925270677,
-0.03368015214800835,
0.006494003813713789,
0.0042706443928182125,
-0.054847247898578644,
-0.042566437274217606,
0.04539903998374939,
-0.027391791343688965,
0.004322030581533909,
0.05402887240052223,
-0.021314838901162148,
-0.06256695091724396,
-0.0017487162258476019,
-0.05765264481306076,
-0.08463092893362045,
-0.003402294358238578,
-0.00033062908914871514,
-0.007398722227662802,
0.03464873880147934,
-0.005904733203351498,
-0.005410879384726286,
0.07687152922153473,
-0.014090745709836483,
0.01784984953701496,
-0.034962281584739685,
-0.001373717444948852,
-0.07090321183204651,
0.033391647040843964,
0.08181535452604294,
0.055645283311605453,
-0.03382650390267372,
-0.017400303855538368,
-0.03920794650912285,
-0.05137347802519798,
0.060535505414009094,
0.029498262330889702,
0.017870206385850906,
0.02046610601246357,
0.05077492818236351,
0.03775794059038162,
0.02268928848206997,
-0.027075493708252907,
-0.071340411901474,
0.03263700008392334,
-0.0022772725205868483,
0.004993428476154804,
0.021960057318210602,
-0.07415227591991425,
0.011502392590045929,
-0.0034183368552476168,
-0.017751816660165787,
0.00782459881156683,
-0.011328737251460552,
0.05772140994668007,
0.022338729351758957,
-0.007818484678864479,
-0.025003403425216675,
0.0125197172164917,
0.07870865613222122,
0.07144614309072495,
-0.010659880936145782,
-0.0627220869064331,
-0.036308322101831436,
0.0513385571539402,
0.009176897816359997,
-0.017722932621836662,
0.018772244453430176,
0.02299456112086773,
-0.026385853067040443,
-0.01963028311729431,
-0.011816366575658321,
0.07770166546106339,
0.04970332235097885,
-0.010020560584962368,
0.02007542923092842,
-0.003994346596300602,
0.047192979604005814,
-0.0432797446846962,
-0.01935618557035923,
-0.11454827338457108,
0.07384173572063446,
-0.0028427341021597385,
0.04060101881623268,
-0.003059886861592531,
0.04862931743264198,
0.008959024213254452,
-0.0007776314741931856,
0.0035727007780224085,
-0.03739620000123978,
0.044965166598558426,
-0.020981278270483017,
-0.02740859054028988,
0.05949406698346138,
0.04452548176050186,
-0.011102534830570221,
0.0020169829949736595,
0.02652929350733757,
-0.014723950996994972,
0.03185953572392464,
-0.004173807334154844,
0.02587282843887806,
-0.04086196795105934,
0.009166654199361801,
0.018595820292830467,
0.026213424280285835,
-0.002705660881474614,
-0.026905763894319534,
-0.011182419955730438,
-0.05979623645544052,
-0.0043767113238573074,
-0.005082684103399515,
0.04656621813774109,
-0.012997613288462162,
-0.01393665000796318,
0.05929505452513695,
0.03751979395747185,
0.023587850853800774,
0.07114254683256149,
0.03368083015084267,
0.017976010218262672,
-0.041240960359573364,
0.0002790756698232144,
-0.00887686014175415,
0.0063183000311255455,
0.01309202704578638,
0.04821426048874855,
0.03804941475391388,
0.03133057802915573,
-0.010735051706433296,
0.0010119654471054673,
-0.0059616947546601295,
-0.015686001628637314,
0.005039686802774668,
-0.01854563131928444,
-0.007764667272567749,
-0.009413653053343296,
-0.024074910208582878,
-0.006966747343540192,
0.04841955006122589,
-0.02783859707415104,
-0.07316439598798752,
0.01789195090532303,
0.020476922392845154,
0.031067194417119026,
0.0015928791835904121,
-0.027668317779898643,
-0.0613466314971447,
0.002545977244153619,
-0.009458367712795734,
-0.004133027046918869,
0.01888919062912464,
-0.0043330020271241665,
0.027898503467440605,
-0.06475844234228134,
-0.01997777260839939,
0.019808055832982063,
0.020552296191453934,
0.053638916462659836,
-0.026992149651050568,
-0.11412862688302994,
0.025606941431760788,
-0.02654106356203556,
0.024761350825428963,
0.006073043216019869,
-0.048596471548080444,
0.013536371290683746,
-0.08426801860332489,
0.027445584535598755,
-0.0180718544870615,
-0.05426228418946266,
-0.05171188712120056,
-0.014858447015285492,
0.04558853805065155,
0.06417973339557648,
-0.00060915487119928,
0.06038423627614975,
-0.004819405265152454,
0.03067614510655403,
-0.09747561812400818,
-0.001144865993410349,
-0.007570092100650072,
0.06776188313961029,
0.007581182289868593,
-0.005072992295026779,
0.016981856897473335,
-0.014672234654426575,
0.00861850194633007,
-0.03925712779164314,
-0.06361139565706253,
-0.0021044621244072914,
-0.031717728823423386,
-0.07176987081766129,
-0.038927894085645676,
-0.0017753767315298319,
-0.025932295247912407,
-0.007429494522511959,
-0.04382048547267914,
-0.10324470698833466,
0.008452299982309341,
0.015062734484672546,
-0.060638900846242905,
0.05826526880264282,
0.06591403484344482,
-0.028138089925050735,
0.017417559400200844,
-0.07251935452222824,
-0.01596318557858467,
-0.012520811520516872,
-0.016243400052189827,
0.014715776778757572,
0.06094231829047203,
-0.013318768702447414,
-0.06227780133485794,
-0.025112811475992203,
-0.015638675540685654,
0.04446733742952347,
-0.020343061536550522,
0.05277811363339424,
0.08501371741294861,
-0.001440734718926251,
0.019795216619968414,
-0.01704939268529415,
-0.0056164562702178955,
-0.016694633290171623,
-0.013549592345952988,
-0.08327007293701172,
-0.03277812525629997,
-0.070428267121315,
-0.05467205494642258,
0.04207010939717293,
-0.035837654024362564,
0.006335644517093897,
-0.031318068504333496,
0.001536055002361536,
-0.0013441169867292047,
0.0031106292735785246,
-0.013504805974662304,
0.01808394119143486,
0.01701444573700428,
-0.03087552636861801,
-0.041129425168037415,
0.012568431906402111,
0.08800332993268967,
-0.009473569691181183,
-0.06205661967396736,
-0.024784546345472336,
-0.003252786584198475,
-0.02894298918545246,
-0.0010124783730134368,
-0.10489977151155472,
0.03153541684150696,
0.004246080759912729,
0.05049210786819458,
0.023813029751181602,
-0.04023842513561249,
0.008836960420012474,
-0.0005818119389005005,
-0.007246316410601139,
0.01305390615016222,
-0.020277714356780052,
0.014123713597655296,
-0.03657842054963112,
-0.0014225199120119214,
0.0797402560710907,
0.08569413423538208,
-0.01718253083527088,
0.023897036910057068,
0.0047383555211126804,
-0.033631522208452225,
0.022551801055669785,
-0.006076285615563393,
-0.05500013008713722,
-0.009568216279149055,
-0.026522312313318253,
0.013950121589004993,
0.01964918151497841,
0.009528250433504581,
0.022944021970033646,
-0.04979712888598442,
-0.024681922048330307,
-0.03350978344678879,
-0.07657970488071442,
0.028877537697553635,
-0.07287140190601349,
-0.04790147393941879,
0.012422054074704647,
-0.0409257635474205,
-0.009113709442317486,
-0.04000530764460564,
0.032876476645469666,
0.0482216440141201,
-0.007355941459536552,
-0.015681257471442223,
0.007332610432058573,
0.053257640451192856,
0.002236216561868787,
-0.0017577806720510125,
-0.01881013996899128,
-0.0068321856670081615,
-0.005061392206698656,
-0.029623262584209442,
-0.008503023535013199,
0.005207490641623735,
0.01802067644894123,
-0.005321828182786703,
-0.035943303257226944,
-0.07513099908828735,
-0.026093309745192528,
0.0320766381919384,
-0.021823948249220848,
0.004714279901236296,
-0.0037578395567834377,
0.026022205129265785,
-0.028036559000611305,
-0.005067487247288227,
-0.04494399204850197,
0.0121914092451334,
-0.032052941620349884,
-0.024426491931080818,
-0.0019358734134584665,
0.034853897988796234,
-0.00977766141295433,
0.011709559708833694,
-0.03414558246731758,
-0.007615821901708841,
0.026789700612425804,
0.01734921522438526,
0.04429428651928902,
-0.0042633418925106525,
-0.03400937467813492,
-0.025282612070441246,
0.052289098501205444,
-0.043360915035009384,
0.03637634217739105,
-0.04388865455985069,
-0.0567685030400753,
0.006283632479608059,
-0.037199173122644424,
-0.08906912058591843,
-0.05830185115337372,
-0.03885030001401901,
0.056349463760852814,
-0.006703893654048443,
-0.00253624701872468,
0.011949578300118446,
-0.013261724263429642,
0.024961795657873154,
-0.03455818444490433,
-0.007659739814698696,
-0.023112917318940163,
-0.03605866804718971,
0.025203188881278038,
0.024978680536150932,
0.0037537310272455215,
-0.007315571885555983,
0.0018330339808017015,
0.015781531110405922,
-0.02284562774002552,
-0.0569988414645195,
-0.002563771791756153,
0.01726366952061653,
0.013215210288763046,
0.0008944699657149613,
-0.028825152665376663,
0.0018258987693116069,
0.008266660384833813,
0.04976687580347061,
0.015272362157702446,
-0.018959153443574905,
-0.00636852765455842,
0.03916312754154205,
0.03608439490199089,
-0.004759245552122593,
0.03258997201919556,
0.018768679350614548,
0.011851981282234192,
0.04841742664575577,
-0.026519063860177994,
0.0007016405579634011,
-0.01742006465792656,
-0.002968805842101574
] |
[
2.1643590927124023,
1.4524728059768677
] |
Quantum Algebra
|
Mathematics
|
math-QA
|
math-ph
|
na
|
2007-03-31T17:28:35
|
It is outlined the possibility to extend the quantum formalism in relation to
the requirements of the general systems theory. It can be done by using a
quantum semantics arising from the deep logical structure of quantum theory. It
is so possible taking into account the logical openness relationship between
observer and system. We are going to show how considering the truth-values of
quantum propositions within the context of the fuzzy sets is here more useful
for systemics . In conclusion we propose an example of formal quantum
coherence.
|
General System theory, Like-Quantum Semantics and Fuzzy Sets
|
physics.gen-ph quant-ph
|
0704.0042
| 2,007
|
[
-0.01945819891989231,
0.07370972633361816,
0.012425437569618225,
-0.06002198904752731,
-0.01975795440375805,
0.02235235646367073,
-0.005394859705120325,
0.012410108000040054,
-0.03497742488980293,
0.028317270800471306,
-0.020221291109919548,
0.04231433570384979,
0.03299891576170921,
0.036478739231824875,
-0.025125084444880486,
-0.002252002479508519,
-0.0010463673388585448,
0.0047362083569169044,
0.03436846658587456,
0.03549344837665558,
0.0090365931391716,
0.02042866311967373,
-0.0068416837602853775,
-0.038188427686691284,
0.05266765132546425,
0.0000012578897212733864,
0.011077444069087505,
0.013287830166518688,
0.003933948930352926,
0.020863210782408714,
0.06047683581709862,
-0.05238427221775055,
0.016662340611219406,
-0.018734702840447426,
-0.03080725111067295,
-0.04094835743308067,
0.0430399551987648,
0.04226486757397652,
0.004384161438792944,
0.022475844249129295,
0.013481124304234982,
0.04493233561515808,
-0.007427926640957594,
-0.05774562060832977,
0.017572909593582153,
-0.01523599773645401,
0.048764485865831375,
0.0021322546526789665,
0.030204201117157936,
-0.06276609003543854,
-0.0141844991594553,
0.023754050955176353,
-0.0021252238657325506,
0.007290244568139315,
0.038771528750658035,
0.024865375831723213,
0.024837570264935493,
0.001631123130209744,
0.022290242835879326,
-0.05508152395486832,
0.014284908771514893,
0.04351913928985596,
-0.011192920617759228,
0.00011585503671085462,
0.025799086317420006,
0.00800113845616579,
-0.03616353124380112,
-0.0027578631415963173,
-0.031947799026966095,
-0.01679043099284172,
0.039243556559085846,
-0.03332913666963577,
-0.024030059576034546,
0.016727734357118607,
0.030725859105587006,
0.012781367637217045,
0.006729084998369217,
0.02379666641354561,
0.03841463103890419,
0.049455251544713974,
-0.050601933151483536,
-0.07530854642391205,
0.0651816576719284,
0.0011976598761975765,
0.03198368847370148,
0.0008850836311466992,
0.0018410308985039592,
-0.03710747882723808,
-0.021584192290902138,
0.05375408008694649,
0.0331987589597702,
-0.05483151599764824,
0.047489434480667114,
0.03343342989683151,
-0.05901919677853584,
0.007957102730870247,
-0.025203058496117592,
-0.028555545955896378,
-0.041718244552612305,
0.01743917353451252,
-0.05294809862971306,
0.02256189100444317,
0.03448256477713585,
-0.03404911234974861,
0.046255238354206085,
0.00288564246147871,
-0.0500711053609848,
0.02679932303726673,
0.00835286732763052,
0.03963322192430496,
-0.0588529147207737,
-0.015891142189502716,
0.026583243161439896,
0.013106548227369785,
-0.021326646208763123,
-0.025196846574544907,
0.06367868185043335,
-0.03808937966823578,
-0.04425360634922981,
0.049629874527454376,
0.055281490087509155,
0.019510289654135704,
-0.01564420759677887,
0.0706694945693016,
-0.006606189999729395,
0.021550767123699188,
-0.062141869217157364,
-0.05206691846251488,
0.016060462221503258,
-0.007713133003562689,
0.011975675821304321,
0.009486344642937183,
-0.027628740295767784,
0.012125439941883087,
-0.010383255779743195,
0.06599708646535873,
0.008489113301038742,
-0.050307586789131165,
0.08844689279794693,
-0.007351981010288,
0.01900455914437771,
-0.0273930411785841,
-0.02238091453909874,
-0.03166315332055092,
0.051762379705905914,
-0.10583922266960144,
0.024890154600143433,
-0.04661658778786659,
-0.012297363951802254,
0.015056801028549671,
0.03619469329714775,
0.06507714092731476,
-0.021449726074934006,
0.032504525035619736,
-0.012056944891810417,
-0.03330445662140846,
-0.047335345298051834,
0.00902558770030737,
0.0025741669815033674,
0.0005515695083886385,
0.030634788796305656,
0.06351181864738464,
-0.023024242371320724,
0.015214175917208195,
-0.006563493516296148,
0.01004820503294468,
0.002513295039534569,
0.017221257090568542,
-0.02825855277478695,
0.05638527497649193,
-0.026048853993415833,
0.01709580607712269,
-0.03213702514767647,
0.0012668565614148974,
0.03436872363090515,
0.036118343472480774,
0.0096995634958148,
-0.028519505634903908,
0.054648637771606445,
0.015063444152474403,
0.018235594034194946,
-0.0470062717795372,
0.030171586200594902,
0.02381216548383236,
0.013310559093952179,
0.04430466145277023,
-0.0020015768241137266,
-0.058998044580221176,
0.008681345731019974,
-0.02133626490831375,
0.010882879607379436,
0.0012873212108388543,
-0.028183259069919586,
0.0015572942793369293,
-0.010136245749890804,
-0.03534162417054176,
0.027051076292991638,
0.027677951380610466,
0.02304636873304844,
-0.04076977074146271,
-0.030961068347096443,
0.029433518648147583,
-0.028294246643781662,
0.014546188525855541,
0.0015957835130393505,
0.05408715456724167,
-0.010676203295588493,
0.028688520193099976,
-0.04367302358150482,
0.0077103422954678535,
0.070978544652462,
-0.009736664593219757,
0.03822363168001175,
0.043982964009046555,
0.004808512516319752,
-0.03172013908624649,
0.05113381892442703,
-0.032999031245708466,
-0.018974166363477707,
0.03960177302360535,
0.0014621210284531116,
-0.0006091844406910241,
0.037246063351631165,
0.00884796679019928,
0.04171512648463249,
-0.003822366939857602,
-0.03421939164400101,
-0.03294054791331291,
-0.058278314769268036,
0.01541823334991932,
-0.03703096881508827,
-0.04761049523949623,
0.03714190050959587,
-0.027446821331977844,
0.027873065322637558,
0.07319238781929016,
0.023559467867016792,
0.028533173725008965,
0.08440786600112915,
0.0638817846775055,
0.03212723135948181,
0.0065344576723873615,
0.029382916167378426,
-0.03876979276537895,
-0.044211722910404205,
0.0027333854231983423,
-0.04059112071990967,
0.006955682300031185,
-0.02848062850534916,
-0.010725107975304127,
-0.018927499651908875,
-0.03224653750658035,
0.0014507739106193185,
-0.027908412739634514,
0.0346568338572979,
-0.045078348368406296,
-0.04378863051533699,
0.043178997933864594,
0.031689126044511795,
-0.049223847687244415,
0.09269291907548904,
-0.05606342852115631,
-0.029345862567424774,
0.007823390886187553,
-0.02658986859023571,
0.026554521173238754,
0.01531047374010086,
-0.046930134296417236,
-0.046766623854637146,
-0.039176709949970245,
0.018548304215073586,
0.030354075133800507,
0.04337688162922859,
0.07831179350614548,
-0.01896068826317787,
0.025305353105068207,
-0.029377104714512825,
0.008140328340232372,
-0.01775527000427246,
-0.032688483595848083,
-0.0802784338593483,
0.005812123883515596,
-0.034300826489925385,
0.020396851003170013,
-0.0250615943223238,
-0.03617797791957855,
0.027771703898906708,
-0.0029177905526012182,
0.047409139573574066,
0.0191936157643795,
0.02409646101295948,
-0.01497525442391634,
0.007974245585501194,
0.055739399045705795,
-0.09834283590316772,
0.05743876472115517,
0.05684181675314903,
-0.004307504277676344,
0.0018272983143106103,
0.05490655079483986,
0.005897550843656063,
0.0165390744805336,
-0.0408778041601181,
0.0169582087546587,
0.030495360493659973,
0.010129586793482304,
-0.013912436552345753,
0.01773786172270775,
-0.0023837320040911436,
-0.02507341280579567,
-0.005949659273028374,
0.03828445076942444,
0.017663724720478058,
-0.031004363670945168,
-0.022780921310186386,
0.030405163764953613,
-0.00024990091333165765,
0.05573520064353943,
0.04775901511311531,
-0.043764062225818634,
0.009483416564762592,
-0.048970505595207214,
0.015905365347862244,
-0.055785711854696274,
0.02589339204132557,
0.07415296882390976,
-0.06878352910280228,
0.01048223115503788,
-0.020802535116672516,
-0.005703173577785492,
0.025048812851309776,
0.014139958657324314,
-0.016707763075828552,
-0.006591613404452801,
-0.032738905400037766,
-0.044892702251672745,
-0.02321556955575943,
0.0034994250163435936,
-0.005852058995515108,
0.002075053285807371,
-0.007223719730973244,
-0.04378536343574524,
0.0257248692214489,
-0.001079830341041088,
-0.03355170413851738,
0.0029704824555665255,
-0.033680327236652374,
0.018691983073949814,
0.04735877737402916,
-0.017900191247463226,
-0.061718638986349106,
0.019239550456404686,
0.00003089496021857485,
0.031001213937997818,
-0.029566744342446327,
0.04680104926228523,
0.0705103799700737,
-0.011243917979300022,
0.07677748054265976,
-0.02922784723341465,
0.03027561865746975,
-0.019557766616344452,
0.029355891048908234,
0.009707720018923283,
0.048740826547145844,
0.06724538654088974,
0.0330364890396595,
0.023543735966086388,
-0.011100038886070251,
-0.003347966820001602,
-0.028889089822769165,
-0.022853415459394455,
0.00336432340554893,
0.034234099090099335,
0.06780818104743958,
-0.027710383757948875,
-0.0508938767015934,
-0.018305087462067604,
-0.03212645277380943,
-0.047149788588285446,
0.055349960923194885,
0.05616495758295059,
0.0476771742105484,
0.017393341287970543,
0.07987560331821442,
0.03047427348792553,
-0.059497494250535965,
-0.014324565418064594,
-0.01664147526025772,
0.036946460604667664,
0.0053339689038693905,
0.010818636044859886,
-0.029663052409887314,
0.03670254722237587,
0.023820290341973305,
0.02264341711997986,
0.036694422364234924,
-0.023681392893195152,
0.01992619037628174,
0.00247806659899652,
-0.05177927389740944,
-0.11063168197870255,
-0.005099751055240631,
0.025548534467816353,
-0.021662337705492973,
-0.030424822121858597,
-0.018963586539030075,
-0.0371837355196476,
0.019595982506871223,
-0.04770549386739731,
0.02183745615184307,
-0.01620336063206196,
0.011804629117250443,
-0.0013259875122457743,
0.030773309990763664,
0.047464482486248016,
0.049139171838760376,
-0.05543475225567818,
0.02421657368540764,
-0.052189651876688004,
-0.03119756281375885,
0.06092175096273422,
0.034879524260759354,
-0.0013566433917731047,
-0.02539634518325329,
-0.008676997385919094,
-0.033976659178733826,
0.047221701592206955,
0.005541760940104723,
-0.035759616643190384,
0.0035894359461963177,
-0.017114220187067986,
0.04117501527070999,
0.034153424203395844,
-0.02876325696706772,
0.012215966358780861,
-0.02411459945142269,
0.010806024074554443,
-0.009363793767988682,
0.034831203520298004,
0.03270687907934189,
-0.009558147750794888,
-0.02834576740860939,
-0.01976291835308075,
0.03967531770467758,
0.04295068979263306,
0.07284686714410782,
0.007354604080319405,
-0.05987216904759407,
-0.07085919380187988,
0.006410837173461914,
0.041563231498003006,
-0.03126884996891022,
0.04058521240949631,
0.051387399435043335,
-0.03600098565220833,
-0.04705347865819931,
-0.020166631788015366,
0.016793373972177505,
0.00969129242002964,
0.03243207186460495,
0.013723565265536308,
-0.04490082710981369,
0.03047776222229004,
-0.01972489431500435,
0.03374199569225311,
-0.09350321441888809,
0.03756250813603401,
-0.011814997531473637,
0.02248714119195938,
-0.00885492842644453,
0.022942280396819115,
0.025241531431674957,
0.006202285178005695,
-0.018136320635676384,
-0.034624695777893066,
0.0453263558447361,
-0.06939106434583664,
0.025528037920594215,
0.051174260675907135,
0.0006576155428774655,
0.0018477094126865268,
0.024090968072414398,
-0.018541553989052773,
-0.011709936894476414,
0.06385977566242218,
0.032886963337659836,
0.05941520258784294,
-0.02501513436436653,
-0.018936196342110634,
0.013202332891523838,
0.021115457639098167,
0.01570366881787777,
0.009426760487258434,
-0.05201601982116699,
-0.03132672607898712,
0.020672673359513283,
-0.02951710857450962,
-0.012144268490374088,
-0.02927950583398342,
-0.04790841415524483,
0.02362416498363018,
0.020731110125780106,
0.053534604609012604,
-0.00373734044842422,
0.02647591009736061,
0.02031620405614376,
-0.11940225213766098,
-0.033503707498311996,
0.00022703860304318368,
0.0029391658026725054,
0.017993001267313957,
0.03079034574329853,
0.027943428605794907,
0.04088210687041283,
-0.055364951491355896,
0.008990437723696232,
0.011792687699198723,
-0.046857964247465134,
0.04335080832242966,
-0.005717922002077103,
0.011207904666662216,
0.023986997082829475,
-0.02525077760219574,
-0.07243815064430237,
0.061054643243551254,
-0.02329644002020359,
-0.08250779658555984,
0.05811165273189545,
0.0314505472779274,
0.06159524247050285,
0.0638488307595253,
-0.0112693440169096,
-0.0254727303981781,
0.03741231560707092,
-0.03172480687499046,
-0.02349119447171688,
0.01989739015698433,
0.005697410553693771,
0.02442600019276142,
-0.015478615649044514,
0.03240509703755379,
0.011443204246461391,
0.04908912256360054,
0.026711851358413696,
-0.08957962691783905,
-0.08106978982686996,
-0.010238340124487877,
0.01040545105934143,
-0.0833149328827858,
-0.033004485070705414,
-0.02344188652932644,
-0.0342920757830143,
-0.07827668637037277,
0.03110707551240921,
0.012396728619933128,
-0.051070842891931534,
-0.00005656705980072729,
-0.002292284741997719,
0.01951303705573082,
0.009635291993618011,
-0.007124743890017271,
0.0123731829226017,
-0.019238648936152458,
-0.004509869962930679,
-0.008433176204562187,
-0.05050698295235634,
0.001884660916402936,
0.046635702252388,
0.030991464853286743,
-0.00956479087471962,
-0.01866874285042286,
-0.004855121485888958,
-0.005396180786192417,
-0.01681423746049404,
-0.05268265679478645,
0.023313459008932114,
-0.04957572743296623,
-0.020413221791386604,
-0.03694789111614227,
-0.021341195330023766,
0.024906134232878685,
0.0008480398682877421,
-0.03646671026945114,
-0.036264825612306595,
0.0008517340756952763,
-0.0603245310485363,
-0.02927994914352894,
0.01603495143353939,
0.03336317837238312,
0.020438851788640022,
0.021888824179768562,
-0.011445150710642338,
-0.003813999006524682,
-0.020334316417574883,
0.02237582392990589,
0.03831181302666664,
-0.027978304773569107,
-0.04498886689543724,
-0.02568356692790985,
-0.04257689788937569,
-0.04325773939490318,
0.06655752658843994,
-0.021249504759907722,
0.06099851801991463,
0.11871480941772461,
0.010002619586884975,
0.03303448110818863,
-0.03608732298016548,
0.008528584614396095,
-0.013968778774142265,
0.03477754816412926,
-0.028698530048131943,
-0.014255207031965256,
0.03192814812064171,
-0.07271385192871094,
0.03643718361854553,
-0.050687920302152634,
0.011247613467276096,
0.002675817348062992,
0.0024603453930467367,
-0.05753099545836449,
0.01007535308599472,
-0.004840620793402195,
0.022786999121308327,
0.005218629725277424,
-0.03719985857605934,
-0.0258758757263422,
0.021854223683476448,
0.0716104805469513,
-0.02045157551765442,
-0.054531775414943695,
0.0005070054321549833,
-0.012618937529623508,
-0.013445627875626087,
0.010480852797627449,
-0.029970252886414528,
-0.030061587691307068,
0.010943579487502575,
0.013029302470386028,
0.023413779214024544,
-0.016662832349538803,
0.025673210620880127,
-0.014357117004692554,
0.029788708314299583,
-0.0026200851425528526,
0.03725118562579155,
-0.020770736038684845,
0.01338122971355915,
0.01172874215990305,
0.0900421068072319,
0.05296311900019646,
-0.033971965312957764,
0.058815013617277145,
-0.014889935962855816,
-0.03206189349293709,
0.03390955924987793,
-0.0486973412334919,
-0.05086350068449974,
-0.004140540957450867,
-0.0026719330344349146,
-0.017765507102012634,
-0.0005369289428927004,
-0.02295640856027603,
-0.021782303228974342,
-0.012953654862940311,
0.021796179935336113,
-0.07614046335220337,
-0.056955236941576004,
0.03527600318193436,
0.0013444620417430997,
-0.061625901609659195,
-0.0356527604162693,
-0.06819558143615723,
-0.009365524165332317,
-0.020463639870285988,
-0.022122448310256004,
0.06274741888046265,
-0.01471818145364523,
-0.0757836177945137,
-0.03307158127427101,
0.03357287123799324,
0.020209915935993195,
0.001192320603877306,
-0.017942922189831734,
-0.011722449213266373,
0.04127631336450577,
-0.008689331822097301,
-0.039417918771505356,
-0.05775538459420204,
0.00920769851654768,
-0.06008918210864067,
-0.018970126286149025,
-0.04788504168391228,
0.025709666311740875,
-0.005568632390350103,
-0.04768970608711243,
0.04323330894112587,
0.03257227689027786,
0.03256918117403984,
-0.035181861370801926,
0.04678086191415787,
-0.040999725461006165,
0.039494216442108154,
0.0020876049529761076,
-0.052704695612192154,
0.012480000965297222,
0.02775542438030243,
-0.0019530319841578603,
0.011454062536358833,
-0.037459053099155426,
0.0009502830798737705,
0.035694241523742676,
0.032262250781059265,
0.0030983551405370235,
-0.025237910449504852,
-0.030753739178180695,
-0.020179904997348785,
0.0018931718077510595,
-0.08026954531669617,
0.03672556206583977,
-0.036343611776828766,
-0.06373286247253418,
0.027534838765859604,
-0.033421166241168976,
0.0015396303497254848,
-0.008180896751582623,
-0.05852922052145004,
0.004427856300026178,
-0.007800639141350985,
0.05121886357665062,
-0.04154428467154503,
-0.023198451846837997,
0.02704029157757759,
-0.04099766165018082,
0.04906269162893295,
-0.05463555455207825,
-0.012880579568445683,
-0.07353859394788742,
0.004016286693513393,
0.02299932949244976,
-0.07222528010606766,
0.012909728102385998,
0.008498366922140121,
0.027637027204036713,
-0.030663110315799713,
-0.050717540085315704,
0.022985845804214478,
0.07769615948200226,
-0.036071762442588806,
-0.06035385653376579,
-0.007809760980308056,
-0.024892140179872513,
0.003668226068839431,
0.01907265931367874,
0.05227423459291458,
-0.02735341526567936,
0.009186888113617897,
0.06083783507347107,
-0.003134811529889703,
0.009084444493055344,
0.02522457391023636,
0.008581805974245071,
0.03489658981561661,
-0.03098471462726593,
0.007420029025524855,
-0.05171145126223564,
0.008390235714614391
] |
[
6.655121803283691,
1.0462088584899902
] |
General Physics
|
General Physics
|
physics-gen-ph
|
quant-ph
|
na
|
2007-03-31T17:31:12
|
We construct a system of nonequilibrium entropy limiters for the lattice
Boltzmann methods (LBM). These limiters erase spurious oscillations without
blurring of shocks, and do not affect smooth solutions. In general, they do the
same work for LBM as flux limiters do for finite differences, finite volumes
and finite elements methods, but for LBM the main idea behind the construction
of nonequilibrium entropy limiter schemes is to transform a field of a scalar
quantity - nonequilibrium entropy. There are two families of limiters: (i)
based on restriction of nonequilibrium entropy (entropy "trimming") and (ii)
based on filtering of nonequilibrium entropy (entropy filtering). The physical
properties of LBM provide some additional benefits: the control of entropy
production and accurate estimate of introduced artificial dissipation are
possible. The constructed limiters are tested on classical numerical examples:
1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven
cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100*100 grid.
All limiter constructions are applicable for both entropic and non-entropic
quasiequilibria.
|
Nonequilibrium entropy limiters in lattice Boltzmann methods
|
cond-mat.stat-mech cond-mat.mtrl-sci
|
0704.0043
| 2,007
|
[
0.008418821729719639,
0.03745285049080849,
0.013381722383201122,
-0.04980191960930824,
0.022950485348701477,
-0.022229142487049103,
0.011469952762126923,
-0.002994473557919264,
-0.06192857399582863,
0.010339010506868362,
-0.041556719690561295,
0.07791677862405777,
0.021020906046032906,
0.005995975807309151,
-0.0012308473233133554,
0.02566627971827984,
0.04142606630921364,
0.023502778261899948,
-0.023999832570552826,
0.010342051275074482,
-0.01999552547931671,
0.022059723734855652,
0.02537216991186142,
-0.07380802184343338,
0.10465596616268158,
-0.002594440011307597,
0.014967614784836769,
0.03893176466226578,
-0.061825189739465714,
0.04769929125905037,
0.03021322749555111,
-0.08735214918851852,
-0.0038433647714555264,
-0.0649917870759964,
-0.035252586007118225,
-0.04274362698197365,
0.07792776823043823,
-0.03899604082107544,
0.0009626278188079596,
-0.008535461500287056,
0.06411956250667572,
-0.05994797125458717,
0.010993138886988163,
-0.012710750102996826,
0.008109763264656067,
0.035357359796762466,
-0.025332897901535034,
-0.007181386463344097,
0.01057901419699192,
0.02796224318444729,
0.004004739224910736,
0.026990743353962898,
-0.008298583328723907,
-0.06088230013847351,
-0.00204044533893466,
0.009350540116429329,
0.00028115633176639676,
-0.04033442959189415,
0.06720459461212158,
-0.028113430365920067,
0.0011995317181572318,
0.023093385621905327,
-0.031815554946660995,
0.023960767313838005,
-0.02052018605172634,
-0.04528732970356941,
-0.049024008214473724,
-0.019758960232138634,
0.023254524916410446,
0.022243063896894455,
0.03792622685432434,
0.02725439891219139,
-0.0332413986325264,
0.02404872328042984,
-0.006142400670796633,
0.035895973443984985,
-0.013750065118074417,
0.040798697620630264,
0.05439410358667374,
-0.0007959460490383208,
-0.03102729842066765,
-0.05382224917411804,
0.03520696237683296,
0.015997225418686867,
0.06463959813117981,
0.031268805265426636,
0.026110585778951645,
0.01376795582473278,
0.0005180631997063756,
0.030606316402554512,
-0.016107747331261635,
-0.022323664277791977,
0.06585855782032013,
0.020024975761771202,
-0.027107419446110725,
0.056475043296813965,
0.005884759593755007,
0.013683966360986233,
0.0022065306548029184,
-0.03937381133437157,
-0.0022904735524207354,
0.04204661026597023,
-0.014690715819597244,
-0.006462292280048132,
0.00482771685346961,
-0.0074942209757864475,
0.00005206207060837187,
-0.010797899216413498,
0.02830304391682148,
-0.02382667176425457,
-0.03788291662931442,
-0.05863785371184349,
0.0013404920464381576,
-0.0025530511047691107,
-0.04127673804759979,
-0.01032022014260292,
0.06049058958888054,
-0.10171134769916534,
-0.021824799478054047,
0.0356387235224247,
0.017787424847483635,
0.0337061807513237,
0.018662631511688232,
-0.006699737627059221,
0.0413375161588192,
0.07830443978309631,
-0.022871607914566994,
0.01078164204955101,
0.013185013085603714,
-0.030540568754076958,
0.014719541184604168,
0.00471664359793067,
-0.005516598466783762,
-0.00000262666094386077,
0.028350962325930595,
0.04933794215321541,
-0.0574466809630394,
-0.0060252961702644825,
0.05287395417690277,
-0.01628134399652481,
-0.010622846893966198,
-0.03589627519249916,
0.007963612675666809,
-0.0005140956491231918,
0.018365224823355675,
-0.09110558032989502,
-0.037752192467451096,
-0.05956282094120979,
-0.032031286507844925,
-0.034134916961193085,
0.015910757705569267,
0.01855173334479332,
0.03974046930670738,
0.03069690614938736,
-0.050688982009887695,
0.0014527682214975357,
0.008487765677273273,
-0.002010191325098276,
0.05355276167392731,
-0.015960274264216423,
0.00010088169801747426,
0.023807330057024956,
-0.006108846049755812,
0.04156295582652092,
-0.054012082517147064,
0.044113676995038986,
0.04919144883751869,
-0.009708002209663391,
0.023743852972984314,
0.008174723014235497,
-0.08091886341571808,
-0.05883234739303589,
-0.032581627368927,
0.012453002855181694,
0.012631363235414028,
0.004130604676902294,
-0.024397937580943108,
0.0032578150276094675,
0.009141652844846249,
-0.026758361607789993,
0.04094909504055977,
-0.005357935559004545,
0.09330147504806519,
0.027811534702777863,
0.012856841087341309,
0.047420255839824677,
-0.011924568563699722,
-0.0019670608453452587,
-0.027844473719596863,
-0.026240259408950806,
0.06921028345823288,
0.013541867956519127,
-0.03993673250079155,
-0.05695755034685135,
-0.008207034319639206,
0.015457028523087502,
0.06765317916870117,
-0.041972652077674866,
-0.031375329941511154,
-0.04695742204785347,
-0.004242226015776396,
-0.011739946901798248,
-0.048700809478759766,
-0.03814059868454933,
0.002937994198873639,
0.05084198713302612,
-0.0023349514231085777,
0.02120816521346569,
0.023887507617473602,
0.0010063158115372062,
0.04470770061016083,
0.0043698642402887344,
-0.012693889439105988,
0.056438148021698,
0.03077062778174877,
-0.011169175617396832,
-0.004141760058701038,
-0.035000886768102646,
-0.026001445949077606,
0.02862684614956379,
0.03856165334582329,
-0.009534145705401897,
0.00078292639227584,
0.011836500838398933,
0.006720161065459251,
0.014470524154603481,
-0.00585945462808013,
0.030730420723557472,
-0.004274540580809116,
0.021770518273115158,
-0.06009620428085327,
-0.010239992290735245,
0.013165752403438091,
-0.05128124728798866,
-0.015817860141396523,
0.01925823464989662,
0.004440355580300093,
0.0365111380815506,
-0.03377151116728783,
0.05548465996980667,
0.03979984670877457,
-0.015800507739186287,
-0.0068466924130916595,
0.004649744369089603,
-0.03614798188209534,
-0.03529428690671921,
-0.021025242283940315,
-0.0034596011973917484,
-0.02834419533610344,
0.003149963915348053,
0.008947241120040417,
0.006709497421979904,
0.007232447620481253,
0.03222859650850296,
0.03719588741660118,
-0.014533176086843014,
-0.030388185754418373,
0.05564074218273163,
-0.04788397252559662,
-0.029155883938074112,
0.07689562439918518,
-0.016489017754793167,
0.025903787463903427,
-0.0304036196321249,
-0.043279487639665604,
-0.012802605517208576,
-0.009161061607301235,
-0.02647683583199978,
0.024272875860333443,
0.029133928939700127,
0.05836600065231323,
0.008282405324280262,
0.05306493118405342,
0.06833088397979736,
0.009950613602995872,
0.05360214412212372,
0.058375176042318344,
0.004810423124581575,
0.005956799723207951,
-0.026450276374816895,
-0.06462893635034561,
-0.018656836822628975,
-0.05131262168288231,
-0.011208320036530495,
-0.04697439447045326,
0.0003498155565466732,
0.043243762105703354,
-0.014140292070806026,
0.06837242841720581,
0.018186470493674278,
-0.0028385429177433252,
0.021047333255410194,
-0.003789173439145088,
0.04085756838321686,
-0.028631508350372314,
0.0464923232793808,
0.05027025565505028,
-0.048054467886686325,
-0.01177933532744646,
0.03992939740419388,
-0.009348288178443909,
0.007758304942399263,
-0.0017993133515119553,
0.05132357403635979,
0.025183439254760742,
0.03400349244475365,
-0.038285475224256516,
-0.029621463268995285,
0.07099847495555878,
0.02794198878109455,
0.013755150139331818,
0.0399484857916832,
-0.013371705077588558,
0.03634130209684372,
-0.0302495826035738,
0.07353030145168304,
0.04971669986844063,
-0.051715392619371414,
0.10931099206209183,
-0.0008835032349452376,
0.061688363552093506,
-0.030659524723887444,
0.03549783304333687,
-0.06233207881450653,
-0.00010162984835915267,
0.02912907488644123,
-0.0057277679443359375,
0.011053541675209999,
-0.017036408185958862,
-0.02783750556409359,
0.008687295019626617,
0.06238739192485809,
0.002674426417797804,
-0.013807782903313637,
-0.04733366146683693,
-0.05508338287472725,
-0.05247828736901283,
0.025881953537464142,
-0.026193812489509583,
-0.004134850110858679,
-0.022527242079377174,
-0.0017167434561997652,
-0.03298674151301384,
-0.04347018897533417,
-0.05014903470873833,
0.01421812642365694,
-0.048250727355480194,
0.004064206965267658,
-0.017121613025665283,
-0.017412599176168442,
-0.00048367827548645437,
0.0009983282070606947,
0.009493757039308548,
-0.03232356160879135,
-0.023116551339626312,
0.021346502006053925,
0.05631154030561447,
-0.012704966589808464,
0.09000223129987717,
0.02472127042710781,
0.02571810968220234,
-0.04352555423974991,
0.028575733304023743,
0.016891714185476303,
0.021656813099980354,
0.02266727387905121,
0.04915594682097435,
0.058180976659059525,
-0.021853068843483925,
-0.09380713105201721,
-0.05531143769621849,
-0.07979691028594971,
0.01824667677283287,
0.039956092834472656,
-0.012317799963057041,
0.03265000134706497,
-0.007938615046441555,
0.0674436092376709,
-0.00887159164994955,
-0.009430808946490288,
0.062606580555439,
-0.015599618665874004,
0.040132950991392136,
-0.028122548013925552,
-0.011078777723014355,
-0.01654481515288353,
-0.018017249181866646,
-0.019348962232470512,
-0.0034210062585771084,
-0.03826986625790596,
0.053094957023859024,
-0.036293890327215195,
-0.02468428760766983,
0.02242983505129814,
-0.021236540749669075,
-0.011665422469377518,
0.04027867317199707,
0.007524827960878611,
0.02995416708290577,
0.015114391222596169,
-0.006806607823818922,
-0.05909942835569382,
-0.043836209923028946,
0.01400751806795597,
-0.003438615472987294,
-0.0404900386929512,
-0.02273864671587944,
-0.034054871648550034,
0.026540353894233704,
-0.006968971341848373,
-0.028277823701500893,
-0.024763641878962517,
-0.0070487093180418015,
-0.07643497735261917,
0.028168508782982826,
-0.04741238057613373,
0.004371842369437218,
-0.020381784066557884,
0.05048105865716934,
-0.015090473927557468,
0.013171039521694183,
0.04550499841570854,
-0.06216535344719887,
0.006953404750674963,
-0.016766181215643883,
-0.02909177727997303,
0.02543213963508606,
-0.023341182619333267,
0.020463963970541954,
-0.06577912718057632,
0.004416037350893021,
0.013627063482999802,
-0.005144453141838312,
0.05672341212630272,
-0.001936679589562118,
-0.024279318749904633,
-0.024855611845850945,
-0.006991199683398008,
-0.05115567892789841,
0.032050639390945435,
0.04512646421790123,
-0.06792569905519485,
0.006135100033134222,
0.003498285776004195,
0.0150041114538908,
0.07266878336668015,
0.05199367552995682,
-0.05391136556863785,
-0.04853494465351105,
0.021876124665141106,
0.022738153114914894,
-0.032210975885391235,
-0.0043386309407651424,
0.0018223236547783017,
0.057109933346509933,
-0.037141863256692886,
-0.026737898588180542,
0.029279861599206924,
0.04026353731751442,
0.08355189114809036,
0.03980422765016556,
0.03221110999584198,
-0.057144712656736374,
0.004436531104147434,
-0.017860179767012596,
-0.00403608800843358,
0.03204244375228882,
0.003033403540030122,
0.037005648016929626,
0.0026839536149054766,
-0.0029510294552892447,
0.010479353368282318,
0.004508627578616142,
0.03202339634299278,
-0.024390414357185364,
-0.04513975977897644,
0.021175803616642952,
-0.029328228905797005,
-0.018767978996038437,
0.0673207938671112,
0.008372507989406586,
0.0063410247676074505,
-0.014176830649375916,
0.003619890194386244,
0.03473084792494774,
0.0333925224840641,
0.01563810184597969,
0.026307187974452972,
-0.012127730995416641,
0.004466549027711153,
-0.0074337986297905445,
0.06896725296974182,
0.011813865974545479,
0.022742770612239838,
-0.0754406601190567,
-0.03901609405875206,
0.052111510187387466,
0.021847445517778397,
-0.011875246651470661,
0.011431029066443443,
-0.05034754425287247,
0.0006615559104830027,
0.010228734463453293,
-0.02285652607679367,
-0.04146341234445572,
0.015187598764896393,
-0.037767503410577774,
-0.06384947150945663,
-0.019712895154953003,
0.001545169623568654,
0.04305950924754143,
0.06749527156352997,
0.066178098320961,
0.05526149645447731,
0.02992267534136772,
-0.04517030343413353,
0.07838819175958633,
-0.05223049968481064,
-0.08952175080776215,
-0.007025604601949453,
0.010928149335086346,
-0.0015778535744175315,
0.05672219768166542,
0.00185451190918684,
-0.08908887207508087,
0.009956168942153454,
-0.027873825281858444,
-0.07673606276512146,
0.013091538101434708,
0.0391787625849247,
-0.03736961632966995,
0.008815537206828594,
-0.009084595367312431,
-0.015533447265625,
-0.012946238741278648,
-0.024520698934793472,
-0.03301212191581726,
0.04607263207435608,
-0.009119710884988308,
-0.016336899250745773,
0.05697659030556679,
0.0009070202358998358,
0.003766931127756834,
-0.010628186166286469,
0.01879849098622799,
-0.03888113424181938,
-0.09866153448820114,
0.014019662514328957,
-0.048855260014534,
-0.06298066675662994,
0.004011417739093304,
-0.023443568497896194,
0.03338899463415146,
-0.07178614288568497,
0.036558717489242554,
-0.04550839215517044,
0.007286726497113705,
-0.03041072189807892,
-0.032107431441545486,
0.04612583667039871,
-0.006007697898894548,
0.0495140440762043,
0.08283565193414688,
-0.0337953045964241,
0.03406279906630516,
-0.12342497706413269,
-0.05724439024925232,
0.03463634103536606,
0.00523714441806078,
0.03029520809650421,
-0.00004620002437150106,
-0.028830111026763916,
0.005397677421569824,
0.04884674400091171,
0.011157169006764889,
-0.01551634632050991,
0.010515782050788403,
-0.05401292443275452,
-0.04298250749707222,
-0.01710187830030918,
-0.02967233583331108,
-0.002042932901531458,
-0.02014412172138691,
-0.021786002442240715,
-0.011375987902283669,
-0.006656144745647907,
-0.001825543469749391,
-0.011094614863395691,
-0.00034061004407703876,
0.005341446492820978,
0.013734432868659496,
-0.04985194280743599,
-0.022176438942551613,
-0.023900272324681282,
-0.056536633521318436,
-0.004031958989799023,
-0.04024346545338631,
-0.013359041884541512,
-0.043882448226213455,
0.028640808537602425,
-0.045156389474868774,
0.0023779955226927996,
0.0055869813077151775,
-0.04128739610314369,
0.014329595491290092,
0.06341198831796646,
-0.003359408350661397,
0.04563406482338905,
0.0006083971238695085,
0.025415591895580292,
-0.0024514871183782816,
-0.013637007214128971,
0.001184192136861384,
-0.035401083528995514,
0.032525863498449326,
-0.03986513987183571,
0.07042960822582245,
-0.018474115058779716,
0.024431003257632256,
-0.043545905500650406,
-0.016482586041092873,
-0.05547003075480461,
-0.004009227268397808,
-0.062096405774354935,
0.01207917183637619,
0.04357253015041351,
-0.026129363104701042,
-0.051362425088882446,
0.04960494488477707,
0.04144176468253136,
0.02315644547343254,
-0.032175611704587936,
0.027973368763923645,
-0.003436381695792079,
0.0014294266002252698,
0.01950005814433098,
-0.0429789237678051,
0.04704668000340462,
0.021347900852560997,
0.03417332097887993,
0.007943885400891304,
-0.01744847372174263,
0.04357980936765671,
0.033660560846328735,
0.02510996349155903,
0.029270997270941734,
-0.0035405426751822233,
0.0444105789065361,
-0.045030947774648666,
-0.035740699619054794,
0.01982203498482704,
0.027725080028176308,
-0.046469561755657196,
0.021785786375403404,
-0.02551874704658985,
0.02391107939183712,
0.04430743306875229,
0.018222013488411903,
-0.024394331499934196,
-0.024502521380782127,
0.016212647780776024,
-0.0009016459807753563,
0.057823121547698975,
-0.013176491484045982,
0.057094305753707886,
-0.030075259506702423,
-0.016114290803670883,
-0.07088737934827805,
0.0020873064640909433,
-0.0243341326713562,
-0.01948070339858532,
-0.03006015531718731,
-0.04044497013092041,
-0.02801896072924137,
-0.04919726029038429,
-0.013555735349655151,
0.014561713673174381,
0.037267547100782394,
0.006216002628207207,
-0.021544363349676132,
0.016809122636914253,
0.016170097514986992,
-0.024593379348516464,
-0.02487104944884777,
-0.01739511825144291,
0.012825277633965015,
0.006683418061584234,
-0.024931838735938072,
-0.03790370002388954,
-0.03538736328482628,
0.010338031686842442,
0.07415186613798141,
0.0031386662740260363,
-0.058089662343263626,
-0.0021499358117580414,
-0.007713650353252888,
-0.03940590098500252,
0.029452957212924957,
0.007925412617623806,
-0.04484037309885025,
-0.007404394447803497,
0.043354228138923645,
-0.042382195591926575,
0.04708817973732948,
0.02900376170873642,
-0.005873064510524273,
0.056896697729825974,
0.018397869542241096,
0.014042938128113747,
-0.003439937252551317,
-0.04790757596492767,
-0.0029135204385966063,
0.07875512540340424,
-0.0026452732272446156,
0.0008691587136127055,
0.013303568586707115,
-0.02768181450664997,
-0.018043886870145798,
0.03712692856788635,
-0.0001532782189315185,
0.04462682083249092,
0.00797420833259821,
-0.044331714510917664,
0.015183267183601856,
0.011104070581495762,
-0.05538830906152725,
-0.021382002159953117,
-0.0054230461828410625,
-0.026296647265553474,
-0.021451428532600403,
0.03227737918496132,
0.006419131066650152,
-0.075249582529068,
0.034797243773937225,
-0.07281360030174255,
0.04670008271932602,
0.011686659418046474,
0.05745817720890045,
0.0019899557810276747,
0.029356898739933968,
-0.027916496619582176,
-0.024061506614089012,
0.05219601094722748,
-0.021593086421489716,
0.0021078060381114483,
-0.020007776096463203,
-0.10767462849617004,
-0.008517616428434849,
0.07477343827486038,
-0.010312214493751526,
0.024793291464447975,
-0.07151398807764053,
0.021601682528853416,
-0.01897806115448475,
0.04040927067399025,
0.01640194095671177,
-0.021284913644194603,
-0.01673705317080021,
0.028902925550937653,
0.0028240098617970943,
0.01936510019004345,
-0.019501589238643646,
0.05485164746642113,
0.05730292201042175,
-0.0096952635794878,
0.038362253457307816,
-0.04458949342370033,
-0.021193798631429672
] |
[
6.562930107116699,
3.8776183128356934
] |
Statistical Mechanics
|
Condensed-Matter Physics
|
cond-mat-stat-mech
|
cond-mat-mtrl-sci
|
na
|
2007-03-31T17:47:54
|
We present a theoretical framework for plasma turbulence in astrophysical
plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks).
The key assumptions are that the turbulence is anisotropic with respect to the
mean magnetic field and frequencies are low compared to the ion cyclotron
frequency. The energy injected at the outer scale scale has to be converted
into heat, which ultimately cannot be done without collisions. A KINETIC
CASCADE develops that brings the energy to collisional scales both in space and
velocity. Its nature depends on the physics of plasma fluctuations. In each of
the physically distinct scale ranges, the kinetic problem is systematically
reduced to a more tractable set of equations. In the "inertial range" above the
ion gyroscale, the kinetic cascade splits into a cascade of Alfvenic
fluctuations, which are governed by the RMHD equations at both the collisional
and collisionless scales, and a passive cascade of compressive fluctuations,
which obey a linear kinetic equation along the moving field lines associated
with the Alfvenic component. In the "dissipation range" between the ion and
electron gyroscales, there are again two cascades: the kinetic-Alfven-wave
(KAW) cascade governed by two fluid-like Electron RMHD equations and a passive
phase-space cascade of ion entropy fluctuations. The latter cascade brings the
energy of the inertial-range fluctuations that was damped by collisionless
wave-particle interaction at the ion gyroscale to collisional scales in the
phase space and leads to ion heating. The KAW energy is similarly damped at the
electron gyroscale and converted into electron heat. Kolmogorov-style scaling
relations are derived for these cascades. Astrophysical and space-physical
applications are discussed in detail.
|
Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in
magnetized weakly collisional plasmas
|
astro-ph nlin.CD physics.plasm-ph physics.space-ph
|
0704.0044
| 2,007
|
[
0.008542696945369244,
0.03211032599210739,
-0.006365271285176277,
-0.04230920225381851,
0.06003604084253311,
0.025850428268313408,
-0.049860451370477676,
0.021965572610497475,
-0.042862165719270706,
-0.008373999036848545,
-0.025851624086499214,
0.09501178562641144,
0.030983613803982735,
0.0101707698777318,
0.016844892874360085,
-0.011140243150293827,
0.03241641819477081,
0.04637981951236725,
-0.015805553644895554,
0.03898674622178078,
-0.05667528882622719,
-0.040980059653520584,
0.02034517005085945,
-0.03973415121436119,
0.11180074512958527,
0.017755728214979172,
0.02270604483783245,
-0.016693267971277237,
-0.006699288729578257,
-0.021389387547969818,
0.0703427791595459,
-0.015310416929423809,
-0.019312283024191856,
-0.05881867557764053,
-0.038500793278217316,
-0.05571651831269264,
0.024913664907217026,
-0.0071628340519964695,
-0.004146283958107233,
-0.018585512414574623,
0.06088360771536827,
-0.03718532621860504,
0.05101402476429939,
0.005896488204598427,
-0.0005956052918918431,
0.05409814044833183,
0.0014696470461785793,
-0.011695319786667824,
-0.00521867023780942,
0.012102600187063217,
-0.041765257716178894,
0.03057936578989029,
-0.007834955118596554,
-0.04439792409539223,
-0.03358453884720802,
-0.004966764245182276,
0.019495271146297455,
-0.0230187326669693,
0.0447375513613224,
0.01780838519334793,
0.0790441557765007,
0.024031654000282288,
-0.017200389876961708,
-0.00510733388364315,
-0.005843886639922857,
-0.06828663498163223,
-0.04108520597219467,
0.03625302016735077,
0.023606717586517334,
-0.018125826492905617,
0.035251419991254807,
-0.017708495259284973,
-0.013092685490846634,
0.005647401325404644,
-0.04351598024368286,
0.005871985573321581,
0.03194092586636543,
-0.002977018477395177,
0.01647518202662468,
0.017651256173849106,
-0.04186128452420235,
0.013841934502124786,
0.06669367104768753,
-0.013828638009727001,
0.03792373836040497,
0.0202134158462286,
-0.002888802206143737,
0.056212205439805984,
-0.07385364919900894,
0.006158430129289627,
-0.0007999535300768912,
-0.010632509365677834,
0.040844518691301346,
-0.03571689501404762,
-0.03975774347782135,
0.04158048704266548,
-0.03385387733578682,
0.08513463288545609,
0.005233484320342541,
-0.06476578861474991,
-0.03369022160768509,
0.020008761435747147,
0.01692049764096737,
-0.002403425518423319,
0.06457225233316422,
-0.005310348700731993,
-0.007547323126345873,
0.026617543771862984,
0.052993591874837875,
-0.01129340659826994,
-0.060222163796424866,
-0.04413197934627533,
0.01277127955108881,
-0.010008892975747585,
-0.006561805959790945,
-0.05326790735125542,
0.0402824841439724,
-0.04600248113274574,
0.005916604306548834,
0.06695576012134552,
0.020196830853819847,
-0.020600689575076103,
-0.038248591125011444,
0.05735402554273605,
0.01851191185414791,
0.03991497680544853,
0.0037538171745836735,
-0.002991500310599804,
0.00327920145355165,
-0.02802562341094017,
0.02692490816116333,
-0.007012184709310532,
-0.0603192113339901,
-0.0036341133527457714,
0.039721760898828506,
0.05335532873868942,
-0.00872673001140356,
-0.00461649289354682,
-0.017819460481405258,
-0.046699848026037216,
0.034039635211229324,
-0.03321314603090286,
0.029004350304603577,
-0.04059578850865364,
-0.0017163511365652084,
-0.031270258128643036,
0.006118236109614372,
-0.061134807765483856,
-0.0005703645874746144,
-0.04024149850010872,
0.02630847506225109,
0.029530778527259827,
0.01566792093217373,
-0.0005852293688803911,
-0.033921364694833755,
-0.02551024965941906,
0.015188580378890038,
0.03757113590836525,
0.007256168872117996,
-0.008023422211408615,
0.01678699441254139,
0.012780620716512203,
0.028572440147399902,
0.0415990985929966,
-0.02305072359740734,
0.008615485392510891,
0.042961206287145615,
0.01903892308473587,
0.021368855610489845,
0.06847082078456879,
-0.07415352016687393,
-0.042431797832250595,
-0.016377367079257965,
-0.006434183102101088,
0.01555324625223875,
0.02414361946284771,
0.009700490161776543,
-0.05876554548740387,
-0.027787480503320694,
-0.01631622016429901,
0.035585690289735794,
-0.0000636901386315003,
0.056630320847034454,
0.01888152025640011,
0.026063507422804832,
0.005146979819983244,
-0.038999784737825394,
-0.01931363344192505,
0.0049833254888653755,
-0.04276891052722931,
0.04832443594932556,
-0.00034241515095345676,
-0.055915575474500656,
-0.044280532747507095,
-0.002658097306266427,
-0.01935999095439911,
0.03782419115304947,
-0.024911874905228615,
-0.06724290549755096,
-0.011604048311710358,
-0.03544948995113373,
0.013187656179070473,
-0.05872654169797897,
0.03148655593395233,
-0.00796497892588377,
0.04693494737148285,
0.01096463855355978,
0.031134871765971184,
0.03086755983531475,
-0.012225938029587269,
0.10403206944465637,
0.02321871928870678,
-0.07804065942764282,
0.026012202724814415,
0.00042027721065096557,
-0.007654921151697636,
-0.004542140755802393,
-0.04669586941599846,
-0.04707915335893631,
0.001962068025022745,
-0.013268131762742996,
-0.023924943059682846,
0.005667155142873526,
-0.0007672632345929742,
0.028738899156451225,
0.005250859074294567,
-0.04908198490738869,
0.009481552988290787,
0.004010885953903198,
-0.047361332923173904,
-0.012057716026902199,
0.0051159942522645,
0.006720791105180979,
-0.045222364366054535,
0.01844944804906845,
-0.0026471572928130627,
-0.03594743832945824,
0.011477765627205372,
0.011411292478442192,
0.07643803209066391,
0.020097604021430016,
0.019393017515540123,
0.029431596398353577,
-0.021669922396540642,
-0.06185569986701012,
-0.05138813704252243,
0.003763774177059531,
0.0077752950601279736,
-0.07815524935722351,
0.019521966576576233,
0.06218495965003967,
-0.02375383861362934,
0.022601718083024025,
0.034387972205877304,
0.030081406235694885,
-0.016069980338215828,
-0.052733853459358215,
0.047238871455192566,
-0.04580118879675865,
-0.02464490570127964,
0.08900563418865204,
-0.01924970932304859,
-0.007260111626237631,
-0.0655188262462616,
-0.05095812678337097,
0.024799780920147896,
-0.004495077766478062,
0.007389410398900509,
-0.020896704867482185,
-0.014982235617935658,
0.020019805058836937,
0.02583981119096279,
0.031142186373472214,
0.05645028501749039,
0.0299399271607399,
0.040523461997509,
0.06558499485254288,
-0.04010439291596413,
0.032342176884412766,
-0.03648665174841881,
-0.0579187348484993,
-0.06916984915733337,
-0.00530402734875679,
-0.053456470370292664,
-0.036854088306427,
0.009623263962566853,
0.04308433458209038,
0.01935165748000145,
0.004749705083668232,
0.023968787863850594,
-0.00811945740133524,
-0.05550432205200195,
-0.011073227040469646,
0.04008586332201958,
-0.01914827525615692,
0.05268292874097824,
0.07278229296207428,
-0.01921948231756687,
0.005461288616061211,
-0.023777009919285774,
0.026226654648780823,
-0.051916539669036865,
0.002772964769974351,
0.0011380156502127647,
-0.014034927822649479,
0.04685860872268677,
-0.004807931371033192,
-0.011787666007876396,
0.018008962273597717,
0.016164101660251617,
0.01604958437383175,
0.04067574813961983,
-0.012673014774918556,
0.03194117173552513,
-0.0154124666005373,
0.03241386264562607,
0.01705946773290634,
-0.016507327556610107,
0.09117718786001205,
0.05228350684046745,
0.03222709149122238,
-0.06922579556703568,
-0.010945986025035381,
-0.07118808478116989,
0.03593272343277931,
0.01851472072303295,
0.005973628722131252,
-0.0006009710486978292,
-0.028530815616250038,
0.017775919288396835,
-0.03821612149477005,
0.04864855483174324,
0.02471947856247425,
-0.021627699956297874,
-0.021220000460743904,
0.006254682783037424,
-0.04058695212006569,
0.010044107213616371,
-0.014215086586773396,
0.031420543789863586,
-0.02975250408053398,
-0.039845481514930725,
-0.049184080213308334,
-0.026071086525917053,
-0.08142617344856262,
0.039481885731220245,
-0.005241401959210634,
-0.017656434327363968,
0.04925857484340668,
-0.02578040398657322,
-0.034195676445961,
0.027781201526522636,
0.025169238448143005,
-0.03181064501404762,
-0.05348098278045654,
0.000048201683966908604,
0.0772213414311409,
-0.039836250245571136,
0.07294519245624542,
0.007919426076114178,
0.0029300253372639418,
-0.04930995777249336,
-0.034416891634464264,
-0.012283976189792156,
0.0018045856850221753,
0.03258379176259041,
0.03673098608851433,
0.034828655421733856,
-0.010713999159634113,
-0.037898022681474686,
-0.047179315239191055,
-0.0211350005120039,
0.043707892298698425,
0.019884098321199417,
0.03819705918431282,
-0.016717132180929184,
0.01636713184416294,
0.05839580297470093,
-0.0034461261238902807,
0.012869545258581638,
0.0361323244869709,
-0.01501617580652237,
0.03486623987555504,
0.013119030743837357,
0.02803288772702217,
-0.028884002938866615,
-0.04300932213664055,
0.03428586944937706,
-0.029536429792642593,
-0.05177935212850571,
0.046751268208026886,
-0.052187804132699966,
-0.06018989160656929,
0.02181864343583584,
0.01757129840552807,
-0.056356340646743774,
0.06397676467895508,
-0.011755610816180706,
0.0750749334692955,
0.04089880734682083,
-0.016863206401467323,
-0.0006717583164572716,
-0.019228151068091393,
-0.01567932218313217,
0.0010791178792715073,
-0.0019424859201535583,
-0.007363115902990103,
-0.07073469460010529,
0.029761245474219322,
-0.024015797302126884,
0.022445570677518845,
0.015083547681570053,
-0.010053412057459354,
-0.075980044901371,
0.04236423224210739,
-0.01349895354360342,
0.028781134635210037,
-0.010162084363400936,
0.04580429941415787,
-0.01732870750129223,
0.011293204501271248,
0.0916985347867012,
-0.005993609316647053,
0.01351832877844572,
-0.04830414429306984,
-0.004570620134472847,
0.01798136532306671,
0.011251206509768963,
0.03011065162718296,
-0.04207264259457588,
0.03381839394569397,
-0.023556247353553772,
-0.02859417535364628,
0.017805645242333412,
-0.05064896121621132,
0.006078151986002922,
-0.024890147149562836,
-0.012307901866734028,
0.003944690339267254,
0.0010954678291454911,
0.03142299875617027,
-0.06556635349988937,
0.027454281225800514,
-0.019882861524820328,
0.03264717385172844,
0.10544398427009583,
0.08903516829013824,
-0.056722208857536316,
-0.06470369547605515,
-0.005870136432349682,
0.02116839960217476,
-0.01090584509074688,
-0.013409147970378399,
0.03864714503288269,
0.09723913669586182,
-0.03064013086259365,
-0.013610524125397205,
-0.004588922951370478,
0.04554161801934242,
0.0012328256852924824,
-0.014840714633464813,
0.0895698294043541,
-0.019559497013688087,
0.0016766763292253017,
0.02455112524330616,
0.018488464877009392,
0.02936575375497341,
-0.030851392075419426,
0.020681185647845268,
0.039774369448423386,
0.024957550689578056,
0.011414316482841969,
-0.017381297424435616,
-0.022237645462155342,
-0.06507541984319687,
0.01753716915845871,
0.04776985943317413,
-0.054003968834877014,
0.025599341839551926,
0.059427279978990555,
0.050818830728530884,
0.0037590237334370613,
0.018058408051729202,
0.016137514263391495,
-0.041795264929533005,
0.022837599739432335,
0.011536271311342716,
0.002321056555956602,
0.01786281354725361,
0.0017214117106050253,
0.0006486225756816566,
0.06514798849821091,
-0.01718210242688656,
0.011951293796300888,
-0.012305859476327896,
0.008889257907867432,
0.017227552831172943,
-0.027022680267691612,
0.03529376909136772,
-0.018948256969451904,
-0.026661690324544907,
-0.02589905820786953,
-0.02797146700322628,
0.01172514446079731,
0.009838424623012543,
0.007883898913860321,
-0.022000936791300774,
-0.05429381877183914,
0.013479609042406082,
0.0260429959744215,
0.006715286523103714,
0.055842816829681396,
0.030290501192212105,
0.10306472331285477,
-0.005289243999868631,
-0.0619543194770813,
0.03402329981327057,
-0.042662739753723145,
0.006649621296674013,
-0.007335453759878874,
-0.039331357926130295,
-0.018217379227280617,
0.022755760699510574,
0.010057906620204449,
-0.09966946393251419,
0.047892678529024124,
-0.015752673149108887,
-0.05355462804436684,
0.05034235864877701,
-0.01888423040509224,
0.001922927680425346,
-0.013284025713801384,
0.0005696137668564916,
-0.02162526734173298,
-0.017454709857702255,
-0.045595794916152954,
-0.0325080007314682,
0.046054355800151825,
-0.009298769757151604,
0.08046221733093262,
-0.01948314532637596,
-0.013018261641263962,
0.0019338406855240464,
-0.006254766136407852,
-0.006373826880007982,
-0.0015479213325306773,
-0.047435540705919266,
0.029992321506142616,
-0.0007403985946439207,
-0.10721249878406525,
0.007339745294302702,
-0.03644212335348129,
0.10510468482971191,
-0.06784213334321976,
-0.001489827991463244,
-0.031491223722696304,
0.04144570231437683,
-0.04656834527850151,
-0.0406244695186615,
-0.02965935878455639,
-0.0019268187461420894,
-0.0012513748370110989,
0.03090433031320572,
0.006481286603957415,
0.05916145071387291,
-0.12406674772500992,
-0.01581461913883686,
-0.04216338321566582,
0.07199191302061081,
-0.001717861625365913,
0.009579352103173733,
-0.0384603850543499,
-0.05107026919722557,
0.045257534831762314,
0.06432630121707916,
-0.06879814714193344,
0.0413501039147377,
0.05525773763656616,
-0.07612860947847366,
-0.03500054404139519,
-0.009080583229660988,
0.027681147679686546,
0.02137017622590065,
-0.010669952258467674,
-0.010333447717130184,
-0.03729410469532013,
-0.009010364301502705,
-0.024879302829504013,
0.07034370303153992,
-0.014746787957847118,
-0.005017291754484177,
-0.0392521470785141,
-0.007399760652333498,
-0.009842537343502045,
-0.05763343349099159,
0.016556354239583015,
-0.011257907375693321,
-0.051685135811567307,
-0.04258832335472107,
-0.02185504324734211,
-0.05750637874007225,
0.008365485817193985,
0.015239328145980835,
-0.017837654799222946,
0.000019314922610647045,
0.014684438705444336,
-0.04713452234864235,
0.0792403519153595,
-0.02417825348675251,
0.0455508679151535,
0.0066662682220339775,
0.0067040640860795975,
-0.014847670681774616,
-0.06033586338162422,
-0.01933283731341362,
-0.006265006028115749,
0.07335083186626434,
-0.038712725043296814,
0.016671301797032356,
-0.030047183856368065,
-0.05470219627022743,
-0.07037098705768585,
-0.00036204728530719876,
-0.08141231536865234,
-0.012370944023132324,
-0.0012675985926762223,
-0.03414712846279144,
-0.020221306011080742,
-0.00250888685695827,
0.016757242381572723,
0.023371534422039986,
0.020071491599082947,
-0.01025919895619154,
0.004314864054322243,
-0.0024101075250655413,
-0.04622473567724228,
-0.02564474381506443,
-0.009169708006083965,
0.04697997123003006,
0.021796023473143578,
0.054484810680150986,
0.002575680147856474,
-0.0159547571092844,
0.021219657734036446,
0.04563412070274353,
0.022463373839855194,
0.006096822675317526,
0.003929642494767904,
0.019094469025731087,
-0.0026136210653930902,
0.036861903965473175,
0.05750570446252823,
0.003868085565045476,
-0.0038676592521369457,
-0.0020289996173232794,
0.020771952345967293,
0.04681198298931122,
0.02523428574204445,
0.006568957585841417,
-0.018820373341441154,
0.009158906526863575,
0.016430916264653206,
0.004623656626790762,
0.01183080580085516,
0.02301003225147724,
-0.039566680788993835,
0.01562441885471344,
-0.06120631471276283,
0.023024702444672585,
0.00800324510782957,
-0.003997524734586477,
-0.012538526207208633,
-0.0627937987446785,
-0.023522362112998962,
-0.04865528270602226,
-0.012193786911666393,
-0.024302445352077484,
-0.03547609597444534,
0.04075692221522331,
-0.014368104748427868,
-0.017668938264250755,
0.018589071929454803,
0.04350685328245163,
-0.00407699029892683,
0.020671823993325233,
0.026985447853803635,
-0.037397123873233795,
-0.02406487800180912,
-0.045492369681596756,
-0.05947934091091156,
0.0022212902549654245,
0.03086794540286064,
0.030728494748473167,
-0.06351203471422195,
0.04911627620458603,
-0.0016941335052251816,
-0.05788220837712288,
0.014203722588717937,
-0.008399424143135548,
0.01403909269720316,
0.042457543313503265,
0.030243488028645515,
-0.018428852781653404,
0.046383440494537354,
-0.013631381094455719,
0.022097501903772354,
0.0586303286254406,
0.007768247276544571,
-0.023434199392795563,
-0.03875168785452843,
0.0005485248402692378,
0.007416849955916405,
-0.019399885088205338,
0.017561472952365875,
0.032443154603242874,
-0.03617658466100693,
0.05081024393439293,
-0.04554038494825363,
0.00987236388027668,
-0.0025396980345249176,
0.03994639962911606,
-0.03853154554963112,
-0.03789450600743294,
0.022215550765395164,
0.055882032960653305,
-0.004673413932323456,
-0.0019861303735524416,
-0.05923774838447571,
0.03622337803244591,
0.00033339974470436573,
-0.03509442135691643,
0.003370435908436775,
-0.046718399971723557,
-0.031931910663843155,
-0.025434015318751335,
0.00011188795178895816,
0.00291841640137136,
0.015017794445157051,
-0.010358904488384724,
-0.013713132590055466,
0.010935379192233086,
-0.01700160838663578,
0.010667108930647373,
0.019403982907533646,
-0.02995411492884159,
-0.016703758388757706,
-0.047293175011873245,
0.008514385670423508,
0.032001446932554245,
-0.009804017841815948,
0.010869689285755157,
0.02084706351161003,
-0.002685008803382516,
-0.00014937660307623446,
0.023050496354699135,
0.03450225293636322,
-0.009477667510509491,
0.044824544340372086,
0.028087861835956573,
-0.0022111269645392895,
0.018707923591136932,
-0.03729706257581711,
-0.01624349132180214,
0.06458823382854462,
0.0010183346457779408,
0.041393134742975235,
-0.02617110125720501,
0.006542895920574665
] |
[
11.189960479736328,
4.9994120597839355
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
nlin-CD
|
physics-plasm-ph
|
2007-03-31T18:09:02
|
This paper considers the propagation of shallow-water solitary and nonlinear
periodic waves over a gradual slope with bottom friction in the framework of a
variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging
method, using a recent development of this theory for perturbed integrable
equations. This general approach enables us not only to improve known results
on the adiabatic evolution of isolated solitary waves and periodic wave trains
in the presence of variable topography and bottom friction, modeled by the
Chezy law, but also importantly, to study the effects of these factors on the
propagation of undular bores, which are essentially unsteady in the system
under consideration. In particular, it is shown that the combined action of
variable topography and bottom friction generally imposes certain global
restrictions on the undular bore propagation so that the evolution of the
leading solitary wave can be substantially different from that of an isolated
solitary wave with the same initial amplitude. This non-local effect is due to
nonlinear wave interactions within the undular bore and can lead to an
additional solitary wave amplitude growth, which cannot be predicted in the
framework of the traditional adiabatic approach to the propagation of solitary
waves in slowly varying media.
|
Evolution of solitary waves and undular bores in shallow-water flows
over a gradual slope with bottom friction
|
nlin.PS nlin.SI
|
0704.0045
| 2,007
|
[
-0.008504029363393784,
0.009805872105062008,
-0.013357575051486492,
-0.019190805032849312,
0.042382434010505676,
0.03598447144031525,
0.0644347071647644,
0.006716828793287277,
-0.020805049687623978,
-0.01997891068458557,
-0.06854003667831421,
0.05349959805607796,
0.05915804207324982,
0.03049362078309059,
-0.055047016590833664,
-0.04988556727766991,
0.016163958236575127,
-0.01808818429708481,
-0.0016588647849857807,
-0.0192404817789793,
-0.032939668744802475,
0.019930757582187653,
0.028827093541622162,
-0.02566990628838539,
0.10549627989530563,
-0.01313878782093525,
0.05495394393801689,
-0.000054599517170572653,
-0.02785026654601097,
0.07479773461818695,
0.033630095422267914,
-0.03299681469798088,
0.037281304597854614,
-0.0024037077091634274,
-0.07789880037307739,
0.00252445787191391,
0.024870848283171654,
-0.027545541524887085,
0.0367959663271904,
0.03050636313855648,
0.03677220270037651,
-0.00446696812286973,
0.004663868807256222,
-0.007990565150976181,
0.02302013523876667,
-0.014582928270101547,
-0.029736287891864777,
-0.0015876423567533493,
0.008747062645852566,
0.03181048855185509,
0.05973924323916435,
-0.021206986159086227,
0.04513330012559891,
-0.03449803963303566,
-0.043017081916332245,
0.03462648764252663,
0.01744679920375347,
-0.05662521347403526,
0.03786550089716911,
-0.0018537496216595173,
-0.006841976661235094,
-0.004449628293514252,
0.013807453215122223,
-0.01734359748661518,
0.01720377244055271,
-0.08198747038841248,
-0.0368523932993412,
-0.01722581498324871,
0.015474957413971424,
-0.03192474693059921,
0.02200515940785408,
-0.05465440824627876,
-0.001093708910048008,
0.017595551908016205,
-0.024888206273317337,
0.02971569262444973,
0.014936789870262146,
-0.014797397889196873,
-0.03249048441648483,
-0.0615961030125618,
-0.008719172328710556,
0.00969996303319931,
0.02942437119781971,
0.03913809359073639,
0.049658652395009995,
-0.02516583912074566,
0.0644339993596077,
0.041175007820129395,
-0.05877992510795593,
0.01639084331691265,
-0.02289721928536892,
0.02623513527214527,
0.023361431434750557,
0.053511835634708405,
-0.019900793209671974,
-0.059093669056892395,
-0.0033425725996494293,
0.06900335103273392,
-0.03276820853352547,
-0.006393804680556059,
-0.04557400569319725,
0.04147258773446083,
0.0293408390134573,
-0.003091538557782769,
0.06647606194019318,
-0.010982801206409931,
-0.01562771387398243,
0.005993377882987261,
0.02551794983446598,
-0.019550800323486328,
-0.02482030913233757,
-0.0315377414226532,
0.02739008516073227,
-0.017849761992692947,
-0.001094601582735777,
-0.02976306341588497,
-0.026414399966597557,
-0.015870356932282448,
0.005977386608719826,
0.041819240897893906,
-0.0027261527720838785,
0.018504342064261436,
-0.019569098949432373,
0.05757627636194229,
0.02805129811167717,
0.05992042273283005,
-0.014779607765376568,
-0.011102975346148014,
0.03864004462957382,
0.027043789625167847,
-0.0030594156123697758,
0.032564274966716766,
-0.03650122880935669,
-0.02582606114447117,
0.04581792280077934,
0.015980105847120285,
-0.04149295389652252,
-0.02568020299077034,
0.015385624021291733,
-0.017156429588794708,
0.015953753143548965,
-0.057886265218257904,
0.008125836960971355,
0.01784258894622326,
0.018626399338245392,
-0.07838764786720276,
0.03650517016649246,
-0.0590100958943367,
-0.02459341287612915,
-0.05462302267551422,
0.017267916351556778,
0.029425926506519318,
0.022421108558773994,
0.020578889176249504,
-0.016115745529532433,
0.015620103105902672,
-0.035489290952682495,
0.03551739826798439,
0.05171791836619377,
-0.02983742021024227,
0.019857652485370636,
0.005852573085576296,
0.046336494386196136,
0.06835543364286423,
-0.04429721459746361,
0.05633839964866638,
0.0005458348314277828,
0.026493044570088387,
0.041891321539878845,
0.052223142236471176,
-0.015491139143705368,
-0.04749191552400589,
-0.020237503573298454,
0.021492019295692444,
0.011329296045005322,
-0.0025378838181495667,
0.02505241520702839,
-0.05862285941839218,
-0.017694571986794472,
0.0021435313392430544,
0.048886753618717194,
-0.008608113043010235,
0.018683765083551407,
-0.013769579119980335,
0.038206443190574646,
0.03213348984718323,
-0.03776993602514267,
-0.04121483862400055,
-0.02796456404030323,
-0.05660251900553703,
0.012922894209623337,
-0.03470515087246895,
-0.07137639820575714,
-0.03793599084019661,
-0.026553815230727196,
-0.01067587360739708,
0.09560002386569977,
-0.027773087844252586,
0.004505611024796963,
-0.016904976218938828,
0.011532459408044815,
0.06841889768838882,
0.024344688281416893,
0.017176948487758636,
-0.010937677696347237,
0.062170542776584625,
-0.015082360245287418,
0.033962346613407135,
0.03316947817802429,
-0.013176344335079193,
0.05081023648381233,
-0.03598345071077347,
-0.028051340952515602,
-0.0025004211347550154,
-0.08498143404722214,
-0.012032045982778072,
0.014500319957733154,
-0.0346902459859848,
-0.016753889620304108,
0.03167732059955597,
0.03694437816739082,
0.009762069210410118,
-0.04771452769637108,
0.021556390449404716,
0.03331403806805611,
-0.0008820450166240335,
-0.030320098623633385,
-0.02495805360376835,
-0.039249490946531296,
-0.009091822430491447,
-0.008799069561064243,
-0.08383523672819138,
0.04308397322893143,
-0.014317965134978294,
-0.01676095463335514,
0.03686649352312088,
-0.01936410367488861,
-0.03134407848119736,
0.0076507325284183025,
0.009850229136645794,
0.03661920130252838,
-0.027729621157050133,
0.046036913990974426,
-0.02931738644838333,
-0.024139991030097008,
-0.019840983673930168,
-0.016447143629193306,
-0.0066694957204163074,
-0.012578803114593029,
0.025958849117159843,
0.06952989846467972,
-0.03757698833942413,
0.025934340432286263,
0.07036798447370529,
0.034099794924259186,
-0.030949058011174202,
-0.0367492139339447,
0.057689934968948364,
0.007593344431370497,
-0.04753422364592552,
0.03909822180867195,
0.005029276013374329,
-0.04432857036590576,
-0.022691231220960617,
-0.03708261251449585,
0.012890944257378578,
0.020359396934509277,
-0.019147686660289764,
-0.012806432321667671,
-0.029722804203629494,
0.026589710265398026,
0.0284804105758667,
0.015941200777888298,
0.06726917624473572,
-0.01760566607117653,
0.008113573305308819,
0.04798721522092819,
-0.01148934569209814,
-0.056805744767189026,
0.00003158819527016021,
-0.051368363201618195,
-0.04113740101456642,
-0.02337433584034443,
-0.018837032839655876,
0.010739981196820736,
0.0014454037882387638,
0.05031716823577881,
-0.015719778835773468,
-0.008419685065746307,
0.06731858104467392,
-0.0314437560737133,
-0.04635924845933914,
0.003084928262978792,
0.1321125030517578,
-0.007564837113022804,
0.06038009002804756,
0.04260196536779404,
-0.028493188321590424,
0.012768318876624107,
0.013883385807275772,
0.05713951960206032,
-0.0233962070196867,
0.007584623526781797,
-0.010489402338862419,
0.0022830860689282417,
-0.003354873973876238,
-0.0028622064273804426,
-0.017363158985972404,
0.07224827259778976,
0.01681707613170147,
0.005795078817754984,
-0.0011111266212537885,
0.014541024342179298,
0.01898631826043129,
-0.0484129935503006,
0.041502274572849274,
0.04057317599654198,
0.008892513811588287,
0.04250490292906761,
0.012476014904677868,
-0.037855636328458786,
-0.015043016523122787,
0.02948720194399357,
-0.02098669856786728,
0.04734665900468826,
0.03480689227581024,
0.0033096664119511843,
0.030195308849215508,
-0.026578230783343315,
0.026024876162409782,
-0.01615959219634533,
0.1066427230834961,
-0.023767033591866493,
-0.040529947727918625,
0.026917217299342155,
-0.0005482520209625363,
0.06139480322599411,
0.041763726621866226,
-0.009736997075378895,
0.006319068372249603,
-0.0016999971121549606,
-0.05356920510530472,
-0.03592575713992119,
-0.034007079899311066,
-0.04292049631476402,
-0.0011320635676383972,
-0.023457996547222137,
-0.004705030471086502,
0.024280758574604988,
0.01441545132547617,
-0.029357464984059334,
-0.015364191494882107,
0.026436692103743553,
0.02700909972190857,
-0.020929036661982536,
0.057357195764780045,
0.05559827387332916,
-0.015525700524449348,
0.0821283683180809,
0.054493147879838943,
0.026006245985627174,
-0.013483528047800064,
0.005117903929203749,
0.010712283663451672,
0.03852999582886696,
0.03374014049768448,
-0.012125070206820965,
0.03874031826853752,
-0.03692864254117012,
-0.04412534087896347,
-0.04351430758833885,
-0.020236847922205925,
0.02619136869907379,
0.027894482016563416,
0.022523541003465652,
-0.004079368896782398,
-0.03160521015524864,
0.03315421938896179,
-0.025189200416207314,
0.024922851473093033,
0.05744963139295578,
-0.0033295995090156794,
0.04091993719339371,
0.021366309374570847,
-0.025228727608919144,
0.052739713340997696,
-0.0907796323299408,
0.006482381839305162,
-0.008830624632537365,
0.0022488522808998823,
0.024198273196816444,
-0.026209797710180283,
-0.005152630619704723,
0.014491981826722622,
-0.00985026452690363,
0.016778867691755295,
0.025412825867533684,
0.050144538283348083,
0.039182521402835846,
-0.0036691066343337297,
-0.05289221182465553,
-0.027171466499567032,
-0.02195088192820549,
0.029219936579465866,
-0.0401221364736557,
0.025130512192845345,
0.02047664485871792,
-0.0699954703450203,
-0.01616494730114937,
-0.02344866655766964,
0.013632508926093578,
-0.00542076863348484,
-0.042990729212760925,
-0.07666291296482086,
0.008592789992690086,
0.015176862478256226,
0.06848012655973434,
-0.03292609751224518,
0.02000923454761505,
0.03170200064778328,
-0.0054921554401516914,
0.07449114322662354,
-0.03259281814098358,
-0.005137618165463209,
-0.03975623473525047,
-0.05070842429995537,
-0.01877351850271225,
0.012673601508140564,
-0.01667153462767601,
-0.061840638518333435,
-0.008451573550701141,
-0.008701353333890438,
-0.007869248278439045,
-0.005465674214065075,
-0.055248696357011795,
0.008538146503269672,
0.026137905195355415,
0.00103943538852036,
0.0040905652567744255,
0.05095699802041054,
0.06425777822732925,
-0.05487335845828056,
0.03087771125137806,
-0.0011496631195768714,
0.06586404889822006,
0.1040681004524231,
0.10181883722543716,
-0.04035455733537674,
0.009210812859237194,
-0.03293062001466751,
-0.012636462226510048,
0.0010771239176392555,
0.00216105068102479,
-0.05741288885474205,
0.09777392446994781,
-0.0013370661763474345,
-0.042597297579050064,
-0.008895168080925941,
0.029518241062760353,
0.005725804250687361,
-0.016554182395339012,
0.042849551886320114,
-0.04020936042070389,
0.022067178040742874,
-0.018856152892112732,
-0.025352708995342255,
-0.0029240900184959173,
-0.013144676573574543,
-0.024363797158002853,
0.043641794472932816,
0.023415740579366684,
-0.00042781521915458143,
0.04878544434905052,
0.01901145838201046,
-0.058182958513498306,
-0.04283326864242554,
0.025769514963030815,
-0.07009351998567581,
-0.005788683425635099,
-0.007501689251512289,
0.02788878232240677,
-0.0297731701284647,
0.01639067567884922,
-0.01688171736896038,
-0.041026294231414795,
0.014795821160078049,
-0.00196667667478323,
0.025730136781930923,
0.006376386620104313,
-0.011055958457291126,
0.036998674273490906,
0.03403152897953987,
-0.0111214779317379,
0.03457513824105263,
-0.04995586723089218,
-0.0701349750161171,
0.02968829683959484,
0.017477301880717278,
-0.025098687037825584,
-0.04693511500954628,
-0.02209775149822235,
0.013154051266610622,
0.002073114737868309,
0.031587835401296616,
-0.0015718117356300354,
0.0499870628118515,
-0.017010563984513283,
-0.06946251541376114,
0.009129241108894348,
0.02545943669974804,
0.008081749081611633,
0.012209692038595676,
0.04886782914400101,
0.042905546724796295,
0.019609002396464348,
-0.0808572843670845,
0.004673654679208994,
-0.0028224021662026644,
-0.064985491335392,
0.0060287038795650005,
0.05780057609081268,
0.010180892422795296,
-0.02181234210729599,
0.047175563871860504,
-0.04896470159292221,
0.016086198389530182,
-0.034463413059711456,
-0.07452251017093658,
0.042479000985622406,
-0.06844006478786469,
0.04251169413328171,
-0.014588890597224236,
-0.0158732570707798,
-0.0036000993568450212,
0.031623151153326035,
-0.060026802122592926,
0.007118286564946175,
0.02260706201195717,
-0.024197716265916824,
0.00814033206552267,
-0.012844560667872429,
0.004466751124709845,
0.03921119496226311,
0.00867883674800396,
0.04005657508969307,
-0.02787196636199951,
-0.046793509274721146,
0.04433495178818703,
-0.027996769174933434,
-0.013869755901396275,
-0.00043816433753818274,
-0.03522823378443718,
0.03234212473034859,
-0.03994019329547882,
-0.035575591027736664,
-0.06193947046995163,
-0.025012722238898277,
-0.07347920536994934,
-0.037433937191963196,
-0.01789228245615959,
0.0066122314892709255,
0.04138263314962387,
0.022865140810608864,
0.010904825292527676,
0.00817883387207985,
-0.08970385789871216,
0.009190453216433525,
0.0012141424231231213,
0.05478399619460106,
0.018930690363049507,
-0.03977639973163605,
-0.03414385765790939,
-0.02201617695391178,
0.012270720675587654,
-0.01023506373167038,
-0.054439742118120193,
-0.0012481317389756441,
-0.026067882776260376,
-0.03293514996767044,
0.03028814308345318,
-0.049085766077041626,
-0.03813669830560684,
0.0001253209775313735,
-0.0014346097595989704,
-0.052946727722883224,
0.02566741779446602,
-0.034220922738313675,
-0.08158814907073975,
0.09900609403848648,
0.0014190498040989041,
0.04041001573204994,
0.008760441094636917,
0.0007756673730909824,
-0.002705167979001999,
-0.012664350681006908,
-0.03824569284915924,
0.0520377941429615,
0.008402375504374504,
-0.03152498975396156,
-0.09706345200538635,
-0.010161234065890312,
0.032534338533878326,
0.08718377351760864,
-0.008831064216792583,
0.01412610337138176,
0.01764005981385708,
-0.0007332367240451276,
0.026613665744662285,
0.009525565430521965,
0.05033483728766441,
-0.029793566092848778,
0.051619891077280045,
-0.002722226781770587,
-0.08925700187683105,
-0.049842674285173416,
-0.08452574908733368,
0.030634351074695587,
-0.008558536879718304,
0.04726645350456238,
-0.04481903836131096,
-0.005131264217197895,
0.0008659770246595144,
0.022466108202934265,
-0.04844692349433899,
-0.011589817702770233,
0.00758405402302742,
-0.03231127932667732,
-0.0834575966000557,
0.012271462008357048,
0.024788614362478256,
0.00149482989218086,
0.006034940481185913,
-0.05868719890713692,
-0.015141894109547138,
-0.05690193921327591,
0.016466446220874786,
0.036191534250974655,
0.019597485661506653,
0.008269507437944412,
0.012998572550714016,
0.06819991022348404,
0.027755359187722206,
-0.013338319025933743,
0.05222426727414131,
0.027921238914132118,
0.034850385040044785,
0.04023852199316025,
0.00013468098768498749,
-0.01725078374147415,
0.013801269233226776,
0.049201659858226776,
0.03318684175610542,
-0.024911440908908844,
0.05843118950724602,
0.05076000094413757,
0.0013821979518979788,
0.019173741340637207,
-0.04620957002043724,
0.0077428314834833145,
0.013984606601297855,
0.011061449535191059,
-0.0002469659666530788,
0.019327662885189056,
-0.006840039975941181,
0.0440300852060318,
-0.02154761366546154,
-0.006148338783532381,
-0.03207620605826378,
-0.04350418969988823,
0.0501602366566658,
0.04221756011247635,
-0.01338106207549572,
0.0028132188599556684,
-0.034505732357501984,
-0.0000927365108509548,
-0.011363564059138298,
-0.03448357433080673,
0.04260881617665291,
0.003206397406756878,
0.0032655554823577404,
0.05736733227968216,
-0.03667056933045387,
0.021797405555844307,
-0.013131584972143173,
0.03327174112200737,
-0.015107803978025913,
-0.007965401746332645,
-0.05484449863433838,
-0.02680942416191101,
-0.05606649070978165,
-0.014431229792535305,
0.016731558367609978,
0.02772759459912777,
-0.0799851045012474,
0.028732474893331528,
0.022253669798374176,
-0.06072593852877617,
0.023877723142504692,
0.0017670103115960956,
0.05521918833255768,
0.023386593908071518,
0.04718783125281334,
-0.06333442032337189,
0.0645761787891388,
-0.030671780928969383,
-0.0667395368218422,
-0.012927819043397903,
-0.013440119102597237,
-0.03314846009016037,
-0.0030789191368967295,
-0.03982119634747505,
-0.011232790537178516,
0.05441772937774658,
-0.011362653225660324,
0.01789131946861744,
0.002124972175806761,
0.009644451551139355,
-0.0385637991130352,
-0.06804092228412628,
-0.020769884809851646,
-0.01867205835878849,
-0.022560233250260353,
-0.05960967391729355,
-0.007654448505491018,
0.018847646191716194,
-0.044725656509399414,
0.005136766470968723,
-0.017804350703954697,
0.02635558508336544,
-0.020873144268989563,
-0.003468800103291869,
-0.03933178260922432,
-0.05321437120437622,
-0.017264505848288536,
-0.06655921787023544,
-0.011241721920669079,
-0.02603144384920597,
0.07586999982595444,
-0.027288366109132767,
-0.04667501896619797,
0.013536974787712097,
-0.025093073025345802,
0.005207302048802376,
-0.011810308322310448,
-0.02314174734055996,
0.002316283993422985,
-0.023055624216794968,
-0.010869797319173813,
0.01561500784009695,
-0.02364356815814972,
0.01823320984840393,
0.008613407611846924,
-0.0062531642615795135,
-0.01871991530060768,
0.03508252277970314,
-0.05109135061502457,
-0.04940303787589073,
0.0020660683512687683,
0.044597525149583817,
-0.017000073567032814,
-0.011259556747972965,
-0.026336845010519028,
0.03453810513019562,
0.0280322153121233,
0.002099027391523123,
-0.016569960862398148,
-0.019904352724552155,
0.0038680077996104956
] |
[
5.695504188537598,
2.9094462394714355
] |
Pattern Formation and Solitons
|
Nonlinear Sciences
|
nlin-PS
|
nlin-SI
|
na
|
2007-04-01T16:37:36
|
In a quantum mechanical model, Diosi, Feldmann and Kosloff arrived at a
conjecture stating that the limit of the entropy of certain mixtures is the
relative entropy as system size goes to infinity. The conjecture is proven in
this paper for density matrices. The first proof is analytic and uses the
quantum law of large numbers. The second one clarifies the relation to channel
capacity per unit cost for classical-quantum channels. Both proofs lead to
generalization of the conjecture.
|
A limit relation for entropy and channel capacity per unit cost
|
quant-ph cs.IT math.IT
|
0704.0046
| 2,007
|
[
-0.03436625376343727,
0.06496534496545792,
0.0012485869228839874,
-0.040033403784036636,
-0.00041972295730374753,
-0.019292747601866722,
0.010006747208535671,
0.03399144113063812,
-0.018924258649349213,
0.022676369175314903,
-0.039548374712467194,
0.029478564858436584,
0.032070863991975784,
-0.013072538189589977,
0.009176719933748245,
0.012953445315361023,
0.03090670332312584,
0.037890274077653885,
-0.003716269275173545,
-0.004548192489892244,
-0.05519748106598854,
-0.029027970507740974,
-0.03669311851263046,
-0.0427439883351326,
0.10050206631422043,
-0.019068531692028046,
0.04604687914252281,
-0.0009437297121621668,
-0.05484326183795929,
0.03236670047044754,
0.06710008531808853,
-0.002649327740073204,
-0.015960831195116043,
-0.08836914598941803,
-0.05225353315472603,
-0.07609164714813232,
0.0464080311357975,
-0.027829023078083992,
-0.006218324415385723,
0.022971607744693756,
0.06755048036575317,
-0.01851402223110199,
0.005502584856003523,
-0.054148007184267044,
-0.015558917075395584,
-0.009054703637957573,
0.017058726400136948,
0.015969011932611465,
0.035954054445028305,
-0.006587399635463953,
-0.011102907359600067,
0.04183352366089821,
-0.02044902928173542,
-0.0448310524225235,
0.009569402784109116,
0.04724463075399399,
0.019818024709820747,
-0.03731654956936836,
0.0504550077021122,
0.0317598395049572,
0.043398674577474594,
0.02496444061398506,
-0.04014474153518677,
0.0017351297428831458,
0.05479876697063446,
-0.05696366727352142,
0.0039392258040606976,
0.011435264721512794,
0.016507292166352272,
0.001300492906011641,
0.0448099821805954,
-0.060559872537851334,
0.026828840374946594,
0.0029698461294174194,
0.02902337722480297,
0.016613611951470375,
0.03379470854997635,
0.015662167221307755,
0.03808426484465599,
0.009406670928001404,
-0.018512453883886337,
-0.06066587194800377,
0.10023505985736847,
0.006377991754561663,
0.07810716331005096,
0.028889581561088562,
0.027630846947431564,
0.022440053522586823,
-0.022622624412178993,
0.09956931322813034,
-0.03533918783068657,
-0.03119298815727234,
0.020538516342639923,
0.06374993920326233,
-0.04789062216877937,
0.015198864974081516,
-0.015748733654618263,
0.016943464055657387,
-0.0012930496595799923,
-0.018708501011133194,
0.005117219407111406,
0.022266503423452377,
0.051696691662073135,
0.003575379028916359,
0.04663645848631859,
0.017553316429257393,
-0.025288766250014305,
-0.018590331077575684,
-0.029450923204421997,
0.002487697172909975,
-0.05880144611001015,
-0.03706370294094086,
0.0071150618605315685,
-0.010820399038493633,
-0.031224461272358894,
-0.01624833233654499,
0.101767897605896,
-0.05752858892083168,
-0.045183662325143814,
0.05530430004000664,
-0.02891649305820465,
0.013392269611358643,
-0.0036408468149602413,
0.059817247092723846,
-0.008568061515688896,
0.08463902026414871,
-0.001949612284079194,
0.017617570236325264,
0.025359896942973137,
-0.01899067498743534,
0.018706247210502625,
0.012201681733131409,
-0.041699688881635666,
-0.021015863865613937,
0.04194114729762077,
0.03630485013127327,
-0.05258473381400108,
-0.04331964999437332,
0.016309311613440514,
0.04002012684941292,
-0.023423491045832634,
-0.04317592829465866,
0.009424389339983463,
-0.005523658823221922,
-0.018189862370491028,
-0.05574570968747139,
0.0005757609033025801,
-0.020404929295182228,
-0.07716841995716095,
-0.019252393394708633,
0.021151915192604065,
0.03150852397084236,
-0.01439356617629528,
0.018103161826729774,
-0.01500120759010315,
-0.004089588299393654,
-0.006437869276851416,
-0.009040088392794132,
0.02399028278887272,
0.00999282393604517,
-0.03535675257444382,
0.03991031274199486,
-0.011893645860254765,
0.028645018115639687,
-0.0647764652967453,
0.003401070134714246,
0.017545826733112335,
0.013568473979830742,
-0.015990914776921272,
-0.0043365866877138615,
-0.03442458435893059,
-0.00878190342336893,
-0.05794708430767059,
-0.007247693836688995,
0.014627406373620033,
0.004189109895378351,
0.0020965805742889643,
-0.016232507303357124,
0.054082971066236496,
-0.004865013062953949,
0.027455918490886688,
-0.008498084731400013,
0.06599782407283783,
0.0468926839530468,
-0.007128531578928232,
0.03815353661775589,
0.018549052998423576,
-0.012297241948544979,
-0.04702121391892433,
-0.04630890116095543,
-0.013091297820210457,
0.04337545111775398,
-0.04561271145939827,
-0.036610715091228485,
0.005180034786462784,
-0.01567668281495571,
0.09294337779283524,
-0.04684757813811302,
0.008209075778722763,
-0.061371780931949615,
-0.025163227692246437,
-0.02284722588956356,
-0.016327157616615295,
0.004017512314021587,
0.0037362577859312296,
0.06648650765419006,
0.00003797541285166517,
0.03608130291104317,
0.024075383320450783,
-0.03392922878265381,
0.06030600517988205,
-0.02329854480922222,
-0.025555793195962906,
0.047730349004268646,
0.009592992253601551,
-0.03318081796169281,
0.01554717868566513,
-0.05742088705301285,
-0.002724142512306571,
0.036278627812862396,
0.017935577780008316,
-0.02166600152850151,
0.02889803797006607,
0.016518402844667435,
0.021288597956299782,
-0.02152579464018345,
-0.021037720143795013,
-0.032507747411727905,
-0.020529499277472496,
0.008871969766914845,
-0.03808598220348358,
-0.04880846291780472,
0.04053954780101776,
0.031521037220954895,
-0.027204478159546852,
0.04200955852866173,
-0.002417014678940177,
0.045994341373443604,
0.028830280527472496,
-0.005129133816808462,
0.04200838506221771,
0.006848334800451994,
0.0031538023613393307,
0.02840784564614296,
-0.08164209127426147,
-0.029566416516900063,
-0.03721390292048454,
-0.03219505399465561,
-0.010525207035243511,
0.026298796758055687,
-0.01378321461379528,
0.01083123404532671,
0.05998902767896652,
0.012900755740702152,
0.04442510008811951,
-0.010595893487334251,
-0.03517591580748558,
0.0414012111723423,
0.031737979501485825,
-0.061880145221948624,
0.020896462723612785,
-0.008349607698619366,
0.02296675369143486,
-0.038505468517541885,
-0.04817740619182587,
0.03576091676950455,
-0.022558584809303284,
-0.034724652767181396,
-0.004255351144820452,
0.009688285179436207,
0.042455077171325684,
0.06143612414598465,
0.03367400914430618,
0.04139068350195885,
-0.0017669341759756207,
0.009372839704155922,
0.043268054723739624,
-0.023422887548804283,
0.012526783160865307,
-0.03811999782919884,
-0.06473170965909958,
-0.016198383644223213,
-0.021388962864875793,
0.020091049373149872,
0.020687628537416458,
-0.00022592236928176135,
-0.01576237753033638,
0.04191717132925987,
0.06344027072191238,
0.036403048783540726,
-0.014671523123979568,
0.06071857362985611,
0.0369420051574707,
0.05682568997144699,
0.002087424509227276,
0.08413729816675186,
0.05271407589316368,
-0.019628111273050308,
0.0035815907176584005,
0.017189204692840576,
-0.013082515448331833,
0.008265555836260319,
-0.021352320909500122,
0.002475126413628459,
0.0741749033331871,
0.05880141258239746,
-0.014551944099366665,
0.03097260557115078,
0.021246518939733505,
0.013459889218211174,
-0.002023349516093731,
0.003998058382421732,
-0.015307674184441566,
-0.012486009858548641,
-0.03859260305762291,
0.018539411947131157,
0.0586978904902935,
0.01018645241856575,
0.06625295430421829,
-0.028079533949494362,
0.0635514184832573,
-0.0640321746468544,
0.019898327067494392,
-0.07038094103336334,
0.036755774170160294,
-0.004716101102530956,
-0.09182655066251755,
0.024101659655570984,
-0.028205618262290955,
-0.02159930393099785,
0.029619459062814713,
-0.007227624300867319,
-0.014987033791840076,
-0.03344827517867088,
-0.02425229921936989,
-0.014281084761023521,
-0.01787651889026165,
0.017314355820417404,
-0.014788825064897537,
0.021020520478487015,
-0.008672022260725498,
-0.014416306279599667,
-0.01013596449047327,
-0.03400827571749687,
-0.022600769996643066,
0.005224793683737516,
-0.06334206461906433,
0.026158416643738747,
0.036257531493902206,
0.0072447084821760654,
-0.06608694046735764,
-0.013587470166385174,
-0.00014248328807298094,
-0.006411666050553322,
-0.019828470423817635,
0.043475374579429626,
0.056883927434682846,
0.004767692182213068,
0.07911207526922226,
-0.03908863663673401,
0.05063945800065994,
-0.051637690514326096,
0.06633306294679642,
-0.026480523869395256,
0.022706715390086174,
0.02996082790195942,
0.012539551593363285,
0.006761912722140551,
-0.021649831905961037,
-0.02592974714934826,
-0.04398265853524208,
-0.06991834193468094,
-0.009351249784231186,
0.05126016214489937,
0.050249870866537094,
-0.04474171996116638,
-0.01910383813083172,
0.014157342724502087,
-0.03531097620725632,
0.009337135590612888,
0.05223851278424263,
0.01385437324643135,
0.004336962942034006,
0.0027438297402113676,
-0.005818829871714115,
0.0013295599492266774,
-0.02886578068137169,
-0.028996294364333153,
0.01540470588952303,
-0.0016915762098506093,
-0.012589874677360058,
-0.06470314413309097,
-0.00826193392276764,
0.005016947165131569,
-0.013907987624406815,
-0.014747199602425098,
0.06633716821670532,
0.008116789162158966,
0.027558816596865654,
0.04149014130234718,
-0.0024796449579298496,
-0.046112947165966034,
-0.012359820306301117,
0.013036098331212997,
0.01233618799597025,
-0.0030196229927241802,
-0.022848088294267654,
-0.01034096535295248,
0.028559565544128418,
-0.04669058695435524,
0.035006582736968994,
-0.006692912429571152,
-0.00032848777482286096,
-0.05942856892943382,
-0.009214812889695168,
0.015933938324451447,
-0.0067783547565341,
-0.05137260630726814,
0.03931724280118942,
0.0036785840056836605,
-0.0349382720887661,
0.017268981784582138,
-0.03647302836179733,
-0.03369266912341118,
0.02161046490073204,
-0.02272389829158783,
-0.004416060633957386,
0.03871850296854973,
0.018028073012828827,
-0.071870356798172,
0.010096649639308453,
0.0340597964823246,
-0.017414892092347145,
0.049296606332063675,
-0.03567719832062721,
0.017885997891426086,
0.013560442253947258,
-0.015615356154739857,
-0.011813068762421608,
0.019155675545334816,
0.028334928676486015,
-0.006938931066542864,
0.01996857300400734,
0.01702112704515457,
0.007457181345671415,
0.07359760254621506,
0.06406132131814957,
-0.01506330631673336,
-0.05731172859668732,
-0.037873730063438416,
0.03818582743406296,
-0.013678297400474548,
0.019631478935480118,
-0.05157935246825218,
0.040727026760578156,
-0.021034441888332367,
-0.027434945106506348,
0.033878859132528305,
0.04173457622528076,
0.03646521642804146,
0.01699461042881012,
0.04484067112207413,
-0.04372798651456833,
0.022179212421178818,
-0.006335586775094271,
-0.03681448847055435,
-0.02622680738568306,
0.052838291972875595,
-0.03189632669091225,
0.03546898439526558,
0.011953762732446194,
0.023444991558790207,
0.021361976861953735,
0.027351850643754005,
-0.02766961045563221,
-0.048671938478946686,
0.0024099687580019236,
-0.04102646932005882,
0.005032156128436327,
0.04613114520907402,
0.021497737616300583,
-0.01206231489777565,
-0.016754213720560074,
0.01664348691701889,
0.013795584440231323,
0.03995521366596222,
0.019729744642972946,
0.013252346776425838,
0.034382592886686325,
-0.01665620319545269,
0.02473500557243824,
0.03775893151760101,
0.016355395317077637,
0.062212683260440826,
-0.06860654056072235,
0.00042592055979184806,
0.029856106266379356,
-0.018736695870757103,
0.000682076730299741,
-0.016086779534816742,
0.01737895794212818,
0.00584501214325428,
-0.01780501753091812,
-0.00219742045737803,
-0.027685919776558876,
-0.02107083424925804,
-0.011429919861257076,
-0.05783183500170708,
-0.0161406472325325,
0.035336241126060486,
0.023187989369034767,
0.07313762605190277,
0.047755707055330276,
0.05276859179139137,
0.047723930329084396,
-0.006190649699419737,
-0.006898077670484781,
-0.0007253825315274298,
-0.08094103634357452,
-0.016106773167848587,
0.050772324204444885,
0.01680416241288185,
-0.003245355561375618,
-0.003753998316824436,
-0.09519975632429123,
-0.008045864291489124,
-0.04080650582909584,
-0.04817451164126396,
0.02099832333624363,
0.024838270619511604,
0.012311681173741817,
0.02767898328602314,
-0.0032528997398912907,
-0.045546773821115494,
-0.0051468415185809135,
0.006062887609004974,
-0.010647494345903397,
0.04433834180235863,
-0.020613232627511024,
0.045922163873910904,
0.013545907102525234,
-0.020250771194696426,
0.025899235159158707,
0.0511951819062233,
0.051840100437402725,
-0.052743855863809586,
-0.09404456615447998,
-0.04015059024095535,
-0.002768986625596881,
-0.04427570477128029,
-0.002235280117020011,
-0.033326655626297,
0.008591375313699245,
-0.06323129683732986,
0.05580882728099823,
-0.06483881920576096,
0.01998434215784073,
0.007041670847684145,
-0.027716955170035362,
0.08167293667793274,
0.04493772238492966,
0.00847867876291275,
0.021826330572366714,
-0.010870003141462803,
0.04860016331076622,
-0.12573330104351044,
-0.025734011083841324,
0.012960292398929596,
0.004419245291501284,
0.055410780012607574,
0.022368747740983963,
-0.013854005374014378,
0.014104127883911133,
0.0019925469532608986,
0.04688989743590355,
-0.03475431352853775,
0.005167946685105562,
-0.06162543222308159,
-0.0403393879532814,
-0.03865135833621025,
-0.0364576019346714,
-0.04772660881280899,
0.009954961948096752,
-0.018426835536956787,
-0.0341460183262825,
0.03468257561326027,
-0.026910901069641113,
-0.05413633584976196,
0.06991687417030334,
0.017411991953849792,
-0.027756957337260246,
-0.025982871651649475,
-0.022065419703722,
-0.044701363891363144,
-0.047214068472385406,
0.004230670165270567,
-0.02367875538766384,
-0.029322978109121323,
-0.039635248482227325,
-0.021546421572566032,
-0.001450435956940055,
0.016779035329818726,
0.06777985394001007,
-0.03394148871302605,
0.0458880178630352,
0.06708405166864395,
-0.026699248701334,
0.028902685269713402,
-0.062302183359861374,
0.011112912558019161,
-0.016152532771229744,
-0.019429560750722885,
0.022995805367827415,
-0.03150624781847,
0.04295233264565468,
-0.03852947801351547,
0.06866004317998886,
0.00164118898101151,
-0.02724599838256836,
-0.02888474240899086,
-0.00003533334893290885,
-0.017239190638065338,
-0.010947700589895248,
-0.07828007638454437,
0.024934465065598488,
0.027184652164578438,
0.009236607700586319,
-0.04864341765642166,
0.04061531648039818,
0.08003599941730499,
0.03586353361606598,
-0.049219463020563126,
-0.04090338200330734,
-0.024979952722787857,
0.005738277453929186,
-0.013210201635956764,
-0.056535754352808,
-0.021984096616506577,
0.04776637628674507,
0.08823757618665695,
0.048734553158283234,
-0.0636485144495964,
-0.019419554620981216,
0.020295022055506706,
0.058582041412591934,
0.01230555772781372,
0.011980999261140823,
-0.02362196333706379,
-0.01286920253187418,
-0.013368364423513412,
0.05343713238835335,
0.08186342567205429,
-0.03642648085951805,
0.040252696722745895,
-0.045693326741456985,
0.02452189475297928,
0.04693225771188736,
-0.015212081372737885,
0.012111897580325603,
-0.03534744307398796,
0.006022310815751553,
0.0046612280420959,
0.03959912061691284,
0.003225760767236352,
0.019677532836794853,
-0.023905791342258453,
-0.0030608149245381355,
-0.05495409294962883,
-0.03951406851410866,
-0.0554177351295948,
-0.022477056831121445,
-0.019823690876364708,
-0.047600749880075455,
-0.05188240483403206,
-0.058908674865961075,
-0.0141049325466156,
0.017737921327352524,
0.024788983166217804,
-0.016167273744940758,
-0.017219481989741325,
0.015064632520079613,
-0.006623419467359781,
0.01668684557080269,
-0.011557359248399734,
-0.037934448570013046,
0.016548385843634605,
-0.01712471805512905,
-0.059905488044023514,
-0.020080773159861565,
-0.016770707443356514,
0.03607136011123657,
0.005044804885983467,
0.0008452965412288904,
-0.03593773767352104,
-0.005688766948878765,
0.07438945770263672,
-0.005376046057790518,
0.023537298664450645,
0.023305637761950493,
0.05408652499318123,
-0.011921210214495659,
0.022447310388088226,
-0.02388245053589344,
0.04181508719921112,
0.004219412337988615,
0.014018252491950989,
0.02917492389678955,
0.04711780697107315,
-0.005599053110927343,
-0.010349228046834469,
-0.024829523637890816,
-0.02341654896736145,
0.017598798498511314,
0.023175308480858803,
0.03922693803906441,
-0.018069151788949966,
-0.037147484719753265,
-0.04606146365404129,
-0.0029833537992089987,
-0.05997081100940704,
0.04766864329576492,
-0.03396714851260185,
-0.10689219832420349,
-0.006274519022554159,
-0.0662335604429245,
-0.061712346971035004,
-0.002783062169328332,
-0.03618815913796425,
0.025305544957518578,
-0.00004874200021731667,
-0.014692580327391624,
-0.011955919675529003,
-0.059637196362018585,
-0.03027864545583725,
-0.05850977823138237,
0.0022444468922913074,
-0.020968981087207794,
0.023978909477591515,
-0.04600691795349121,
0.00846728216856718,
-0.022914918139576912,
-0.06294216215610504,
0.022526942193508148,
0.020593857392668724,
-0.000914214993827045,
-0.07014109194278717,
-0.07170836627483368,
-0.002565693110227585,
0.0411907322704792,
0.005348258651793003,
-0.04066133499145508,
-0.042236823588609695,
-0.009652522392570972,
0.008614080026745796,
0.04899859428405762,
0.008482730947434902,
0.0319262370467186,
0.04001004621386528,
0.015986239537596703,
-0.027331864461302757,
0.05259987339377403,
-0.0198111142963171,
0.032885678112506866,
0.04422016814351082,
0.007790267001837492,
0.016285059973597527,
-0.022320743650197983,
0.010457877069711685
] |
[
6.335170269012451,
0.9260620474815369
] |
Quantum Physics
|
General Physics
|
quant-ph
|
math-IT
|
na
|
2007-04-01T13:06:50
|
The intelligent acoustic emission locator is described in Part I, while Part
II discusses blind source separation, time delay estimation and location of two
simultaneously active continuous acoustic emission sources.
The location of acoustic emission on complicated aircraft frame structures is
a difficult problem of non-destructive testing. This article describes an
intelligent acoustic emission source locator. The intelligent locator comprises
a sensor antenna and a general regression neural network, which solves the
location problem based on learning from examples. Locator performance was
tested on different test specimens. Tests have shown that the accuracy of
location depends on sound velocity and attenuation in the specimen, the
dimensions of the tested area, and the properties of stored data. The location
accuracy achieved by the intelligent locator is comparable to that obtained by
the conventional triangulation method, while the applicability of the
intelligent locator is more general since analysis of sonic ray paths is
avoided. This is a promising method for non-destructive testing of aircraft
frame structures by the acoustic emission method.
|
Intelligent location of simultaneously active acoustic emission sources:
Part I
|
cs.NE cs.AI
|
0704.0047
| 2,007
|
[
0.049774497747421265,
-0.011572875082492828,
-0.015367635525763035,
-0.05618061497807503,
0.01494630891829729,
-0.015416530892252922,
0.02823377400636673,
0.03323302045464516,
-0.06783153861761093,
-0.0019341273000463843,
-0.06017422303557396,
0.03209426999092102,
0.0026028892025351524,
0.00010847899102373049,
0.017371810972690582,
-0.06914697587490082,
0.006220846902579069,
0.009516318328678608,
-0.00772471446543932,
-0.0025283589493483305,
-0.001803334685973823,
-0.02420949563384056,
-0.006369021255522966,
-0.0355507992208004,
0.09102319926023483,
-0.020919401198625565,
-0.015032545663416386,
0.006162950303405523,
-0.05025598034262657,
-0.030459577217698097,
0.025087401270866394,
-0.1139402762055397,
0.017480140551924706,
0.012146282941102982,
-0.05906142666935921,
-0.017427315935492516,
0.04937717318534851,
-0.013665121980011463,
0.005322916433215141,
0.076438769698143,
0.04116329550743103,
-0.043150197714567184,
0.005872238427400589,
-0.004448061343282461,
0.05771798640489578,
0.021167343482375145,
0.017533624544739723,
-0.031522322446107864,
0.062443528324365616,
-0.0213233083486557,
-0.006901048123836517,
0.010157863609492779,
-0.009097451344132423,
0.0033985129557549953,
0.0301457978785038,
-0.01523634698241949,
-0.03700423613190651,
-0.012537730857729912,
0.03715424984693527,
-0.03351464867591858,
0.012755874544382095,
0.07601410895586014,
-0.0703517496585846,
0.021603984758257866,
0.009644804522395134,
-0.04972154274582863,
-0.030684279277920723,
-0.00800376571714878,
-0.031352657824754715,
-0.02360566519200802,
0.036904651671648026,
-0.012617086991667747,
0.03319714963436127,
0.00040223522228188813,
-0.033157672733068466,
0.0034439910668879747,
0.014466429129242897,
-0.001719101332128048,
-0.022582918405532837,
0.0813412293791771,
0.034638598561286926,
-0.021740460768342018,
0.024105481803417206,
-0.012240627780556679,
0.04276749864220619,
0.02041354961693287,
-0.003915091976523399,
0.030276350677013397,
0.005614016205072403,
0.03203268721699715,
0.014223632402718067,
0.05423785373568535,
0.049791183322668076,
0.05524016544222832,
-0.0060068233869969845,
0.046125441789627075,
-0.08090314269065857,
0.05747080594301224,
-0.001831113826483488,
-0.00794228259474039,
-0.002046670066192746,
0.01208498701453209,
-0.03602388873696327,
0.04192788898944855,
0.038710299879312515,
-0.029132211580872536,
0.009281781502068043,
-0.023361166939139366,
-0.027654150500893593,
-0.010196514427661896,
-0.04554622247815132,
-0.03799229487776756,
0.052782125771045685,
0.011773135513067245,
-0.06412062048912048,
-0.042991913855075836,
0.03645707294344902,
-0.07307660579681396,
0.000752078543882817,
0.05642601102590561,
0.011894232593476772,
-0.025828678160905838,
0.033403970301151276,
-0.024331772699952126,
0.020931368693709373,
-0.0025013056583702564,
-0.057443615049123764,
0.000830314529594034,
-0.008422674611210823,
0.011376063339412212,
-0.0026115754153579473,
0.012123508378863335,
0.015681881457567215,
0.010637898929417133,
0.05115196481347084,
0.04125441238284111,
0.01117638312280178,
-0.09386948496103287,
0.0361051931977272,
0.022678423672914505,
0.05379195511341095,
-0.004973721224814653,
0.04445050284266472,
-0.04273043945431709,
0.049080248922109604,
-0.04631052911281586,
-0.00032781774643808603,
-0.05178500711917877,
-0.023173989728093147,
-0.019709991291165352,
0.020726408809423447,
-0.002124857623130083,
0.01025827694684267,
-0.007005216088145971,
-0.01852293312549591,
-0.03266064450144768,
-0.020222986117005348,
0.004628281574696302,
0.048933401703834534,
-0.00017243195907212794,
-0.045194245874881744,
0.020672617480158806,
-0.007892352528870106,
0.06251391023397446,
-0.013331430964171886,
0.026368368417024612,
-0.011916612274944782,
0.013705412857234478,
0.05992730334401131,
0.040853701531887054,
-0.03424307703971863,
0.011850373819470406,
0.01168761309236288,
-0.02655913308262825,
0.047575026750564575,
-0.02202632464468479,
0.03638613224029541,
-0.04624819755554199,
0.00996700581163168,
-0.015112279914319515,
0.04735470563173294,
-0.025676602497696877,
-0.006459907162934542,
0.03489307686686516,
-0.011879146099090576,
0.00043750955956056714,
-0.012307251803576946,
-0.08025187999010086,
-0.013425336219370365,
-0.029223764315247536,
0.01222429983317852,
-0.039863716810941696,
-0.056457072496414185,
-0.040178265422582626,
-0.06717318296432495,
-0.013543345034122467,
0.049272388219833374,
-0.02379215694963932,
0.057009387761354446,
0.022371670231223106,
-0.03536839783191681,
-0.019604414701461792,
-0.016212834045290947,
0.0019847648218274117,
-0.025242691859602928,
0.014345469884574413,
0.04326261952519417,
-0.030216306447982788,
-0.01707187481224537,
0.022690368816256523,
0.044921983033418655,
0.04000464826822281,
0.02900782972574234,
0.03385363519191742,
-0.01755484566092491,
0.002086726250126958,
0.01200067438185215,
-0.04094027727842331,
0.010377389378845692,
-0.01194771472364664,
0.047655001282691956,
-0.0059505063109099865,
0.051975008100271225,
-0.04184465855360031,
0.04544612765312195,
0.03305304795503616,
-0.01480206847190857,
-0.014676010236144066,
-0.046197470277547836,
-0.0294489748775959,
-0.03427565470337868,
-0.06508418917655945,
0.07135358452796936,
-0.0042561753652989864,
0.056959785521030426,
-0.010555438697338104,
0.01368663553148508,
0.030892817303538322,
0.016625475138425827,
0.08133850246667862,
0.013337853364646435,
-0.00759731512516737,
-0.017176968976855278,
-0.0279835294932127,
-0.07857375591993332,
-0.031201161444187164,
-0.01376723125576973,
-0.04728458449244499,
-0.02073345147073269,
0.0263520535081625,
0.0047624059952795506,
0.03435101732611656,
0.0033223130740225315,
0.012821638025343418,
0.03503523766994476,
-0.033512067049741745,
-0.033504750579595566,
0.04960116371512413,
-0.02465095743536949,
-0.06541921198368073,
0.017912544310092926,
-0.055964212864637375,
0.03405552729964256,
-0.040614452213048935,
-0.03092755749821663,
0.014607371762394905,
0.0268393661826849,
-0.030387232080101967,
-0.030817102640867233,
-0.059794653207063675,
-0.020489275455474854,
-0.010005377233028412,
0.0729948878288269,
0.03202067315578461,
0.018489263951778412,
0.07755569368600845,
0.029383469372987747,
0.005746068898588419,
-0.014073719270527363,
0.010262192226946354,
-0.05751902982592583,
-0.0075202942825853825,
-0.043165143579244614,
-0.07610582560300827,
0.015965161845088005,
0.02085854858160019,
0.03337250277400017,
0.000755728455260396,
0.05054818093776703,
-0.013468199409544468,
-0.005059097893536091,
-0.01339784823358059,
0.009779254905879498,
0.024883663281798363,
-0.05713537707924843,
0.049433182924985886,
0.037468187510967255,
-0.012459516525268555,
0.027026858180761337,
-0.023237118497490883,
0.0320880301296711,
0.029747381806373596,
0.026162520051002502,
-0.030345140025019646,
0.02105998620390892,
-0.02271283231675625,
-0.014702076092362404,
-0.021341869607567787,
0.0380559079349041,
0.025754109025001526,
-0.04593732953071594,
0.004443506710231304,
0.04182891547679901,
-0.0043098209425807,
0.017022335901856422,
0.0213111974298954,
0.011143587529659271,
0.001337079331278801,
0.09773944318294525,
0.07971891015768051,
0.012060451321303844,
-0.0030265364330261946,
-0.0003416451800148934,
-0.035801783204078674,
0.026215344667434692,
0.05096271634101868,
0.0678723081946373,
0.028442395851016045,
-0.04277762770652771,
-0.015807542949914932,
0.016479933634400368,
0.0649944543838501,
-0.0481867790222168,
-0.012394679710268974,
-0.010835603810846806,
-0.01377391628921032,
0.030868491157889366,
0.07204950600862503,
-0.03725278377532959,
0.03479889780282974,
0.07770133018493652,
0.010470091365277767,
-0.00852241925895214,
-0.047680314630270004,
-0.07203907519578934,
-0.011753244325518608,
-0.009757990948855877,
0.005116249900311232,
-0.0015283467946574092,
-0.014932838268578053,
-0.04199930280447006,
-0.0035073854960501194,
0.008713035844266415,
0.0089749526232481,
-0.03309844806790352,
0.022662635892629623,
0.047936584800481796,
-0.013188048265874386,
0.06229158118367195,
0.04407485947012901,
0.022364264354109764,
-0.011866522021591663,
0.061995357275009155,
-0.007190810516476631,
0.0034514996223151684,
-0.01700982078909874,
0.041376467794179916,
0.002260238630697131,
0.016471531242132187,
-0.03404795005917549,
0.0051361010409891605,
-0.020217329263687134,
-0.034899212419986725,
0.038655251264572144,
-0.018529025837779045,
-0.0073278299532830715,
-0.07896745204925537,
-0.0062519703060388565,
-0.011651123873889446,
0.018741467967629433,
-0.005287287291139364,
-0.005519954487681389,
0.0395670048892498,
0.0013550823787227273,
0.05255992338061333,
-0.009880661964416504,
-0.025655193254351616,
-0.025465484708547592,
0.002049730159342289,
-0.07717619091272354,
-0.015246492810547352,
-0.03762045130133629,
-0.11253379285335541,
-0.012280752882361412,
-0.010090494528412819,
-0.029645325616002083,
0.039590198546648026,
0.007217888720333576,
0.002309649484232068,
0.02131880261003971,
-0.0075844042003154755,
-0.03679788112640381,
0.004380036145448685,
0.011717348359525204,
-0.04536442086100578,
0.025256630033254623,
0.011366404592990875,
-0.015812845900654793,
0.025903820991516113,
-0.002204975113272667,
-0.026840006932616234,
0.022186212241649628,
-0.0317414253950119,
-0.058294642716646194,
0.045655690133571625,
-0.03732677921652794,
0.06969475001096725,
0.03143749758601189,
-0.010702728293836117,
-0.010675905272364616,
-0.0009049887303262949,
0.06458912044763565,
0.017409387975931168,
-0.03654974699020386,
-0.020231034606695175,
-0.008316637016832829,
0.010662400163710117,
0.012779127806425095,
0.011741526424884796,
-0.06174865737557411,
0.019662484526634216,
-0.05878311023116112,
0.0458059124648571,
0.02711312286555767,
-0.04706437885761261,
0.07181431353092194,
0.04988829046487808,
-0.0007405128562822938,
0.05958353728055954,
-0.014461331069469452,
-0.014343583025038242,
-0.03407419100403786,
0.008798819966614246,
-0.01009279489517212,
0.01795705035328865,
0.0862744078040123,
0.04251307249069214,
-0.03345736116170883,
-0.0337083674967289,
0.03467971831560135,
0.025026485323905945,
-0.006167672574520111,
-0.04304663464426994,
0.018902895972132683,
0.07667891681194305,
-0.012217145413160324,
0.014028494246304035,
-0.01240143645554781,
0.11744043231010437,
0.024876559153199196,
0.020032690837979317,
0.05480613932013512,
-0.07782912999391556,
0.00010204598220298067,
-0.007276901975274086,
-0.0025145888794213533,
-0.0151428347453475,
-0.02775990590453148,
-0.018030090257525444,
0.04504993557929993,
-0.023877795785665512,
0.005271900910884142,
-0.0034128043334931135,
0.053038690239191055,
-0.011816425248980522,
-0.015701262280344963,
0.03919127956032753,
-0.01944076456129551,
-0.015203068032860756,
0.040072523057460785,
0.022153569385409355,
-0.04161277040839195,
-0.042997341603040695,
-0.03088895045220852,
-0.014197622425854206,
-0.01712225377559662,
-0.028625430539250374,
0.000572021643165499,
-0.011718853376805782,
-0.008074549026787281,
0.049417972564697266,
0.00747675122693181,
-0.027877511456608772,
-0.03633784130215645,
-0.040540967136621475,
-0.053389158099889755,
-0.048908207565546036,
0.021203581243753433,
-0.018844030797481537,
-0.02942996844649315,
-0.008424082770943642,
0.001637171139009297,
0.002244421513751149,
0.008763146586716175,
-0.036766551434993744,
0.015501989983022213,
0.026212451979517937,
-0.07276562601327896,
-0.04834877699613571,
0.0305025577545166,
0.01031506061553955,
0.053959254175424576,
-0.016130762174725533,
0.015146450139582157,
-0.002376060700044036,
-0.07196830958127975,
0.07030382752418518,
0.06677866727113724,
-0.0937240719795227,
0.03467123955488205,
0.04879136383533478,
0.0719926580786705,
0.0016200601821765304,
0.03245164081454277,
-0.0734533816576004,
0.01769578829407692,
-0.06356026232242584,
-0.0632614940404892,
0.07389268279075623,
-0.026033475995063782,
-0.0041066608391702175,
0.028849849477410316,
-0.01141009759157896,
-0.0010454099392518401,
-0.003149312222376466,
0.010328500531613827,
-0.01029029581695795,
-0.04337894171476364,
0.02086479961872101,
-0.01182989589869976,
0.021879009902477264,
0.0060494099743664265,
0.028974926099181175,
-0.018560945987701416,
0.01635374315083027,
-0.06080782413482666,
-0.028328850865364075,
0.01412276178598404,
0.00018307277059648186,
-0.05845656618475914,
0.044336847960948944,
-0.009218077175319195,
0.061908263713121414,
-0.06616755574941635,
0.03477880358695984,
-0.04591067507863045,
-0.046141453087329865,
-0.016300810500979424,
0.004682712722569704,
-0.04605013132095337,
0.008063280023634434,
0.019886095076799393,
0.014507868327200413,
0.03336840495467186,
0.021514395251870155,
-0.05586373805999756,
-0.027307217940688133,
0.039951398968696594,
0.04439058154821396,
0.029869887977838516,
0.013157953508198261,
-0.024281669408082962,
-0.031374722719192505,
0.041012365370988846,
0.03948028013110161,
-0.003348262282088399,
0.04011160135269165,
0.01734222285449505,
-0.03371981531381607,
0.014101146720349789,
-0.01233613584190607,
-0.022083783522248268,
0.012487219646573067,
-0.021021397784352303,
-0.006241618189960718,
0.025425460189580917,
-0.012171902693808079,
-0.019002703949809074,
0.05250187963247299,
-0.014595163986086845,
0.002072108443826437,
-0.07315374910831451,
0.004107646644115448,
-0.06563246250152588,
-0.07820336520671844,
-0.04680313169956207,
0.048791322857141495,
0.013597420416772366,
-0.012881691567599773,
-0.04558117687702179,
-0.008733449503779411,
0.00608198344707489,
0.08356737345457077,
-0.04073483124375343,
0.01361891906708479,
0.05683913826942444,
0.02516460046172142,
0.0484687015414238,
0.006723642814904451,
-0.04842788353562355,
-0.03500623255968094,
-0.0038775564171373844,
-0.03646063432097435,
-0.02283252216875553,
0.02204536646604538,
-0.02832494117319584,
0.07668859511613846,
-0.05877313017845154,
0.04734732210636139,
-0.03385506197810173,
0.06185755878686905,
-0.018090393394231796,
-0.006843349896371365,
-0.01244133897125721,
-0.004240986425429583,
0.006111036520451307,
-0.030987096950411797,
-0.05482449382543564,
0.019470591098070145,
0.04969475790858269,
0.009531494230031967,
0.010086520574986935,
0.01748448796570301,
-0.04952000454068184,
-0.06518682837486267,
0.011280332691967487,
0.0029200841672718525,
0.021014777943491936,
0.03439762443304062,
0.06193499267101288,
0.006931392941623926,
0.03335651010274887,
-0.0042947460897266865,
0.04444512724876404,
0.02732231840491295,
0.0030168716330081224,
0.0023850055877119303,
0.018402917310595512,
-0.01948411762714386,
-0.007513588760048151,
-0.002333043608814478,
-0.003567202016711235,
-0.020109664648771286,
0.03361625596880913,
0.021596379578113556,
0.026649150997400284,
-0.010175483301281929,
-0.01622171513736248,
-0.020679127424955368,
0.003528689034283161,
-0.02295108698308468,
-0.05343923345208168,
-0.027342557907104492,
0.01180711854249239,
-0.013207501731812954,
-0.061765216290950775,
-0.02804490551352501,
-0.0702238604426384,
-0.029700763523578644,
-0.012941934168338776,
0.015948960557579994,
-0.009111410938203335,
-0.03541009500622749,
-0.03246768191456795,
-0.05829395353794098,
0.05098789557814598,
-0.016041887924075127,
0.008016839623451233,
-0.004461564123630524,
-0.019765907898545265,
0.014823839999735355,
0.02453353814780712,
-0.006324112880975008,
-0.06128391623497009,
0.041207730770111084,
-0.016226360574364662,
-0.02839401178061962,
-0.007330363616347313,
-0.013835446909070015,
-0.07771256566047668,
0.0015566484071314335,
0.010079281404614449,
0.010065577924251556,
-0.0854879766702652,
0.005525125190615654,
-0.028711462393403053,
-0.008468793705105782,
-0.005391341168433428,
0.003056248649954796,
0.03539692610502243,
-0.00044228151091374457,
0.056989703327417374,
0.0163226630538702,
0.08133400231599808,
-0.023909511044621468,
-0.04201178252696991,
0.04052402824163437,
0.05076884850859642,
-0.0024977740831673145,
0.014471031725406647,
-0.023136502131819725,
0.032243940979242325,
0.04625767841935158,
0.0567595437169075,
-0.09214602410793304,
-0.010594576597213745,
0.023779621347784996,
0.013134032487869263,
-0.02037118561565876,
-0.04205819219350815,
0.012493823654949665,
0.0059286137111485004,
-0.07539434731006622,
0.042089659720659256,
0.016614725813269615,
-0.03586093708872795,
0.05644475668668747,
0.016988804563879967,
0.06910772621631622,
0.0015945648774504662,
0.008486333303153515,
0.026176733896136284,
-0.03330317139625549,
-0.0227791890501976,
-0.010797517374157906,
-0.02215336076915264,
0.0031268924940377474,
0.003922684118151665,
-0.05477343872189522,
0.01607060246169567,
0.005175981670618057,
-0.032039251178503036,
0.00831521488726139,
-0.01197228766977787,
-0.02162998728454113,
-0.0552988164126873,
-0.03074079565703869,
0.04503006488084793,
0.0431319922208786,
-0.04926958680152893,
-0.025442352518439293,
0.010758810676634312,
0.014381533488631248,
-0.004707249812781811,
-0.006380725651979446,
0.06296046078205109,
-0.023904671892523766,
0.04221680387854576,
0.11422453820705414,
-0.016496147960424423,
0.0066812774166464806,
-0.00008683920896146446,
0.019171636551618576,
0.02633950486779213,
-0.004800770897418261,
-0.0045557329431176186,
0.005499871913343668,
0.0032347445376217365
] |
[
3.5580222606658936,
12.671149253845215
] |
Neural and Evolutionary Computing
|
Computer Science
|
cs-NE
|
cs-AI
|
na
|
2007-03-31T19:17:47
|
We report on the analysis of selected single source data sets from the first
round of the Mock LISA Data Challenges (MLDC) for white dwarf binaries. We
implemented an end-to-end pipeline consisting of a grid-based coherent
pre-processing unit for signal detection, and an automatic Markov Chain Monte
Carlo post-processing unit for signal evaluation. We demonstrate that signal
detection with our coherent approach is secure and accurate, and is increased
in accuracy and supplemented with additional information on the signal
parameters by our Markov Chain Monte Carlo approach. We also demonstrate that
the Markov Chain Monte Carlo routine is additionally able to determine
accurately the noise level in the frequency window of interest.
|
Inference on white dwarf binary systems using the first round Mock LISA
Data Challenges data sets
|
gr-qc astro-ph
|
0704.0048
| 2,007
|
[
-0.048761073499917984,
0.014464739710092545,
-0.010868516750633717,
-0.07977867871522903,
0.018660936504602432,
-0.02942308969795704,
0.04162346199154854,
-0.0008027677540667355,
-0.058831095695495605,
-0.01074284128844738,
-0.08013909310102463,
0.09039144217967987,
0.03136426955461502,
0.03714499995112419,
-0.013662644661962986,
-0.01713389903306961,
0.050137367099523544,
-0.02323003299534321,
-0.0021477099508047104,
0.0037980887573212385,
0.004719960503280163,
0.006765672005712986,
-0.04974841699004173,
-0.03393622487783432,
0.0947740226984024,
-0.00007809336966602132,
0.019602810963988304,
0.041156962513923645,
-0.07413279265165329,
0.054926689714193344,
0.05658045783638954,
-0.03035176917910576,
0.0368536151945591,
-0.02458438277244568,
-0.022401941940188408,
0.0015394518850371242,
0.0041305869817733765,
-0.05669105798006058,
-0.001353878527879715,
0.04845674708485603,
0.026828652247786522,
-0.007369984872639179,
0.01030715648084879,
-0.0051093390211462975,
-0.0022716280072927475,
-0.0029711746610701084,
0.01131381094455719,
-0.025066865608096123,
0.03911445662379265,
0.02631356380879879,
0.009324958547949791,
0.045806195586919785,
0.03853405639529228,
0.03470959514379501,
0.011248263530433178,
0.0433352068066597,
0.001862633042037487,
-0.02742687612771988,
0.05920526385307312,
-0.023424295708537102,
0.011595798656344414,
0.04729840159416199,
-0.09945370256900787,
-0.013140903785824776,
-0.022568339481949806,
-0.0664399266242981,
-0.04409584030508995,
-0.005075498484075069,
0.008573089726269245,
-0.02314813621342182,
0.05732497572898865,
-0.0135307302698493,
0.017639346420764923,
0.008231902495026588,
0.0011841215891763568,
0.0204884372651577,
0.01931126043200493,
-0.03615117073059082,
0.000732686254195869,
0.010937288403511047,
0.012338679283857346,
-0.045105479657649994,
0.025369970127940178,
0.03609754890203476,
0.03761115297675133,
0.01598742976784706,
0.0005377060733735561,
0.03624388203024864,
-0.04170158877968788,
0.0779702290892601,
-0.00898792315274477,
0.027764184400439262,
0.008200052194297314,
0.05527520924806595,
-0.021664904430508614,
0.005141363479197025,
-0.0794743224978447,
0.04752155765891075,
-0.0068175713531672955,
-0.007519529666751623,
-0.010861024260520935,
0.07012790441513062,
-0.023765545338392258,
0.013784839771687984,
0.008356696926057339,
0.010897345840930939,
-0.002023617969825864,
-0.020384764298796654,
0.00123842793982476,
-0.02281082235276699,
-0.09044934809207916,
-0.00808112695813179,
0.035350069403648376,
0.0008585339528508484,
-0.018858464434742928,
0.003656929126009345,
0.07239874452352524,
-0.07293182611465454,
-0.02595391497015953,
0.04692566394805908,
0.0046774293296039104,
-0.04181396961212158,
-0.04159931838512421,
0.02714718133211136,
0.00041709738434292376,
0.028820691630244255,
-0.06615784019231796,
-0.003134162398055196,
0.01514302846044302,
-0.0032019480131566525,
-0.017836961895227432,
0.0019089620327576995,
-0.04300834983587265,
0.03471917286515236,
0.04853205755352974,
0.0789135992527008,
-0.005592763423919678,
-0.03192288801074028,
0.01880922168493271,
-0.02549125626683235,
-0.03059443272650242,
0.02791527844965458,
-0.01996421441435814,
-0.03450344502925873,
0.05225561186671257,
-0.0339837484061718,
-0.01703748106956482,
-0.027770958840847015,
-0.03387393802404404,
0.004660538863390684,
0.011230106465518475,
0.06617304682731628,
0.04315250739455223,
0.033648956567049026,
-0.020107097923755646,
-0.05339280143380165,
-0.022227654233574867,
0.030239613726735115,
-0.02810528315603733,
0.009603059850633144,
-0.00928505789488554,
0.0009040969889611006,
0.0037062333431094885,
0.044133927673101425,
-0.0004856634477619082,
0.003770741168409586,
0.03135077655315399,
0.0376286506652832,
0.04302462190389633,
0.062364235520362854,
-0.02898339554667473,
-0.07041716575622559,
-0.0021617345046252012,
-0.01736392080783844,
0.004576905630528927,
0.018318092450499535,
0.012490326538681984,
-0.05725511536002159,
0.044444214552640915,
0.027155594900250435,
0.06902417540550232,
-0.019811013713479042,
0.030499864369630814,
0.03787664696574211,
-0.02533343993127346,
-0.026192782446742058,
-0.01969827152788639,
-0.025711987167596817,
0.0294721107929945,
0.008791573345661163,
-0.0027824726421386003,
-0.014963178895413876,
-0.0744280144572258,
-0.055975113064050674,
0.027526356279850006,
-0.04295925050973892,
0.044612519443035126,
-0.07305196672677994,
0.009677356109023094,
-0.02120528742671013,
-0.005276401527225971,
0.0017412719316780567,
-0.06780554354190826,
0.050488829612731934,
-0.02650654874742031,
0.03278065472841263,
0.029186038300395012,
-0.010494819842278957,
0.029331272467970848,
0.0465095192193985,
0.03193957358598709,
0.0072023081593215466,
0.009943167679011822,
0.026534708216786385,
0.026450440287590027,
0.00905770342797041,
-0.00918603129684925,
-0.0241813063621521,
-0.022667864337563515,
0.021716060116887093,
0.014982837252318859,
-0.06894712150096893,
0.004057042300701141,
0.001073189196176827,
0.017741959542036057,
0.007890056818723679,
-0.07378995418548584,
-0.00010557632776908576,
-0.06842678040266037,
-0.003967674449086189,
-0.006268889177590609,
-0.05172785744071007,
0.0153890922665596,
-0.00625009648501873,
0.021041152998805046,
0.006755459122359753,
0.00007311798981390893,
-0.0020445375703275204,
0.028380151838064194,
0.07296835631132126,
0.012089035473763943,
0.017354775220155716,
0.020665518939495087,
-0.038445066660642624,
-0.06537735462188721,
-0.03304314985871315,
0.0009539755992591381,
-0.016426552087068558,
-0.0024412269704043865,
0.016096793115139008,
-0.008606437593698502,
0.02883175201714039,
0.019101262092590332,
0.002111350651830435,
0.05571755766868591,
-0.04226994886994362,
-0.047989360988140106,
0.035783011466264725,
-0.043360259383916855,
0.0023645292967557907,
0.03018827922642231,
-0.04671631380915642,
-0.014121073298156261,
-0.020904168486595154,
0.04745778441429138,
0.00781226297840476,
0.010904878377914429,
-0.05928017199039459,
0.00797982420772314,
-0.04268784075975418,
0.020844990387558937,
-0.0047683026641607285,
0.11688341200351715,
0.0283571258187294,
0.009598278440535069,
0.061450984328985214,
0.04916342347860336,
-0.004146034829318523,
0.013438797555863857,
0.03255566209554672,
-0.087782122194767,
-0.036817070096731186,
0.0025236394722014666,
-0.06855833530426025,
-0.007797508500516415,
0.020987078547477722,
0.031076835468411446,
-0.03079974092543125,
0.021164095029234886,
0.0233655646443367,
-0.024567971006035805,
-0.006415535695850849,
-0.0074348230846226215,
0.03568623214960098,
0.0033071914222091436,
0.026108283549547195,
0.04368630051612854,
0.0038666115142405033,
0.03311567008495331,
0.0018751121824607253,
0.023252129554748535,
0.047780778259038925,
0.0035820056218653917,
-0.045389268547296524,
0.0193970687687397,
-0.012288833037018776,
0.014127003028988838,
0.02218622714281082,
-0.0014990096678957343,
-0.02242189086973667,
-0.024429330602288246,
0.05492635443806648,
-0.01224453840404749,
-0.020610788837075233,
0.013694402761757374,
0.03771975636482239,
0.025413768365979195,
0.040998466312885284,
0.031254250556230545,
0.016972487792372704,
0.02235102467238903,
0.00376083143055439,
-0.0035404409281909466,
-0.0859907865524292,
0.00921094324439764,
0.052144359797239304,
0.05064079910516739,
0.013453682884573936,
-0.0533132329583168,
0.01964639686048031,
0.059757087379693985,
0.03437002748250961,
0.013057521544396877,
0.03239930048584938,
-0.0411139652132988,
-0.013013733550906181,
-0.016045130789279938,
0.042241744697093964,
-0.023449577391147614,
0.04946951940655708,
0.018539512529969215,
-0.01673295348882675,
-0.023877087980508804,
-0.018686365336179733,
-0.05890032276511192,
-0.02395465038716793,
-0.009053799323737621,
-0.0019291916396468878,
0.07072523981332779,
-0.006820135749876499,
-0.03973797708749771,
-0.0018348938319832087,
0.005437988322228193,
0.002033875323832035,
0.0012856420362368226,
0.06395731121301651,
0.022012369707226753,
0.003959925379604101,
0.05596072971820831,
0.03216470405459404,
0.022786030545830727,
-0.023876363411545753,
0.06038837134838104,
0.02569231390953064,
0.036290671676397324,
-0.004484905861318111,
0.016869015991687775,
0.058429617434740067,
0.032416533678770065,
-0.04443839192390442,
-0.04214709997177124,
0.009172781370580196,
0.01772741600871086,
0.08443942666053772,
0.0248251985758543,
0.005143025424331427,
-0.0669272318482399,
0.012045200914144516,
0.010873324237763882,
0.015851719304919243,
0.004421379417181015,
-0.007250607945024967,
0.04151076450943947,
-0.01766165904700756,
0.004610614851117134,
-0.0902315005660057,
-0.042910072952508926,
0.008446311578154564,
0.022580809891223907,
-0.04778706282377243,
0.012194064445793629,
-0.04155561327934265,
-0.06338363140821457,
0.019201956689357758,
0.011699299328029156,
-0.03627098724246025,
0.02718997560441494,
-0.009543303400278091,
0.012914707884192467,
0.014358717948198318,
-0.03724314644932747,
-0.028779011219739914,
0.034942563623189926,
0.004691737238317728,
-0.037316251546144485,
-0.024679122492671013,
-0.08557113260030746,
-0.06939774751663208,
0.04933614283800125,
-0.008373143151402473,
0.005789131857454777,
-0.02821478806436062,
-0.011682875454425812,
-0.07641877979040146,
0.028945328667759895,
-0.00569990836083889,
0.09096893668174744,
-0.005577506963163614,
0.01930742897093296,
0.011721085757017136,
0.012086853384971619,
0.027919605374336243,
-0.017133895307779312,
-0.012778709642589092,
-0.07222533971071243,
0.018053973093628883,
0.017823420464992523,
0.003994561266154051,
0.011314011178910732,
-0.014836649410426617,
0.04640169069170952,
-0.007505246438086033,
0.019480178132653236,
0.06260450184345245,
-0.024217849597334862,
0.0006636434118263423,
0.05697964131832123,
0.005543615203350782,
-0.023125775158405304,
-0.025939540937542915,
0.03485798463225365,
-0.11221487075090408,
0.014116150327026844,
-0.010911465622484684,
0.029629984870553017,
0.1456817090511322,
0.051080264151096344,
-0.048655301332473755,
-0.016292229294776917,
0.04380790516734123,
0.014104499481618404,
-0.009179013781249523,
-0.010008670389652252,
0.04284004494547844,
0.10807406902313232,
-0.007805329281836748,
0.00965658575296402,
-0.007202246226370335,
0.057675644755363464,
0.04455915465950966,
0.034465473145246506,
0.0004527670971583575,
-0.006861854810267687,
0.03157588467001915,
0.03427301347255707,
0.0009454868850298226,
-0.013800526969134808,
-0.05559133365750313,
0.053547415882349014,
0.04338059946894646,
-0.00886011216789484,
-0.007860258221626282,
0.03346065804362297,
0.00006178106559673324,
-0.02496802806854248,
-0.03258490189909935,
0.014649704098701477,
-0.04306131228804588,
0.022405460476875305,
0.04763484373688698,
0.021892959251999855,
-0.014219017699360847,
-0.040469225496053696,
-0.02009122632443905,
-0.03360382094979286,
0.05296817794442177,
0.017623156309127808,
-0.010860546492040157,
-0.02720646932721138,
-0.03640628978610039,
-0.014417082071304321,
-0.006797376088798046,
0.032180946320295334,
0.03064919263124466,
-0.061950329691171646,
-0.06519471108913422,
0.0026304919738322496,
-0.0023339774925261736,
-0.02464648149907589,
0.014205989427864552,
-0.0057862126268446445,
0.0010838030138984323,
0.021588662639260292,
-0.004534624982625246,
0.004133034497499466,
0.008032340556383133,
-0.04094364866614342,
-0.04457295686006546,
-0.02700062096118927,
-0.015183869749307632,
-0.03726205229759216,
0.051699455827474594,
0.037638742476701736,
0.04895137622952461,
-0.01495471689850092,
-0.06052487716078758,
0.025135474279522896,
-0.007903626188635826,
-0.04213592782616615,
-0.0014900348614901304,
-0.01668071746826172,
0.03620536997914314,
0.01872428134083748,
0.004724232014268637,
-0.1158299669623375,
-0.013191997073590755,
-0.005688105709850788,
-0.04887167736887932,
-0.03910648822784424,
0.0026389474514871836,
-0.008110643364489079,
0.0030238304752856493,
-0.024006986990571022,
-0.00007152101898100227,
0.008422321639955044,
-0.006520251277834177,
-0.027009110897779465,
0.003782761748880148,
0.027089057490229607,
0.015045377425849438,
0.022937852889299393,
0.029682230204343796,
0.01855492778122425,
0.009018618613481522,
0.016380352899432182,
-0.07130651921033859,
0.010653886012732983,
0.05759076029062271,
-0.054725874215364456,
-0.1481807678937912,
0.02766876295208931,
-0.010513611137866974,
0.031505364924669266,
-0.06126242130994797,
0.0017259652959182858,
-0.01582065038383007,
0.006432554218918085,
-0.04273086413741112,
-0.050463855266571045,
-0.007473638281226158,
-0.026284808292984962,
-0.014703099615871906,
-0.014855909161269665,
0.007456865627318621,
-0.006034011021256447,
-0.04603157937526703,
-0.04116164147853851,
0.009403354488313198,
-0.03929520770907402,
0.005269257817417383,
0.0063958121463656425,
-0.02672574855387211,
-0.018065549433231354,
0.022549260407686234,
-0.006243348587304354,
-0.007094834465533495,
0.01865122839808464,
0.013032439164817333,
-0.009328984655439854,
-0.02253110334277153,
-0.016926579177379608,
-0.011872668750584126,
-0.02283378504216671,
0.039769381284713745,
0.02171453647315502,
0.022671805694699287,
-0.022187061607837677,
0.012097526341676712,
0.024396028369665146,
-0.008890660479664803,
0.005547569133341312,
-0.042130276560783386,
0.021118415519595146,
-0.038790568709373474,
-0.02626936510205269,
-0.045721836388111115,
0.022528905421495438,
0.015212896279990673,
-0.0005394748877733946,
-0.03070654533803463,
0.005229426547884941,
0.009766417555510998,
0.008619842119514942,
-0.009490354917943478,
0.02039010263979435,
-0.015076328068971634,
-0.05030227452516556,
0.012439226731657982,
0.017005328088998795,
-0.010542863979935646,
0.01764831691980362,
-0.04294554889202118,
-0.001253240741789341,
-0.043185796588659286,
-0.01332679484039545,
-0.06647113710641861,
0.07017678022384644,
0.024173855781555176,
-0.01123416144400835,
-0.020365433767437935,
0.006701076868921518,
-0.03982393071055412,
-0.019006524235010147,
-0.058285728096961975,
0.025835080072283745,
0.03561447560787201,
0.0061636860482394695,
-0.06637415289878845,
0.045434556901454926,
0.0671587586402893,
-0.0034167328849434853,
0.009622317738831043,
0.02197573147714138,
-0.015466373413801193,
-0.006093773525208235,
-0.006995068863034248,
-0.03149650990962982,
0.01740185171365738,
0.032288238406181335,
0.07755863666534424,
0.09387528896331787,
0.004550222773104906,
-0.009808529168367386,
0.00385948340408504,
0.0145500423386693,
0.034145355224609375,
0.07893653959035873,
0.05959267541766167,
0.0019344042520970106,
0.009223475120961666,
0.05748509615659714,
0.033747777342796326,
0.041446503251791,
0.040407445281744,
-0.01649925485253334,
0.058194685727357864,
0.023996418341994286,
-0.007886654697358608,
-0.004994342103600502,
-0.010225827805697918,
-0.01967400126159191,
-0.03415197506546974,
-0.03347143158316612,
-0.022552018985152245,
0.04686575010418892,
-0.08238545805215836,
-0.007416179869323969,
-0.0757802426815033,
-0.014289657585322857,
0.00008191135566448793,
-0.0031189636792987585,
-0.03591972216963768,
-0.03895946219563484,
0.013156749308109283,
-0.02521098591387272,
-0.0633416473865509,
-0.0016236455412581563,
0.01972053386271,
-0.03786078095436096,
-0.04445597901940346,
-0.01738969050347805,
-0.007456113118678331,
-0.007472045253962278,
0.014086621813476086,
-0.023946018889546394,
0.01766388863325119,
-0.04456787183880806,
-0.04510200768709183,
-0.013338049873709679,
-0.03278971090912819,
0.015217874199151993,
0.047423895448446274,
0.028793776407837868,
-0.059634171426296234,
-0.03447626531124115,
-0.006273753009736538,
-0.10306920856237411,
-0.02448989823460579,
-0.018037116155028343,
0.04162658751010895,
-0.0310011375695467,
0.04511545971035957,
-0.05238334834575653,
0.05753907188773155,
-0.01880646124482155,
0.009430421516299248,
0.045345790684223175,
0.07084830850362778,
0.018342243507504463,
0.0022348808124661446,
0.017500579357147217,
0.0038852524012327194,
-0.034990426152944565,
-0.010509492829442024,
-0.051484834402799606,
-0.009112277999520302,
-0.02495778538286686,
-0.0387086346745491,
0.026895906776189804,
0.024001406505703926,
0.03151420131325722,
-0.04053675755858421,
-0.0574658140540123,
0.08247276395559311,
0.022734584286808968,
-0.0683966875076294,
-0.020270539447665215,
0.03549329563975334,
0.05919300392270088,
-0.015175404958426952,
-0.014762588776648045,
-0.01843891851603985,
-0.014677312225103378,
-0.011030714027583599,
0.00044319420703686774,
0.029211295768618584,
-0.004322784021496773,
0.024665726348757744,
-0.07732027769088745,
0.018394483253359795,
-0.030606785789132118,
-0.005167752038687468,
-0.001880478928796947,
-0.019822724163532257,
0.00364225497469306,
-0.05460723489522934,
-0.071260467171669,
0.03287261351943016,
0.04654191434383392,
-0.012801796197891235,
-0.007657232694327831,
0.00008324346708832309,
-0.02218884788453579,
0.004080521408468485,
-0.015700720250606537,
0.02624179609119892,
0.006209710147231817,
-0.008507193997502327,
0.04456297308206558,
-0.07200637459754944,
0.03092900477349758,
-0.02742324024438858,
-0.002228414174169302,
0.07538463920354843,
0.018927203491330147,
-0.0014961392153054476,
-0.0035297125577926636,
0.024938924238085747
] |
[
14.793452262878418,
3.6742045879364014
] |
General Relativity and Quantum Cosmology
|
General Physics
|
gr-qc
|
astro-ph
|
na
|
2007-04-02T09:23:25
|
We present an algorithm that produces the classification list of smooth Fano
d-polytopes for any given d. The input of the algorithm is a single number,
namely the positive integer d. The algorithm has been used to classify smooth
Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano
6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.
|
An algorithm for the classification of smooth Fano polytopes
|
math.CO
|
0704.0049
| 2,007
|
[
0.02171468548476696,
0.05014538764953613,
0.0025046684313565493,
-0.037172842770814896,
-0.039336685091257095,
-0.028185807168483734,
0.028901712968945503,
0.018200697377324104,
-0.019284935668110847,
0.007262899540364742,
-0.11992806941270828,
0.04596761614084244,
0.043577007949352264,
0.004283060319721699,
0.03044930100440979,
0.018030330538749695,
-0.012990185059607029,
0.002305936999619007,
-0.03489275276660919,
-0.03237786516547203,
0.013288023881614208,
-0.00342353293672204,
-0.002132234163582325,
-0.006700770929455757,
0.09125982224941254,
0.025470396503806114,
-0.0058881426230072975,
0.00476080784574151,
-0.07640015333890915,
0.015647543594241142,
0.0355735644698143,
0.0005916300578974187,
0.02082986943423748,
0.008100448176264763,
-0.03612712770700455,
-0.0125193540006876,
0.05368734896183014,
-0.02115434966981411,
0.04193401709198952,
0.036553993821144104,
0.04875291511416435,
0.04271203652024269,
-0.0006211701547726989,
0.05744976922869682,
-0.010218136012554169,
-0.032269109040498734,
0.017379408702254295,
-0.02213856764137745,
0.025615356862545013,
-0.03744090721011162,
0.014193505048751831,
0.041575461626052856,
0.008323767222464085,
-0.0837012305855751,
-0.053466781973838806,
0.03057265281677246,
-0.01637553609907627,
-0.08605267852544785,
0.025211280211806297,
-0.012655683793127537,
-0.023081989958882332,
0.060478828847408295,
-0.020452287048101425,
0.025154775008559227,
0.01614568755030632,
-0.03265302628278732,
-0.004735866561532021,
0.045150917023420334,
-0.01998385600745678,
0.00360633316449821,
0.027905400842428207,
-0.008843504823744297,
0.05625111237168312,
0.023015029728412628,
-0.05186336860060692,
-0.06084584817290306,
0.038661252707242966,
-0.04265337437391281,
0.017717255279421806,
-0.03416547551751137,
0.048732269555330276,
-0.016126321628689766,
0.036314707249403,
-0.006213454995304346,
-0.0039430223405361176,
-0.01581190526485443,
-0.02488607168197632,
-0.003992369864135981,
-0.06818804144859314,
-0.018385224044322968,
-0.003588738851249218,
0.040885429829359055,
0.006439669989049435,
0.05635245889425278,
-0.04125088080763817,
0.05158689618110657,
-0.06538303196430206,
0.06006559357047081,
-0.024126900359988213,
-0.06604098528623581,
0.02086460590362549,
0.03449828177690506,
0.03783745318651199,
-0.03236394003033638,
0.07739725708961487,
0.0310450978577137,
0.01691141352057457,
-0.00488084414973855,
0.013302724808454514,
-0.03373970463871956,
-0.02537253312766552,
0.0039574927650392056,
-0.01890055276453495,
-0.0010179373202845454,
-0.026724284514784813,
-0.009319107979536057,
0.01105435099452734,
-0.06247571483254433,
-0.01049642451107502,
0.11598441749811172,
-0.0017559557454660535,
-0.013278515078127384,
-0.004206104204058647,
-0.0030611467082053423,
0.02850920893251896,
-0.04537483677268028,
-0.04093122482299805,
-0.002404713537544012,
0.024693138897418976,
-0.021868407726287842,
0.05173381790518761,
-0.0023936626967042685,
-0.03919893503189087,
0.0033360326196998358,
0.020742200314998627,
0.04320328310132027,
-0.003126674797385931,
-0.0077943382784724236,
0.07179725170135498,
-0.03685057908296585,
0.03742885962128639,
0.02784927375614643,
0.00950966589152813,
0.01696728728711605,
0.030625568702816963,
-0.03953283652663231,
-0.007279766723513603,
-0.07020233571529388,
-0.05409450829029083,
0.01771729812026024,
0.04647451266646385,
0.043985843658447266,
0.02921910211443901,
0.026032911613583565,
-0.036161888390779495,
-0.03524962440133095,
0.007076915353536606,
0.05440407246351242,
0.025605591014027596,
0.00862352829426527,
0.03284349665045738,
0.017227452248334885,
-0.07925325632095337,
0.02420511282980442,
-0.058267779648303986,
-0.010357852093875408,
0.010323936119675636,
0.023108866065740585,
-0.019232284277677536,
0.04821192845702171,
-0.030166825279593468,
0.022464973852038383,
0.03958052396774292,
-0.01941034197807312,
0.02867138385772705,
-0.038249969482421875,
-0.016037480905652046,
0.000037221336242510006,
0.013162066228687763,
-0.013011632487177849,
0.07672899961471558,
0.00780944898724556,
0.012670328840613365,
0.04360054433345795,
-0.036352235823869705,
-0.00857897475361824,
0.006518905516713858,
-0.04767778888344765,
0.008054444566369057,
-0.015073935501277447,
0.029757918789982796,
0.05380380153656006,
-0.006657658144831657,
-0.05165337398648262,
0.023148132488131523,
-0.01578519120812416,
0.05168896168470383,
-0.03900507465004921,
0.024833401665091515,
-0.06373276561498642,
0.028906073421239853,
-0.04438067600131035,
-0.012681839987635612,
0.035433921962976456,
-0.04574470594525337,
0.04219672828912735,
0.026019660755991936,
-0.011576694436371326,
0.014983193017542362,
-0.017986003309488297,
0.002140436787158251,
-0.016364308074116707,
0.0023909802548587322,
0.028376463800668716,
-0.028325993567705154,
0.019194433465600014,
-0.02381848730146885,
-0.023679623380303383,
-0.029157737269997597,
0.008651478216052055,
0.05742424353957176,
-0.04397893697023392,
-0.0704784169793129,
0.0038936659693717957,
0.027789020910859108,
-0.004997250158339739,
-0.027634525671601295,
0.021966852247714996,
-0.04926653206348419,
-0.007115921471267939,
-0.04745058715343475,
-0.08152930438518524,
0.004706110805273056,
-0.003925174009054899,
-0.008839129470288754,
0.0053267101757228374,
-0.019211364910006523,
0.05324752628803253,
0.0032949140295386314,
0.0017675971612334251,
0.02402884140610695,
-0.004554813262075186,
-0.003657632740214467,
-0.022716499865055084,
-0.08184319734573364,
-0.037973079830408096,
-0.03445617854595184,
0.004179763607680798,
0.0009978493908420205,
0.03317883238196373,
-0.023890824988484383,
0.013093551620841026,
0.03550363704562187,
0.08787841349840164,
0.03244272246956825,
-0.047516290098428726,
-0.06656397134065628,
0.041489552706480026,
0.04784344509243965,
-0.05993252247571945,
0.08471950143575668,
-0.024224229156970978,
0.018147241324186325,
-0.02768069878220558,
-0.062064751982688904,
-0.002257833257317543,
0.045368365943431854,
-0.03627653792500496,
-0.034857127815485,
0.0021900238934904337,
-0.0011650474043563008,
0.0441131629049778,
0.03242627903819084,
-0.02670014277100563,
-0.06141906976699829,
0.01544075645506382,
0.032950762659311295,
-0.0326969176530838,
-0.02924528159201145,
0.02798285521566868,
-0.022961724549531937,
-0.07700423896312714,
-0.048097092658281326,
-0.012201289646327496,
-0.014509336091578007,
0.04371190816164017,
-0.010025891475379467,
0.00893375463783741,
0.002290126634761691,
0.026020154356956482,
0.002003673231229186,
0.0017340169288218021,
0.02705533429980278,
-0.01327933557331562,
0.03695032373070717,
0.04662885144352913,
0.04360639303922653,
-0.011652735993266106,
0.045743465423583984,
0.016538964584469795,
0.018659433349967003,
-0.007647859398275614,
0.0148383853957057,
0.007381985895335674,
0.060407452285289764,
-0.010867792181670666,
0.043538399040699005,
0.00976009201258421,
-0.013673173263669014,
-0.04447542503476143,
0.0043524098582565784,
0.03963594511151314,
-0.01760862208902836,
0.027503065764904022,
-0.010122069157660007,
0.036149635910987854,
0.03926384076476097,
0.04013819247484207,
0.02414233237504959,
-0.03476417809724808,
0.017340058460831642,
-0.04767460376024246,
0.048216868191957474,
-0.07812738418579102,
-0.014162205159664154,
0.034744277596473694,
0.040157075971364975,
0.0306402500718832,
-0.004402543883770704,
-0.030350182205438614,
0.03845704346895218,
0.025304362177848816,
-0.03222443908452988,
-0.00750760268419981,
-0.049427058547735214,
-0.029017725959420204,
-0.03804263472557068,
0.0024519076105207205,
0.0035115822684019804,
-0.039288319647312164,
-0.002616166602820158,
-0.022633375599980354,
-0.07210483402013779,
-0.07733646035194397,
-0.025714002549648285,
-0.01608102209866047,
0.021916445344686508,
-0.009408962912857533,
0.03448174148797989,
0.010385739617049694,
-0.03359634056687355,
-0.011330771259963512,
0.010840516537427902,
-0.051177047193050385,
0.010663371533155441,
0.037870701402425766,
0.013024484738707542,
-0.050459351390600204,
0.005040437448769808,
0.049111537635326385,
0.0578867606818676,
0.03538227081298828,
0.02033199556171894,
-0.037703339010477066,
0.01898905634880066,
-0.009728251956403255,
0.007461206056177616,
0.033843744546175,
0.018214629963040352,
-0.004918195307254791,
0.00038926838897168636,
-0.07219689339399338,
0.050963714718818665,
0.02365226484835148,
-0.01159506756812334,
0.021488578990101814,
-0.0666271448135376,
0.00870154332369566,
0.03388117253780365,
-0.016533978283405304,
0.07211319357156754,
-0.02443169429898262,
0.06613456457853317,
0.012645695358514786,
0.0009657939081080258,
0.02507564052939415,
-0.04460011050105095,
-0.011893865652382374,
0.0076012699864804745,
-0.019592056050896645,
0.038649462163448334,
-0.021040096879005432,
-0.01920437440276146,
0.025019675493240356,
0.010327432304620743,
-0.03355337306857109,
0.021294577047228813,
0.043330248445272446,
-0.07772710174322128,
0.006407018750905991,
-0.0714646652340889,
-0.09195471554994583,
0.04357815161347389,
-0.011110927909612656,
-0.02820528857409954,
-0.006019901484251022,
-0.02057165838778019,
-0.038313884288072586,
0.03602517396211624,
0.03513308987021446,
-0.04946945235133171,
-0.0032932551112025976,
-0.04097701236605644,
-0.04555998370051384,
0.006271278485655785,
0.009922616183757782,
0.03200790658593178,
-0.0030668326653540134,
0.05384582281112671,
-0.029072310775518417,
-0.011095035821199417,
0.05867611989378929,
-0.05753037706017494,
0.0019400302553549409,
-0.05107344314455986,
-0.006506574805825949,
0.06721516698598862,
0.039693426340818405,
0.029804160818457603,
-0.04655880481004715,
0.03372509032487869,
0.031883805990219116,
-0.0523330494761467,
0.003959628287702799,
-0.06211115047335625,
0.014235489070415497,
0.02260027639567852,
-0.0007904463564045727,
-0.005824388470500708,
0.029414992779493332,
0.05099402368068695,
-0.01644744910299778,
0.002266218652948737,
-0.032451335340738297,
0.0433928407728672,
0.05355845391750336,
0.04057467356324196,
-0.022932197898626328,
-0.019815830513834953,
0.02954665943980217,
0.05579615756869316,
-0.0059339189901947975,
-0.0035095741041004658,
0.036087680608034134,
0.04677342623472214,
0.0014435196062549949,
-0.011265825480222702,
-0.05311879143118858,
0.0661417618393898,
0.09060762822628021,
0.10298265516757965,
0.019184991717338562,
-0.011895151808857918,
-0.00788874551653862,
-0.025654548779129982,
0.00006818294787080958,
-0.0204391460865736,
0.021172568202018738,
0.010669885203242302,
0.07021337747573853,
-0.019726231694221497,
0.02209804765880108,
-0.022818032652139664,
0.011688200756907463,
-0.05294171720743179,
-0.0013188559096306562,
-0.015761099755764008,
-0.01975119858980179,
0.00006938253500266,
0.04187212511897087,
0.049314629286527634,
-0.05406434088945389,
0.00158553512301296,
-0.024836065247654915,
0.0026322859339416027,
0.01899033784866333,
-0.0013493943260982633,
-0.0007473388686776161,
0.000010224481229670346,
-0.003702228656038642,
0.0004410205001477152,
0.045705005526542664,
-0.0133634302765131,
0.01860879920423031,
-0.032106246799230576,
-0.05282002314925194,
0.03498062863945961,
-0.0033438499085605145,
0.018473949283361435,
-0.03420356288552284,
0.01938020996749401,
0.009311140514910221,
0.02827654778957367,
-0.0003377835964784026,
0.025844261050224304,
0.013078534044325352,
-0.0005242906045168638,
-0.05867709964513779,
0.03509717062115669,
-0.009513910859823227,
0.012921854853630066,
0.05685548484325409,
0.049267955124378204,
0.06831498444080353,
0.00698618171736598,
-0.07021594792604446,
0.016514543443918228,
0.0020702031906694174,
-0.05175331234931946,
0.010663428343832493,
0.014734276570379734,
-0.02829885482788086,
-0.009716448374092579,
-0.0134203489869833,
-0.06821783632040024,
0.006688757333904505,
-0.011889785528182983,
-0.10510031133890152,
0.05164756998419762,
-0.029397496953606606,
0.024307463318109512,
0.001228125300258398,
-0.06001456081867218,
-0.028336023911833763,
-0.03476438671350479,
-0.019677596166729927,
-0.06388571858406067,
-0.004206154961138964,
0.023426536470651627,
0.07866605371236801,
0.008337622508406639,
0.02383529394865036,
-0.0031956741586327553,
-0.012534448876976967,
-0.009725173935294151,
-0.04147208482027054,
-0.055583707988262177,
0.03212849795818329,
-0.04796473681926727,
-0.050629980862140656,
-0.008839594200253487,
-0.025548122823238373,
0.030376052483916283,
-0.06244025379419327,
0.011943574994802475,
0.007631476037204266,
-0.014145432971417904,
-0.04317373409867287,
-0.008155781775712967,
-0.020480507984757423,
-0.024571875110268593,
-0.008700392208993435,
0.011225257068872452,
-0.00042560978909023106,
0.0077252560295164585,
-0.12763164937496185,
-0.022314980626106262,
0.007216162979602814,
0.018782898783683777,
-0.0023461731616407633,
0.01615891605615616,
-0.07111194729804993,
0.03618348017334938,
0.091888427734375,
-0.004536118358373642,
-0.06540239602327347,
0.029658691957592964,
0.014076139777898788,
-0.00001612720006960444,
-0.03075091540813446,
-0.009387322701513767,
-0.0031456423457711935,
0.027061600238084793,
0.026883354410529137,
-0.03303567320108414,
0.02973899431526661,
-0.025373373180627823,
-0.03997611626982689,
-0.0114828422665596,
0.004884067922830582,
0.023996662348508835,
-0.007056393660604954,
-0.024153729900717735,
-0.009381220676004887,
-0.005060440860688686,
0.012263895943760872,
-0.03188837319612503,
0.004698425531387329,
-0.02463284321129322,
-0.06508924067020416,
0.017784953117370605,
0.04915839433670044,
0.09724637120962143,
-0.05040750652551651,
-0.08200378715991974,
0.07198896259069443,
-0.002361621940508485,
0.07148899883031845,
0.008159522898495197,
0.05230560526251793,
0.028318822383880615,
0.03524419292807579,
-0.04051133617758751,
-0.05635819211602211,
-0.026744406670331955,
-0.07319110631942749,
0.05163240432739258,
-0.05350671708583832,
0.0498538576066494,
-0.04638652130961418,
0.006807420868426561,
-0.07977033406496048,
-0.005937847308814526,
-0.03770030662417412,
0.008181632496416569,
0.015608606860041618,
-0.047203198075294495,
-0.030018573626875877,
0.028114713728427887,
0.050509944558143616,
0.007087253965437412,
-0.05225148797035217,
-0.017974955961108208,
-0.009608418680727482,
-0.016747264191508293,
-0.014350002631545067,
-0.0759921744465828,
0.028266841545701027,
0.03587935492396355,
0.12017781287431717,
0.035159144550561905,
-0.03225657716393471,
-0.02925293520092964,
-0.023008503019809723,
0.08348827809095383,
-0.024508804082870483,
0.0031478097662329674,
0.01389418076723814,
0.005321325734257698,
0.008136790245771408,
0.04756036400794983,
0.08151377737522125,
-0.02178957685828209,
0.023669110611081123,
-0.011609220877289772,
-0.039191145449876785,
0.0326450951397419,
-0.02033551223576069,
-0.002158505143597722,
0.056370969861745834,
0.03455233573913574,
-0.02466663159430027,
-0.052227266132831573,
-0.006163984537124634,
-0.00230453722178936,
-0.018111879006028175,
-0.01134271826595068,
0.009915740229189396,
-0.036589570343494415,
-0.02066742070019245,
-0.013129967264831066,
0.005648767109960318,
-0.03511425107717514,
0.011691074818372726,
-0.018585631623864174,
0.00263233226723969,
0.004658988676965237,
0.001053051557391882,
-0.004309171810746193,
-0.0324084535241127,
-0.004593404475599527,
0.019859734922647476,
-0.036850716918706894,
-0.01209251582622528,
0.01904069073498249,
0.021704910323023796,
-0.019508711993694305,
-0.006214114837348461,
-0.03308413177728653,
-0.04086519777774811,
0.04576174542307854,
0.005547158420085907,
0.020779646933078766,
-0.040376272052526474,
-0.025053489953279495,
0.005095719825476408,
-0.039691340178251266,
-0.013300875201821327,
0.04280032217502594,
-0.015682371333241463,
0.018854375928640366,
0.07244732975959778,
-0.004094094969332218,
0.030801409855484962,
-0.05085248500108719,
-0.02291294001042843,
-0.06137273833155632,
0.0176535677164793,
0.03050285577774048,
-0.0031119929626584053,
-0.007045643404126167,
-0.010178410448133945,
0.04047746956348419,
0.021705826744437218,
0.03257521986961365,
0.007397093344479799,
-0.004278034437447786,
-0.04533035308122635,
-0.009729276411235332,
-0.009887696243822575,
0.016859082505106926,
-0.0034495689906179905,
0.0013692928478121758,
0.005110056139528751,
0.02400495670735836,
-0.041289567947387695,
-0.008000873029232025,
-0.04665723443031311,
0.06278076022863388,
0.02658211439847946,
0.05427046865224838,
0.008140434511005878,
-0.04205605760216713,
-0.004412747919559479,
-0.006069533061236143,
-0.036806635558605194,
0.007390023209154606,
0.00598423695191741,
-0.02252448908984661,
0.011133546940982342,
0.011305241845548153,
0.011822810396552086,
0.04069366678595543,
-0.010746380314230919,
0.009374548681080341,
-0.017767755314707756,
-0.041580911725759506,
0.03149230033159256,
0.029384862631559372,
0.017678800970315933,
-0.029794523492455482,
0.007824063301086426,
0.009432503953576088,
-0.002562082139775157,
-0.03086089715361595,
0.052687231451272964,
0.027524322271347046,
-0.004339707549661398,
0.03023536130785942,
-0.014663186855614185,
0.019582409411668777,
0.009317571297287941,
0.04939643293619156,
0.07893546670675278,
0.02535931020975113,
0.030217479914426804,
-0.045087046921253204,
0.005628096405416727
] |
[
0.3292221426963806,
0.7491114139556885
] |
Combinatorics
|
Mathematics
|
math-CO
|
na
|
na
|
2007-04-01T18:53:13
|
Part I describes an intelligent acoustic emission locator, while Part II
discusses blind source separation, time delay estimation and location of two
continuous acoustic emission sources.
Acoustic emission (AE) analysis is used for characterization and location of
developing defects in materials. AE sources often generate a mixture of various
statistically independent signals. A difficult problem of AE analysis is
separation and characterization of signal components when the signals from
various sources and the mode of mixing are unknown. Recently, blind source
separation (BSS) by independent component analysis (ICA) has been used to solve
these problems. The purpose of this paper is to demonstrate the applicability
of ICA to locate two independent simultaneously active acoustic emission
sources on an aluminum band specimen. The method is promising for
non-destructive testing of aircraft frame structures by acoustic emission
analysis.
|
Intelligent location of simultaneously active acoustic emission sources:
Part II
|
cs.NE cs.AI
|
0704.0050
| 2,007
|
[
0.04542442783713341,
-0.012241996824741364,
-0.007213972974568605,
-0.07593552768230438,
-0.002320758765563369,
-0.013556362129747868,
0.04414895921945572,
0.02727551944553852,
-0.05640765652060509,
0.000970186258200556,
-0.03439198434352875,
0.06767714768648148,
-0.0014693269040435553,
0.0011701697949320078,
0.02326371893286705,
-0.06453463435173035,
0.024231184273958206,
0.009410479106009007,
-0.018606794998049736,
0.009199458174407482,
0.007077249698340893,
-0.026792380958795547,
-0.012365290895104408,
-0.03400694951415062,
0.10114507377147675,
-0.02524121105670929,
-0.01161995530128479,
0.023945501074194908,
-0.053012665361166,
-0.026265818625688553,
0.013829630799591541,
-0.08800161629915237,
0.026336584240198135,
0.012125731445848942,
-0.0343334935605526,
-0.0024921996518969536,
0.06306951493024826,
0.02454342134296894,
-0.015958432108163834,
0.07991977781057358,
0.04082535579800606,
-0.05463125556707382,
0.02352043427526951,
-0.01915815845131874,
0.0392298586666584,
0.028875650838017464,
0.009896207600831985,
-0.02080794796347618,
0.029836926609277725,
-0.01857856847345829,
0.010683364234864712,
0.022107049822807312,
-0.0006748057203367352,
-0.00845850259065628,
0.010896904394030571,
-0.0013914378359913826,
-0.031346771866083145,
-0.01931646093726158,
0.048034343868494034,
-0.004214948508888483,
-0.011371273547410965,
0.07304958254098892,
-0.0780508741736412,
0.035285938531160355,
0.011849086731672287,
-0.052101049572229385,
-0.009158413857221603,
-0.033442914485931396,
-0.020789671689271927,
-0.0391993448138237,
0.026362275704741478,
-0.03386383131146431,
0.051814112812280655,
0.002742393407970667,
-0.031033650040626526,
-0.011615343391895294,
0.0029325359500944614,
0.007878037169575691,
-0.014720664359629154,
0.06437418609857559,
0.026104038581252098,
-0.04882413521409035,
0.06193754822015762,
-0.002688807900995016,
0.040281180292367935,
0.024878032505512238,
0.0076186638325452805,
0.0401010625064373,
-0.014300224371254444,
0.026260333135724068,
0.02221807651221752,
0.04410310834646225,
0.05571305379271507,
0.05388379096984863,
-0.002798395697027445,
0.05263112112879753,
-0.08418057858943939,
0.06880606710910797,
-0.02879634127020836,
-0.012585695832967758,
-0.0042192344553768635,
0.011774133890867233,
-0.03369336202740669,
0.0383862741291523,
0.05103021115064621,
-0.014056420885026455,
0.0031635190825909376,
-0.01721830666065216,
-0.0354195237159729,
-0.008022523485124111,
-0.0673660933971405,
-0.03376415744423866,
0.034528329968452454,
0.014517196454107761,
-0.04634350538253784,
-0.03741183504462242,
0.045037735253572464,
-0.07254377752542496,
0.023160848766565323,
0.020141584798693657,
0.0037676698993891478,
-0.05103655532002449,
0.018682420253753662,
-0.026446301490068436,
0.0056459903717041016,
-0.008213281631469727,
-0.05691319331526756,
0.005452536046504974,
0.01872912608087063,
-0.013532249256968498,
-0.012867999263107777,
0.0011541825952008367,
0.04205184802412987,
0.01578092761337757,
0.051447805017232895,
0.009813427925109863,
-0.001412546611391008,
-0.05718439817428589,
0.019993091002106667,
0.031104622408747673,
0.03464427590370178,
-0.002575246151536703,
0.017041662707924843,
-0.04260564222931862,
0.03906591981649399,
-0.031003238633275032,
-0.017913222312927246,
-0.05939273536205292,
-0.03157150000333786,
-0.002442780416458845,
0.0258487518876791,
0.01719537377357483,
0.024036716669797897,
-0.013155590742826462,
-0.019879745319485664,
-0.034416720271110535,
-0.02378009259700775,
-0.0085431057959795,
0.0242630485445261,
-0.022941311821341515,
-0.028025174513459206,
0.016438428312540054,
-0.0010275383247062564,
0.06313701719045639,
-0.010446569882333279,
0.02610054612159729,
-0.010629133321344852,
0.01463359221816063,
0.09297237545251846,
0.044368140399456024,
-0.041633568704128265,
0.019196318462491035,
-0.014074108563363552,
-0.004371133167296648,
0.04845137894153595,
-0.016401251778006554,
0.04665142670273781,
-0.06714220345020294,
0.04104787856340408,
0.01141300518065691,
0.03228449076414108,
-0.003090619808062911,
-0.025051269680261612,
0.03474859893321991,
0.026048406958580017,
-0.0171836968511343,
-0.0002741554344538599,
-0.07142876088619232,
-0.01726783812046051,
-0.01909785158932209,
-0.01423911564052105,
-0.0554833747446537,
-0.08003741502761841,
-0.03219398856163025,
-0.04189286753535271,
-0.02290159836411476,
0.047455284744501114,
-0.016196589916944504,
0.04571723937988281,
0.00741909584030509,
-0.03847881034016609,
-0.019799495115876198,
-0.053611624985933304,
0.029507750645279884,
-0.023558450862765312,
0.03444446623325348,
0.011112232692539692,
-0.019567733630537987,
-0.03515201807022095,
0.020129352807998657,
0.034760069102048874,
0.0474356934428215,
0.008447116240859032,
0.012376431375741959,
-0.021169589832425117,
-0.009295144118368626,
0.018237009644508362,
-0.0487215481698513,
-0.003484548069536686,
0.009205556474626064,
0.054444849491119385,
0.013642198406159878,
0.0328449010848999,
-0.02728918194770813,
0.039756614714860916,
0.027740683406591415,
-0.012165432795882225,
-0.010721038095653057,
-0.05656181275844574,
-0.02765442244708538,
-0.03429712355136871,
-0.0633455440402031,
0.07922206073999405,
-0.0067830439656972885,
0.021494053304195404,
0.0026950291357934475,
0.00011253342381678522,
0.03739091753959656,
0.009652149863541126,
0.06751984357833862,
-0.002032575896009803,
0.0012303163530305028,
-0.015968194231390953,
-0.02339075319468975,
-0.06458398699760437,
-0.01875961199402809,
0.00336334016174078,
-0.018486013635993004,
-0.016045723110437393,
0.011997989378869534,
-0.007651152554899454,
0.023986442014575005,
-0.029489688575267792,
0.002965193009003997,
0.00555306626483798,
-0.04030785709619522,
-0.009159409441053867,
0.06417148560285568,
-0.019258754327893257,
-0.05704245716333389,
0.009961209259927273,
-0.08564362674951553,
0.0379495844244957,
-0.05575433373451233,
-0.029932064935564995,
0.017192907631397247,
0.015096163377165794,
-0.04850829765200615,
-0.03678099811077118,
-0.06834631413221359,
-0.034668002277612686,
0.003237061435356736,
0.07449058443307877,
0.04984989017248154,
0.028197573497891426,
0.07539739459753036,
0.01881638914346695,
-0.0024699203204363585,
-0.02151520922780037,
0.019519316032528877,
-0.06398309022188187,
-0.001648471923545003,
-0.018751097843050957,
-0.06011343374848366,
0.006767167244106531,
0.055649738758802414,
0.037825461477041245,
-0.0023953476920723915,
0.03006955422461033,
-0.006400489713996649,
-0.0051306262612342834,
-0.028172502294182777,
0.005626564379781485,
0.03896252438426018,
-0.0767488107085228,
0.059059929102659225,
0.03161632642149925,
-0.03891495242714882,
0.0016208513407036662,
0.002763614756986499,
0.033237259835004807,
0.037883270531892776,
0.022319845855236053,
-0.021460818126797676,
0.021793760359287262,
-0.011973817832767963,
-0.017612844705581665,
-0.03539222478866577,
0.0375412181019783,
0.017510395497083664,
-0.024028010666370392,
-0.00765245221555233,
0.04816291853785515,
-0.007587726693600416,
-0.0155791025608778,
0.01999429054558277,
0.01336562167853117,
-0.009032451547682285,
0.06120797619223595,
0.05782347172498703,
-0.0008975448436103761,
0.005306415259838104,
0.030324405059218407,
-0.03182113543152809,
0.024210087954998016,
0.03487352654337883,
0.05985729768872261,
0.014870804734528065,
-0.03906743973493576,
0.002725818194448948,
-0.007569220848381519,
0.04059840738773346,
-0.05438068136572838,
-0.00891189370304346,
-0.0041694664396345615,
-0.010172950103878975,
0.00925299059599638,
0.05608270689845085,
-0.03708937019109726,
0.045884471386671066,
0.08676717430353165,
0.026947366073727608,
0.000996976625174284,
-0.04211341589689255,
-0.07821467518806458,
-0.03613041713833809,
0.0066164531745016575,
0.023743702098727226,
0.0060380869545042515,
-0.010094651021063328,
-0.02660319022834301,
0.015939826145768166,
0.020822474732995033,
0.006742914207279682,
-0.02860894612967968,
0.03247106075286865,
0.08350887894630432,
-0.025537382811307907,
0.046033091843128204,
0.051993731409311295,
0.013234779238700867,
-0.04725252091884613,
0.05780528113245964,
-0.02054140344262123,
0.012467076070606709,
-0.030341627076268196,
0.05236116051673889,
-0.0036053231451660395,
0.04714277759194374,
-0.06646865606307983,
-0.0017750670667737722,
-0.008080964908003807,
-0.04303109645843506,
0.04126277565956116,
0.004921106621623039,
-0.010898697189986706,
-0.05123034119606018,
-0.0035595856606960297,
-0.0016485792584717274,
0.018347997218370438,
0.005868767388164997,
-0.014081434346735477,
0.04530473053455353,
0.01593027636408806,
0.03479931876063347,
-0.021484430879354477,
-0.03810393437743187,
0.02269842103123665,
-0.02675497904419899,
-0.09797223657369614,
0.008796866983175278,
-0.030242903158068657,
-0.11653362214565277,
-0.020278597250580788,
-0.03285897895693779,
-0.010813850909471512,
0.019809268414974213,
0.012324508279561996,
0.020653419196605682,
0.02080715261399746,
-0.028818758204579353,
-0.03366965427994728,
-0.010183564387261868,
0.03716902807354927,
-0.03126385062932968,
0.05571489408612251,
0.026020430028438568,
-0.040415648370981216,
0.0507936105132103,
-0.0005004483973607421,
-0.022786641493439674,
0.00005790485374745913,
-0.03955251723527908,
-0.0376625582575798,
0.04078452289104462,
-0.0279835257679224,
0.05820905417203903,
0.03879599645733833,
0.013147315941751003,
-0.02026771754026413,
0.006516924127936363,
0.04526904970407486,
-0.018251117318868637,
-0.006694632116705179,
-0.02374250441789627,
-0.012708180584013462,
-0.004141415469348431,
-0.001756911282427609,
0.0014121878193691373,
-0.06803159415721893,
-0.012737691402435303,
-0.03143604099750519,
0.04067249596118927,
0.004316989332437515,
-0.06316893547773361,
0.08733402192592621,
0.038558654487133026,
0.04981599375605583,
0.04067280888557434,
-0.0006847709300927818,
-0.005323793273419142,
-0.05078435316681862,
0.01299623679369688,
-0.001377951237373054,
0.03733034431934357,
0.09398892521858215,
0.07610557228326797,
-0.031150704249739647,
-0.031007621437311172,
0.028361765667796135,
0.028361663222312927,
-0.02009638398885727,
-0.04249577969312668,
0.027501022443175316,
0.07918089628219604,
-0.0171221811324358,
0.04002479091286659,
-0.001880369265563786,
0.10997162759304047,
0.02956528589129448,
0.051482513546943665,
0.038658156991004944,
-0.05306735634803772,
-0.005904781632125378,
-0.004815477412194014,
-0.0018287381390109658,
-0.026406126096844673,
-0.0027461666613817215,
-0.022855455055832863,
0.05373498052358627,
-0.02740941382944584,
0.014705250971019268,
0.005893031135201454,
0.040163613855838776,
-0.003570857923477888,
-0.011588050983846188,
0.0255630724132061,
-0.014013712294399738,
-0.029066704213619232,
0.03897875174880028,
0.028149619698524475,
-0.022911151871085167,
-0.025822574272751808,
-0.016607770696282387,
-0.0311175175011158,
-0.02112673968076706,
-0.03273415192961693,
-0.007410543039441109,
-0.029388882219791412,
-0.022389547899365425,
0.04403040185570717,
0.030604396015405655,
-0.007314575836062431,
-0.03693965822458267,
-0.04320191964507103,
-0.050781216472387314,
0.004563490394502878,
0.034403447061777115,
-0.01640857756137848,
-0.038356103003025055,
-0.006690370850265026,
-0.01979060284793377,
0.015382620505988598,
0.03463893383741379,
0.019264960661530495,
0.02016611583530903,
0.028054598718881607,
-0.05915660411119461,
0.011934764683246613,
0.021780189126729965,
0.024503421038389206,
0.04776306450366974,
0.01454576663672924,
0.014945127069950104,
-0.0031816393602639437,
-0.03154221922159195,
0.08802059292793274,
0.04297696053981781,
-0.0939498096704483,
0.023017840459942818,
0.02577449381351471,
0.06796086579561234,
0.005352668929845095,
0.05178854614496231,
-0.07494901865720749,
0.01708824932575226,
-0.05697006732225418,
-0.05901828780770302,
0.06332403421401978,
-0.03932911902666092,
-0.005160057917237282,
0.043998293578624725,
-0.010548326186835766,
-0.02595699205994606,
0.015792323276400566,
-0.013213696889579296,
0.001518899924121797,
-0.00468040443956852,
-0.007155848667025566,
0.00885534193366766,
0.0009458840359002352,
0.00241885450668633,
0.028265180066227913,
-0.00450524128973484,
0.024713780730962753,
-0.05507897213101387,
-0.015869934111833572,
0.0264536514878273,
0.004651274532079697,
-0.05906069278717041,
0.0488412082195282,
-0.005786262918263674,
0.09680882841348648,
-0.05434659123420715,
0.057075899094343185,
-0.03492022305727005,
-0.03897855058312416,
-0.000568066374398768,
0.008368615061044693,
-0.03092588484287262,
0.011935051530599594,
0.024558421224355698,
0.003808216657489538,
0.02613764815032482,
0.02673971839249134,
-0.0557473860681057,
-0.006145271006971598,
0.0544632188975811,
0.025032272562384605,
0.02164391800761223,
-0.025892270728945732,
-0.05156385898590088,
-0.029745442792773247,
0.024216676130890846,
0.031672682613134384,
0.01920173317193985,
0.03812306746840477,
0.02954157069325447,
-0.02831561118364334,
0.006767396815121174,
-0.023480352014303207,
0.006124061997979879,
0.006283072289079428,
-0.0003616199246607721,
-0.026914015412330627,
0.02772451564669609,
-0.025131309404969215,
-0.027147509157657623,
0.04957401007413864,
-0.010576954111456871,
0.007037110161036253,
-0.09443841129541397,
0.011369339190423489,
-0.053594231605529785,
-0.0713634043931961,
-0.0465116985142231,
0.011328469030559063,
0.003888456616550684,
0.008811288513243198,
-0.04963791370391846,
-0.013542772270739079,
0.016211939975619316,
0.05891779065132141,
-0.011402907781302929,
0.02170676551759243,
0.03566046804189682,
0.01814180612564087,
0.02819400280714035,
-0.007466247770935297,
-0.06838690489530563,
-0.04616493359208107,
-0.028037413954734802,
-0.037929467856884,
-0.035771943628787994,
0.007244299165904522,
-0.04153100401163101,
0.051173072308301926,
-0.04826604574918747,
0.04675270617008209,
-0.034161921590566635,
0.04398521035909653,
-0.02380051277577877,
-0.010877072811126709,
-0.034867312759160995,
-0.030033493414521217,
0.03257102519273758,
-0.023725172504782677,
-0.06078297272324562,
0.018582500517368317,
0.06865737587213516,
0.026877472177147865,
-0.007857934571802616,
0.009938256815075874,
-0.05167487636208534,
-0.04898865148425102,
0.02174147590994835,
-0.006887947209179401,
0.018787283450365067,
0.02194732427597046,
0.07330981642007828,
0.0188115444034338,
0.037329114973545074,
-0.004515547305345535,
0.05477495491504669,
0.0215731430798769,
0.01955009251832962,
0.007479812018573284,
0.004454218782484531,
-0.01566043309867382,
-0.0005737442406825721,
0.008177798241376877,
0.007377001456916332,
-0.04489732161164284,
0.0394972525537014,
0.021999457851052284,
0.032951924949884415,
-0.006521130446344614,
-0.019352778792381287,
0.008289434015750885,
0.0013681082054972649,
-0.019100304692983627,
-0.027020838111639023,
-0.019017895683646202,
0.01904095523059368,
0.006617172155529261,
-0.061205148696899414,
-0.0014428665162995458,
-0.059985894709825516,
-0.036279261112213135,
0.005856235045939684,
-0.001696134451776743,
-0.0013746157055720687,
-0.03836571052670479,
-0.03212607651948929,
-0.03486171364784241,
0.04753522202372551,
-0.0023245736956596375,
0.012623704969882965,
0.007704241666942835,
-0.023013347759842873,
0.01403894368559122,
0.018216988071799278,
-0.021887198090553284,
-0.029796060174703598,
0.01907106675207615,
-0.036818064749240875,
-0.044961217790842056,
-0.011594136245548725,
-0.027302902191877365,
-0.05555542930960655,
0.0035411349963396788,
0.012049658223986626,
-0.007580250967293978,
-0.0970456600189209,
0.013859213329851627,
-0.027825767174363136,
-0.020292634144425392,
-0.019570432603359222,
-0.01590193435549736,
0.050389163196086884,
0.006956954021006823,
0.043295640498399734,
0.016152577474713326,
0.07489046454429626,
-0.029284991323947906,
-0.023348970338702202,
0.049978192895650864,
0.04891291260719299,
0.008875276893377304,
0.004758074879646301,
-0.04106244072318077,
0.01703333668410778,
0.0492478609085083,
0.01827082224190235,
-0.09965342283248901,
-0.03369506075978279,
0.014388937503099442,
-0.008730117231607437,
-0.006002967245876789,
-0.018920769914984703,
0.014941541478037834,
-0.01671849563717842,
-0.08745808154344559,
0.05345011129975319,
0.028668586164712906,
-0.05024930089712143,
0.06275337934494019,
0.04545340687036514,
0.06234932318329811,
-0.014144917018711567,
0.006134969647973776,
0.021234354004263878,
-0.009948614984750748,
-0.03176083043217659,
-0.021584341302514076,
-0.01825299672782421,
0.038252491503953934,
0.0007316361297853291,
-0.05775086581707001,
-0.00767036247998476,
-0.01866317167878151,
-0.050906743854284286,
-0.010762462392449379,
-0.028538303449749947,
-0.02446102909743786,
-0.07800759375095367,
-0.06626645475625992,
0.022183159366250038,
0.06473439931869507,
-0.021461227908730507,
-0.04152343049645424,
0.022204354405403137,
0.006637327838689089,
-0.02041076496243477,
0.019540240988135338,
0.04450702667236328,
-0.009750323370099068,
0.03421549126505852,
0.09307795763015747,
-0.038557421416044235,
0.015619316138327122,
0.0006976619479246438,
-0.02667158842086792,
0.019678719341754913,
0.006135836709290743,
-0.025358088314533234,
0.005005299113690853,
-0.027360044419765472
] |
[
5.112495422363281,
7.985459804534912
] |
Neural and Evolutionary Computing
|
Computer Science
|
cs-NE
|
cs-AI
|
na
|
2007-04-02T18:17:41
|
A novel way of picturing the processing of quantum information is described,
allowing a direct visualization of teleportation of quantum states and
providing a simple and intuitive understanding of this fascinating phenomenon.
The discussion is aimed at providing physicists a method of explaining
teleportation to non-scientists. The basic ideas of quantum physics are first
explained in lay terms, after which these ideas are used with a graphical
description, out of which teleportation arises naturally.
|
Visualizing Teleportation
|
physics.ed-ph quant-ph
|
0704.0051
| 2,007
|
[
-0.019185516983270645,
0.09021108597517014,
-0.0010487736435607076,
-0.060049355030059814,
0.006533344276249409,
-0.005331209860742092,
-0.005808460526168346,
0.003432805882766843,
-0.021435651928186417,
0.02380080707371235,
-0.027628140524029732,
0.043357450515031815,
0.07382360845804214,
0.008022069931030273,
0.004847078584134579,
-0.0035644317977130413,
0.027613582089543343,
-0.016684312373399734,
0.0435585118830204,
-0.01736057549715042,
-0.010911679826676846,
-0.0038748779334127903,
-0.0034325867891311646,
-0.0323781780898571,
0.009600804187357426,
-0.008252201601862907,
-0.02140861004590988,
0.000843371613882482,
-0.012677605263888836,
0.013767913915216923,
0.05071045085787773,
-0.05661899596452713,
-0.025762811303138733,
-0.020171593874692917,
-0.0575103797018528,
-0.049176543951034546,
0.004025544039905071,
-0.03319054841995239,
0.008203992620110512,
0.06980253010988235,
-0.016282591968774796,
-0.03265547379851341,
-0.020744023844599724,
-0.07386593520641327,
0.026902535930275917,
0.010220804251730442,
0.07001931220293045,
-0.023196395486593246,
0.008115435019135475,
-0.03770563006401062,
-0.026276806369423866,
0.0245808195322752,
0.00015056077972985804,
0.009290428832173347,
0.03199459984898567,
-0.012403304688632488,
-0.02134520374238491,
-0.02540147304534912,
0.1272057741880417,
-0.0361335463821888,
0.04309244453907013,
0.08426595479249954,
-0.022776175290346146,
0.0017321810591965914,
0.04903959110379219,
-0.016395529732108116,
-0.0758548229932785,
0.06594183295965195,
0.003913387656211853,
0.0006333961500786245,
0.03820693865418434,
-0.003403621958568692,
-0.034120410680770874,
0.006777252070605755,
0.0315546989440918,
0.054537806659936905,
0.020187390968203545,
-0.022239526733756065,
0.020143279805779457,
0.04088496044278145,
-0.004026312846690416,
-0.07685745507478714,
-0.01431579515337944,
-0.0019035525619983673,
0.06240877881646156,
-0.015906112268567085,
-0.014877413399517536,
-0.004123442806303501,
-0.0618380531668663,
0.02481955662369728,
-0.006102481856942177,
0.004703726153820753,
0.0897340178489685,
0.06028766557574272,
-0.08633461594581604,
0.003461417043581605,
-0.03641042858362198,
-0.001550628338009119,
-0.017774982377886772,
-0.021123431622982025,
-0.0028208510484546423,
0.023390937596559525,
0.008885525166988373,
-0.020536262542009354,
0.052225202322006226,
-0.004926452878862619,
0.015500430949032307,
-0.011377030983567238,
0.019968541339039803,
0.01768779568374157,
-0.06360509246587753,
-0.05417841300368309,
0.0007901845965534449,
0.01387347187846899,
0.004047413356602192,
-0.026161331683397293,
0.04275500029325485,
-0.06078123301267624,
0.012061106972396374,
0.0669475644826889,
-0.006239817477762699,
0.045906323939561844,
0.03271681070327759,
-0.003633086336776614,
0.049670908600091934,
0.04074610397219658,
-0.02766590565443039,
-0.036297574639320374,
0.011504740454256535,
-0.028619660064578056,
0.013555909506976604,
0.0019737340044230223,
-0.05586904287338257,
0.04652072489261627,
0.002456319984048605,
0.06809240579605103,
0.02766476757824421,
-0.06332843005657196,
0.027182022109627724,
-0.010863964445888996,
0.034213677048683167,
-0.04135451838374138,
-0.048321545124053955,
-0.0348614901304245,
0.035229749977588654,
-0.06291501969099045,
-0.004021217115223408,
-0.023136334493756294,
0.00012743796105496585,
-0.03420903906226158,
0.030319062992930412,
-0.002057121368125081,
-0.01671825908124447,
0.01270334143191576,
0.0251255314797163,
-0.03951061889529228,
0.0038598678074777126,
0.009842046536505222,
0.03359106928110123,
0.05202644690871239,
0.020086107775568962,
0.0026364633813500404,
-0.04566360265016556,
0.06470686942338943,
-0.05882812663912773,
-0.010231191292405128,
0.04823236167430878,
-0.035368382930755615,
0.06357450783252716,
-0.013315296731889248,
-0.017101453617215157,
-0.005154605023562908,
-0.038320716470479965,
-0.0034959728363901377,
0.003370073391124606,
0.01648031175136566,
0.04048899933695793,
-0.04520832747220993,
-0.006657017860561609,
-0.015283090062439442,
0.03308810293674469,
-0.05321614816784859,
0.00716850720345974,
0.018235184252262115,
0.016353799030184746,
-0.007360884454101324,
0.007740323897451162,
0.017801206558942795,
-0.015027491375803947,
-0.0669562891125679,
-0.024519503116607666,
-0.04001461714506149,
-0.027640121057629585,
-0.07466167956590652,
-0.027884772047400475,
-0.06580497324466705,
0.07237636297941208,
-0.008204762823879719,
0.027458060532808304,
-0.05023598670959473,
-0.014542881399393082,
0.023770589381456375,
-0.028981544077396393,
0.01971021667122841,
-0.033998772501945496,
0.046932585537433624,
0.0188481155782938,
0.015522790141403675,
-0.033226169645786285,
-0.010974240489304066,
0.06662968546152115,
0.02920409105718136,
0.025917770341038704,
-0.0012982890475541353,
-0.03779945522546768,
0.007530412171036005,
0.02604658529162407,
-0.035078007727861404,
-0.030898185446858406,
0.05504262074828148,
0.026219243183732033,
-0.03800395503640175,
0.006256430875509977,
0.025030657649040222,
0.04414387419819832,
0.00841226615011692,
-0.09208737313747406,
-0.05253280699253082,
-0.03359435498714447,
-0.018700245767831802,
-0.03467288985848427,
-0.0013806347269564867,
0.008357522077858448,
0.03302726149559021,
-0.00136479118373245,
0.023464351892471313,
-0.03351117670536041,
0.031375277787446976,
0.06347305327653885,
0.07155077904462814,
0.047324806451797485,
-0.017549119889736176,
0.016365302726626396,
-0.015652015805244446,
-0.06547101587057114,
0.0007508648559451103,
0.027392055839300156,
-0.0438484363257885,
-0.021380942314863205,
-0.021643422544002533,
-0.0015638035256415606,
-0.04365119710564613,
-0.013014355674386024,
0.0454196073114872,
0.034113071858882904,
-0.011516934260725975,
-0.04638553783297539,
0.03956715762615204,
-0.015711847692728043,
-0.060951873660087585,
0.015264417976140976,
-0.043838195502758026,
0.006614033132791519,
-0.02129190042614937,
-0.0560973696410656,
0.002586233662441373,
0.049704063683748245,
0.0396706648170948,
-0.04678002744913101,
-0.07639366388320923,
-0.03484032675623894,
0.03912128508090973,
0.0004588391457218677,
0.02641909383237362,
0.005780874751508236,
-0.005798396188765764,
-0.006154615432024002,
-0.005803872365504503,
-0.01892954297363758,
-0.04969519004225731,
-0.10494330525398254,
0.00702004274353385,
-0.10085911303758621,
0.011112110689282417,
0.019096894189715385,
-0.048232849687337875,
0.056702665984630585,
-0.0015517714200541377,
-0.002821193542331457,
0.04518928751349449,
0.023315444588661194,
-0.011554677970707417,
0.009602866135537624,
0.017058320343494415,
-0.03492778539657593,
0.0638611689209938,
0.08045404404401779,
-0.006023084744811058,
-0.0007987874560058117,
0.027891268953680992,
0.0010294101666659117,
-0.0206539835780859,
0.05094579979777336,
0.03246903792023659,
0.01041839737445116,
0.006931082811206579,
-0.004534142091870308,
0.007376908790320158,
0.009380179457366467,
0.00858153123408556,
-0.022185318171977997,
0.03081420250236988,
-0.0031590110156685114,
0.013163971714675426,
-0.03701424598693848,
0.009403751231729984,
0.036318764090538025,
0.05423279479146004,
0.08673964440822601,
0.04989609867334366,
0.014109905809164047,
-0.006752318236976862,
0.01827235519886017,
-0.02718745917081833,
0.056244175881147385,
0.057583101093769073,
-0.021491268649697304,
0.01730821467936039,
-0.005471617914736271,
-0.03137568011879921,
-0.028686892241239548,
0.005539288278669119,
-0.05892826244235039,
-0.07647906243801117,
-0.05102140083909035,
-0.04733661934733391,
-0.014721209183335304,
0.05201420187950134,
0.019884871318936348,
-0.04864970222115517,
0.03124026395380497,
-0.07752235233783722,
-0.06096654012799263,
-0.011487416923046112,
0.009181339293718338,
0.015206093899905682,
-0.014971877448260784,
-0.0004169040475971997,
0.05955373868346214,
-0.04911685362458229,
-0.044253554195165634,
0.044210877269506454,
0.0174435805529356,
-0.002980319084599614,
-0.06316791474819183,
0.06357520073652267,
0.006660017184913158,
-0.02667958289384842,
0.0605812668800354,
-0.005045084748417139,
-0.010898019187152386,
-0.009324313141405582,
0.03685703128576279,
-0.027085203677415848,
0.02062145806849003,
-0.011415272019803524,
-0.010081403888761997,
0.04010320454835892,
0.0233272947371006,
-0.044184260070323944,
-0.02762184478342533,
-0.04930693656206131,
-0.008653318509459496,
0.006589324679225683,
0.05483584105968475,
0.007708280347287655,
-0.06706507503986359,
-0.011557190679013729,
0.005869394168257713,
0.0036450682673603296,
0.022286690771579742,
0.01165331993252039,
0.06594529747962952,
0.027845177799463272,
0.045203302055597305,
0.028956647962331772,
-0.028544830158352852,
-0.0030914656817913055,
-0.011673718690872192,
0.015068774111568928,
0.0008726344094611704,
-0.050943076610565186,
0.0015480347210541368,
0.01723238080739975,
-0.0009006155305542052,
0.012106130830943584,
0.056513238698244095,
0.005135471001267433,
0.055145181715488434,
-0.024764811620116234,
-0.03435627371072769,
-0.05276108533143997,
0.0023854735773056746,
-0.030980810523033142,
-0.023105885833501816,
0.004122338257730007,
-0.0010187765583395958,
-0.025250079110264778,
0.06548933684825897,
-0.033220671117305756,
0.004164212848991156,
0.05917386710643768,
-0.03937666490674019,
-0.06543227285146713,
-0.01028685923665762,
0.06370582431554794,
0.04852483794093132,
-0.00006163834041217342,
-0.0016565085388720036,
0.027232082560658455,
-0.0038536186330020428,
0.09017016738653183,
0.03943490609526634,
-0.004438857082277536,
-0.0257419440895319,
-0.008907470852136612,
0.011074998416006565,
0.0062051801942288876,
-0.018287580460309982,
-0.04479661211371422,
0.02033650316298008,
-0.0060188970528542995,
0.04759163409471512,
0.02024080418050289,
-0.0678940936923027,
-0.016238734126091003,
0.017755215987563133,
0.03855457529425621,
0.0383293442428112,
0.06374973058700562,
0.07039951533079147,
-0.0330551452934742,
0.02098134532570839,
-0.01595320552587509,
-0.014694975689053535,
0.06172403693199158,
0.04387426748871803,
0.02407718077301979,
-0.03880147635936737,
-0.04133210331201553,
0.0311505738645792,
0.012836440466344357,
-0.0005133773083798587,
-0.007589675951749086,
0.06669826805591583,
-0.03177202120423317,
0.01364555861800909,
-0.011747131124138832,
0.02185712195932865,
0.034063708037137985,
0.021564049646258354,
0.09801746159791946,
-0.044693224132061005,
0.015479358844459057,
-0.01078771147876978,
0.014760367572307587,
-0.01247509103268385,
-0.0016829584492370486,
0.02396439202129841,
-0.016465667635202408,
-0.03139634430408478,
0.013877076096832752,
0.03557797893881798,
0.03217104449868202,
-0.001532493275590241,
-0.04073045402765274,
0.013741256669163704,
-0.014484701678156853,
-0.01975362002849579,
0.04640284553170204,
0.04404062032699585,
-0.001906136516481638,
0.010521242395043373,
-0.0626489520072937,
-0.010877516120672226,
0.010925495997071266,
-0.014470648020505905,
0.09619156271219254,
-0.06414421647787094,
-0.02675825171172619,
0.028813090175390244,
0.0019312724471092224,
-0.009857474826276302,
-0.008075178600847721,
-0.03812664374709129,
-0.10451092571020126,
0.011294864118099213,
0.004892473574727774,
0.003539253957569599,
-0.04337597265839577,
0.016361936926841736,
0.03477269411087036,
-0.013964192941784859,
0.029962200671434402,
0.01065881084650755,
-0.0060049924068152905,
0.0005348777631297708,
-0.09800495207309723,
-0.009019587188959122,
0.04254325106739998,
-0.018270812928676605,
0.037491269409656525,
-0.012002965435385704,
0.007034823298454285,
0.005706035532057285,
-0.06839785724878311,
0.01140295434743166,
0.0010726319160312414,
-0.05322265625,
0.046834029257297516,
0.001441226457245648,
-0.009493675082921982,
-0.012645544484257698,
0.011999540962278843,
-0.09137637913227081,
0.052755650132894516,
-0.0757741704583168,
-0.020062526687979698,
0.04974273964762688,
0.01802353747189045,
-0.009953770786523819,
0.06497768312692642,
0.0280438419431448,
-0.03583312779664993,
0.001443491317331791,
-0.02211141400039196,
-0.0004175583308096975,
0.029772114008665085,
0.014025218784809113,
0.04984878748655319,
0.006793640088289976,
0.029428282752633095,
0.0052820839919149876,
0.06880585104227066,
0.03613186255097389,
-0.03447049856185913,
-0.07718288898468018,
-0.008999914862215519,
0.010864528827369213,
-0.029605576768517494,
0.014818276278674603,
-0.03451722487807274,
0.03700410947203636,
-0.059293922036886215,
0.018976928666234016,
-0.009633535519242287,
-0.01072152890264988,
-0.034864384680986404,
-0.04317920655012131,
0.029472336173057556,
-0.004741801414638758,
0.06476116925477982,
0.07019685208797455,
0.02085963822901249,
0.024694709107279778,
-0.03229681774973869,
-0.023116162046790123,
0.012519437819719315,
0.03553479537367821,
0.021336577832698822,
0.00463295029476285,
-0.009581713937222958,
-0.04961225017905235,
0.026424558833241463,
-0.005651730112731457,
-0.04942968487739563,
0.05813233181834221,
-0.02438059076666832,
-0.07979399710893631,
-0.01971128210425377,
-0.011661535128951073,
-0.00025396686396561563,
0.014029859565198421,
-0.03404909744858742,
-0.043712317943573,
0.0030847059097141027,
-0.04979454353451729,
-0.0247541144490242,
0.04720859229564667,
0.017972873523831367,
-0.04653589800000191,
0.011680014431476593,
-0.007596158422529697,
-0.07295434176921844,
-0.01855488494038582,
0.0064965905621647835,
0.017203468829393387,
0.0048334309831261635,
-0.036283981055021286,
0.013707690872251987,
-0.02533349022269249,
-0.03931000828742981,
0.01992049627006054,
0.015962984412908554,
0.016061410307884216,
0.10173477232456207,
-0.007853158749639988,
0.016414228826761246,
-0.01344056986272335,
-0.041924670338630676,
0.02768837660551071,
0.005330098792910576,
-0.021162360906600952,
-0.045472756028175354,
-0.013208023272454739,
-0.04308486729860306,
0.06345217674970627,
-0.04107266664505005,
-0.0031561970245093107,
-0.028432926163077354,
0.015818670392036438,
-0.04754197597503662,
0.05145879462361336,
-0.024383705109357834,
0.015182782895863056,
0.034158188849687576,
-0.01790528930723667,
-0.0275897067040205,
0.026830129325389862,
0.08367133140563965,
-0.018506277352571487,
-0.033487409353256226,
-0.03094448149204254,
0.008975458331406116,
0.004233280662447214,
0.032628823071718216,
-0.0052497112192213535,
0.019700156524777412,
-0.014254149980843067,
0.020955007523298264,
0.0017428059363737702,
-0.051158804446458817,
0.016898948699235916,
-0.0363977774977684,
0.0051752119325101376,
0.03819306194782257,
-0.009266761131584644,
0.014064246788620949,
-0.0477098748087883,
0.02260088361799717,
0.0665895864367485,
0.0245750080794096,
-0.007291525602340698,
0.03892459720373154,
0.024802295491099358,
-0.00546229537576437,
0.0316651351749897,
0.006588820833712816,
-0.02853325940668583,
-0.07199617475271225,
-0.05092443898320198,
-0.023483963683247566,
-0.0143914008513093,
-0.027026107534766197,
0.02410663291811943,
-0.014219372533261776,
0.0006560496403835714,
-0.05572490766644478,
-0.05980498716235161,
0.04201677441596985,
-0.022220732644200325,
-0.03142806515097618,
-0.020200705155730247,
0.010364067740738392,
-0.014331931248307228,
-0.0020255660638213158,
-0.003430318320170045,
0.007197918836027384,
-0.021343059837818146,
-0.030654266476631165,
-0.009973736479878426,
0.04012299329042435,
0.023146633058786392,
0.012623438611626625,
-0.032108888030052185,
0.013537343591451645,
-0.016378585249185562,
0.014367367140948772,
-0.08822712302207947,
-0.035910360515117645,
0.010263018310070038,
-0.015437699854373932,
0.011756694875657558,
-0.05039985105395317,
0.07027572393417358,
0.0022385548800230026,
-0.009000221267342567,
-0.0047787027433514595,
0.0281786248087883,
0.07472586631774902,
0.010574499145150185,
0.0131074832752347,
-0.026296265423297882,
0.0036139334551990032,
0.0020739748142659664,
-0.06522168219089508,
0.04561026021838188,
0.01365270558744669,
-0.007541893515735865,
0.02369970828294754,
0.0006348565220832825,
0.026456529274582863,
0.09065686911344528,
0.03743521496653557,
-0.013221400789916515,
-0.0014586502220481634,
0.023160742595791817,
0.012831772677600384,
0.012133810669183731,
0.014252780005335808,
0.008709671907126904,
0.017434721812605858,
-0.07062815129756927,
0.03604210168123245,
-0.02478359453380108,
-0.0011512170312926173,
0.007640223018825054,
0.008602458983659744,
0.0033883738797158003,
0.007111947517842054,
0.04463648423552513,
0.04421934112906456,
-0.024954065680503845,
-0.001561095006763935,
-0.0464167557656765,
0.005833649076521397,
-0.03537578880786896,
-0.022837139666080475,
-0.019926832988858223,
0.004224860109388828,
0.0036101213190704584,
-0.026170002296566963,
0.004534189123660326,
-0.0007090828730724752,
-0.010144646279513836,
-0.05559930577874184,
-0.06394151598215103,
0.04163461923599243,
0.04245159029960632,
-0.05857822299003601,
0.01565520465373993,
0.00203096866607666,
-0.017631150782108307,
0.01728927344083786,
0.04579494521021843,
0.0019239357206970453,
-0.019389688968658447,
0.01852763630449772,
0.06187157332897186,
-0.004257885739207268,
-0.0015054710675030947,
-0.011045636609196663,
0.013914237730205059,
0.039968930184841156,
-0.0686776340007782,
0.014590679667890072,
-0.050129592418670654,
0.041377510875463486
] |
[
6.737797737121582,
0.5494744777679443
] |
Physics Education
|
General Physics
|
physics-ed-ph
|
quant-ph
|
na
|
2007-03-31T20:07:39
|
We study space-time symmetries in scalar quantum field theory (including
interacting theories) on static space-times. We first consider Euclidean
quantum field theory on a static Riemannian manifold, and show that the
isometry group is generated by one-parameter subgroups which have either
self-adjoint or unitary quantizations. We analytically continue the
self-adjoint semigroups to one-parameter unitary groups, and thus construct a
unitary representation of the isometry group of the associated Lorentzian
manifold. The method is illustrated for the example of hyperbolic space, whose
Lorentzian continuation is Anti-de Sitter space.
|
Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries
|
hep-th
|
0704.0052
| 2,007
|
[
-0.011668641120195389,
0.043617647141218185,
-0.03109689988195896,
-0.037582267075777054,
0.008180681616067886,
0.03223569318652153,
0.04265392944216728,
0.01031589973717928,
-0.038276925683021545,
0.025032473728060722,
-0.05055136978626251,
0.039184585213661194,
-0.02033841423690319,
0.05146455392241478,
-0.017563335597515106,
-0.014215351082384586,
0.04119473695755005,
0.02284623496234417,
0.004430245142430067,
-0.03456658869981766,
-0.020086174830794334,
-0.019137175753712654,
0.03191373869776726,
-0.024599362164735794,
0.09324582666158676,
-0.005700321402400732,
0.056397151201963425,
0.004177727736532688,
-0.021764768287539482,
-0.03191434592008591,
0.06274949014186859,
0.03322545066475868,
0.017307400703430176,
-0.04938402399420738,
-0.01948941871523857,
-0.08445291221141815,
0.03470083698630333,
-0.018674883991479874,
-0.011826211586594582,
0.051233746111392975,
0.041426852345466614,
-0.052397266030311584,
-0.015441539697349072,
-0.03047998435795307,
0.01856687292456627,
-0.00256793643347919,
0.021413451060652733,
0.043557170778512955,
0.05594194680452347,
0.009304152801632881,
-0.009974694810807705,
0.038379546254873276,
0.020303349941968918,
-0.07086676359176636,
-0.038702331483364105,
0.006126503460109234,
0.00802875030785799,
-0.011528898030519485,
0.06615588068962097,
0.051779281347990036,
-0.020068228244781494,
0.032739169895648956,
-0.020133091136813164,
0.032212480902671814,
0.012410401366651058,
-0.0009016080293804407,
-0.04652046412229538,
-0.028240082785487175,
-0.05280030146241188,
-0.017656125128269196,
0.03533452749252319,
-0.046106256544589996,
0.03659342601895332,
0.04271410033106804,
-0.013938603922724724,
0.016766848042607307,
0.017139462754130363,
0.005545633379369974,
-0.025892486795783043,
-0.018265319988131523,
-0.015717675909399986,
-0.0644158273935318,
0.0172642283141613,
0.007914936169981956,
0.09706975519657135,
-0.004179233685135841,
0.028111543506383896,
0.04877474159002304,
-0.06192200258374214,
0.03338070586323738,
0.020169345661997795,
0.0019582530949264765,
0.05593640357255936,
0.06220060959458351,
-0.04178905859589577,
0.03632722795009613,
-0.034692663699388504,
0.028610626235604286,
-0.04120118170976639,
-0.05652065947651863,
-0.0012034677201882005,
0.036426346749067307,
0.03244313597679138,
0.0538923516869545,
0.049973197281360626,
0.042495399713516235,
0.014025630429387093,
0.011868057772517204,
0.02054186910390854,
0.010628740303218365,
-0.07798313349485397,
0.006205400452017784,
-0.004801606293767691,
-0.017723744735121727,
-0.04145180061459541,
-0.040846988558769226,
0.047289855778217316,
-0.10452178865671158,
-0.008347203023731709,
0.05440131574869156,
0.001546105952002108,
0.039349623024463654,
0.032190367579460144,
-0.022988053038716316,
0.010807151906192303,
0.032995760440826416,
-0.07826410233974457,
-0.04640327766537666,
0.0131813520565629,
-0.02693161740899086,
0.03668821230530739,
0.018537474796175957,
-0.0677628219127655,
0.036240775138139725,
-0.03308508172631264,
0.042744386941194534,
-0.018147986382246017,
-0.020645279437303543,
0.03166792914271355,
0.0106849055737257,
0.017092440277338028,
-0.020566800609230995,
0.012845100834965706,
-0.003254018956795335,
-0.01893835887312889,
-0.0726771280169487,
0.0509970560669899,
-0.09679856151342392,
-0.02374659664928913,
-0.015860626474022865,
0.0014043606352061033,
0.043096888810396194,
0.0378379300236702,
0.04938434436917305,
0.013328501023352146,
-0.048454560339450836,
-0.01087423600256443,
0.03179636225104332,
0.07834749668836594,
-0.02130245603621006,
0.042077165096998215,
0.017956333234906197,
-0.03620434179902077,
0.006180956959724426,
-0.018616383895277977,
0.008769676089286804,
0.014739724807441235,
-0.008757541887462139,
0.03546973317861557,
0.04711640253663063,
-0.0485989935696125,
-0.022574158385396004,
-0.050749409943819046,
-0.02404078096151352,
0.0015709782019257545,
0.02925778739154339,
-0.035779692232608795,
-0.026637164875864983,
-0.0289072934538126,
0.02978704497218132,
0.050623733550310135,
-0.0677616149187088,
0.029689835384488106,
0.017900146543979645,
0.002688867971301079,
0.03057304583489895,
-0.03347094729542732,
-0.011045997962355614,
-0.06520383805036545,
0.017872707918286324,
0.032107263803482056,
0.021221915259957314,
-0.026364417746663094,
-0.010744997300207615,
-0.030635910108685493,
-0.0076528978534042835,
0.06676755845546722,
0.0038343677297234535,
-0.007692513056099415,
-0.028160259127616882,
0.021367942914366722,
0.019274013116955757,
-0.07070265710353851,
0.022053178399801254,
-0.002778224181383848,
0.07232123613357544,
0.011806254275143147,
-0.010891280137002468,
0.024542659521102905,
-0.00734836095944047,
0.08298767358064651,
0.040700946003198624,
0.02696509286761284,
0.01906680501997471,
-0.01154804416000843,
0.013906662352383137,
0.03866448625922203,
-0.07792676240205765,
-0.0450676754117012,
0.057934269309043884,
0.048941999673843384,
0.0027622845955193043,
0.04874084144830704,
0.025983573868870735,
0.04967596009373665,
0.01025904156267643,
-0.07008598744869232,
-0.027235230430960655,
-0.03415033966302872,
-0.014750156551599503,
-0.032435521483421326,
-0.0253489688038826,
0.030161097645759583,
0.006627100054174662,
0.014878768473863602,
0.007590755820274353,
0.011500679887831211,
0.04935310035943985,
0.011709469370543957,
0.047729093581438065,
0.04235457628965378,
0.036031533032655716,
-0.019987063482403755,
-0.01706366240978241,
-0.03950648754835129,
-0.022748252376914024,
-0.00014499582175631076,
-0.0096354391425848,
-0.05433035269379616,
0.012415006756782532,
-0.0114307701587677,
-0.014923806302249432,
-0.024255577474832535,
0.003339397022500634,
0.005435108672827482,
-0.045465949922800064,
-0.03091544657945633,
0.03710954263806343,
-0.06298133730888367,
-0.08764335513114929,
0.053882770240306854,
-0.06173788756132126,
0.0009225927642546594,
-0.022844301536679268,
-0.013952231965959072,
-0.034439776092767715,
0.029824115335941315,
0.009320983663201332,
-0.0002749801496975124,
-0.028322692960500717,
0.021055227145552635,
0.046373989433050156,
0.0442219041287899,
0.06113981828093529,
-0.03470998257398605,
0.009352460503578186,
0.011051692068576813,
-0.020185142755508423,
-0.03761948645114899,
-0.007449571043252945,
0.010608210228383541,
-0.03851206600666046,
-0.07275622338056564,
0.01211747620254755,
0.0035881001967936754,
0.01361904013901949,
0.04565972834825516,
0.0026146031450480223,
0.01850091852247715,
0.02746627666056156,
0.0022700733970850706,
0.018559027463197708,
0.009483544155955315,
0.03185243532061577,
0.015457561239600182,
0.06341956555843353,
0.023199494928121567,
-0.04360362887382507,
-0.011872148141264915,
-0.0065484000369906425,
-0.060237154364585876,
0.007490025367587805,
0.0582229420542717,
-0.027430476620793343,
0.01680111326277256,
-0.04555419832468033,
-0.01497672963887453,
-0.047159530222415924,
0.04143879562616348,
-0.0049929325468838215,
-0.059076424688100815,
0.01588929444551468,
-0.01647254079580307,
0.010183291509747505,
-0.05705655366182327,
0.02704795077443123,
0.02513602189719677,
-0.016212118789553642,
0.08585552126169205,
-0.0050286781042814255,
-0.007106182165443897,
-0.004715800751000643,
0.012414750643074512,
-0.02367766760289669,
0.03817475959658623,
0.02673635259270668,
-0.021203527227044106,
0.03108065016567707,
-0.038620732724666595,
-0.05508553609251976,
0.035798195749521255,
0.0377131849527359,
-0.0038180281408131123,
-0.026206960901618004,
-0.02400200441479683,
0.014994601719081402,
-0.0488014742732048,
-0.002955392235890031,
-0.04825304448604584,
-0.012570340186357498,
0.003297565272077918,
-0.0131546501070261,
-0.04544414207339287,
-0.005494703538715839,
-0.01127123273909092,
0.05923691764473915,
-0.01531823631376028,
-0.01420512143522501,
0.030370740219950676,
0.03254281356930733,
-0.05183276906609535,
0.0028853383846580982,
0.02658933959901333,
-0.017002206295728683,
-0.03460632264614105,
0.04598173499107361,
0.0788671225309372,
0.013116536661982536,
0.036461081355810165,
-0.021996555849909782,
-0.012278489768505096,
-0.01378362812101841,
0.00868155900388956,
0.01913616620004177,
0.011595449410378933,
0.012368006631731987,
-0.024952510371804237,
-0.023550748825073242,
0.01737154647707939,
-0.011033223941922188,
0.00726605299860239,
-0.05443641543388367,
0.0016315426910296082,
0.054315246641635895,
-0.0019097456242889166,
-0.02751217409968376,
-0.026150112971663475,
0.002415897324681282,
-0.006258152890950441,
-0.03458404913544655,
0.07911305874586105,
0.019060654565691948,
0.03935148939490318,
0.021055467426776886,
0.034890204668045044,
0.0434611551463604,
-0.07138167321681976,
-0.0014246910577639937,
-0.04243927076458931,
-0.0034511382691562176,
0.01888900063931942,
-0.04657479748129845,
-0.022854460403323174,
0.006419242825359106,
0.006347768474370241,
-0.02087840810418129,
0.01012072991579771,
0.018859364092350006,
0.017228849232196808,
-0.018061339855194092,
-0.016616396605968475,
-0.05249212682247162,
0.0059609804302453995,
-0.0030030047055333853,
-0.043931994587183,
0.003984511364251375,
-0.0219013262540102,
-0.07883990556001663,
0.05307358130812645,
0.019295038655400276,
0.01352870836853981,
0.03858716040849686,
0.019015751779079437,
-0.11937247961759567,
0.03371717780828476,
0.02536642551422119,
0.06799907982349396,
-0.04814271256327629,
0.006308953743427992,
-0.03365589678287506,
-0.02938368357717991,
0.06615206599235535,
0.03401576727628708,
-0.046025246381759644,
-0.04297206923365593,
0.0007066702819429338,
0.02113351598381996,
-0.013391785323619843,
-0.04331003874540329,
-0.06708835810422897,
0.03902897983789444,
0.007478463463485241,
0.014342894777655602,
0.021062271669507027,
-0.0733642578125,
-0.012777226977050304,
-0.0018979307496920228,
0.01239107921719551,
-0.036834344267845154,
0.011715948581695557,
0.08708858489990234,
-0.04754560813307762,
0.010283863171935081,
-0.022022558376193047,
0.006098420824855566,
0.05664423853158951,
0.03740060329437256,
-0.0449240542948246,
-0.039835672825574875,
-0.0315101332962513,
0.03567802160978317,
0.044868361204862595,
0.007680528797209263,
0.0525679886341095,
0.038087114691734314,
-0.021003130823373795,
-0.023668522015213966,
0.02047165483236313,
0.04409102723002434,
0.032940011471509933,
-0.00688380328938365,
0.02602831833064556,
0.00779375433921814,
0.035308435559272766,
-0.03523653373122215,
-0.036122459918260574,
-0.06747090816497803,
0.05376261845231056,
-0.023409588262438774,
0.06581288576126099,
0.023317646235227585,
0.03764791414141655,
0.009131068363785744,
-0.009361689910292625,
-0.012427995912730694,
0.012467015534639359,
0.0054188622161746025,
-0.04079374298453331,
-0.039609890431165695,
-0.005311364307999611,
0.05124056339263916,
0.0005980820278637111,
-0.0006342381238937378,
-0.00323318550363183,
0.0018864740850403905,
0.047529783099889755,
0.022551892325282097,
0.0309913232922554,
-0.007440965157002211,
0.014636777341365814,
-0.017027121037244797,
0.02200106903910637,
0.029811354354023933,
0.008785136975347996,
-0.04504109546542168,
0.026906073093414307,
-0.019835714250802994,
-0.03751499205827713,
0.024696452543139458,
-0.02635020948946476,
-0.003975323401391506,
0.040487516671419144,
0.05211276188492775,
-0.02284282073378563,
-0.001603809418156743,
0.020373385399580002,
0.028641197830438614,
-0.046750232577323914,
-0.050993796437978745,
0.04579827934503555,
0.008930510841310024,
0.029542140662670135,
0.04363010451197624,
0.05787675827741623,
0.05112864449620247,
0.007733503356575966,
0.04372374713420868,
-0.0041200583800673485,
-0.05746223405003548,
-0.024878034368157387,
-0.031006811186671257,
0.032105207443237305,
0.036110054701566696,
-0.014394144527614117,
-0.02797766774892807,
0.04228651523590088,
-0.036313846707344055,
-0.06414205580949783,
0.014003202319145203,
-0.0051842667162418365,
0.02600334770977497,
0.02050388790667057,
0.015581317245960236,
-0.022453084588050842,
0.06309407949447632,
-0.07330916076898575,
0.030147826299071312,
0.06053388491272926,
-0.005062902346253395,
0.0461469329893589,
-0.062423791736364365,
-0.020430855453014374,
0.017932763323187828,
-0.004146832041442394,
0.0002885061257984489,
-0.03274373710155487,
-0.07588286697864532,
0.04513177648186684,
0.0042655374854803085,
-0.02376549504697323,
0.003909749444574118,
-0.043913643807172775,
0.022962119430303574,
-0.05090980976819992,
-0.011526813730597496,
-0.03553817421197891,
0.01956893689930439,
-0.04088371619582176,
-0.06187639757990837,
0.013465032912790775,
0.011349639855325222,
-0.0027475703973323107,
0.029177263379096985,
0.0009210246498696506,
0.013511951081454754,
-0.08248202502727509,
0.0036266783718019724,
-0.0560583770275116,
0.0731758400797844,
-0.019596630707383156,
0.03307965770363808,
0.005844624247401953,
0.014785208739340305,
0.011621217243373394,
-0.0314498133957386,
-0.0364835225045681,
0.03567996621131897,
-0.03506040945649147,
-0.10032092779874802,
-0.000022200383682502434,
-0.021889930590987206,
-0.008363253436982632,
0.017894454300403595,
-0.044430091977119446,
-0.07972268760204315,
0.017702288925647736,
-0.008082069456577301,
-0.029801983386278152,
0.06065569818019867,
0.02510000765323639,
-0.010400216095149517,
-0.028611555695533752,
-0.014378715306520462,
0.01762482151389122,
-0.01462271437048912,
0.01958703249692917,
-0.002411056309938431,
0.011426190845668316,
-0.046150460839271545,
-0.020888708531856537,
-0.005298792850226164,
0.012893269769847393,
0.11407052725553513,
-0.007577013690024614,
0.0620526559650898,
0.07866344600915909,
-0.05058113485574722,
0.019251301884651184,
0.01664462313055992,
-0.0033638973254710436,
-0.01747140847146511,
0.009991285391151905,
-0.08993109315633774,
0.0183115154504776,
-0.0038704301696270704,
-0.05176888406276703,
0.05597300827503204,
-0.011441908776760101,
-0.01833552122116089,
-0.035283345729112625,
0.014966352842748165,
-0.0013321660226210952,
-0.028624380007386208,
-0.045544855296611786,
0.01719382032752037,
0.006381297018378973,
0.0028301801066845655,
-0.04426629841327667,
0.0325140655040741,
0.044906504452228546,
0.04778459668159485,
-0.038599807769060135,
0.008371957577764988,
-0.018330439925193787,
0.003116614418104291,
0.0011480922112241387,
-0.02456001192331314,
0.035181473940610886,
-0.015313330106437206,
0.04069359228014946,
-0.000043577703763730824,
0.005315088201314211,
0.0299480352550745,
0.011402794159948826,
-0.020187409594655037,
0.00894462876021862,
0.01636912301182747,
0.0015155336586758494,
-0.013299891725182533,
-0.012059507891535759,
0.11734695732593536,
0.06818670779466629,
-0.04043339937925339,
0.024366118013858795,
-0.006095061544328928,
-0.009900432080030441,
0.05533425882458687,
0.022514954209327698,
-0.02900511585175991,
-0.02067854441702366,
-0.009723115712404251,
0.008850814774632454,
-0.05490443855524063,
-0.0057962797582149506,
0.02998732030391693,
-0.011376175098121166,
-0.024316860362887383,
-0.007471118122339249,
0.002894097473472357,
0.03296617045998573,
-0.06468448042869568,
-0.03867084160447121,
0.00025422096950933337,
-0.037465646862983704,
-0.03535136207938194,
-0.04597897455096245,
-0.015763437375426292,
0.07354797422885895,
-0.03491796925663948,
-0.023504741489887238,
-0.006983735598623753,
0.04906001687049866,
0.006846367381513119,
0.007329417858272791,
-0.016469312831759453,
-0.026266740635037422,
0.0007577958167530596,
-0.046158161014318466,
-0.027324829250574112,
0.009436273016035557,
0.008024078793823719,
-0.021151240915060043,
-0.06267047673463821,
-0.06261928379535675,
0.0023849408607929945,
-0.0014333428116515279,
-0.00910272728651762,
0.017394796013832092,
-0.027294257655739784,
0.0067318822257220745,
-0.015897925943136215,
0.00643862783908844,
-0.0073103755712509155,
0.006083441432565451,
0.013410745188593864,
-0.049781449139118195,
0.008199919015169144,
0.014814506284892559,
0.03158900886774063,
-0.009040813893079758,
-0.035959191620349884,
0.012187935411930084,
0.04713061451911926,
0.007979222573339939,
0.08368367701768875,
-0.017343794927001,
-0.08218207955360413,
-0.011572517454624176,
0.06714481115341187,
-0.013363326899707317,
0.014542735181748867,
-0.012083567678928375,
-0.029101194813847542,
-0.016252124682068825,
-0.007964735850691795,
-0.0767868310213089,
-0.008793625049293041,
-0.04631759226322174,
0.10494619607925415,
-0.029090167954564095,
-0.014108005911111832,
0.0004088752903044224,
-0.04618950933218002,
0.03735145926475525,
-0.036126505583524704,
0.0030720580834895372,
-0.024199269711971283,
-0.033628787845373154,
0.004822493996471167,
-0.011235582642257214,
0.012515775859355927,
-0.033956028521060944,
0.03538496792316437,
0.010628322139382362,
-0.025960391387343407,
-0.028553009033203125,
-0.04437483102083206,
-0.02366018295288086,
0.01595636084675789,
-0.012678050436079502,
0.009456590749323368,
0.046357713639736176,
0.014523956924676895,
0.017198769375681877,
0.060072533786296844,
-0.015475576743483543,
-0.03779264912009239,
-0.02468430995941162,
0.08760643750429153,
-0.026821818202733994,
0.028506917878985405,
0.044475238770246506,
0.009158392436802387,
0.04683178290724754,
-0.012633254751563072,
0.017601778730750084,
-0.048888031393289566,
-0.005078263580799103
] |
[
11.910377502441406,
1.335047721862793
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-03-31T20:14:41
|
The aim of the present paper is to provide a global presentation of the
theory of special Finsler manifolds. We introduce and investigate globally (or
intrinsically, free from local coordinates) many of the most important and most
commonly used special Finsler manifolds: locally Minkowskian, Berwald,
Landesberg, general Landesberg, $P$-reducible, $C$-reducible,
semi-$C$-reducible, quasi-$C$-reducible, $P^{*}$-Finsler, $C^{h}$-recurrent,
$C^{v}$-recurrent, $C^{0}$-recurrent, $S^{v}$-recurrent, $S^{v}$-recurrent of
the second order, $C_{2}$-like, $S_{3}$-like, $S_{4}$-like, $P_{2}$-like,
$R_{3}$-like, $P$-symmetric, $h$-isotropic, of scalar curvature, of constant
curvature, of $p$-scalar curvature, of $s$-$ps$-curvature. The global
definitions of these special Finsler manifolds are introduced. Various
relationships between the different types of the considered special Finsler
manifolds are found. Many local results, known in the literature, are proved
globally and several new results are obtained. As a by-product, interesting
identities and properties concerning the torsion tensor fields and the
curvature tensor fields are deduced. Although our investigation is entirely
global, we provide; for comparison reasons, an appendix presenting a local
counterpart of our global approach and the local definitions of the special
Finsler spaces considered.
|
A Global Approach to the Theory of Special Finsler Manifolds
|
math.DG gr-qc
|
0704.0053
| 2,007
|
[
0.02726302482187748,
0.016558831557631493,
0.0029352717101573944,
0.0018644656520336866,
0.007653180509805679,
0.03632481396198273,
0.04719247668981552,
0.030830375850200653,
-0.07302024215459824,
0.029552869498729706,
-0.08263060450553894,
0.0403984859585762,
-0.002045903354883194,
-0.023069443181157112,
0.005682581569999456,
-0.04831651598215103,
0.007739895489066839,
-0.02528207376599312,
-0.018512235954403877,
0.0012937415158376098,
-0.047415491193532944,
-0.026482077315449715,
-0.004543433431535959,
-0.012260204181075096,
0.0827605202794075,
0.00275935186073184,
0.05035242810845375,
-0.02928341180086136,
-0.038231220096349716,
-0.0035007901024073362,
0.03820769116282463,
-0.038091644644737244,
0.005742788314819336,
-0.06995376199483871,
0.00491374870762229,
-0.06126869097352028,
0.07440639287233353,
-0.005914401262998581,
-0.0072279563173651695,
0.06119754537940025,
0.028721017763018608,
0.03317316621541977,
0.009291978552937508,
-0.00169404037296772,
0.026980360969901085,
0.02028554119169712,
-0.027201829478144646,
0.020053375512361526,
0.04071297124028206,
0.01766149513423443,
-0.041662395000457764,
0.04239656403660774,
0.016853144392371178,
-0.07923173159360886,
-0.025993673130869865,
-0.008695687167346478,
0.041265759617090225,
0.009910202585160732,
0.036855459213256836,
0.003200457664206624,
0.0038790865801274776,
0.03001311607658863,
-0.04980429634451866,
0.02941553108394146,
-0.02437901869416237,
-0.06660455465316772,
-0.046848878264427185,
0.008517829701304436,
0.0069271656684577465,
-0.015857866033911705,
0.026959022507071495,
-0.0019398300210013986,
0.07006193697452545,
0.005599112715572119,
-0.01944124326109886,
-0.020190544426441193,
-0.027584191411733627,
-0.03613964840769768,
0.03001551702618599,
0.020358994603157043,
0.003369317390024662,
-0.013624738901853561,
0.027054017409682274,
0.03301968425512314,
0.06749003380537033,
0.00944176409393549,
0.037365756928920746,
0.040272731333971024,
-0.051945943385362625,
-0.0025425616186112165,
0.02710709720849991,
-0.0037646624259650707,
0.07732260227203369,
0.08724600076675415,
-0.027232348918914795,
-0.014931031502783298,
0.014570571482181549,
0.021801816299557686,
-0.053659044206142426,
-0.07491069287061691,
-0.0035162554122507572,
0.05390411242842674,
0.015355749055743217,
0.0554804690182209,
0.07183609902858734,
0.010358824394643307,
0.0769680067896843,
0.034638047218322754,
0.06576360017061234,
-0.013923404738307,
-0.059972312301397324,
0.01729664020240307,
0.017901644110679626,
0.01563999243080616,
-0.04554733633995056,
-0.037126339972019196,
0.03481857106089592,
-0.11955565214157104,
0.009769842028617859,
0.07942131161689758,
-0.00015322418767027557,
-0.024630308151245117,
0.022319970652461052,
0.06725717335939407,
0.007420126814395189,
0.0684375911951065,
-0.03645998239517212,
-0.03590334579348564,
0.05018262192606926,
0.008900629356503487,
0.046119485050439835,
0.014146627858281136,
-0.04419074207544327,
-0.008560004644095898,
0.04206803813576698,
0.049374472349882126,
-0.06709101051092148,
0.00750041613355279,
0.017139960080385208,
-0.02374408207833767,
0.026058737188577652,
-0.017470596358180046,
-0.007854292169213295,
-0.0002382157399551943,
0.018139248713850975,
-0.06732126325368881,
0.03399159014225006,
-0.05038098245859146,
-0.028972197324037552,
-0.011826308444142342,
0.046275943517684937,
-0.008636589162051678,
0.000758552982006222,
0.009925393387675285,
-0.03833688795566559,
-0.03190784901380539,
0.0007667028112336993,
0.009777420200407505,
0.07496905326843262,
-0.004745590500533581,
0.014755469746887684,
0.025055862963199615,
0.040047965943813324,
0.050033725798130035,
-0.02938726171851158,
0.06590701639652252,
0.03491820767521858,
0.0007596930954605341,
0.023855123668909073,
-0.032986123114824295,
-0.0261857770383358,
0.0014194087125360966,
-0.00810573436319828,
-0.02151838317513466,
0.021922249346971512,
-0.06988877803087234,
-0.022893767803907394,
-0.05578786879777908,
-0.007235490716993809,
-0.005671504884958267,
-0.05738811939954758,
-0.006708618253469467,
0.04756834730505943,
0.015648454427719116,
0.0006202845834195614,
0.10986711829900742,
-0.03536764532327652,
-0.01835607923567295,
-0.04821031168103218,
-0.01218993030488491,
0.011168439872562885,
0.056614555418491364,
0.023376954719424248,
0.012740091420710087,
0.019530313089489937,
0.055956609547138214,
0.03617728874087334,
-0.019082173705101013,
-0.036692578345537186,
-0.007062740158289671,
0.007232489064335823,
-0.01623355969786644,
-0.05406598746776581,
-0.00122844148427248,
-0.015557622537016869,
0.04921545460820198,
0.002335640136152506,
-0.035438623279333115,
0.07216684520244598,
0.022171083837747574,
0.0898829773068428,
-0.06250827014446259,
0.010912834666669369,
0.015560421161353588,
-0.0013611712493002415,
0.032365139573812485,
0.00372884888201952,
-0.016353709623217583,
-0.015001747757196426,
0.008224633522331715,
0.04733278602361679,
0.019876623526215553,
0.022619254887104034,
0.019632354378700256,
0.04699394851922989,
0.003477207850664854,
-0.01982632279396057,
-0.0024807180743664503,
0.007929913699626923,
-0.019821172580122948,
-0.050132639706134796,
-0.08234699815511703,
0.08571905642747879,
0.03386823087930679,
-0.011858111247420311,
-0.017994282767176628,
0.004544263705611229,
0.0371258370578289,
0.053833238780498505,
0.05808088183403015,
-0.006444371305406094,
-0.015238362364470959,
0.015726011246442795,
-0.0016523918602615595,
-0.02297658659517765,
-0.003184025874361396,
0.03447077423334122,
-0.044551365077495575,
-0.005751124117523432,
0.013051728717982769,
-0.005917685572057962,
-0.02493203617632389,
0.04885760322213173,
0.030955877155065536,
0.051904741674661636,
-0.013386891223490238,
-0.01225077360868454,
0.06842238456010818,
0.0018836894305422902,
-0.05945650860667229,
0.02047506347298622,
0.010355315171182156,
-0.019416814669966698,
-0.02190159074962139,
-0.09495412558317184,
0.03993792086839676,
0.017331598326563835,
-0.009245512075722218,
0.014537478797137737,
-0.015524722635746002,
-0.023768147453665733,
0.005522382911294699,
0.05030496418476105,
0.1260182410478592,
-0.05151595175266266,
0.01516471616923809,
-0.006945572327822447,
-0.05256214365363121,
-0.05346599593758583,
0.005779382307082415,
-0.025833996012806892,
0.0087820403277874,
-0.020481647923588753,
-0.03527725115418434,
-0.002519299741834402,
0.020795002579689026,
0.016873536631464958,
0.015858689323067665,
0.007372110616415739,
0.05321047082543373,
-0.01853768154978752,
-0.012604555115103722,
-0.010328308679163456,
-0.0007648773607797921,
0.001825534040108323,
0.06730641424655914,
0.013248060829937458,
-0.01905161701142788,
-0.010073697194457054,
0.01644822582602501,
0.04310283064842224,
0.0027500803116708994,
0.006888910662382841,
-0.021194903180003166,
0.00742775434628129,
-0.04474621266126633,
-0.020263560116291046,
-0.05598512664437294,
0.07216234505176544,
0.0031802633311599493,
-0.05252017453312874,
-0.022414246574044228,
-0.005304147023707628,
-0.03030596673488617,
-0.05094224214553833,
0.07792896032333374,
0.04557251185178757,
0.005851105321198702,
0.035537246614694595,
-0.015516569837927818,
-0.0067128995433449745,
-0.0410999059677124,
-0.0036040404811501503,
-0.09321056306362152,
0.03909390792250633,
0.039976753294467926,
-0.031074367463588715,
-0.007128273136913776,
-0.05584098398685455,
-0.019585831090807915,
-0.03686899319291115,
0.025881893932819366,
-0.05643780902028084,
-0.01553097553551197,
-0.04375318065285683,
0.012242740020155907,
-0.06666156649589539,
0.04710861295461655,
-0.0031264140270650387,
-0.021818920969963074,
0.058260973542928696,
-0.01813303492963314,
-0.08918944001197815,
-0.033034902065992355,
-0.06220044940710068,
0.03690874204039574,
-0.005945871584117413,
-0.026786787435412407,
0.036853350698947906,
0.02327083982527256,
-0.06264711171388626,
0.010406582616269588,
0.035726163536310196,
-0.006691425573080778,
0.0010395494755357504,
0.04781270772218704,
0.03394153341650963,
-0.04512878507375717,
0.03950829431414604,
-0.015798106789588928,
0.029279738664627075,
-0.04906135052442551,
0.011530940420925617,
0.03393884748220444,
0.02300131507217884,
0.04130203276872635,
0.01958681270480156,
-0.018450021743774414,
-0.030918920412659645,
-0.019526181742548943,
-0.024887187406420708,
-0.02377578429877758,
0.0264785997569561,
0.01780541241168976,
0.0018107277574017644,
-0.036179691553115845,
-0.05614635720849037,
-0.0048012207262218,
-0.08372295647859573,
-0.03817904740571976,
0.055390045046806335,
-0.019599182531237602,
0.008860195055603981,
0.025463012978434563,
0.0035374327562749386,
0.01848931610584259,
-0.03248871490359306,
0.00401231599971652,
-0.011217104271054268,
0.014512941241264343,
0.02826797403395176,
-0.03410281613469124,
-0.0319637730717659,
0.0054484023712575436,
0.03852743282914162,
0.001758974976837635,
0.06970680505037308,
0.04892795532941818,
-0.03617284446954727,
-0.004273548256605864,
-0.03481709584593773,
-0.07266584783792496,
-0.01053039450198412,
-0.01922706328332424,
-0.027891980484128,
0.018501438200473785,
-0.05416053906083107,
-0.07815947383642197,
0.050508640706539154,
-0.00884360633790493,
0.03881410136818886,
-0.023738902062177658,
0.03356800973415375,
-0.10884897410869598,
0.1110580712556839,
-0.011191905476152897,
0.03334185853600502,
-0.05383111163973808,
0.006734867580235004,
-0.029392220079898834,
0.008767146617174149,
0.0025577552150934935,
0.0172558780759573,
0.005315139889717102,
0.021811027079820633,
0.003722622524946928,
0.021010829135775566,
-0.016606980934739113,
-0.011909489519894123,
-0.060568686574697495,
0.03189823031425476,
-0.00018607842503115535,
-0.0013845330104231834,
0.00033143049222417176,
-0.038269445300102234,
-0.007611340843141079,
-0.025447996333241463,
-0.028997737914323807,
-0.01875259168446064,
0.03483593836426735,
0.07529271394014359,
0.014569607563316822,
0.015850072726607323,
-0.014454124495387077,
0.01631358079612255,
0.04313506558537483,
0.050576698035001755,
-0.015276335179805756,
0.007331032771617174,
-0.004459059797227383,
-0.028227195143699646,
-0.003411647630855441,
-0.0049047009088099,
0.03781285136938095,
0.05048435926437378,
-0.0018087178468704224,
-0.0007959360955283046,
-0.020079687237739563,
0.017239723354578018,
-0.0009323434205725789,
0.012365804985165596,
0.00261468393728137,
0.04774168133735657,
0.011277828365564346,
0.0341094508767128,
-0.00970522966235876,
-0.03997831791639328,
0.023844366893172264,
-0.017450306564569473,
-0.016869166865944862,
0.016590921208262444,
0.024862881749868393,
0.015757694840431213,
-0.045781075954437256,
0.011311916634440422,
0.008709260262548923,
0.03025791607797146,
-0.015355336479842663,
-0.020801465958356857,
0.022971399128437042,
0.036381110548973083,
0.009225565008819103,
-0.039044979959726334,
-0.0223971176892519,
0.02778352051973343,
0.013608605600893497,
0.01138682197779417,
-0.011035432107746601,
-0.029132887721061707,
-0.02629007026553154,
-0.016572102904319763,
0.04647842422127724,
0.017062958329916,
0.03940564766526222,
-0.02989652380347252,
0.0025343785528093576,
0.018792126327753067,
-0.012664847075939178,
0.0011188412318006158,
-0.017608365043997765,
-0.0033943939488381147,
0.026892920956015587,
0.013004536740481853,
0.00316421315073967,
0.005589490290731192,
0.012768911197781563,
0.02908567525446415,
-0.009898639284074306,
-0.0008142503211274743,
0.03203527256846428,
-0.050151899456977844,
-0.0012256292393431067,
0.044974058866500854,
0.057798922061920166,
0.00542956730350852,
-0.03862732648849487,
0.022227413952350616,
-0.0008191595552489161,
-0.013562454842031002,
-0.03413412347435951,
0.0004006056406069547,
-0.03903575614094734,
0.03105783276259899,
-0.0056608933955430984,
-0.06187017634510994,
0.012259874492883682,
-0.06349653005599976,
-0.040010951459407806,
0.06348519772291183,
-0.07298674434423447,
-0.028699154034256935,
0.005634748842567205,
0.026002677157521248,
-0.015042225830256939,
0.014607821591198444,
-0.046705830842256546,
0.009801757521927357,
0.030544860288500786,
0.027921928092837334,
0.03888075798749924,
-0.030908530578017235,
-0.022979235276579857,
-0.05079130828380585,
0.004193473607301712,
0.013571858406066895,
-0.02830677665770054,
-0.04928179830312729,
0.03567750006914139,
0.0006703116814605892,
-0.037621162831783295,
-0.018738599494099617,
-0.02934616059064865,
0.05798314884305,
-0.09286949038505554,
0.055210087448358536,
-0.020367996767163277,
0.0307437926530838,
-0.046222951263189316,
-0.03828926384449005,
0.0012859435519203544,
0.02576710842549801,
-0.010962261818349361,
-0.015947511419653893,
-0.009270964190363884,
-0.051895562559366226,
-0.08564001321792603,
-0.010585920885205269,
-0.009178615175187588,
0.06477198004722595,
-0.01721295528113842,
-0.00453835679218173,
0.003199974074959755,
-0.004394629970192909,
0.012534328736364841,
0.03277275711297989,
-0.055173005908727646,
0.035758960992097855,
0.0026681851595640182,
-0.023227548226714134,
-0.03497599437832832,
0.0014016615459695458,
-0.01808641292154789,
0.0009239586652256548,
-0.03861243650317192,
-0.058749690651893616,
0.028297891840338707,
0.027222586795687675,
-0.07502623647451401,
0.029918452724814415,
-0.012962752021849155,
0.044371265918016434,
0.025839652866125107,
-0.04021839797496796,
-0.052237458527088165,
-0.009415827691555023,
0.026599133387207985,
0.05209845304489136,
0.023522691801190376,
0.002846660790964961,
-0.038642384111881256,
-0.006869936361908913,
0.04740900546312332,
0.07102420926094055,
-0.0313071608543396,
0.024861231446266174,
0.07205673307180405,
-0.005050573963671923,
0.017189687117934227,
0.026612943038344383,
0.0681956484913826,
0.047300856560468674,
-0.035301364958286285,
-0.053553204983472824,
-0.04836144670844078,
-0.03440437093377113,
-0.060971032828092575,
0.045227933675050735,
-0.028106048703193665,
0.0327049121260643,
-0.06748013943433762,
0.038406312465667725,
-0.04282403737306595,
0.02527698129415512,
-0.00016382156172767282,
-0.017339088022708893,
0.037215013056993484,
-0.0882251188158989,
-0.016263239085674286,
-0.0007440808112733066,
0.025456903502345085,
0.013389610685408115,
-0.002044738968834281,
-0.0338582880795002,
0.0156356580555439,
-0.012082692235708237,
0.014610344544053078,
-0.015460564754903316,
0.00821384321898222,
-0.0015164959477260709,
0.08507302403450012,
0.03467102721333504,
-0.017798224464058876,
0.0059877727180719376,
-0.02273915708065033,
0.05909549817442894,
0.008218551985919476,
-0.020308202132582664,
0.024229813367128372,
-0.001536601921543479,
0.00942058302462101,
0.08181855827569962,
0.058975860476493835,
-0.026724135503172874,
0.011777611449360847,
0.009094081819057465,
-0.04202323034405708,
0.0009982975898310542,
-0.021264713257551193,
-0.003980150446295738,
0.012760959565639496,
-0.028782900422811508,
0.01241534948348999,
-0.006870766635984182,
-0.03363365679979324,
-0.014581378549337387,
-0.0016049579717218876,
-0.014538097195327282,
-0.03472725301980972,
-0.027991311624646187,
0.1007685512304306,
-0.010533277876675129,
-0.011364597827196121,
-0.03146126866340637,
0.008038763888180256,
-0.027249712496995926,
-0.002752624684944749,
-0.0016482719220221043,
0.022556867450475693,
0.006151652429252863,
-0.0379137322306633,
0.03789415955543518,
0.06478352844715118,
-0.041430678218603134,
0.00423795823007822,
-0.025330910459160805,
-0.00658193975687027,
0.03072343021631241,
-0.030681109055876732,
-0.004684753250330687,
-0.02122139185667038,
0.04286744073033333,
0.002298906212672591,
-0.0014775412855669856,
-0.06059657782316208,
0.017035817727446556,
-0.018643086776137352,
-0.02700343355536461,
0.025709029287099838,
-0.047596387565135956,
0.0045786271803081036,
0.002303431276232004,
0.038342174142599106,
-0.05189092457294464,
0.04584663361310959,
-0.023183295503258705,
-0.021633261814713478,
-0.07584424316883087,
0.026998553425073624,
-0.028557268902659416,
0.04667949676513672,
-0.014064356684684753,
0.008333288133144379,
0.04625285044312477,
0.005731254816055298,
0.01825159601867199,
0.024871842935681343,
-0.016311775892972946,
-0.05755627900362015,
-0.008180621080100536,
-0.04416118189692497,
0.0022448250092566013,
-0.01746445521712303,
-0.07109961658716202,
-0.0052814781665802,
-0.028297165408730507,
-0.021923227235674858,
-0.052464455366134644,
-0.03779218718409538,
0.0611177496612072,
0.022081606090068817,
0.007032215595245361,
-0.001805959502235055,
-0.04674733802676201,
0.06487249583005905,
-0.007380501367151737,
-0.027759557589888573,
-0.0015340209938585758,
-0.035664960741996765,
0.017970815300941467,
-0.03895701840519905,
0.030130930244922638,
-0.07579757273197174,
-0.0008093485375866294,
0.03533390536904335,
-0.038919031620025635,
-0.023887893185019493,
-0.012346720322966576,
0.0022119113709777594,
-0.027265455573797226,
0.009028241969645023,
-0.04306598752737045,
0.019889144226908684,
0.01393409539014101,
0.00009446265903534368,
-0.006849000696092844,
0.015382375568151474,
0.011094076558947563,
0.03314971178770065,
0.026228981092572212,
-0.006996878422796726,
-0.043395061045885086,
0.008520719595253468,
0.0004461659409571439,
0.08666809648275375,
0.018912317231297493,
-0.00011055006325477734,
-0.032168351113796234,
0.007156693376600742
] |
[
2.97037410736084,
1.6908063888549805
] |
Differential Geometry
|
Mathematics
|
math-DG
|
gr-qc
|
na
|
2007-04-02T18:14:21
|
In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with
$0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the
elements in these spaces, their interpolation properties, and the behavior of
singular integrals and other operators acting on them.
|
The Hardy-Lorentz Spaces $H^{p,q}(R^n)$
|
math.CA math.FA
|
0704.0054
| 2,007
|
[
0.003255218733102083,
0.015844250097870827,
-0.008246099576354027,
0.05037196725606918,
0.03481023386120796,
0.028242893517017365,
0.018229294568300247,
0.031180109828710556,
-0.029490390792489052,
-0.013762311078608036,
-0.07271768897771835,
0.016605224460363388,
-0.005064839962869883,
-0.018546834588050842,
-0.00004299513602745719,
-0.04389504715800285,
0.0564938522875309,
-0.002215813612565398,
-0.0341510996222496,
-0.017195556312799454,
-0.0395662859082222,
-0.020344678312540054,
-0.037971775978803635,
-0.09814101457595825,
0.09309718012809753,
0.03798487409949303,
0.05951983481645584,
-0.03008555807173252,
-0.07446639984846115,
-0.0004099935758858919,
0.01059237401932478,
-0.05736330896615982,
-0.05109703168272972,
-0.06552615761756897,
-0.033119745552539825,
-0.03023429960012436,
0.08183468878269196,
0.02064632624387741,
0.008060470223426819,
0.01382013875991106,
0.023312054574489594,
-0.025857342407107353,
0.034888215363025665,
-0.048347342759370804,
0.005880135577172041,
0.010938096791505814,
0.00919303484261036,
0.04193420335650444,
0.059612955898046494,
0.04364462569355965,
-0.03697945550084114,
0.013565466739237309,
-0.00954313576221466,
-0.08174300938844681,
-0.02006058767437935,
0.026211196556687355,
0.01692681759595871,
-0.021312879398465157,
0.04196338355541229,
-0.015038951300084591,
0.006435273680835962,
0.04578578844666481,
-0.03540008142590523,
0.017652126029133797,
0.018455643206834793,
-0.018943069502711296,
-0.02178739756345749,
0.03762334957718849,
0.0023903583642095327,
-0.03502591699361801,
0.03597349300980568,
-0.011133642867207527,
-0.023007936775684357,
0.03703228011727333,
-0.060555361211299896,
0.026157774031162262,
0.006524768192321062,
0.03754991665482521,
0.04109768196940422,
0.03659145161509514,
-0.025919903069734573,
-0.03796916827559471,
0.06339361518621445,
0.04275653883814812,
0.007456523831933737,
0.05518043786287308,
0.05494849383831024,
0.01070735789835453,
-0.044446635991334915,
0.03895404562354088,
0.034454479813575745,
0.016944874078035355,
0.05633864179253578,
0.04285841062664986,
-0.06134280934929848,
-0.006715092342346907,
-0.01826324313879013,
-0.0016088502015918493,
-0.005244874861091375,
-0.04166347160935402,
0.01547812670469284,
0.0204231608659029,
0.02803167700767517,
-0.016414619982242584,
0.022122416645288467,
-0.011442271992564201,
0.044224970042705536,
-0.015281802974641323,
-0.0014051849720999599,
0.0025352099910378456,
-0.04818696901202202,
-0.025296831503510475,
0.02087719365954399,
-0.043131180107593536,
-0.017276424914598465,
0.009655861184000969,
0.034059077501297,
-0.0884503722190857,
0.03547797352075577,
0.08715960383415222,
0.06583502888679504,
0.0448712557554245,
-0.0018608963582664728,
0.017830658704042435,
0.028263401240110397,
0.03061562404036522,
-0.09595877677202225,
0.006457539740949869,
-0.0031952951103448868,
-0.09047137945890427,
0.011576296761631966,
0.032568830996751785,
-0.022876592352986336,
0.0034504837822169065,
-0.039321526885032654,
0.01941375806927681,
-0.008263648487627506,
-0.04991217330098152,
0.030984139069914818,
-0.05811941623687744,
-0.00824596919119358,
-0.012178844772279263,
0.00821659155189991,
-0.01849762536585331,
0.020137593150138855,
-0.06308753788471222,
0.02616886980831623,
-0.035716596990823746,
-0.051419321447610855,
0.03281831741333008,
-0.009744515642523766,
0.026512427255511284,
0.01744476892054081,
0.09420892596244812,
-0.039187002927064896,
-0.012361573986709118,
0.04314805567264557,
0.002144600497558713,
0.03930852562189102,
0.02493276633322239,
-0.0032759823370724916,
0.07957470417022705,
-0.05036589503288269,
0.04897800832986832,
-0.05610724166035652,
0.03453097492456436,
0.05851415917277336,
-0.01263177115470171,
0.004645744804292917,
0.022480804473161697,
-0.015205638483166695,
-0.03179696202278137,
-0.01288700569421053,
0.02032569982111454,
-0.012285870499908924,
0.003318389877676964,
0.02664257399737835,
-0.033547040075063705,
-0.01385139487683773,
0.013004534877836704,
-0.001342680654488504,
0.021725613623857498,
0.056046389043331146,
0.0002916701487265527,
0.02999074012041092,
0.03435758501291275,
-0.03378841653466225,
-0.06727860122919083,
-0.03537597507238388,
-0.06358882784843445,
0.04123590886592865,
0.06014060229063034,
-0.003484909189864993,
-0.05391121655702591,
0.002232481725513935,
-0.017633991315960884,
0.0015133933629840612,
-0.039626430720090866,
0.01859268918633461,
-0.05312124639749527,
0.004448018502444029,
-0.005350051447749138,
0.018490275368094444,
0.03644710034132004,
0.014577249996364117,
0.018452027812600136,
-0.022527728229761124,
-0.009711320511996746,
0.04147364944219589,
0.018210386857390404,
0.06559451669454575,
-0.020220469683408737,
-0.00224739545956254,
-0.020926794037222862,
-0.006197253242135048,
0.004504559561610222,
-0.05337509885430336,
-0.022121446207165718,
0.013230456970632076,
0.0384073480963707,
0.03242397680878639,
0.019776249304413795,
0.0038419952616095543,
-0.008179857395589352,
-0.023289643228054047,
-0.03782901540398598,
-0.002686596941202879,
0.04072609543800354,
-0.018592288717627525,
-0.027940601110458374,
-0.02098015323281288,
-0.005899695213884115,
0.039947547018527985,
-0.03449608385562897,
-0.02418181113898754,
0.014936394989490509,
-0.04342615604400635,
0.07545606791973114,
-0.003943291958421469,
0.0790347158908844,
0.024688826873898506,
0.0070112887769937515,
-0.02167978510260582,
0.00828593596816063,
-0.03016878291964531,
0.007500757463276386,
-0.023076403886079788,
-0.03421730920672417,
-0.08682481199502945,
-0.029160678386688232,
0.006298988126218319,
-0.038183536380529404,
0.02378110960125923,
0.04734024032950401,
0.002853970043361187,
0.002212687162682414,
-0.02587265335023403,
-0.012220824137330055,
-0.007132460363209248,
-0.09577272832393646,
0.00335264066234231,
-0.032358139753341675,
-0.03323179483413696,
-0.017802400514483452,
-0.0739557072520256,
-0.0026072210166603327,
0.05564532056450844,
-0.016871245577931404,
0.05424703657627106,
-0.023296654224395752,
0.015612712129950523,
0.04875662177801132,
0.08808992803096771,
0.04729301109910011,
-0.04273979738354683,
-0.02737933024764061,
0.011191722005605698,
-0.05691366642713547,
0.004913841374218464,
0.0016151455929502845,
-0.023397060111165047,
-0.014446461573243141,
-0.043509554117918015,
0.04714944586157799,
-0.05487486720085144,
-0.006406857632100582,
0.00428070779889822,
0.005598767194896936,
0.018031233921647072,
0.047262318432331085,
-0.04352767765522003,
-0.008950675837695599,
0.016598045825958252,
0.03261797875165939,
-0.004695262759923935,
0.03253084048628807,
0.06895358115434647,
-0.028936801478266716,
-0.047927096486091614,
0.009918317198753357,
-0.008794231340289116,
0.028090404346585274,
0.046677958220243454,
0.01500198245048523,
0.024110330268740654,
0.015109539963304996,
-0.0213429294526577,
-0.01140834391117096,
0.004702422767877579,
-0.00478771235793829,
-0.01043904572725296,
0.01801704242825508,
-0.01395668275654316,
0.026843929663300514,
-0.037055812776088715,
0.019734196364879608,
-0.000345381791703403,
-0.03532716631889343,
0.06075122952461243,
0.029546964913606644,
0.03260019049048424,
-0.08585231006145477,
0.03276054188609123,
-0.1327565610408783,
0.019016845151782036,
0.027785196900367737,
-0.0003823439765255898,
0.023133227601647377,
-0.023483695462346077,
-0.024690527468919754,
-0.03387540951371193,
0.02370574325323105,
-0.013115168549120426,
0.002873382531106472,
-0.03608059883117676,
0.0009937103604897857,
0.0018539634766057134,
0.028997736051678658,
-0.026450442150235176,
-0.03959580883383751,
0.045630086213350296,
-0.04669713228940964,
-0.002355269156396389,
-0.008696286007761955,
0.00547905545681715,
0.004424564074724913,
-0.022744761779904366,
-0.004373189061880112,
0.03300906717777252,
0.009806014597415924,
-0.0448840968310833,
-0.030701810494065285,
0.02322702296078205,
-0.03032558411359787,
0.011195654049515724,
-0.012116089463233948,
0.03692154958844185,
-0.005352790001779795,
0.063285231590271,
0.031239202246069908,
0.017782624810934067,
-0.017327647656202316,
-0.007693171966820955,
-0.0015464936150237918,
-0.01898845098912716,
0.01688939891755581,
-0.014492878690361977,
0.016435330733656883,
-0.031706906855106354,
0.015015263110399246,
0.01953928731381893,
-0.02434217557311058,
0.04884618520736694,
0.04747102037072182,
-0.009633551351726055,
-0.0038510537706315517,
-0.0342695415019989,
-0.00036402756813913584,
0.018392471596598625,
-0.015266167931258678,
-0.0018980383174493909,
0.0225632693618536,
0.05308453366160393,
0.04418126866221428,
0.044702399522066116,
0.028737269341945648,
-0.01507251150906086,
-0.004709404427558184,
-0.003712035482749343,
-0.04121352359652519,
0.020754583179950714,
-0.019597603008151054,
0.004742398392409086,
0.01799703761935234,
-0.0026363073848187923,
-0.053483348339796066,
0.07741809636354446,
-0.03936470299959183,
0.00441741244867444,
0.033108390867710114,
-0.045177094638347626,
-0.040668588131666183,
-0.018540600314736366,
-0.03132525831460953,
0.007217950653284788,
0.032833438366651535,
-0.03310561925172806,
-0.054873060435056686,
0.0654527023434639,
-0.009871701709926128,
-0.02867134101688862,
-0.03304664045572281,
0.013788091950118542,
-0.05080718547105789,
0.020409051328897476,
0.02080545388162136,
0.0032675722613930702,
0.017259037122130394,
0.028058066964149475,
-0.012928645126521587,
-0.013396388851106167,
0.06440304219722748,
-0.0133706359192729,
-0.04613347351551056,
-0.019687015563249588,
0.015215946361422539,
0.042628951370716095,
0.010445701889693737,
0.014840858057141304,
-0.03647536784410477,
0.039521411061286926,
-0.007944162003695965,
0.03845203295350075,
0.04446149244904518,
-0.061083126813173294,
-0.07068325579166412,
-0.030254818499088287,
0.007484147325158119,
0.011721414513885975,
0.07246774435043335,
0.05819464102387428,
-0.05850007012486458,
-0.010614166967570782,
0.06211221590638161,
-0.0009166237432509661,
0.04890935868024826,
0.01898735947906971,
-0.01190294697880745,
-0.0454714335501194,
-0.04470289871096611,
-0.0002999744610860944,
-0.07724322378635406,
-0.006373248528689146,
0.011654121801257133,
0.06995619833469391,
0.011583668179810047,
-0.004866443574428558,
-0.017229072749614716,
0.05861400440335274,
0.06009533256292343,
0.016434721648693085,
-0.0044847894459962845,
-0.022445073351264,
0.04415934905409813,
-0.04530273750424385,
-0.004290789365768433,
-0.08797089755535126,
0.025169964879751205,
-0.022821549326181412,
0.05535713583230972,
0.04261136054992676,
0.0166091900318861,
0.01906782016158104,
-0.036716528236866,
0.014670162461698055,
-0.019452404230833054,
-0.02543989010155201,
-0.021822761744260788,
-0.04613201692700386,
0.028144443407654762,
0.007900788448750973,
-0.019451593980193138,
-0.04048294574022293,
-0.0057260412722826,
-0.0028975787572562695,
-0.0020720360334962606,
0.007422428112477064,
-0.013551926240324974,
0.025334417819976807,
0.005845597013831139,
-0.003583188634365797,
0.06469526886940002,
0.04037708416581154,
0.01661049760878086,
-0.037423476576805115,
-0.04757385700941086,
0.013969257473945618,
0.01813407801091671,
0.01545833982527256,
0.006885729264467955,
0.002136408817023039,
0.04876231402158737,
0.020341746509075165,
-0.005225148051977158,
0.010791853070259094,
0.012345833703875542,
0.006942285690456629,
-0.049001000821590424,
-0.0074910796247422695,
0.005158592946827412,
0.03570560738444328,
0.049132559448480606,
0.07538215070962906,
0.0643795058131218,
0.036065295338630676,
0.0010152158793061972,
0.015431844629347324,
-0.007832838222384453,
-0.06932302564382553,
0.013146782293915749,
-0.009354871697723866,
0.0023606126196682453,
0.04218963161110878,
-0.05704544484615326,
-0.004555911757051945,
0.03315848484635353,
-0.02495177462697029,
-0.0857938900589943,
-0.012606893666088581,
0.004941703751683235,
0.04069257900118828,
0.03176630288362503,
-0.009830608032643795,
-0.03498318791389465,
0.02839062735438347,
-0.07789601385593414,
0.024452509358525276,
-0.007520005572587252,
0.002270752564072609,
0.05428890511393547,
-0.03641744330525398,
0.018937723711133003,
0.0020812577567994595,
0.028667211532592773,
-0.008822541683912277,
-0.006852095481008291,
-0.07260646671056747,
0.04460614174604416,
-0.04129224643111229,
0.027443308383226395,
0.033776648342609406,
-0.07021549344062805,
0.0482681542634964,
-0.06099306046962738,
0.00854041613638401,
-0.03951587900519371,
0.045226242393255234,
-0.03261777386069298,
-0.07116049528121948,
0.004582223016768694,
0.017728138715028763,
0.03776371851563454,
-0.0058869789354503155,
0.030176090076565742,
0.006886012386530638,
-0.06510193645954132,
-0.011695667169988155,
-0.029505720362067223,
0.029644927009940147,
-0.015056591480970383,
-0.031071731820702553,
-0.007202360779047012,
0.03656679391860962,
0.06030646711587906,
-0.020492924377322197,
-0.03172682225704193,
0.05532902479171753,
-0.009232396259903908,
-0.023399682715535164,
-0.0127078453078866,
-0.01463081780821085,
-0.020687054842710495,
-0.009367327205836773,
-0.029687190428376198,
-0.03993263095617294,
0.04793442785739899,
-0.03146021440625191,
-0.023920411244034767,
0.09667040407657623,
0.03935456648468971,
0.042250920087099075,
-0.010545472614467144,
-0.04634648561477661,
-0.039641499519348145,
-0.016502052545547485,
0.029743537306785583,
0.020606448873877525,
-0.02028348110616207,
-0.03945014253258705,
0.0031883337069302797,
0.036024075001478195,
0.04209313169121742,
0.058998603373765945,
-0.058103907853364944,
0.07154002040624619,
0.06470612436532974,
0.00025462647317908704,
0.013810086995363235,
-0.009304826147854328,
-0.0002729694824665785,
0.011296210810542107,
0.023612255230545998,
-0.06017231196165085,
-0.032883170992136,
0.05108978599309921,
-0.07567645609378815,
0.051354702562093735,
-0.008161009289324284,
0.006248386111110449,
-0.05116887390613556,
0.011062871664762497,
-0.047866128385066986,
-0.045135170221328735,
-0.023401794955134392,
0.005627150181680918,
0.026360878720879555,
-0.050223708152770996,
-0.01617005467414856,
-0.042886875569820404,
0.015347546897828579,
0.034894682466983795,
0.00533737987279892,
0.006406361702829599,
-0.024002768099308014,
-0.00923798605799675,
0.017305195331573486,
0.009092689491808414,
-0.00046246807323768735,
0.00621927622705698,
0.07201195508241653,
0.02429940551519394,
-0.019722066819667816,
0.0005714139551855624,
-0.012821312993764877,
0.009350430220365524,
0.042536187916994095,
0.0072246151976287365,
-0.011685446836054325,
-0.030727673321962357,
0.031811024993658066,
0.04426625743508339,
0.05564773082733154,
-0.02378401905298233,
0.006417168769985437,
0.005883857607841492,
-0.03097950480878353,
0.01859043538570404,
-0.007175731007009745,
-0.06151827052235603,
-0.01625531166791916,
-0.03257012367248535,
-0.0007988765137270093,
0.030378062278032303,
-0.0175528172403574,
0.014559196308255196,
-0.009591707959771156,
-0.039443936198949814,
-0.04605536535382271,
-0.05502628907561302,
0.014868482016026974,
-0.02934832125902176,
-0.008477910421788692,
0.010780016891658306,
-0.05668875202536583,
-0.03705502301454544,
0.024911275133490562,
0.04307091608643532,
-0.018651781603693962,
-0.021734580397605896,
-0.04794584959745407,
-0.04474647715687752,
0.05569654703140259,
-0.016397008672356606,
-0.002816224005073309,
0.033669613301754,
-0.0683201402425766,
-0.007581882644444704,
-0.05774322524666786,
0.014305668883025646,
-0.060622215270996094,
0.009241815656423569,
-0.021581893786787987,
0.02406287007033825,
-0.007388400379568338,
-0.023591622710227966,
-0.042681630700826645,
-0.017485905438661575,
0.05514451116323471,
-0.05449104681611061,
0.05441330000758171,
-0.027795545756816864,
0.016661982983350754,
0.014833437278866768,
0.04569070041179657,
-0.008677368052303791,
-0.008385956287384033,
0.013866211287677288,
0.010109391994774342,
0.05141627788543701,
0.003348066471517086,
-0.008308950811624527,
0.023175213485956192,
0.08129936456680298,
-0.02067197673022747,
0.08250301331281662,
-0.004291116259992123,
0.028940672054886818,
-0.06642869114875793,
0.02349936030805111,
-0.03590254485607147,
0.016705941408872604,
-0.015356679446995258,
-0.004335080739110708,
0.0009582348866388202,
-0.02121611312031746,
-0.04634615033864975,
-0.013560528866946697,
-0.04479367658495903,
0.029233820736408234,
0.044594500213861465,
0.03320007771253586,
-0.02533421665430069,
-0.08616452664136887,
0.06966497749090195,
-0.020746812224388123,
-0.04344164580106735,
-0.002734976587817073,
0.0010492360452190042,
0.038017891347408295,
-0.013921779580414295,
-0.013802248053252697,
-0.018040668219327927,
0.009971003979444504,
-0.0027902768924832344,
-0.015414551831781864,
-0.01662372052669525,
-0.06676508486270905,
-0.04529373347759247,
0.01326588075608015,
0.035833485424518585,
-0.0809294655919075,
0.020813802257180214,
0.0156905148178339,
0.046918731182813644,
-0.01972549967467785,
-0.0413564071059227,
-0.00538087310269475,
0.054757215082645416,
0.10715287178754807,
0.014494217932224274,
0.03321376070380211,
-0.02104347199201584,
0.01331888884305954,
0.049101538956165314,
-0.0005314820446074009,
0.05807702615857124,
0.00414503226056695,
0.006381950341165066
] |
[
3.0915699005126953,
3.4379777908325195
] |
Classical Analysis and ODEs
|
Mathematics
|
math-CA
|
math-FA
|
na
|
2007-04-01T20:46:31
|
Potassium intercalation in graphite is investigated by first-principles
theory. The bonding in the potassium-graphite compound is reasonably well
accounted for by traditional semilocal density functional theory (DFT)
calculations. However, to investigate the intercalate formation energy from
pure potassium atoms and graphite requires use of a description of the graphite
interlayer binding and thus a consistent account of the nonlocal dispersive
interactions. This is included seamlessly with ordinary DFT by a van der Waals
density functional (vdW-DF) approach [Phys. Rev. Lett. 92, 246401 (2004)]. The
use of the vdW-DF is found to stabilize the graphite crystal, with crystal
parameters in fair agreement with experiments. For graphite and
potassium-intercalated graphite structural parameters such as binding
separation, layer binding energy, formation energy, and bulk modulus are
reported. Also the adsorption and sub-surface potassium absorption energies are
reported. The vdW-DF description, compared with the traditional semilocal
approach, is found to weakly soften the elastic response.
|
Potassium intercalation in graphite: A van der Waals density-functional
study
|
cond-mat.soft cond-mat.mtrl-sci
|
0704.0055
| 2,007
|
[
0.043077223002910614,
0.05573677271604538,
0.007552322931587696,
-0.027201620861887932,
-0.021510247141122818,
0.00928270909935236,
-0.02503945305943489,
0.02310365065932274,
-0.033629946410655975,
0.012514106929302216,
-0.02463085763156414,
0.037566158920526505,
-0.000988793675787747,
-0.031796615570783615,
-0.0010766414925456047,
0.017593977972865105,
0.023971719667315483,
-0.0059048025868833065,
-0.001225796528160572,
0.028682006523013115,
-0.11196239292621613,
-0.05111423879861832,
-0.049116604030132294,
-0.026503222063183784,
0.05649130046367645,
0.004800661001354456,
-0.006457091309130192,
0.02827097848057747,
-0.022699827328324318,
0.03960076719522476,
0.027226386591792107,
-0.007873459719121456,
0.0002136045804945752,
-0.05918470025062561,
-0.03990844637155533,
-0.0007198089151643217,
0.04389871656894684,
-0.019160695374011993,
-0.04682750627398491,
-0.03432682156562805,
-0.011868275701999664,
-0.026709843426942825,
0.016539191827178,
-0.007365027442574501,
0.0380370058119297,
0.009338382631540298,
-0.03085283190011978,
-0.020005712285637856,
0.007152468431740999,
0.016155805438756943,
-0.06416646391153336,
0.06827124953269958,
0.027120167389512062,
-0.03641199693083763,
-0.02327894978225231,
-0.01279514841735363,
0.03835335001349449,
0.017847763374447823,
0.04966570436954498,
-0.056513432413339615,
0.06449783593416214,
0.010337023064494133,
-0.008550290018320084,
0.033152781426906586,
0.06417802721261978,
-0.10000359266996384,
-0.045727211982011795,
0.03325936198234558,
0.02544102631509304,
-0.06991535425186157,
0.006666149478405714,
0.008724849671125412,
0.011044615879654884,
0.0427393838763237,
-0.04456699639558792,
0.009472405537962914,
0.050221312791109085,
-0.019171619787812233,
0.028670931234955788,
0.006398344412446022,
0.01927570067346096,
0.0011991355568170547,
0.060867056250572205,
-0.017285050824284554,
0.051712505519390106,
-0.02217525616288185,
0.007121813017874956,
0.03966936469078064,
-0.05513661727309227,
0.06130138039588928,
0.02143106609582901,
0.0031504309736192226,
0.03731406852602959,
0.014046918600797653,
-0.03773084655404091,
0.0034555629827082157,
-0.00523236021399498,
0.031898003071546555,
-0.0014307143865153193,
-0.07179266959428787,
-0.012367636896669865,
-0.03752268850803375,
0.035383887588977814,
0.043165095150470734,
0.03543435409665108,
0.023884709924459457,
0.019078055396676064,
0.0035646778997033834,
0.02985912188887596,
-0.024151241406798363,
-0.05198187008500099,
0.024935398250818253,
0.0027027472387999296,
0.015225740149617195,
0.028507724404335022,
-0.015717454254627228,
0.013289243914186954,
-0.07462846487760544,
0.01605825126171112,
0.015569965355098248,
0.015769412741065025,
0.006513569038361311,
0.01446310244500637,
-0.011804893612861633,
0.007923781871795654,
-0.015150139108300209,
-0.04862010106444359,
-0.015417138114571571,
0.00223335693590343,
-0.00782014336436987,
0.010506308637559414,
0.01780722104012966,
-0.03608580306172371,
-0.006678813137114048,
0.009887578897178173,
0.008420795202255249,
-0.06482207775115967,
-0.05514740198850632,
-0.037372078746557236,
-0.05164490267634392,
-0.03697601333260536,
-0.03370708227157593,
-0.04921302944421768,
-0.016051335260272026,
0.02962184138596058,
-0.055077943950891495,
-0.0005765992682427168,
-0.02309473603963852,
-0.036650534719228745,
0.0038718157447874546,
0.03445084020495415,
0.0188510213047266,
0.06150444224476814,
-0.026003405451774597,
-0.011818012222647667,
-0.0667622908949852,
0.03369784727692604,
-0.02529633417725563,
0.08118956536054611,
0.014629469253122807,
-0.00290583330206573,
0.025246933102607727,
-0.01995021477341652,
0.06142645701766014,
-0.015919432044029236,
-0.018072357401251793,
0.09236564487218857,
-0.004881995264440775,
0.05538470670580864,
0.05252056568861008,
-0.0322561077773571,
-0.04714959114789963,
-0.015846792608499527,
-0.023376749828457832,
-0.027419138699769974,
0.023039253428578377,
0.01487746648490429,
-0.06578747183084488,
0.006471196189522743,
-0.013871016912162304,
0.04201855510473251,
-0.008336291648447514,
0.015811746940016747,
0.07084089517593384,
-0.0008830838487483561,
0.017274433746933937,
-0.00031269664759747684,
0.0227164588868618,
-0.01833702251315117,
-0.009356147609651089,
-0.0092984763905406,
-0.0126434825360775,
-0.044848766177892685,
-0.08851096034049988,
0.03157075494527817,
-0.03392396867275238,
0.06671231985092163,
0.006473838351666927,
-0.024177201092243195,
-0.05056614428758621,
-0.033276889473199844,
-0.03972412273287773,
-0.046143703162670135,
0.02242487668991089,
0.014078875072300434,
0.006333664525300264,
-0.02012738399207592,
0.004661376588046551,
0.05504102632403374,
-0.04965860769152641,
0.024549385532736778,
-0.029265012592077255,
-0.02384924702346325,
0.047714728862047195,
0.01661044918000698,
-0.015551571734249592,
0.0055527463555336,
-0.02663271687924862,
-0.053387705236673355,
0.010587535798549652,
-0.008875016123056412,
0.014283495023846626,
0.03135468065738678,
0.07433377206325531,
0.035809215158224106,
-0.01745632104575634,
-0.025917483493685722,
0.019513508304953575,
-0.044352106750011444,
0.006191516760736704,
-0.07812908291816711,
-0.007393230684101582,
-0.011923610232770443,
0.017982926219701767,
-0.011771191842854023,
0.08642522990703583,
-0.08436572551727295,
-0.009802122600376606,
0.0185001939535141,
0.016473228111863136,
0.011123377829790115,
0.022325938567519188,
0.014329057186841965,
-0.021517645567655563,
-0.06434366852045059,
-0.008617211133241653,
-0.02461228519678116,
0.00581524008885026,
-0.025030214339494705,
0.03360377252101898,
0.0564749538898468,
0.036713212728500366,
-0.017576996237039566,
-0.00027535666595213115,
0.018640195950865746,
-0.00838034600019455,
-0.0799243375658989,
0.01820741780102253,
-0.0073289042338728905,
-0.09405294805765152,
0.04918987676501274,
-0.04574411362409592,
0.004774213302880526,
-0.01796972006559372,
-0.03330577164888382,
0.011052997782826424,
0.012811664491891861,
-0.04751203954219818,
-0.012210851535201073,
-0.010846973396837711,
-0.014985308982431889,
0.03661021217703819,
0.0452549085021019,
0.05652652308344841,
-0.021582258865237236,
-0.009046858176589012,
0.06534560769796371,
-0.06912115216255188,
0.00163108273409307,
-0.0406544990837574,
-0.08554615080356598,
0.0005422496469691396,
-0.030234048143029213,
-0.005531210917979479,
-0.014149579219520092,
0.05266762897372246,
0.056442975997924805,
-0.011780687607824802,
0.04217065870761871,
-0.012295989319682121,
-0.0039979564025998116,
-0.011165190488100052,
-0.012471056543290615,
0.06779763847589493,
-0.030479544773697853,
0.018051261082291603,
0.0685637816786766,
-0.05950348824262619,
-0.0024151289835572243,
0.0730268806219101,
0.017860708758234978,
-0.010002142749726772,
0.030718691647052765,
0.015171393752098083,
-0.009402645751833916,
0.02266710437834263,
0.019714385271072388,
-0.022709829732775688,
-0.0021754701156169176,
-0.01181667298078537,
-0.015647200867533684,
0.04256512224674225,
0.009651568718254566,
0.010211590677499771,
-0.07553394138813019,
0.01369972713291645,
0.032473377883434296,
0.024278920143842697,
0.07394354790449142,
-0.004129288252443075,
0.053962476551532745,
-0.007139769848436117,
0.044965460896492004,
-0.029228484258055687,
-0.017839359119534492,
0.06999172270298004,
-0.04774055257439613,
0.004630149807780981,
-0.008587402291595936,
0.038826651871204376,
0.00909654051065445,
0.05851699411869049,
-0.006252472288906574,
-0.04408513754606247,
-0.031445909291505814,
-0.01237810030579567,
-0.022009436041116714,
0.002390963723883033,
-0.0267967376857996,
0.023284900933504105,
-0.04305770620703697,
-0.03427491337060928,
-0.0368175245821476,
-0.03776206448674202,
-0.01586361788213253,
0.033971983939409256,
-0.02971493825316429,
0.01295854989439249,
0.0259403008967638,
-0.010498914867639542,
-0.0645056888461113,
-0.005673007573932409,
0.05523763969540596,
0.007951645180583,
-0.020508086308836937,
0.03152470663189888,
0.06301287561655045,
0.007875041104853153,
0.018532173708081245,
0.013385651633143425,
0.030820641666650772,
-0.028019467368721962,
0.06532583385705948,
-0.01708798110485077,
-0.023341309279203415,
0.03331705555319786,
0.003355732886120677,
0.04159960895776749,
0.021378645673394203,
-0.025756852701306343,
-0.05344897136092186,
-0.04691777378320694,
0.03664722293615341,
0.07678746432065964,
0.06619349867105484,
0.006241475231945515,
-0.05210665613412857,
-0.025048358365893364,
-0.02391347475349903,
-0.012139840051531792,
0.05126038193702698,
0.028812889009714127,
0.05600990727543831,
0.015900693833827972,
0.01691626012325287,
0.02285982109606266,
-0.10560575127601624,
0.04020235314965248,
-0.03370516374707222,
0.0029665078036487103,
-0.008041500113904476,
-0.030492175370454788,
-0.05007348582148552,
0.019779151305556297,
-0.04399522766470909,
-0.0029079162050038576,
-0.007036576047539711,
0.008575711399316788,
-0.013996081426739693,
-0.043601080775260925,
-0.04095245152711868,
-0.051043227314949036,
-0.01645493321120739,
-0.07141155004501343,
0.029644137248396873,
-0.0002710523549467325,
-0.011618577875196934,
-0.0819159746170044,
0.061503227800130844,
-0.037365179508924484,
-0.0003691537131089717,
0.002791167236864567,
-0.036085110157728195,
-0.08711545914411545,
0.023215267807245255,
0.010543689131736755,
0.014113987796008587,
-0.005043142009526491,
-0.009948774240911007,
-0.037688516080379486,
0.002714504487812519,
0.06577090919017792,
-0.029641587287187576,
-0.0011448547011241317,
0.0046914671547710896,
0.03903847932815552,
0.037057019770145416,
-0.0021683115046471357,
-0.016596052795648575,
0.017211342230439186,
-0.0016667959280312061,
0.015384139493107796,
0.028566624969244003,
0.0027008645702153444,
-0.06535506248474121,
0.01143709011375904,
0.031835947185754776,
0.02370515652000904,
-0.019063416868448257,
0.027138687670230865,
0.0404379665851593,
-0.02660377509891987,
0.025464830920100212,
0.04499517381191254,
0.017705107107758522,
0.05448557063937187,
-0.007802183739840984,
0.012505639344453812,
-0.016476141288876534,
-0.012966878712177277,
0.023254262283444405,
-0.031837597489356995,
0.005610604304820299,
0.027667798101902008,
0.08178598433732986,
0.010889139026403427,
-0.008753973990678787,
-0.01954548805952072,
0.05687820538878441,
0.07964488863945007,
0.04289562255144119,
0.02124493569135666,
-0.019476240500807762,
0.0063200597651302814,
-0.009151400066912174,
0.0364442802965641,
-0.0032725895289331675,
0.023492678999900818,
-0.00760348467156291,
0.06106045842170715,
0.011770675890147686,
-0.0053482879884541035,
0.01075949240475893,
0.046753279864788055,
-0.005334131419658661,
-0.021788233891129494,
0.037358373403549194,
-0.04882677271962166,
0.032013025134801865,
-0.013346820138394833,
0.037035562098026276,
0.027954595163464546,
-0.025158623233437538,
0.0178275927901268,
-0.029693108052015305,
0.0176861472427845,
0.011155115440487862,
0.0032769658137112856,
-0.026323959231376648,
0.02471143566071987,
0.0741405263543129,
0.01261167787015438,
0.03698427230119705,
0.02450593374669552,
0.007371372077614069,
-0.004114951007068157,
0.06217053532600403,
0.05170029029250145,
0.047023795545101166,
0.0326496958732605,
0.027858208864927292,
0.012129752896726131,
-0.016985997557640076,
-0.023455971851944923,
0.000018660040950635448,
0.0445818156003952,
0.06317999213933945,
-0.08690209686756134,
-0.01471865363419056,
0.03543773293495178,
-0.022628657519817352,
0.021190250292420387,
0.042954932898283005,
0.06012236699461937,
0.0487649142742157,
-0.06837750226259232,
0.036701492965221405,
-0.013255651108920574,
-0.0629463717341423,
0.010904235765337944,
-0.0015641903737559915,
0.02112015150487423,
-0.0512046292424202,
-0.019955923780798912,
-0.06575243175029755,
0.03690890222787857,
-0.027212370187044144,
-0.0544847771525383,
0.03256543353199959,
-0.030872611328959465,
-0.023273391649127007,
0.03904309496283531,
0.008062551729381084,
0.043585170060396194,
0.020182183012366295,
-0.060824498534202576,
-0.034092992544174194,
0.0413360558450222,
0.00765033345669508,
0.06926208734512329,
0.007403931114822626,
0.04717843607068062,
-0.00162807188462466,
0.03430476039648056,
-0.02453979104757309,
-0.01795155741274357,
-0.023079819977283478,
0.022708222270011902,
0.028448333963751793,
-0.07713928073644638,
0.023941412568092346,
-0.04523874819278717,
0.02902749739587307,
-0.06286638975143433,
0.052462466061115265,
-0.031573232263326645,
0.01737426035106182,
-0.03534394130110741,
-0.006128653418272734,
0.013805883005261421,
-0.0024126525968313217,
0.002618369646370411,
0.02389296516776085,
0.00011159475252497941,
0.08750700950622559,
-0.07591742277145386,
-0.004088075365871191,
-0.03962774947285652,
0.04800906777381897,
-0.042526692152023315,
-0.04607138782739639,
-0.01697908714413643,
-0.009458616375923157,
0.03064868412911892,
-0.008772579953074455,
-0.011046896688640118,
0.0349748320877552,
0.011710479855537415,
-0.03969511762261391,
-0.04925002157688141,
0.006701543461531401,
-0.016945820301771164,
-0.0031308981124311686,
0.01712079904973507,
-0.05126545950770378,
-0.01129341684281826,
0.014054302126169205,
-0.07367311418056488,
0.041369788348674774,
-0.023243920877575874,
0.007111263927072287,
0.005816023796796799,
-0.030861597508192062,
-0.02765013463795185,
-0.05221739411354065,
-0.01141588855534792,
0.04748744145035744,
0.0013126218691468239,
0.012674261815845966,
-0.029832884669303894,
0.008243732154369354,
0.011936741881072521,
0.006179940886795521,
-0.034834783524274826,
0.012308516539633274,
-0.005407118238508701,
0.023946380242705345,
0.035985615104436874,
-0.05632142722606659,
-0.01107015274465084,
0.012290776707231998,
0.04234294220805168,
0.0049012224189937115,
-0.044100236147642136,
0.006125863641500473,
-0.06397708505392075,
0.07415290176868439,
-0.03571292385458946,
0.052204765379428864,
-0.05728054791688919,
0.011511417105793953,
-0.037931930273771286,
-0.015470398589968681,
-0.0554729662835598,
0.05265377461910248,
0.015122356824576855,
-0.0353374108672142,
0.013996854424476624,
0.0034351178910583258,
0.06049739941954613,
-0.009637117385864258,
0.01769893802702427,
-0.004155975766479969,
-0.017045412212610245,
-0.04311400651931763,
0.057702913880348206,
-0.011657172814011574,
-0.03731774911284447,
0.0017729977844282985,
0.03557194769382477,
-0.021151255816221237,
-0.08527609705924988,
0.020601630210876465,
0.01558663696050644,
0.07094242423772812,
-0.004453917499631643,
-0.036723583936691284,
0.023939384147524834,
-0.01572350040078163,
0.0043948437087237835,
0.060718048363924026,
0.08378578722476959,
-0.04070151969790459,
0.01628400757908821,
0.0329245924949646,
0.023454610258340836,
0.005587439984083176,
-0.007288561202585697,
0.032222915440797806,
0.025149071589112282,
-0.04008512943983078,
-0.018171826377511024,
0.011265816166996956,
-0.014332061633467674,
0.031227033585309982,
-0.05563628673553467,
-0.015613270923495293,
-0.028952619060873985,
-0.059876758605241776,
-0.002671794965863228,
-0.021614741533994675,
-0.020097967237234116,
0.029867911711335182,
-0.014247171580791473,
-0.042769480496644974,
0.021223820745944977,
-0.013139712624251842,
-0.02918393723666668,
-0.023334184661507607,
0.035244449973106384,
-0.019664572551846504,
0.048461366444826126,
0.05393989756703377,
-0.002232960192486644,
-0.04278665781021118,
0.011269972659647465,
-0.01025197934359312,
-0.03695034980773926,
-0.06293994933366776,
0.015016155317425728,
0.023726588115096092,
-0.007087293546646833,
0.0026492509059607983,
-0.04869483783841133,
0.03844883665442467,
0.047086864709854126,
-0.0620921291410923,
-0.044194530695676804,
0.01611553132534027,
0.03224899619817734,
0.03209532052278519,
0.0300699882209301,
-0.037250224500894547,
0.01783551089465618,
0.025887146592140198,
0.0024886103346943855,
0.011697005480527878,
0.027156325057148933,
-0.0026495372876524925,
-0.013954674825072289,
0.05120338127017021,
-0.04123864322900772,
0.08513981848955154,
0.01631913334131241,
0.05543416738510132,
-0.023469533771276474,
-0.008812213316559792,
-0.07667765021324158,
0.021869713440537453,
0.01622283272445202,
0.025578292086720467,
-0.010342449881136417,
-0.025758592411875725,
-0.00816419068723917,
-0.009521733969449997,
-0.0500691719353199,
-0.024392019957304,
0.00038681208388879895,
0.03706922382116318,
0.06566076725721359,
0.01974320411682129,
0.000889561022631824,
-0.025170721113681793,
0.0020083950366824865,
-0.05662156268954277,
0.01628890261054039,
0.02216554991900921,
-0.004221134819090366,
-0.013216556049883366,
0.040548115968704224,
-0.04642951115965843,
-0.011674207635223866,
0.013177824206650257,
-0.018137691542506218,
-0.05636243894696236,
0.0006118502933532,
-0.06277653574943542,
0.029201433062553406,
0.043960630893707275,
-0.0080367811024189,
-0.08204657584428787,
-0.01701872982084751,
-0.003669542260468006,
-0.05393734946846962,
-0.020754586905241013,
-0.019225716590881348,
-0.02135859616100788,
0.02816511131823063,
0.0860389843583107,
-0.040752626955509186,
-0.006376620847731829,
-0.0136713907122612,
-0.02203269675374031,
0.017302727326750755,
0.04282859340310097,
0.02729836292564869,
-0.055026907473802567,
-0.02669125236570835
] |
[
9.905170440673828,
-1.9895354509353638
] |
Soft Condensed Matter
|
Condensed-Matter Physics
|
cond-mat-soft
|
cond-mat-mtrl-sci
|
na
|
2007-03-31T21:51:45
|
We study a simple model of a nematic liquid crystal made of parallel
ellipsoidal particles interacting via a repulsive Gaussian law. After
identifying the relevant solid phases of the system through a careful
zero-temperature scrutiny of as many as eleven candidate crystal structures, we
determine the melting temperature for various pressure values, also with the
help of exact free energy calculations. Among the prominent features of this
model are pressure-driven reentrant melting and the stabilization of a columnar
phase for intermediate temperatures.
|
Phase diagram of Gaussian-core nematics
|
cond-mat.soft cond-mat.mtrl-sci
|
0704.0056
| 2,007
|
[
-0.0020030997693538666,
0.05449426546692848,
0.002244452014565468,
-0.04761727899312973,
0.039366308599710464,
0.004320930223912001,
-0.041133712977170944,
0.012417010962963104,
-0.055921681225299835,
0.05304691195487976,
-0.08402932435274124,
0.04449130594730377,
0.022094709798693657,
-0.03490307182073593,
-0.01906752400100231,
0.03973933681845665,
0.014921745285391808,
-0.009277936071157455,
0.0013790111988782883,
0.05957740172743797,
-0.03416190296411514,
-0.05347585305571556,
-0.03442839905619621,
-0.06810227781534195,
0.08765345811843872,
0.012670611962676048,
0.023518318310379982,
0.036321334540843964,
-0.12202555686235428,
0.0493292473256588,
0.037277884781360626,
-0.009443194605410099,
-0.002843643305823207,
-0.044621486216783524,
-0.045263826847076416,
-0.055687498301267624,
0.062146782875061035,
-0.0171066727489233,
-0.007246303837746382,
0.038718316704034805,
0.03254717215895653,
0.006235905922949314,
0.027138544246554375,
-0.01747533492743969,
0.02790834568440914,
0.06277773529291153,
0.016766786575317383,
-0.019443748518824577,
-0.01198899932205677,
0.015021245926618576,
-0.02059873938560486,
0.07227811962366104,
0.025621559470891953,
-0.07865146547555923,
-0.05478261038661003,
-0.009870946407318115,
-0.0009796336526051164,
0.011223237961530685,
0.005081071052700281,
-0.003674854524433613,
0.011045034043490887,
0.058712802827358246,
-0.043584514409303665,
0.015649279579520226,
0.004955887328833342,
-0.04158676043152809,
-0.06691385060548782,
0.02313082665205002,
0.011422498151659966,
-0.060651522129774094,
0.02911505289375782,
-0.00020885517005808651,
-0.016810929402709007,
0.02920982800424099,
0.008102699182927608,
-0.027526607736945152,
-0.003833297174423933,
-0.0072828009724617004,
-0.021219799295067787,
-0.0270029678940773,
-0.004358835984021425,
0.0020852964371442795,
0.02986067160964012,
0.02172933891415596,
0.06680255383253098,
0.012898962944746017,
0.0037575671449303627,
0.0418890006840229,
-0.09880194813013077,
-0.008172301575541496,
0.03857794031500816,
0.008417011238634586,
0.012590461410582066,
0.05705614015460014,
0.017187628895044327,
0.0013660397380590439,
0.023251548409461975,
0.029132699593901634,
0.030095359310507774,
-0.06105048581957817,
-0.014528431929647923,
-0.005834936164319515,
0.004153153859078884,
-0.033327654004096985,
0.046546097844839096,
0.026916110888123512,
0.024783141911029816,
-0.003380877198651433,
0.02236808091402054,
-0.012343928217887878,
-0.04434914514422417,
-0.011142046190798283,
-0.01054638996720314,
0.01653887704014778,
-0.017818588763475418,
-0.051081135869026184,
0.06337502598762512,
-0.07271724194288254,
-0.007519572041928768,
0.045891910791397095,
0.04021235182881355,
-0.010955993086099625,
0.0390804298222065,
0.06541123986244202,
0.0031765971798449755,
0.030418332666158676,
0.015322423540055752,
-0.027478132396936417,
-0.03185943886637688,
0.004990415181964636,
-0.04298420250415802,
-0.00415509520098567,
-0.028947383165359497,
-0.020418591797351837,
0.05946371331810951,
0.07418203353881836,
-0.028827441856265068,
-0.0031246808357536793,
-0.017821025103330612,
-0.009547026827931404,
-0.0007154384511522949,
0.016698623076081276,
-0.008721772581338882,
-0.012802273966372013,
0.00827355869114399,
-0.06900676339864731,
0.012814942747354507,
-0.03968624770641327,
-0.006989430170506239,
-0.006921777501702309,
-0.011607546359300613,
0.05553998053073883,
-0.004464578814804554,
0.04172971844673157,
-0.0332174114882946,
-0.032774750143289566,
0.011007389053702354,
-0.015044542029500008,
0.028786540031433105,
-0.0030318875797092915,
0.0644196942448616,
-0.023891447111964226,
-0.02331511117517948,
0.062459979206323624,
-0.08218877762556076,
0.03422106057405472,
0.021993793547153473,
0.034991342574357986,
0.06917484104633331,
0.025759214535355568,
-0.0514177642762661,
-0.034170687198638916,
-0.06284788995981216,
0.05532240867614746,
0.052161429077386856,
-0.003786466782912612,
-0.013552205637097359,
-0.01816631853580475,
0.05414891615509987,
-0.02370378188788891,
0.028108391910791397,
-0.03767642006278038,
0.05375426635146141,
0.045939333736896515,
-0.00561931449919939,
0.037300124764442444,
0.029120665043592453,
0.014116398990154266,
0.011401871219277382,
0.005232209339737892,
-0.014675518497824669,
0.019717104732990265,
-0.06672930717468262,
-0.011047152802348137,
0.08838487416505814,
-0.002311290241777897,
0.05729496106505394,
-0.027209116145968437,
-0.00897906068712473,
-0.01459448877722025,
0.0036246259696781635,
0.017818139865994453,
-0.032444823533296585,
0.03601896017789841,
-0.003207635134458542,
0.06291063874959946,
0.02931254915893078,
0.02064327895641327,
-0.0016737414989620447,
0.026636913418769836,
0.06294864416122437,
0.036698032170534134,
-0.03834458440542221,
0.029445882886648178,
0.0064155119471251965,
0.030661167576909065,
-0.0015567033551633358,
-0.06610662490129471,
-0.038746755570173264,
0.09594445675611496,
-0.02054726891219616,
-0.0037390764337033033,
-0.012122240848839283,
-0.008871541358530521,
0.03987536579370499,
-0.04143514856696129,
-0.04664475843310356,
0.02756083384156227,
-0.037373192608356476,
-0.04023259878158569,
-0.06172209233045578,
-0.05318724364042282,
0.006206074729561806,
0.00045611642417497933,
0.007339571136981249,
-0.02427373081445694,
0.008601585403084755,
0.031846508383750916,
0.026362046599388123,
0.09151610732078552,
-0.0012971347896382213,
0.009867497719824314,
0.012676546350121498,
-0.06911605596542358,
-0.08165212720632553,
-0.03463849797844887,
-0.011691016145050526,
0.00868514645844698,
-0.01661503128707409,
0.03555402532219887,
0.01356168556958437,
0.0014765250962227583,
-0.014261349104344845,
0.012856263667345047,
0.014498844742774963,
-0.00933096930384636,
-0.00665883906185627,
0.05013415962457657,
-0.005276826675981283,
-0.07061821967363358,
0.049550868570804596,
-0.04184611886739731,
-0.03822258114814758,
-0.019713595509529114,
-0.04865172505378723,
0.011541738174855709,
-0.007796917576342821,
-0.03393111005425453,
-0.017627203837037086,
0.0023032529279589653,
-0.014922859147191048,
0.028816569596529007,
0.09364007413387299,
0.05215808376669884,
0.0022521954961121082,
0.02150065265595913,
0.06127583980560303,
-0.021646177396178246,
0.010219687595963478,
0.008328213356435299,
-0.03845556825399399,
-0.03895142301917076,
-0.04174455255270004,
-0.020576361566781998,
-0.010595226660370827,
0.02239665947854519,
0.033453453332185745,
0.024856913834810257,
0.009336239658296108,
0.009299207478761673,
0.023974129930138588,
-0.0022098904009908438,
0.04290634021162987,
0.058702725917100906,
0.011643311008810997,
0.009011141955852509,
0.06704390048980713,
-0.029588934034109116,
-0.01240108348429203,
0.03363897651433945,
-0.026115041226148605,
0.028315631672739983,
-0.028397973626852036,
0.05042392387986183,
-0.01332941185683012,
0.040622156113386154,
0.0022850350942462683,
0.0086791617795825,
0.026912065222859383,
0.005530900321900845,
-0.028318995609879494,
0.0531928725540638,
0.010980376973748207,
0.03142804279923439,
-0.04075692966580391,
0.03142271563410759,
0.028305254876613617,
0.016186002641916275,
0.10619746893644333,
0.015881022438406944,
-0.01193405594676733,
-0.0355827771127224,
0.05271325260400772,
-0.07278875261545181,
-0.023610977455973625,
0.04578395187854767,
0.012683109380304813,
0.024746308103203773,
-0.0381753072142601,
-0.013704302720725536,
0.015204363502562046,
0.0638045221567154,
-0.009436175227165222,
0.012413091957569122,
0.004028528928756714,
-0.014711233787238598,
-0.024539638310670853,
-0.002015151083469391,
0.000007463284873665543,
0.022911436855793,
0.015048949979245663,
-0.009541604667901993,
-0.00670728599652648,
-0.04616013541817665,
0.0023714324925094843,
-0.024127095937728882,
-0.04183822125196457,
-0.024730242788791656,
0.01933608390390873,
-0.016979405656456947,
-0.004493818152695894,
-0.03528319671750069,
0.009397925809025764,
-0.05520880967378616,
-0.0024755389895290136,
-0.03517177328467369,
0.028250277042388916,
-0.038324903696775436,
0.052490413188934326,
-0.0037948882672935724,
0.026970915496349335,
-0.04560855031013489,
0.018445510417222977,
0.05351018160581589,
-0.005282163619995117,
0.014325374737381935,
0.003580219577997923,
0.04552442952990532,
0.02476511150598526,
-0.058890365064144135,
-0.021756572648882866,
-0.07109534740447998,
-0.0003031158703379333,
0.016088902950286865,
0.04029589518904686,
0.047049056738615036,
-0.07585965096950531,
-0.012124304659664631,
-0.02257712557911873,
0.015380906872451305,
0.07174175977706909,
-0.012459313496947289,
0.014007008634507656,
0.02788633108139038,
-0.004876820836216211,
0.03590650111436844,
-0.03811201453208923,
-0.013822326436638832,
-0.0351310670375824,
-0.06306082755327225,
0.04389384761452675,
-0.03959887474775314,
0.000653402297757566,
-0.009286532178521156,
0.0017962127458304167,
-0.032527100294828415,
0.03452490642666817,
0.030549420043826103,
-0.005039449315518141,
-0.010869905352592468,
-0.01974656991660595,
-0.08632160723209381,
-0.02126569114625454,
-0.062377188354730606,
-0.003065968630835414,
-0.005105552263557911,
-0.037287987768650055,
-0.08980170637369156,
0.0498422309756279,
-0.02276657335460186,
-0.006016680039465427,
0.04724862053990364,
-0.014056402258574963,
-0.07263138890266418,
0.04503098130226135,
0.025771159678697586,
0.015890171751379967,
-0.00953345000743866,
0.026024354621767998,
-0.021031659096479416,
-0.003199891420081258,
0.020364655181765556,
-0.04336310178041458,
0.0030151456594467163,
-0.04633358120918274,
-0.003773918142542243,
0.03890835866332054,
0.012325108982622623,
-0.0300128273665905,
-0.08368852734565735,
0.05149194598197937,
0.027609145268797874,
-0.015284916386008263,
0.02000228688120842,
-0.04043539986014366,
0.022454561665654182,
-0.004468564409762621,
0.028625860810279846,
-0.005201610736548901,
0.07644636183977127,
0.005923560820519924,
-0.04944262653589249,
0.035395652055740356,
-0.008641787804663181,
0.032405510544776917,
0.08691106736660004,
0.05893727019429207,
-0.01926371455192566,
-0.06642261147499084,
-0.012071477249264717,
0.04804638400673866,
-0.0011745634255930781,
-0.03574623540043831,
0.027874423190951347,
0.06906703859567642,
-0.04257043078541756,
-0.0014633112587034702,
0.06376060843467712,
0.06175994873046875,
0.04881565272808075,
-0.014835204929113388,
-0.0012153153074905276,
-0.027698172256350517,
0.0318182073533535,
-0.024081172421574593,
0.009593929164111614,
0.030752617865800858,
-0.02062639221549034,
0.052948497235774994,
0.036835893988609314,
-0.010783425532281399,
0.003441722597926855,
0.048319753259420395,
0.040433406829833984,
-0.016051556915044785,
-0.010933739133179188,
0.04971658065915108,
-0.044130053371191025,
0.05967620015144348,
0.026946548372507095,
0.020940963178873062,
0.0010433655697852373,
-0.024836422875523567,
-0.044612184166908264,
-0.016153767704963684,
0.052845485508441925,
-0.012119313701987267,
0.008729464374482632,
-0.0014945963630452752,
0.023886390030384064,
-0.01538662426173687,
0.01386195793747902,
0.00786558911204338,
-0.005960408132523298,
-0.017852051183581352,
-0.04393908008933067,
0.06240291893482208,
0.015570300631225109,
0.03588975965976715,
0.028273150324821472,
-0.042296458035707474,
-0.03681396692991257,
0.013746881857514381,
0.002040420426055789,
-0.0044142999686300755,
0.006985390093177557,
-0.029937129467725754,
-0.07059437781572342,
0.00818953849375248,
-0.011086109094321728,
0.02353961579501629,
0.021543459966778755,
0.054479509592056274,
0.05688701942563057,
0.007252594921737909,
-0.01663750596344471,
-0.032748475670814514,
0.0029847738333046436,
-0.05587495490908623,
0.010353746823966503,
0.008038796484470367,
-0.00890059769153595,
-0.0035192084033042192,
0.030361942946910858,
-0.058633312582969666,
0.00876713078469038,
-0.0035228945780545473,
-0.07382164895534515,
0.031816188246011734,
-0.047498781234025955,
-0.05294300243258476,
0.008421022444963455,
-0.0014544298173859715,
0.007839455269277096,
0.03407171741127968,
-0.08730960637331009,
-0.026988036930561066,
0.03595394268631935,
0.029340820387005806,
-0.0230164285749197,
-0.01693480834364891,
0.04831323027610779,
0.012853965163230896,
0.053022533655166626,
0.015139729715883732,
0.004628280643373728,
-0.07336404174566269,
0.04196647182106972,
-0.024938177317380905,
-0.05810006335377693,
0.00836683064699173,
-0.03233480453491211,
0.023883093148469925,
-0.06405407190322876,
0.0472119003534317,
-0.001525588915683329,
0.004210633225739002,
-0.021704785525798798,
-0.0284129548817873,
-0.051136262714862823,
-0.03700883314013481,
-0.0038995835930109024,
0.0062154680490493774,
0.0365767702460289,
0.006939871236681938,
-0.09833753108978271,
-0.04424455389380455,
0.009597783908247948,
-0.005276873242110014,
-0.003624812699854374,
0.06482955068349838,
-0.027959199622273445,
0.006284624338150024,
0.06025887280702591,
0.010315589606761932,
-0.04442290589213371,
-0.008888733573257923,
-0.010870560072362423,
0.0073461285792291164,
0.01887604407966137,
-0.0616220086812973,
0.01793477311730385,
0.006131904665380716,
0.017188988626003265,
-0.05893387645483017,
0.025200599804520607,
-0.01161027792841196,
-0.028497887775301933,
0.038657113909721375,
0.011176486499607563,
0.013690811581909657,
-0.04613466560840607,
-0.004866685718297958,
-0.021562544628977776,
-0.0005902103730477393,
0.015089507214725018,
-0.015221081674098969,
-0.027268679812550545,
-0.03190210834145546,
-0.041235197335481644,
0.0061336844228208065,
0.006364786997437477,
-0.0033971278462558985,
-0.026499245315790176,
0.04837686941027641,
0.013721168972551823,
-0.030170273035764694,
0.049715541303157806,
-0.022304855287075043,
0.01706211268901825,
-0.00010744424071162939,
0.024896716699004173,
-0.0164274163544178,
-0.10518936812877655,
0.013564818538725376,
-0.056017886847257614,
0.06217386573553085,
0.004411596804857254,
-0.01390836387872696,
-0.03778791055083275,
-0.03006695955991745,
-0.0339391864836216,
0.009176467545330524,
-0.09637917578220367,
0.004985618870705366,
-0.018409796059131622,
-0.032098330557346344,
-0.013984308578073978,
0.005004929378628731,
0.018259266391396523,
0.013152360916137695,
-0.04305555298924446,
-0.00935226771980524,
-0.011146009899675846,
-0.005196550395339727,
0.04509495198726654,
-0.04747192934155464,
0.009027262218296528,
0.047159332782030106,
0.019214486703276634,
0.0545005165040493,
-0.05806887149810791,
-0.03996121510863304,
0.016669031232595444,
0.008807414211332798,
0.0012971273390576243,
-0.002316015539690852,
-0.0013266205787658691,
0.04782222583889961,
0.020355690270662308,
0.04597536474466324,
0.000026623371013556607,
-0.000061949816881679,
0.003781525883823633,
-0.013530443422496319,
0.007956648245453835,
0.06187085807323456,
0.00464233011007309,
-0.020573725923895836,
-0.003699086606502533,
-0.008320750668644905,
0.0327860526740551,
0.026614435017108917,
0.0065812962129712105,
0.015238656662404537,
-0.009471600875258446,
-0.010465717874467373,
-0.04692379757761955,
-0.007808645721524954,
0.001995174679905176,
-0.03510534018278122,
-0.06594495475292206,
-0.07044528424739838,
-0.026150355115532875,
-0.0584363229572773,
0.008974193595349789,
0.01376343984156847,
-0.010924719274044037,
0.0164090096950531,
-0.009551013819873333,
0.05202949047088623,
-0.002946503460407257,
-0.03486833721399307,
-0.017695561051368713,
-0.020810844376683235,
0.0028872478287667036,
0.03242897242307663,
0.03731487691402435,
-0.046560805290937424,
-0.016515327617526054,
-0.0024228685069829226,
0.04594133794307709,
-0.03955158218741417,
-0.035469647496938705,
0.009814529679715633,
0.006227831821888685,
-0.04046677425503731,
0.002693291986361146,
0.0011841596569865942,
0.02791506052017212,
0.01213191170245409,
0.013831283897161484,
-0.007572205271571875,
0.058626703917980194,
-0.060278020799160004,
-0.017662115395069122,
0.017712337896227837,
0.025597194209694862,
-0.009142950177192688,
0.02159307524561882,
-0.04499460384249687,
-0.008521758951246738,
0.03973750025033951,
-0.014125480316579342,
0.09482109546661377,
0.005890501197427511,
-0.007544318214058876,
-0.045826587826013565,
0.005058566574007273,
-0.017162473872303963,
0.022933829575777054,
-0.007344455923885107,
-0.09548231959342957,
0.04071597754955292,
-0.021988598629832268,
-0.05730254948139191,
-0.04075662046670914,
0.013513020239770412,
0.08592585474252701,
0.02744665928184986,
-0.02228856459259987,
0.006486502010375261,
-0.045585811138153076,
0.04021736979484558,
-0.011244549416005611,
-0.016875984147191048,
-0.029536757618188858,
0.018403636291623116,
-0.036641787737607956,
0.032160285860300064,
0.004041760694235563,
-0.046173565089702606,
-0.0017592982621863484,
-0.024056855589151382,
-0.021822882816195488,
-0.03461797535419464,
-0.07159551978111267,
0.07480419427156448,
0.05168553441762924,
0.026290403679013252,
-0.010908032767474651,
-0.029320435598492622,
0.017848500981926918,
-0.02822396717965603,
-0.016147756949067116,
0.005373681429773569,
-0.02640223130583763,
0.05496182292699814,
0.020030314102768898,
-0.0719372108578682,
0.008113469928503036,
-0.02922912873327732,
0.04776492714881897,
0.040328774601221085,
0.039411384612321854,
0.05219794437289238,
-0.007603494916111231,
0.0121372751891613
] |
[
7.947846412658691,
3.701660394668579
] |
Soft Condensed Matter
|
Condensed-Matter Physics
|
cond-mat-soft
|
cond-mat-mtrl-sci
|
na
|
2007-04-01T19:58:35
|
We study the interplay of crystal field splitting and Hund coupling in a
two-orbital model which captures the essential physics of systems with two
electrons or holes in the e_g shell. We use single site dynamical mean field
theory with a recently developed impurity solver which is able to access strong
couplings and low temperatures. The fillings of the orbitals and the location
of phase boundaries are computed as a function of Coulomb repulsion, exchange
coupling and crystal field splitting. We find that the Hund coupling can drive
the system into a novel Mott insulating phase with vanishing orbital
susceptibility. Away from half-filling, the crystal field splitting can induce
an orbital selective Mott state.
|
High-spin to low-spin and orbital polarization transitions in
multiorbital Mott systems
|
cond-mat.str-el
|
0704.0057
| 2,007
|
[
-0.013861243613064289,
0.06735154241323471,
0.00409170426428318,
-0.010144648142158985,
-0.004716123919934034,
0.0365024171769619,
-0.023258619010448456,
0.018382633104920387,
0.04410853609442711,
0.024027103558182716,
-0.03975095599889755,
0.03247937560081482,
0.0015644008526578546,
-0.04183030128479004,
-0.006468830164521933,
-0.0063747684471309185,
0.030746404081583023,
-0.004358598962426186,
0.016127055510878563,
-0.005758220795542002,
-0.04630124568939209,
-0.004334890749305487,
-0.034306108951568604,
-0.028219083324074745,
0.0704682394862175,
0.04586975276470184,
0.04896019026637077,
-0.023679101839661598,
-0.011155497282743454,
0.045871298760175705,
0.03447398915886879,
-0.054769426584243774,
-0.006546344142407179,
-0.04954388737678528,
-0.06326252967119217,
-0.03913332149386406,
0.038572944700717926,
0.006513947155326605,
-0.05207470804452896,
0.029970942065119743,
0.06466028094291687,
-0.02945295348763466,
0.02360038459300995,
-0.059955958276987076,
0.014184316620230675,
-0.01304977759718895,
0.025435304269194603,
-0.01698426529765129,
-0.0006902735913172364,
-0.004722494166344404,
0.000388100219424814,
0.06753943115472794,
0.0496230386197567,
-0.060808006674051285,
-0.005491899326443672,
0.01080743782222271,
-0.01563267968595028,
-0.009255114942789078,
0.05445065349340439,
-0.03867929428815842,
0.02563595585525036,
0.043888118118047714,
-0.013651493936777115,
0.02153387852013111,
0.02159074693918228,
-0.014955061487853527,
-0.01110342051833868,
0.027649739757180214,
0.0031139168422669172,
-0.03275192156434059,
0.009198147803544998,
0.011444125324487686,
0.014317733235657215,
0.04100319743156433,
-0.024112097918987274,
0.01679690182209015,
0.010929613374173641,
-0.01775391958653927,
0.010217788629233837,
-0.007956207729876041,
0.011642750352621078,
-0.018649902194738388,
0.03681827709078789,
0.026862196624279022,
0.026896780356764793,
-0.008485929109156132,
0.03655358403921127,
0.021555518731474876,
-0.09136927872896194,
0.020299196243286133,
-0.004432160872966051,
-0.021448658779263496,
-0.006153807044029236,
0.012646221555769444,
-0.04746094346046448,
0.03753070905804634,
0.027036603540182114,
0.04306419938802719,
-0.023268336430191994,
-0.042330946773290634,
-0.012226028367877007,
0.02073335461318493,
-0.011601155623793602,
0.026030156761407852,
0.08306081593036652,
0.07146906852722168,
-0.01451851800084114,
-0.006422813981771469,
0.04412342980504036,
0.07555290311574936,
-0.10186579078435898,
-0.004446351435035467,
0.0003034050459973514,
-0.014612991362810135,
-0.0284078661352396,
0.0054845791310071945,
0.04951560124754906,
-0.06116102263331413,
-0.028195001184940338,
-0.012080524116754532,
0.0021645231172442436,
-0.003909463528543711,
-0.002189669292420149,
0.021201416850090027,
0.0029781810007989407,
0.02094179578125477,
-0.04868946969509125,
-0.07371029257774353,
0.026967570185661316,
0.014976238831877708,
-0.022239193320274353,
0.011406091041862965,
-0.015138724818825722,
-0.01338149979710579,
0.021076949313282967,
0.017844874411821365,
-0.005427734926342964,
-0.04398777335882187,
0.03100833296775818,
-0.004903198219835758,
0.003510397393256426,
-0.033946435898542404,
-0.03527745231986046,
0.0018273340538144112,
0.009851077571511269,
-0.06833214312791824,
0.05856597051024437,
-0.04544006660580635,
-0.01858077570796013,
-0.010855620726943016,
0.019616112112998962,
0.03429270163178444,
0.03872866928577423,
0.05609887093305588,
-0.01145867072045803,
-0.07307012379169464,
-0.023107420653104782,
0.005391050595790148,
0.06962067633867264,
-0.03043733909726143,
0.019005045294761658,
-0.006579401437193155,
-0.06684845685958862,
0.030139176174998283,
-0.03670851141214371,
0.015046635642647743,
0.018498824909329414,
0.04124932736158371,
0.015358836390078068,
0.01954122632741928,
-0.027555635198950768,
-0.04571948200464249,
-0.010551916435360909,
-0.005172457545995712,
0.022077882662415504,
0.059860408306121826,
-0.021589066833257675,
-0.02565637230873108,
0.0318467915058136,
0.02258213236927986,
0.10304483771324158,
-0.004516213200986385,
0.04473118856549263,
0.040819380432367325,
0.051655568182468414,
-0.019916744902729988,
-0.020232409238815308,
-0.012543635442852974,
-0.06026620417833328,
-0.024112768471240997,
0.0426974780857563,
0.013408430851995945,
-0.028829365968704224,
-0.03137907758355141,
-0.01278685312718153,
-0.0028300690464675426,
0.08557216823101044,
-0.036404937505722046,
-0.044216372072696686,
-0.05103720352053642,
-0.01791500858962536,
-0.023427775129675865,
-0.08207622915506363,
-0.014284582808613777,
-0.0030035388190299273,
0.06056173890829086,
-0.0019324251916259527,
0.040241580456495285,
0.03898465633392334,
-0.019116129726171494,
0.04727867990732193,
0.0198220182210207,
-0.02458138018846512,
0.0009925606427714229,
-0.032787855714559555,
0.03909771889448166,
0.053344711661338806,
-0.05981077626347542,
-0.02655097469687462,
0.055916622281074524,
0.053682684898376465,
-0.009881047531962395,
0.042077820748090744,
0.016049962490797043,
0.05455159395933151,
0.00020864752877969295,
-0.028440067544579506,
-0.00021920108702033758,
-0.03417269513010979,
-0.02239105850458145,
-0.06563196331262589,
0.004211930092424154,
0.04204115644097328,
-0.007057465147227049,
0.024336695671081543,
0.007664643693715334,
-0.04919842258095741,
-0.0007472735014744103,
-0.009416298009455204,
0.04701231047511101,
0.025395561009645462,
0.025574762374162674,
-0.03176293894648552,
-0.024499958381056786,
-0.03072834573686123,
-0.0168276596814394,
0.009643183089792728,
0.06069847568869591,
-0.02173939161002636,
0.037593476474285126,
0.04234347492456436,
0.001093636848963797,
-0.005856775678694248,
-0.02174615114927292,
-0.012390573509037495,
-0.006318091880530119,
-0.052978407591581345,
0.06887613236904144,
-0.06559275835752487,
-0.016603384166955948,
0.029844122007489204,
-0.09354738891124725,
0.014980888925492764,
-0.017679639160633087,
0.01566130481660366,
0.0025910583790391684,
0.04194876179099083,
-0.06766313314437866,
-0.021997978910803795,
-0.041270215064287186,
0.0009416512912139297,
0.07876002043485641,
0.042500194162130356,
0.05484404414892197,
0.0018568881787359715,
-0.022601373493671417,
0.015419090166687965,
0.005094904452562332,
-0.024789458140730858,
-0.03124324046075344,
-0.09115148335695267,
-0.02983776479959488,
-0.027434535324573517,
0.000857302627991885,
-0.0006200550706125796,
0.04692036658525467,
0.022494029253721237,
0.003838245291262865,
0.000992636545561254,
0.019837873056530952,
0.012459464371204376,
-0.005846006795763969,
-0.0058573526330292225,
0.0993497222661972,
-0.0033864756114780903,
-0.02211882546544075,
0.029926789924502373,
-0.025820162147283554,
-0.00006489029328804463,
0.06632508337497711,
0.001979815773665905,
0.020944764837622643,
0.003999731037765741,
0.021846896037459373,
-0.005911270156502724,
-0.009479044005274773,
-0.014451079070568085,
-0.031508684158325195,
-0.03402472659945488,
0.009759364649653435,
-0.01466206181794405,
0.07154980301856995,
0.019814733415842056,
0.024079544469714165,
-0.033891525119543076,
0.026566587388515472,
-0.03688478469848633,
0.0208524689078331,
0.08305098861455917,
-0.056348465383052826,
-0.013456515036523342,
0.007034498266875744,
0.0065998053178191185,
-0.052962224930524826,
-0.027595048770308495,
0.07475403696298599,
-0.015428237617015839,
-0.0027529385406523943,
-0.02602226473391056,
0.0113139683380723,
-0.0034990301355719566,
0.019269626587629318,
-0.04285440593957901,
-0.01781766302883625,
-0.005815779324620962,
0.01527259312570095,
0.007120919413864613,
0.06889339536428452,
-0.0432983860373497,
-0.02505466155707836,
0.00034170137951150537,
-0.07070252299308777,
-0.043408047407865524,
-0.057077016681432724,
-0.028929146006703377,
-0.014190166257321835,
-0.06237395480275154,
-0.002332716016098857,
0.032895833253860474,
0.008467864245176315,
-0.048010338097810745,
0.016936562955379486,
-0.005745242815464735,
0.03108731471002102,
-0.03932991623878479,
-0.0034480991307646036,
0.020643465220928192,
-0.00687644025310874,
0.07011622935533524,
0.030103979632258415,
0.017687685787677765,
-0.06883247941732407,
0.036408837884664536,
0.014125648885965347,
-0.00905842985957861,
0.03216760978102684,
-0.013964840210974216,
0.021624376997351646,
0.02527087740600109,
-0.034444864839315414,
-0.045471061021089554,
-0.07256855815649033,
0.016232779249548912,
0.05829109996557236,
0.058719903230667114,
-0.025515712797641754,
-0.05691834166646004,
-0.015686122700572014,
0.009575805626809597,
-0.017051631584763527,
0.02188907563686371,
0.030723538249731064,
0.026544557884335518,
0.058404065668582916,
0.04374556988477707,
-0.0046145254746079445,
-0.0430377796292305,
0.01066679134964943,
-0.02907443791627884,
-0.015142437070608139,
-0.007281692698597908,
0.008115085773169994,
-0.02170768938958645,
0.039044339209795,
0.03565780073404312,
-0.040938496589660645,
0.056569430977106094,
-0.04842834547162056,
0.021372072398662567,
-0.02227230928838253,
-0.06710933893918991,
-0.09115700423717499,
-0.01806013099849224,
-0.054046545177698135,
-0.03529459238052368,
0.012041876092553139,
-0.03000064194202423,
-0.022771235555410385,
0.050235193222761154,
-0.007112193387001753,
0.014542396180331707,
0.018001271411776543,
-0.007913674227893353,
-0.05146125331521034,
0.08727733790874481,
-0.0008753967704251409,
0.029207810759544373,
0.043493758887052536,
0.03837715461850166,
-0.03214852884411812,
-0.03567618876695633,
0.04853662848472595,
0.00041899093776009977,
-0.014305626042187214,
-0.022158712148666382,
-0.000022532103685080074,
0.0023377847392112017,
-0.014233938418328762,
0.022489773109555244,
-0.01835709437727928,
0.04823301360011101,
-0.0014417626662179828,
-0.014259792864322662,
-0.014026490040123463,
-0.05133576691150665,
-0.0014230995438992977,
-0.00562900397926569,
-0.0198835339397192,
-0.01243502739816904,
0.06233162432909012,
0.058804579079151154,
-0.07861511409282684,
-0.0047299363650381565,
0.013039453886449337,
0.03422375023365021,
0.007779241539537907,
0.04184304177761078,
-0.05785056948661804,
0.0018970448290929198,
-0.043062563985586166,
0.017974723130464554,
-0.010208888910710812,
-0.017439961433410645,
0.05451175943017006,
0.07573883980512619,
-0.056569766253232956,
0.014862172305583954,
0.0129723334684968,
0.021078456193208694,
0.07728025317192078,
-0.040285661816596985,
0.03724868223071098,
-0.013705321587622166,
0.021209068596363068,
-0.04055783897638321,
0.016677306964993477,
-0.022062145173549652,
0.015776552259922028,
0.03575103357434273,
0.0307999886572361,
-0.021689357236027718,
0.003891650354489684,
0.03484906628727913,
0.02106344699859619,
0.002503477269783616,
-0.06639482825994492,
0.019138768315315247,
-0.08815954625606537,
0.03474261611700058,
0.01707700453698635,
0.042821746319532394,
0.011902552098035812,
0.03512649983167648,
0.03801971673965454,
-0.015077097341418266,
0.019030863419175148,
0.011539059691131115,
0.026003407314419746,
-0.02653355523943901,
-0.04430463910102844,
0.010997640900313854,
0.03379271924495697,
0.013623291626572609,
0.00022260686091613024,
-0.042306795716285706,
0.008960677310824394,
0.026155229657888412,
0.021600915119051933,
0.009717203676700592,
0.041378483176231384,
-0.00959409587085247,
0.006444311235100031,
-0.017937693744897842,
0.025383347645401955,
-0.012107116170227528,
0.020155036821961403,
0.01237763836979866,
-0.09164067357778549,
0.0027743901591748,
-0.017073264345526695,
0.019489426165819168,
0.04313971474766731,
0.03352511301636696,
0.028024017810821533,
0.01656930148601532,
-0.05171149969100952,
0.015123502351343632,
0.007004023063927889,
-0.052338626235723495,
-0.03616955503821373,
-0.03789670765399933,
0.005071769468486309,
0.012292732484638691,
0.0010122882667928934,
-0.06383407860994339,
0.06273538619279861,
-0.010169638320803642,
-0.07345456629991531,
0.03796203061938286,
0.030548665672540665,
0.0011736431624740362,
0.06003112718462944,
0.01057373732328415,
0.014075417071580887,
0.06272067129611969,
-0.023115545511245728,
-0.005163135938346386,
0.009487361647188663,
-0.008663353510200977,
0.050848644226789474,
-0.003989345859736204,
0.012014741078019142,
0.011138444766402245,
0.02200273983180523,
0.017432957887649536,
-0.04240090027451515,
-0.07576734572649002,
0.014797043986618519,
-0.01952965185046196,
-0.03759871423244476,
-0.008679249323904514,
-0.03473767638206482,
0.022089703008532524,
-0.044848743826150894,
0.03354606032371521,
-0.013010854832828045,
-0.008526620455086231,
-0.033979445695877075,
-0.01876952312886715,
-0.008891599252820015,
-0.01932016760110855,
0.03512556850910187,
0.03276131674647331,
0.010099783539772034,
0.004891715478152037,
-0.020401861518621445,
-0.038630057126283646,
-0.01135204080492258,
0.022359641268849373,
-0.03142803534865379,
-0.002832692349329591,
0.005670605227351189,
-0.014248490333557129,
-0.011891448870301247,
0.006441987585276365,
0.008099201135337353,
-0.004304289352148771,
0.017466062679886818,
-0.016872357577085495,
0.025259636342525482,
-0.012764835730195045,
0.004372984170913696,
-0.017578471451997757,
0.025909719988703728,
-0.04384570196270943,
0.020296264439821243,
-0.03396805748343468,
-0.061215635389089584,
0.035469330847263336,
0.011195276863873005,
-0.01613360457122326,
-0.012541019357740879,
-0.010623275302350521,
-0.05576542019844055,
-0.01866152137517929,
0.01169741339981556,
-0.02424975484609604,
-0.0391736663877964,
-0.05806877091526985,
-0.0038766672369092703,
0.03128017485141754,
0.022808415815234184,
0.04364477097988129,
0.008711490780115128,
0.05876411125063896,
0.07074274122714996,
-0.012577218003571033,
0.01041355449706316,
-0.01110809575766325,
-0.004523439798504114,
-0.007163400761783123,
-0.021306991577148438,
-0.04571346193552017,
-0.04445359855890274,
-0.03229460492730141,
0.006870660465210676,
0.05183269828557968,
0.05674990639090538,
-0.013721039518713951,
0.003145757131278515,
-0.034211546182632446,
-0.02269112691283226,
-0.01987031288444996,
-0.03174660727381706,
-0.005396748892962933,
0.05966293439269066,
0.01536564715206623,
-0.07067179679870605,
0.04985718056559563,
-0.006025451235473156,
0.023313265293836594,
-0.037728793919086456,
-0.023504171520471573,
-0.016380131244659424,
-0.013854832388460636,
0.02521894872188568,
-0.05083688348531723,
0.004623247776180506,
0.025991227477788925,
0.08048593252897263,
0.09030701965093613,
-0.007983813993632793,
0.003297569463029504,
0.07002148777246475,
0.019638292491436005,
0.03973521292209625,
0.03696560859680176,
-0.001932059763930738,
0.010279613547027111,
-0.018086718395352364,
0.07343636453151703,
0.06550481170415878,
-0.043038349598646164,
0.05441328138113022,
-0.007416168227791786,
0.03852393478155136,
0.03535262122750282,
0.002745879115536809,
-0.014995203353464603,
0.03439868614077568,
-0.08947811275720596,
-0.009743771515786648,
-0.004826760850846767,
0.016094660386443138,
0.018097391352057457,
-0.058952491730451584,
-0.040594276040792465,
-0.08647197484970093,
-0.03808612376451492,
0.005257249344140291,
-0.10143852978944778,
-0.045053303241729736,
-0.0641622245311737,
0.027370454743504524,
-0.042886849492788315,
-0.045455098152160645,
0.006270443554967642,
0.028557512909173965,
-0.054850853979587555,
-0.017979003489017487,
-0.012976950034499168,
0.038718082010746,
0.018063325434923172,
-0.03238784149289131,
-0.004581789020448923,
0.007311679422855377,
-0.018497468903660774,
0.010925681330263615,
-0.03933503106236458,
0.013909934088587761,
0.05242183804512024,
0.034514475613832474,
0.02124800905585289,
-0.042231861501932144,
-0.04642287269234657,
0.04421953484416008,
-0.06945408880710602,
-0.030158506706357002,
0.02835957333445549,
0.022509675472974777,
0.005707516800612211,
0.03799067437648773,
-0.018514757975935936,
0.02730288915336132,
-0.001876496709883213,
-0.011539734899997711,
0.07108720391988754,
0.020482435822486877,
0.012224583886563778,
0.037568289786577225,
-0.007613392546772957,
0.0083380788564682,
0.06268133223056793,
0.010584583505988121,
0.03772719204425812,
-0.03349735960364342,
-0.010001973249018192,
-0.07415590435266495,
-0.0004219123802613467,
0.03043377958238125,
0.041158389300107956,
-0.03659714385867119,
-0.030193092301487923,
0.04802023246884346,
0.00007971184822963551,
-0.09113599359989166,
0.012372137047350407,
-0.019310830160975456,
0.0796566754579544,
-0.028702901676297188,
0.006660246755927801,
-0.019447896629571915,
-0.04420416057109833,
-0.006452381145209074,
-0.03355061262845993,
0.05690579488873482,
-0.0783490240573883,
-0.0445631667971611,
-0.02655421383678913,
-0.01830466277897358,
0.0361260324716568,
-0.06842846423387527,
0.007029954344034195,
-0.015896549448370934,
-0.02129250019788742,
0.0018477176781743765,
-0.05872177332639694,
0.050126124173402786,
0.07105842232704163,
0.025507230311632156,
-0.06775590777397156,
-0.06281094253063202,
-0.02898562327027321,
-0.006182361859828234,
0.0326228030025959,
-0.007875299081206322,
-0.038709383457899094,
0.04950975999236107,
0.055482178926467896,
-0.019650915637612343,
0.012944679707288742,
0.00023440970107913017,
-0.0001464317028876394,
0.034010887145996094,
-0.0014187602791935205,
0.0077500357292592525,
-0.005297370254993439,
0.05012400448322296
] |
[
7.961111545562744,
-2.9347989559173584
] |
Strongly Correlated Electrons
|
Condensed-Matter Physics
|
cond-mat-str-el
|
na
|
na
|
2007-03-31T21:59:26
|
I shall present three arguments for the proposition that intelligent life is
very rare in the universe. First, I shall summarize the consensus opinion of
the founders of the Modern Synthesis (Simpson, Dobzhanski, and Mayr) that the
evolution of intelligent life is exceedingly improbable. Second, I shall
develop the Fermi Paradox: if they existed they'd be here. Third, I shall show
that if intelligent life were too common, it would use up all available
resources and die out. But I shall show that the quantum mechanical principle
of unitarity (actually a form of teleology!) requires intelligent life to
survive to the end of time. Finally, I shall argue that, if the universe is
indeed accelerating, then survival to the end of time requires that intelligent
life, though rare, to have evolved several times in the visible universe. I
shall argue that the acceleration is a consequence of the excess of matter over
antimatter in the universe. I shall suggest experiments to test these claims.
|
Intelligent Life in Cosmology
|
physics.pop-ph
|
0704.0058
| 2,007
|
[
0.017154453322291374,
0.07937867939472198,
0.0004675006784964353,
-0.026070134714245796,
0.026309864595532417,
0.07467325776815414,
-0.01613892987370491,
0.041191328316926956,
0.002847584430128336,
0.032391466200351715,
-0.05351840704679489,
0.017236554995179176,
0.02997826784849167,
0.03807626664638519,
-0.033984292298555374,
-0.025500886142253876,
0.05663565918803215,
-0.02911888249218464,
0.050528060644865036,
0.03086308389902115,
-0.031729038804769516,
-0.0246831476688385,
0.003172840690240264,
0.006204497534781694,
0.08551715314388275,
-0.0049712820909917355,
0.036911945790052414,
-0.0038637076504528522,
-0.013181800954043865,
0.009255948476493359,
0.08373291045427322,
-0.0375509150326252,
0.040288425981998444,
-0.04556373134255409,
0.009739412926137447,
-0.06010705605149269,
0.06359006464481354,
0.016792915761470795,
0.020626522600650787,
0.057007573544979095,
-0.01587100885808468,
-0.022274566814303398,
0.010481237433850765,
-0.027721533551812172,
0.038141146302223206,
0.026216929778456688,
0.00579668115824461,
-0.013595803640782833,
0.08667857199907303,
-0.049390483647584915,
-0.03230857104063034,
0.03678438812494278,
0.0008604257018305361,
-0.018688300624489784,
-0.0013703186996281147,
0.0156682338565588,
-0.021101785823702812,
-0.05363517627120018,
0.02208883687853813,
-0.015347464010119438,
0.042131174355745316,
0.0074309660121798515,
0.008090291172266006,
0.0001520863443147391,
0.08049888163805008,
-0.030582154169678688,
-0.020440446212887764,
0.06124243140220642,
0.021190937608480453,
-0.0248553566634655,
0.010676421225070953,
-0.08631806820631027,
-0.01425473764538765,
0.03258664160966873,
-0.007158719934523106,
0.07036332786083221,
0.013191957958042622,
0.005009629298001528,
-0.00025645620189607143,
0.014526180922985077,
-0.023643506690859795,
-0.018763108178973198,
0.03962582349777222,
0.02676064893603325,
0.011125460267066956,
-0.04595014080405235,
-0.016634875908493996,
-0.03040110133588314,
-0.03178637847304344,
0.04735921323299408,
0.04271963983774185,
0.030055228620767593,
0.04757490009069443,
-0.021571403369307518,
-0.05554892495274544,
0.0001904787204694003,
-0.05383514240384102,
0.031940389424562454,
-0.010825499892234802,
0.018098823726177216,
-0.036207303404808044,
0.003040570067241788,
0.003030295018106699,
-0.014583176001906395,
0.040018074214458466,
-0.004077604506164789,
-0.009489216841757298,
-0.004927980247884989,
0.007538552395999432,
-0.010244358330965042,
-0.04613608494400978,
-0.047696176916360855,
0.028498919680714607,
-0.02905987575650215,
-0.029396148398518562,
-0.025405092164874077,
0.04799376055598259,
-0.03611932694911957,
-0.005003016907721758,
0.06295395642518997,
-0.01098185870796442,
0.012722741812467575,
0.020129017531871796,
0.0012295849155634642,
-0.02736736461520195,
0.024135148152709007,
-0.03424600511789322,
-0.05143364891409874,
-0.01806807890534401,
0.015443925745785236,
-0.030500413849949837,
0.04687391221523285,
-0.04467896372079849,
0.01587860845029354,
0.005622268188744783,
0.04788288101553917,
-0.03605588898062706,
-0.054430313408374786,
0.02277190238237381,
0.024107296019792557,
0.07680083066225052,
-0.042132604867219925,
0.017627330496907234,
-0.04116326943039894,
-0.03086019679903984,
-0.027950530871748924,
-0.0033774087205529213,
-0.020391374826431274,
-0.039900749921798706,
0.012692665681242943,
-0.00408177450299263,
0.0618276484310627,
0.011137137189507484,
0.05741756781935692,
-0.05240488052368164,
-0.039939116686582565,
-0.039045557379722595,
0.046251993626356125,
0.009770378470420837,
-0.024673892185091972,
-0.01180205773562193,
0.021296484395861626,
-0.07484323531389236,
0.07075515389442444,
-0.013274414464831352,
0.05573945492506027,
0.01934613101184368,
-0.04481633007526398,
0.007785489782691002,
0.04303978383541107,
-0.05869033560156822,
-0.032842397689819336,
0.011431924998760223,
0.016872955486178398,
0.0010588684817776084,
-0.03604013845324516,
-0.010311135090887547,
-0.06093398854136467,
-0.07920487225055695,
-0.04526204988360405,
0.044392939656972885,
-0.0882817879319191,
-0.00125272071454674,
0.049420151859521866,
0.00579244177788496,
-0.010863198898732662,
0.032228559255599976,
-0.0015851183561608195,
-0.022254742681980133,
-0.01329077873378992,
0.020433470606803894,
-0.004557231906801462,
-0.0028368989005684853,
-0.06939813494682312,
0.0026441116351634264,
-0.03786499798297882,
0.08634697645902634,
0.0021722251549363136,
0.02017877623438835,
-0.0452578142285347,
-0.01677430234849453,
-0.014013772830367088,
-0.05294562131166458,
-0.02284124307334423,
-0.011048072949051857,
0.014871739782392979,
-0.001015116460621357,
0.06358657777309418,
0.010244714096188545,
-0.0025552448350936174,
0.08873725682497025,
-0.014131905511021614,
-0.007393181324005127,
0.03940298408269882,
-0.03547067195177078,
-0.0019910007249563932,
0.043772753328084946,
-0.03608020395040512,
-0.012435868382453918,
0.032997146248817444,
0.04223330691456795,
-0.019107192754745483,
-0.011957678012549877,
-0.0004024060326628387,
0.055556539446115494,
0.013737107627093792,
-0.07565628737211227,
-0.045693300664424896,
-0.03103540651500225,
0.013429315760731697,
-0.024623000994324684,
-0.005281134508550167,
0.07462659478187561,
-0.040700480341911316,
-0.0042121680453419685,
0.026487555354833603,
0.004630919545888901,
0.0009122293558903039,
0.045438751578330994,
0.05159120634198189,
-0.0048612928949296474,
0.019765034317970276,
-0.006609906442463398,
-0.042054433375597,
0.002556899096816778,
-0.07059959322214127,
-0.01087690144777298,
-0.056184232234954834,
-0.022328905761241913,
0.009722483344376087,
0.016968611627817154,
-0.015661515295505524,
0.03676877170801163,
0.050910454243421555,
0.008499727584421635,
-0.03512357920408249,
-0.02301274985074997,
0.08412159979343414,
-0.037124183028936386,
0.004050958901643753,
0.10839538276195526,
-0.04788238927721977,
0.014693901874125004,
-0.016688011586666107,
-0.046169448643922806,
0.021671442314982414,
0.0095162782818079,
-0.0028876163996756077,
-0.021293623372912407,
-0.005792402196675539,
-0.013078962452709675,
0.018343841657042503,
-0.013707826845347881,
0.07430659979581833,
0.007659506518393755,
0.025812048465013504,
-0.004979886580258608,
-0.014158429577946663,
-0.011646758764982224,
-0.01584436185657978,
-0.05632408335804939,
0.006294615101069212,
-0.0371880903840065,
-0.01773754507303238,
0.008171902038156986,
-0.026778247207403183,
0.0012582571944221854,
0.011553112417459488,
0.0201101116836071,
0.00676848366856575,
-0.02686263993382454,
-0.025446679443120956,
-0.004263066686689854,
0.06545845419168472,
-0.02770346589386463,
0.057811107486486435,
0.03147273510694504,
-0.01287085097283125,
-0.035733919590711594,
-0.0200184416025877,
0.051541224122047424,
-0.02334398590028286,
0.055518489331007004,
0.004575949162244797,
0.02950567752122879,
-0.014628997072577477,
-0.01792893558740616,
-0.0039105783216655254,
-0.0022669252939522266,
-0.04411974921822548,
0.02468913048505783,
0.004131121560931206,
0.008141481317579746,
0.001355415559373796,
-0.023043813183903694,
0.029077978804707527,
0.019648699089884758,
-0.0069579812698066235,
0.13547448813915253,
0.0018280695658177137,
0.028373241424560547,
-0.037858717143535614,
-0.043581850826740265,
-0.06351011991500854,
0.04293181002140045,
0.053772587329149246,
-0.04732707515358925,
0.011932693421840668,
-0.014359140768647194,
0.0039547826163470745,
-0.03149484097957611,
0.0312246885150671,
-0.03494300693273544,
-0.014061558060348034,
-0.067854143679142,
-0.010832691565155983,
-0.013310756534337997,
0.05095846205949783,
-0.021440114825963974,
0.008032890036702156,
0.015175717882812023,
0.014543694444000721,
-0.03597042337059975,
0.013408361934125423,
-0.03314707428216934,
-0.007290401495993137,
0.016158318147063255,
-0.018950501456856728,
0.0714913085103035,
0.02184257283806801,
-0.02422904595732689,
-0.024631721898913383,
0.03267189487814903,
0.02996143326163292,
-0.029353365302085876,
0.00969950295984745,
0.04038179665803909,
0.012192442081868649,
0.10358960926532745,
-0.012454329058527946,
0.02053300105035305,
-0.021074268966913223,
0.0492110550403595,
-0.03513810783624649,
0.04816630855202675,
0.03486085683107376,
0.006505830679088831,
0.012639440596103668,
0.03042517602443695,
-0.005780704319477081,
-0.0007420937181450427,
-0.0384003110229969,
-0.01509104110300541,
0.060633741319179535,
0.058327388018369675,
-0.034416861832141876,
-0.045944929122924805,
0.016539249569177628,
-0.029389705508947372,
-0.008454428054392338,
0.05749569833278656,
0.002983675105497241,
0.022785114124417305,
-0.02650921605527401,
0.048110198229551315,
0.02156384103000164,
-0.026546118780970573,
-0.03568648919463158,
-0.020631125196814537,
0.016867833212018013,
-0.02317744493484497,
-0.017862683162093163,
-0.04474298283457756,
-0.009957967326045036,
0.007832367904484272,
-0.052653588354587555,
0.044340915977954865,
-0.01308052334934473,
0.011808323673903942,
0.005416809115558863,
-0.07502732425928116,
-0.06793739646673203,
0.02211916260421276,
0.015343871898949146,
-0.03404299542307854,
-0.017800606787204742,
-0.008839476853609085,
-0.0546160489320755,
0.06511355936527252,
-0.034771356731653214,
0.03932017832994461,
0.06502576917409897,
0.016283519566059113,
-0.05932554230093956,
0.015511021949350834,
-0.03307435289025307,
0.02200162038207054,
-0.07496093213558197,
0.01551474817097187,
-0.00181307434104383,
0.027285706251859665,
0.034677546471357346,
-0.012083332985639572,
0.0073160030879080296,
-0.021049611270427704,
0.000662030593957752,
-0.022489486262202263,
0.004269768018275499,
-0.03477843105792999,
0.006203539669513702,
0.03912609443068504,
0.01834653504192829,
-0.023352311924099922,
0.06638891994953156,
-0.0053561232052743435,
-0.014868221245706081,
0.011686014011502266,
0.018200507387518883,
-0.00260384869761765,
0.04685399681329727,
0.06265440583229065,
-0.061964504420757294,
0.001019127550534904,
0.005455114413052797,
0.02490045502781868,
0.09144770354032516,
0.032538339495658875,
-0.006371764466166496,
-0.027425616979599,
0.00031650636810809374,
0.02772487699985504,
0.0006480497540906072,
-0.006908823736011982,
0.051615916192531586,
0.030966874212026596,
-0.024400906637310982,
-0.001485896180383861,
0.000873351062182337,
0.023529531434178352,
0.04434571787714958,
-0.04177442938089371,
0.03163951262831688,
0.0008417594362981617,
0.03717859834432602,
0.006908218841999769,
-0.0007886883686296642,
-0.017554782330989838,
0.0008311832789331675,
0.03679054230451584,
0.011128743179142475,
-0.033666275441646576,
0.029038280248641968,
0.0324641577899456,
0.03183590993285179,
-0.06420645117759705,
-0.028307214379310608,
-0.015096080489456654,
-0.06378471106290817,
-0.0112767294049263,
0.054116345942020416,
0.03869567811489105,
-0.06754507124423981,
-0.026128845289349556,
-0.01062183640897274,
-0.02427120879292488,
0.03398573771119118,
-0.03575054556131363,
0.007220233324915171,
-0.020808696746826172,
-0.02436908707022667,
0.0004117442585993558,
0.0016774089308455586,
0.016145803034305573,
0.025549788028001785,
-0.025969326496124268,
-0.02610543556511402,
0.018842259421944618,
-0.025135893374681473,
-0.010863804258406162,
0.0006300563691183925,
-0.04580170661211014,
0.022417336702346802,
0.005549141671508551,
0.017990540713071823,
-0.04597688093781471,
0.013307190500199795,
-0.004201643168926239,
-0.0847700983285904,
-0.019267018884420395,
0.004544255323708057,
0.0316389724612236,
0.02509460411965847,
0.032139889895915985,
0.0381736159324646,
-0.011251273564994335,
-0.00546333659440279,
0.025871004909276962,
-0.0022114505991339684,
-0.022769782692193985,
0.03639894351363182,
-0.007368652615696192,
0.02159145101904869,
0.02883019484579563,
-0.03832518309354782,
-0.04792829230427742,
0.012664781883358955,
-0.030936269089579582,
-0.058118704706430435,
0.04386525973677635,
-0.017419995740056038,
0.009251518175005913,
0.015123059041798115,
-0.025403916835784912,
-0.03432418033480644,
0.010170836001634598,
0.020214637741446495,
-0.033188387751579285,
0.022135257720947266,
0.004949631635099649,
-0.005801514722406864,
-0.005277400370687246,
-0.01764870434999466,
0.03114325739443302,
0.021923651918768883,
0.03782569244503975,
-0.015346670523285866,
-0.13148421049118042,
0.05681569129228592,
0.05962095409631729,
-0.05938621610403061,
-0.010709510184824467,
-0.027773182839155197,
0.05717969313263893,
-0.02503935433924198,
0.018739717081189156,
-0.011190056800842285,
0.015151195228099823,
0.0004824934003408998,
-0.0456889308989048,
0.011372119188308716,
-0.021005067974328995,
0.05969231575727463,
0.0441717766225338,
0.008465241640806198,
-0.02213989943265915,
-0.11569815129041672,
-0.019402053207159042,
-0.03728252649307251,
0.007110578939318657,
0.029667556285858154,
0.045477211475372314,
-0.009279974736273289,
-0.013764902018010616,
0.032958824187517166,
0.0451371856033802,
-0.025409331545233727,
0.04715173691511154,
0.02954048104584217,
-0.1007431223988533,
-0.030476858839392662,
-0.025312498211860657,
-0.04273254796862602,
0.023406540974974632,
-0.017689481377601624,
-0.030737323686480522,
0.026598487049341202,
-0.023416073992848396,
-0.005361329764127731,
0.0485650934278965,
-0.03672117739915848,
0.04667069762945175,
-0.02313767559826374,
0.003299442119896412,
-0.01829661801457405,
-0.06308091431856155,
-0.02549586445093155,
-0.0019875825382769108,
-0.023401176556944847,
-0.05691919103264809,
-0.05270533263683319,
0.005080279894173145,
-0.03473979979753494,
0.09117601066827774,
-0.006216439418494701,
0.043894071131944656,
0.017129559069871902,
-0.016278425231575966,
0.03742102533578873,
0.029354257509112358,
-0.01724044606089592,
0.0025476431474089622,
0.00040605946560390294,
-0.03879253938794136,
-0.010821569710969925,
-0.01572001352906227,
-0.033859092742204666,
0.08193003386259079,
-0.03144272044301033,
-0.02701103687286377,
0.017278321087360382,
0.018469292670488358,
-0.03999185934662819,
0.01239189226180315,
-0.08121417462825775,
-0.02446839027106762,
-0.0166659876704216,
-0.008663552813231945,
-0.026630740612745285,
0.039352867752313614,
0.08039892464876175,
-0.019594058394432068,
-0.032708436250686646,
0.0037215615157037973,
0.015131037682294846,
-0.02981121651828289,
0.020518362522125244,
-0.03557119145989418,
0.0270429328083992,
-0.015097200870513916,
0.018488507717847824,
0.029666751623153687,
-0.05009612813591957,
0.023833461105823517,
0.0272555872797966,
0.010419046506285667,
0.03299636021256447,
0.05406209081411362,
0.03008989803493023,
0.022349948063492775,
-0.03268062323331833,
0.046303004026412964,
0.009568381123244762,
0.0024668839760124683,
0.015265105292201042,
0.00176471087615937,
0.01389675959944725,
0.015416779555380344,
-0.020839471369981766,
0.004817554727196693,
-0.041219212114810944,
-0.0038266496267169714,
-0.01204668078571558,
0.009286487475037575,
-0.036610450595617294,
0.03520013391971588,
-0.002763838041573763,
-0.010178470984101295,
-0.09314437210559845,
-0.0254510510712862,
0.037488482892513275,
-0.04264587536454201,
-0.010892522521317005,
-0.07589513808488846,
-0.05382185056805611,
-0.030597100034356117,
-0.01287844032049179,
-0.025904905050992966,
0.02337287925183773,
0.04111663997173309,
0.025208957493305206,
0.0240849107503891,
0.03256874531507492,
-0.024897335097193718,
-0.07107152789831161,
0.013679527677595615,
0.005289186257869005,
0.011736591346561909,
-0.06127272546291351,
-0.03520394116640091,
-0.06238945201039314,
-0.030393894761800766,
-0.009895242750644684,
0.01629054546356201,
-0.08300057798624039,
0.014356148429214954,
0.0024788419250398874,
-0.0404721274971962,
0.011428678408265114,
0.06364737451076508,
0.03572200611233711,
0.008788952603936195,
0.055298466235399246,
-0.027645280584692955,
0.04652026295661926,
-0.00015249199350364506,
0.008517995476722717,
-0.00891992449760437,
0.05614137649536133,
-0.019846918061375618,
0.026589922606945038,
-0.0012542650802060962,
0.03505063056945801,
0.035730112344026566,
0.018701380118727684,
0.04143649339675903,
-0.039757922291755676,
0.018941672518849373,
-0.030528299510478973,
0.02552238292992115,
-0.05479521304368973,
0.03485073149204254,
-0.04001227766275406,
-0.0575786754488945,
0.03981330990791321,
0.005182966124266386,
-0.008839642629027367,
0.016846975311636925,
-0.003607605118304491,
0.020613158121705055,
0.023097356781363487,
0.050359178334474564,
-0.0025764438323676586,
-0.07014003396034241,
0.016516754403710365,
-0.0761542096734047,
0.04888572543859482,
-0.033870745450258255,
0.014718263410031796,
-0.1160057857632637,
-0.03636781871318817,
0.01628117263317108,
-0.007489574141800404,
0.0295226089656353,
0.03667217120528221,
-0.02376086451113224,
-0.03561031073331833,
-0.08065640181303024,
0.028178459033370018,
0.04984564706683159,
0.010187195613980293,
-0.019681554287672043,
-0.002225840464234352,
-0.06911227852106094,
0.012076219543814659,
0.07335438579320908,
0.015761325135827065,
0.04271863400936127,
0.012315665371716022,
0.0640956461429596,
-0.027035025879740715,
0.01946520060300827,
0.0023731798864901066,
-0.0035751210525631905,
0.006891352124512196,
-0.0014169326750561595,
0.027941180393099785,
0.0005174599355086684,
-0.026815177872776985
] |
[
12.9801025390625,
6.815321445465088
] |
Popular Physics
|
General Physics
|
physics-pop-ph
|
na
|
na
|
2007-03-31T22:16:50
|
We derive masses and radii for both components in the single-lined eclipsing
binary HAT-TR-205-013, which consists of a F7V primary and a late M-dwarf
secondary. The system's period is short, $P=2.230736 \pm 0.000010$ days, with
an orbit indistinguishable from circular, $e=0.012 \pm 0.021$. We demonstrate
generally that the surface gravity of the secondary star in a single-lined
binary undergoing total eclipses can be derived from characteristics of the
light curve and spectroscopic orbit. This constrains the secondary to a unique
line in the mass-radius diagram with $M/R^2$ = constant. For HAT-TR-205-013, we
assume the orbit has been tidally circularized, and that the primary's rotation
has been synchronized and aligned with the orbital axis. Our observed line
broadening, $V_{\rm rot} \sin i_{\rm rot} = 28.9 \pm 1.0$ \kms, gives a primary
radius of $R_{\rm A} = 1.28 \pm 0.04$ \rsun. Our light curve analysis leads to
the radius of the secondary, $R_{\rm B} = 0.167 \pm 0.006$ \rsun, and the
semimajor axis of the orbit, $a = 7.54 \pm 0.30 \rsun = 0.0351 \pm 0.0014$ AU.
Our single-lined spectroscopic orbit and the semimajor axis then yield the
individual masses, $M_{\rm B} = 0.124 \pm 0.010$ \msun and $M_{\rm A} = 1.04
\pm 0.13$ \msun. Our result for HAT-TR-205-013 B lies above the theoretical
mass-radius models from the Lyon group, consistent with results from
double-lined eclipsing binaries. The method we describe offers the opportunity
to study the very low end of the stellar mass-radius relation.
|
The Mass and Radius of the Unseen M-Dwarf Companion in the Single-Lined
Eclipsing Binary HAT-TR-205-013
|
astro-ph
|
0704.0059
| 2,007
|
[
-0.0635460764169693,
0.005603916011750698,
-0.022323060780763626,
-0.052256107330322266,
0.00045470744953490794,
0.020036444067955017,
0.04036002233624458,
-0.038212377578020096,
-0.02562272734940052,
-0.030171912163496017,
-0.04866955801844597,
0.05593276023864746,
0.04687194153666496,
0.013576987199485302,
0.04381873831152916,
-0.010815431363880634,
0.012639625929296017,
-0.03880908340215683,
-0.003725110087543726,
0.024018796160817146,
-0.028507588431239128,
-0.0014584519667550921,
-0.049155328422784805,
-0.026947742328047752,
0.07737728953361511,
0.009917001239955425,
0.03806418180465698,
0.0114815142005682,
-0.07129775732755661,
0.04886231571435928,
0.04396308958530426,
-0.049388203769922256,
0.025288207456469536,
-0.012691290117800236,
-0.02313421480357647,
-0.04472923278808594,
0.06755220890045166,
0.015255080536007881,
-0.01282053254544735,
0.01886017434298992,
0.033416666090488434,
-0.0331374816596508,
0.024642396718263626,
-0.023531315848231316,
0.02534610964357853,
-0.016588689759373665,
0.021728968247771263,
-0.011860732920467854,
0.05051673948764801,
0.00043896865099668503,
0.02645682916045189,
0.0637994334101677,
0.04773861914873123,
-0.04831536114215851,
-0.04488717392086983,
0.011894493363797665,
0.013532436452805996,
-0.037675414234399796,
0.027386194095015526,
-0.027217913419008255,
0.03865090012550354,
0.01328900083899498,
-0.06428342312574387,
0.02217651531100273,
0.03133534640073776,
-0.03580619394779205,
-0.030547956004738808,
0.012897813692688942,
-0.018630830571055412,
-0.03354421630501747,
0.03147299215197563,
-0.0059084221720695496,
0.023764682933688164,
0.03148796781897545,
-0.026510046795010567,
-0.02284565195441246,
0.005555456038564444,
-0.016974609345197678,
-0.043717630207538605,
-0.01692941039800644,
0.03637224808335304,
-0.052733078598976135,
0.024758610874414444,
0.031493183225393295,
0.022332631051540375,
0.004880229942500591,
-0.03036528080701828,
0.0349174402654171,
-0.10846683382987976,
0.05713184177875519,
0.0010440044570714235,
0.016357973217964172,
0.05351122096180916,
0.012554936110973358,
0.008247820660471916,
0.014724315144121647,
0.004209847189486027,
0.031162839382886887,
-0.01630169339478016,
-0.020252861082553864,
0.027111245319247246,
0.04262404143810272,
-0.016820639371871948,
0.006826562341302633,
0.10801145434379578,
0.06405279785394669,
0.012087888084352016,
0.009370584972202778,
0.044040050357580185,
-0.016121573746204376,
-0.08484438061714172,
-0.021613791584968567,
-0.003314293222501874,
-0.008444168604910374,
-0.005131097044795752,
-0.04892420023679733,
0.025072423741221428,
-0.07111348956823349,
-0.01315860915929079,
0.030747748911380768,
0.026883073151111603,
-0.02750268206000328,
-0.003197442041710019,
0.07064584642648697,
-0.030003167688846588,
-0.026792610064148903,
-0.032966259866952896,
-0.03863922506570816,
0.0434478260576725,
0.004680054262280464,
-0.06382616609334946,
-0.008645661175251007,
-0.05346035957336426,
-0.04046317934989929,
0.06631387770175934,
0.074684739112854,
-0.0025270998012274504,
-0.020704668015241623,
-0.049334753304719925,
-0.03457309305667877,
0.015993768349289894,
0.03431272879242897,
0.026222821325063705,
-0.06952866166830063,
0.01967514678835869,
-0.029822560027241707,
-0.01748954877257347,
-0.015464945696294308,
-0.03759642317891121,
-0.013108785264194012,
0.018160264939069748,
0.050420768558979034,
-0.011466347612440586,
0.022554786875844002,
-0.07089972496032715,
-0.05252274125814438,
-0.012523974291980267,
0.0035006587859243155,
0.014185224659740925,
-0.010213630273938179,
0.04802484065294266,
0.03085208497941494,
-0.05535602569580078,
0.030696233734488487,
-0.01640366017818451,
0.028691019862890244,
0.0027913888916373253,
0.04832595959305763,
0.008965847082436085,
0.044999271631240845,
-0.053467534482479095,
-0.03178371861577034,
-0.020646123215556145,
0.013745944947004318,
0.0010075565660372376,
-0.011261774227023125,
0.016952456906437874,
-0.005898769479244947,
-0.00018946053751278669,
0.061101991683244705,
0.08553341776132584,
-0.0060914866626262665,
0.05061888322234154,
0.014441406354308128,
0.0010456916643306613,
-0.0037081632763147354,
0.02777610532939434,
-0.01352875679731369,
-0.023272180929780006,
-0.01501929759979248,
0.004659287631511688,
0.01977468468248844,
0.036678705364465714,
-0.052755966782569885,
0.028710372745990753,
-0.034416086971759796,
0.08022885024547577,
0.005535430740565062,
-0.018396945670247078,
-0.026632212102413177,
-0.06886903196573257,
-0.031926143914461136,
-0.014576843939721584,
-0.0063276709988713264,
-0.02363686077296734,
0.035749711096286774,
0.014066683128476143,
0.05155586451292038,
0.05148639157414436,
0.028238840401172638,
0.05086107552051544,
0.01688026823103428,
0.002926725195720792,
0.004301454406231642,
-0.01623702235519886,
0.004991572350263596,
-0.00388926500454545,
-0.041050851345062256,
-0.02249538153409958,
0.014637193642556667,
0.0517924539744854,
-0.023958967998623848,
0.032554373145103455,
-0.023535218089818954,
0.050181712955236435,
0.03433487191796303,
-0.02248932607471943,
0.03341304138302803,
-0.005114099010825157,
-0.05308479070663452,
0.021770291030406952,
-0.030664218589663506,
0.03580986708402634,
0.024696605280041695,
0.0018770464230328798,
-0.03744971379637718,
0.034533049911260605,
0.05857488140463829,
0.036716628819704056,
0.06062044948339462,
0.07817821949720383,
-0.012933628633618355,
-0.020546920597553253,
-0.047408007085323334,
-0.05230661481618881,
0.020984116941690445,
-0.013837190344929695,
0.04249676689505577,
-0.01661362498998642,
0.04426436871290207,
-0.018704909831285477,
0.024243587628006935,
0.05744398012757301,
0.0017474479973316193,
0.021088523790240288,
-0.04295651987195015,
-0.07503541558980942,
0.004987579770386219,
-0.08239217847585678,
-0.044402237981557846,
0.001589612802490592,
-0.03598986566066742,
0.03011036291718483,
-0.041694626212120056,
-0.003269332693889737,
-0.0008090524934232235,
-0.06036701053380966,
-0.049437347799539566,
0.02877708151936531,
0.0049965474754571915,
0.05664336308836937,
0.03587793931365013,
0.046693477779626846,
0.06770722568035126,
-0.009885343722999096,
0.027190295979380608,
0.04479954391717911,
-0.03319938853383064,
0.019336417317390442,
0.015028527937829494,
-0.05612315610051155,
-0.03384717181324959,
-0.019670642912387848,
-0.0025438806042075157,
0.009137592278420925,
0.02055162377655506,
-0.0004784006450790912,
0.007091926876455545,
-0.004194584209471941,
0.041844867169857025,
-0.04214458540081978,
-0.000645090825855732,
0.021042846143245697,
0.05880805477499962,
0.0454605408012867,
0.016281163319945335,
0.06156638637185097,
0.07879503071308136,
-0.023657310754060745,
-0.024129871279001236,
-0.0050431955605745316,
0.02465977519750595,
-0.03911735862493515,
0.00525953434407711,
-0.01781686767935753,
0.018252216279506683,
-0.02090327814221382,
-0.043747156858444214,
0.0358896479010582,
-0.014002840034663677,
-0.02466288022696972,
0.045677583664655685,
0.016141949221491814,
0.019276773557066917,
-0.02567891962826252,
0.03482825309038162,
-0.05365076661109924,
-0.017646556720137596,
0.030760889872908592,
0.03939265012741089,
-0.020284082740545273,
-0.027923405170440674,
0.0011549362679943442,
-0.06415462493896484,
0.022796520963311195,
0.012752985581755638,
0.029069634154438972,
0.03362560644745827,
-0.018116505816578865,
0.039759717881679535,
-0.01792925037443638,
0.03548805043101311,
-0.03035799041390419,
0.011692767962813377,
-0.01686595194041729,
0.04680771008133888,
0.02249564230442047,
0.051737818866968155,
-0.008104474283754826,
0.004225687589496374,
0.005811023060232401,
-0.018893234431743622,
-0.03718606382608414,
-0.03883158788084984,
0.01025227177888155,
0.0026799989864230156,
-0.030173350125551224,
-0.026610879227519035,
0.07271252572536469,
-0.009975366294384003,
-0.05436908081173897,
-0.03159618377685547,
-0.0057999552227556705,
-0.02044817991554737,
0.0036989469081163406,
0.056605059653520584,
0.05300399288535118,
-0.015176923014223576,
0.04466521739959717,
-0.03471813723444939,
0.0008480739197693765,
-0.0439961776137352,
0.025452181696891785,
0.055838149040937424,
0.04265210032463074,
0.02763131447136402,
-0.03506813570857048,
0.020625105127692223,
0.034779805690050125,
-0.03357618302106857,
-0.08446021378040314,
-0.04792026802897453,
0.06452640146017075,
0.03097856231033802,
0.015492687001824379,
-0.018425164744257927,
-0.039040353149175644,
0.0004484860983211547,
-0.024915743619203568,
0.02778264880180359,
0.07739298790693283,
0.014944829978048801,
0.0012572272680699825,
0.026328323408961296,
0.007229134440422058,
-0.018469788134098053,
-0.04576260223984718,
0.019789092242717743,
0.028321711346507072,
-0.04366292059421539,
-0.009698777459561825,
-0.024027477949857712,
-0.021212682127952576,
-0.033451735973358154,
0.03729714825749397,
0.011884389445185661,
0.07757861912250519,
-0.03836777061223984,
0.020758284255862236,
0.013334650546312332,
-0.08924511075019836,
-0.05943728983402252,
-0.005140981636941433,
0.032396938651800156,
-0.05348360165953636,
-0.007175439037382603,
-0.02214125357568264,
-0.029584242030978203,
0.052131667733192444,
0.002281761961057782,
0.02407957799732685,
0.06481146067380905,
0.008581453002989292,
-0.06832505017518997,
0.010597179643809795,
0.03211323171854019,
0.01518503949046135,
-0.033547405153512955,
-0.0018273383611813188,
-0.01741846464574337,
-0.02966970205307007,
0.021811289712786674,
-0.009539094753563404,
-0.017605887725949287,
-0.04256333038210869,
0.013411523774266243,
0.013742401264607906,
-0.030453702434897423,
-0.020252810791134834,
-0.04109789803624153,
0.0517844595015049,
-0.016260264441370964,
-0.00025606100098229945,
0.04432351514697075,
-0.06061480566859245,
0.010039453394711018,
0.046948377043008804,
-0.009181764908134937,
-0.012899328023195267,
0.01222273986786604,
0.019807441160082817,
-0.06685013324022293,
-0.05315914750099182,
-0.029646361246705055,
0.01561775617301464,
0.03362177684903145,
0.08905624598264694,
-0.06037453934550285,
-0.0499831847846508,
0.012820937670767307,
0.03530358523130417,
-0.013225271366536617,
-0.024505233392119408,
0.017822321504354477,
0.057420749217271805,
-0.059251345694065094,
0.03099176660180092,
-0.010586882010102272,
0.09109484404325485,
-0.008275357075035572,
0.022527102380990982,
0.0026334545109421015,
0.005529110319912434,
0.04118054360151291,
0.01735738478600979,
-0.05875160172581673,
0.027142487466335297,
0.010197944939136505,
0.04994858801364899,
0.08705826103687286,
-0.043212249875068665,
0.06876805424690247,
0.006692889146506786,
0.023609014227986336,
-0.005455655977129936,
-0.048197828233242035,
0.017245540395379066,
-0.051870062947273254,
0.0026919282972812653,
0.0881221741437912,
0.010569090023636818,
0.03240369260311127,
-0.05806472897529602,
0.031235668808221817,
0.019259536638855934,
0.08341637253761292,
0.03044828772544861,
-0.02774491161108017,
-0.004264873452484608,
0.027346322312951088,
-0.056419339030981064,
0.01725945435464382,
0.022805633023381233,
0.010638970881700516,
-0.02500174753367901,
-0.0570986345410347,
0.004326545633375645,
0.013653582893311977,
0.050511568784713745,
-0.009388579055666924,
0.013959555886685848,
0.00947568379342556,
0.012712543830275536,
0.04661199450492859,
0.057108718901872635,
0.040680840611457825,
-0.07056477665901184,
-0.05741133168339729,
0.00037916135624982417,
0.022196829319000244,
-0.008826355449855328,
0.05507584661245346,
0.025165613740682602,
0.020412806421518326,
0.008987396955490112,
-0.05007157474756241,
0.04905034601688385,
0.06855878233909607,
-0.0199216790497303,
0.022541595622897148,
-0.004124411381781101,
-0.017303191125392914,
0.0011132345534861088,
-0.04246380552649498,
-0.054830435663461685,
0.027318758890032768,
-0.027357012033462524,
-0.06050912290811539,
0.03643010929226875,
-0.05376100540161133,
-0.024718111380934715,
0.015066348947584629,
0.014387420378625393,
-0.0166794341057539,
-0.023619068786501884,
-0.039660628885030746,
-0.0012770028552040458,
0.043479423969984055,
0.024876106530427933,
-0.019204964861273766,
-0.03042520582675934,
-0.009828967973589897,
-0.029042888432741165,
0.03590025752782822,
0.00402391841635108,
-0.041212208569049835,
-0.02943222038447857,
0.0545068122446537,
0.007080873474478722,
-0.044831112027168274,
0.053277820348739624,
-0.013256830163300037,
0.005990260746330023,
-0.021294014528393745,
-0.0002545268216636032,
-0.014996937476098537,
-0.01108548790216446,
-0.03473956882953644,
-0.061916641891002655,
-0.007978791370987892,
0.03576520085334778,
0.022150708362460136,
0.021948648616671562,
0.05526474490761757,
-0.043825872242450714,
-0.10786424577236176,
-0.009805827401578426,
-0.012405849061906338,
0.014777136035263538,
-0.048529062420129776,
-0.009432599879801273,
-0.04964546859264374,
0.007501524407416582,
0.005650138016790152,
0.033117033541202545,
0.011520113795995712,
0.022852875292301178,
0.03774715214967728,
-0.0506703145802021,
-0.058596428483724594,
-0.017886100336909294,
0.010305507108569145,
0.02011331357061863,
0.0345880500972271,
-0.01618032157421112,
0.005593164823949337,
-0.060401495546102524,
0.0007882490172050893,
0.00018786231521517038,
-0.027702996507287025,
0.01874311827123165,
-0.01902134157717228,
-0.05344558507204056,
-0.06204066053032875,
-0.058026090264320374,
0.05502578988671303,
-0.0012495132395997643,
0.019156083464622498,
-0.021573398262262344,
-0.045287858694791794,
-0.009403831325471401,
0.039941027760505676,
0.08814810961484909,
-0.03157956898212433,
0.029789716005325317,
0.030822204425930977,
-0.005216851364821196,
0.030298812314867973,
-0.023905344307422638,
-0.02047140896320343,
-0.020734645426273346,
0.014809241518378258,
-0.016775328665971756,
-0.04195784404873848,
-0.04576985910534859,
-0.022576017305254936,
0.0023495289497077465,
0.037160780280828476,
-0.05819106101989746,
-0.03802815079689026,
-0.007206268142908812,
-0.07566197216510773,
0.005631483159959316,
-0.12000367790460587,
-0.010566472075879574,
0.006220991723239422,
0.01818300038576126,
-0.07241189479827881,
0.01935378834605217,
-0.0010218849638476968,
0.02548256143927574,
-0.0631922110915184,
-0.02136189304292202,
-0.032053954899311066,
0.03289518877863884,
0.03803572431206703,
-0.017388125881552696,
0.041943952441215515,
0.06750302016735077,
0.03074178285896778,
0.055353276431560516,
-0.023362373933196068,
-0.03385625034570694,
0.0042982506565749645,
-0.002224765485152602,
0.02077409438788891,
0.006190910004079342,
0.019311435520648956,
0.036122068762779236,
0.00021592347184196115,
0.017849555239081383,
0.057334624230861664,
-0.03675080090761185,
0.1087731420993805,
0.016210516914725304,
-0.005599095486104488,
0.010323761031031609,
0.015900421887636185,
0.004515216685831547,
-0.05374078452587128,
-0.0379457026720047,
0.019043346866965294,
0.036719586700201035,
-0.00984068214893341,
0.04098311811685562,
-0.05194902420043945,
-0.010379862040281296,
-0.04072045907378197,
-0.03208475932478905,
0.022215288132429123,
-0.018396727740764618,
-0.031343262642621994,
-0.04892309755086899,
-0.0374615378677845,
-0.05691124126315117,
0.03172871097922325,
0.004361160099506378,
0.004629266448318958,
-0.011275690980255604,
-0.021541327238082886,
-0.028140192851424217,
-0.001021940028294921,
0.009452070109546185,
0.017777040600776672,
-0.0022256893571466208,
-0.027304040268063545,
-0.037734586745500565,
-0.01711484231054783,
0.03594325855374336,
-0.013689682818949223,
0.008952402509748936,
0.023147763684391975,
0.011768457479774952,
-0.05845646560192108,
-0.014431824907660484,
-0.014180696569383144,
-0.04178721085190773,
0.01759941689670086,
0.026570918038487434,
-0.012540002353489399,
-0.013092678971588612,
0.03642674908041954,
-0.009549306705594063,
0.017901740968227386,
0.028692493215203285,
0.04759608209133148,
-0.010376126505434513,
0.06095626950263977,
-0.012367448769509792,
0.009943615645170212,
-0.015233523212373257,
-0.025628870353102684,
0.01700478233397007,
-0.0022940055932849646,
0.025731010362505913,
-0.018595974892377853,
-0.03993022069334984,
-0.03623046725988388,
-0.013760432600975037,
-0.02510732226073742,
0.0219589751213789,
-0.02743302658200264,
-0.004313228651881218,
-0.01985470950603485,
-0.04376957193017006,
-0.07978670299053192,
0.00642935186624527,
0.02828642725944519,
0.07135884463787079,
-0.004678167402744293,
-0.011873065494000912,
0.018180906772613525,
-0.055177949368953705,
-0.0066928560845553875,
-0.0403205081820488,
0.016614308580756187,
0.008206167258322239,
0.0032490352168679237,
-0.061068471521139145,
-0.011006440967321396,
-0.00392866600304842,
-0.0707942470908165,
0.029825491830706596,
0.0016588961007073522,
-0.01417919248342514,
-0.00231810100376606,
-0.06074487045407295,
0.037740275263786316,
0.025633828714489937,
0.0038722583558410406,
0.041130002588033676,
0.022345129400491714,
-0.00048334026359952986,
-0.032948222011327744,
0.0329270102083683,
-0.02128423936665058,
-0.02459385059773922,
0.01605282910168171,
-0.027944205328822136,
-0.008378906175494194,
0.007815415039658546,
0.023678559809923172,
-0.03194071352481842,
0.031865645200014114,
0.036861877888441086,
0.033048272132873535,
-0.040712371468544006,
0.027985768392682076
] |
[
14.186405181884766,
8.195050239562988
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
na
|
na
|
2007-03-31T22:24:53
|
We investigate the Coulomb excitation of low-lying states of unstable nuclei
in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is
shown that the cross sections for the $E1$ and $E2$ transitions are larger at
lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb
distortion are found to be both relevant for energies as low as 10 MeV/nucleon
and as high as 500 MeV/nucleon. Implications for studies at radioactive beam
facilities are discussed.
|
Coulomb excitation of unstable nuclei at intermediate energies
|
nucl-th
|
0704.0060
| 2,007
|
[
-0.0038594596553593874,
0.03727197274565697,
0.007825493812561035,
-0.03654617816209793,
0.06854458898305893,
0.06454313546419144,
-0.017073536291718483,
0.07295103371143341,
-0.02361299842596054,
0.012597454711794853,
-0.05005330219864845,
0.050057463347911835,
-0.02782684564590454,
0.0031427424401044846,
0.028355563059449196,
-0.01716308481991291,
0.07843625545501709,
-0.0075418041087687016,
0.028183646500110626,
0.06327284872531891,
-0.06032828986644745,
0.012478863820433617,
-0.05901371315121651,
-0.04724515974521637,
0.14061732590198517,
0.05476082116365433,
0.01595773734152317,
-0.005461542867124081,
-0.03313868120312691,
0.052596017718315125,
0.03527553379535675,
-0.07613465189933777,
-0.02536618895828724,
-0.0430583618581295,
-0.05701480060815811,
-0.043289147317409515,
0.04806246608495712,
-0.0223371721804142,
0.017332542687654495,
0.02850121073424816,
0.020665520802140236,
-0.03663090616464615,
0.033397212624549866,
-0.03977517411112785,
0.010635912418365479,
0.02741149067878723,
0.00819480698555708,
-0.01144949346780777,
-0.013573821634054184,
-0.023182857781648636,
-0.029689595103263855,
-0.00611246470361948,
-0.0026030647568404675,
-0.0058376300148665905,
0.0038542281836271286,
-0.012735175900161266,
-0.0665886178612709,
-0.04659275710582733,
0.05848544463515282,
0.01835162378847599,
0.058207422494888306,
0.06191560998558998,
-0.022298790514469147,
-0.028104806318879128,
0.03870833292603493,
-0.05397574231028557,
-0.040794745087623596,
0.01796243153512478,
0.0033621862530708313,
-0.014275886118412018,
0.0333075225353241,
-0.05686955526471138,
-0.05518031120300293,
0.03310784325003624,
-0.014714900404214859,
-0.042242441326379776,
0.035053908824920654,
-0.005445660091936588,
0.012376940809190273,
0.02006847783923149,
0.008594988845288754,
-0.036091867834329605,
0.04640008881688118,
-0.004075384698808193,
0.020802857354283333,
0.030720429494976997,
-0.00282071391120553,
0.0666472539305687,
-0.057762496173381805,
0.031915124505758286,
0.016560876742005348,
-0.00794810801744461,
0.01967466063797474,
0.0392867736518383,
-0.06598114967346191,
0.03638468682765961,
0.01388544775545597,
0.09128078818321228,
-0.009770031087100506,
-0.03669257462024689,
0.006669191177934408,
0.015793491154909134,
-0.002259285654872656,
0.033346451818943024,
0.01570364087820053,
0.024686725810170174,
-0.003992997109889984,
-0.03317326307296753,
0.024354202672839165,
-0.015814678743481636,
-0.07992624491453171,
-0.03629117086529732,
-0.007909937761723995,
-0.006706685293465853,
-0.023427758365869522,
0.000020362822397146374,
0.02805132232606411,
-0.05086277425289154,
-0.011084814555943012,
0.05503394454717636,
0.019465774297714233,
0.013781661167740822,
0.00829799473285675,
0.0077285305596888065,
0.008190549910068512,
-0.005132258404046297,
-0.025118127465248108,
-0.007833773270249367,
0.04655638709664345,
0.0038583080749958754,
-0.0027733775787055492,
0.010663008317351341,
-0.036394089460372925,
-0.02785862609744072,
0.07987792789936066,
0.07709689438343048,
-0.00017654303519520909,
-0.02505706250667572,
0.013179055415093899,
-0.048848170787096024,
0.06528972089290619,
0.05391324684023857,
0.007244649808853865,
-0.030063221231102943,
0.02002110332250595,
-0.046073462814092636,
0.024166326969861984,
0.03599840775132179,
-0.061428435146808624,
0.03268800303339958,
0.013129203580319881,
-0.018244413658976555,
0.02343251183629036,
0.046294547617435455,
-0.024187088012695312,
-0.014624831266701221,
-0.01022946834564209,
-0.024231482297182083,
-0.007363887969404459,
0.04943954199552536,
0.0048002456314861774,
0.03149918094277382,
-0.08789312094449997,
0.06757505983114243,
-0.049541838467121124,
0.024938933551311493,
-0.011733924970030785,
0.017061280086636543,
0.0134302182123065,
0.021224264055490494,
-0.03858790174126625,
-0.02515610307455063,
-0.025366362184286118,
-0.03592477738857269,
-0.019621646031737328,
-0.01815207675099373,
0.01660551130771637,
-0.04463863745331764,
0.025411734357476234,
-0.012238912284374237,
0.051402777433395386,
0.017272597178816795,
0.01209709607064724,
0.046689797192811966,
0.0405367873609066,
-0.008598885498940945,
0.008966964669525623,
-0.030959831550717354,
-0.050678789615631104,
-0.011517832055687904,
0.007783092092722654,
0.030688917264342308,
-0.0925525575876236,
-0.10394550114870071,
-0.027761362493038177,
-0.048199333250522614,
0.03800762817263603,
-0.03957636281847954,
0.01494246069341898,
-0.020403053611516953,
-0.017323441803455353,
0.0024053589440882206,
-0.08734245598316193,
0.013683146797120571,
0.0003661754308268428,
0.027435751631855965,
-0.013526031747460365,
-0.007762509863823652,
0.014014718122780323,
-0.02848670817911625,
0.06111719459295273,
0.013837842270731926,
-0.030518120154738426,
0.021516241133213043,
-0.0453888364136219,
0.04653468728065491,
0.024902919307351112,
-0.04896707087755203,
-0.01275404542684555,
0.07838785648345947,
-0.028914324939250946,
-0.0031146975234150887,
-0.012098339386284351,
0.01165307778865099,
0.0672018751502037,
0.022106777876615524,
-0.04346955940127373,
0.01746186427772045,
-0.03643481433391571,
-0.0068139382638037205,
-0.09606819599866867,
0.025183849036693573,
0.00840699952095747,
-0.013024287298321724,
-0.032695550471544266,
-0.0164173673838377,
-0.023644182831048965,
-0.006599383894354105,
0.0429544523358345,
0.033548370003700256,
-0.005209994502365589,
0.012362342327833176,
-0.007287772372364998,
-0.02323015220463276,
-0.08185475319623947,
-0.04529513418674469,
0.002085902029648423,
-0.017233600839972496,
-0.024845952168107033,
-0.029682956635951996,
0.022508742287755013,
-0.006226365454494953,
0.04904082417488098,
0.06209958344697952,
-0.004847866017371416,
-0.04636124148964882,
-0.05652646720409393,
0.07911001145839691,
-0.015947457402944565,
-0.01700417511165142,
0.00910343136638403,
-0.05690458044409752,
0.030165454372763634,
-0.013464465737342834,
-0.04942183569073677,
0.03871484100818634,
0.02506418153643608,
-0.036792878061532974,
-0.00683735404163599,
-0.05950068309903145,
0.006295043975114822,
0.053409475833177567,
0.016902396455407143,
0.04051986709237099,
0.011704273521900177,
-0.016335617750883102,
0.04945988208055496,
-0.05657980963587761,
-0.007424829062074423,
-0.06985315680503845,
-0.08166765421628952,
-0.00015689298743382096,
0.0034797443076968193,
0.0006751562468707561,
0.0007710691425018013,
-0.002055472694337368,
-0.0039762635715305805,
-0.052391473203897476,
0.05791071429848671,
0.029170913621783257,
-0.004642130807042122,
-0.04327128082513809,
0.013481471687555313,
0.025176001712679863,
0.05785563215613365,
0.01632697694003582,
0.04893738776445389,
-0.03305456414818764,
-0.05350084230303764,
0.025347482413053513,
-0.006040827836841345,
-0.023785991594195366,
-0.01683301106095314,
-0.038151104003190994,
-0.020320510491728783,
0.014964969828724861,
0.030018294230103493,
0.012097829021513462,
-0.015089589171111584,
-0.008224557153880596,
-0.05303395912051201,
-0.00889303907752037,
-0.048687394708395004,
0.04396698623895645,
-0.06503061205148697,
0.025377728044986725,
-0.005369283724576235,
0.014197842217981815,
0.08952716737985611,
0.005150691606104374,
0.021493107080459595,
0.003446861868724227,
0.03420572727918625,
-0.08382384479045868,
-0.008871554397046566,
0.04918539151549339,
0.015880858525633812,
-0.003938119392842054,
-0.005480925552546978,
-0.015244885347783566,
0.025612564757466316,
0.018565993756055832,
-0.03499117121100426,
-0.011203103698790073,
0.005105321295559406,
-0.03209357336163521,
-0.019786348566412926,
0.0736355260014534,
-0.018386870622634888,
0.0036074568051844835,
0.04537934809923172,
-0.037274058908224106,
-0.026070408523082733,
-0.07235897332429886,
0.043253809213638306,
0.0132438400760293,
-0.013630668632686138,
-0.019317910075187683,
-0.0021138594020158052,
-0.04121898487210274,
-0.03840303793549538,
-0.008010153658688068,
0.01744847185909748,
-0.039949800819158554,
-0.01598428189754486,
0.0005027438746765256,
0.005666869692504406,
-0.030154071748256683,
0.057012639939785004,
0.04577360674738884,
-0.004473148845136166,
-0.02796015702188015,
0.03037000261247158,
0.0012177317403256893,
0.0038382578641176224,
0.0293483417481184,
-0.03482915088534355,
0.035469744354486465,
0.027706047520041466,
-0.03341515362262726,
-0.058738064020872116,
-0.03212221711874008,
0.02849792130291462,
0.02644357830286026,
-0.018692055717110634,
-0.014810464344918728,
-0.02990684285759926,
0.059538863599300385,
-0.003085822332650423,
0.011988596059381962,
0.061112675815820694,
-0.04059028625488281,
0.006964012049138546,
0.004179087933152914,
0.006794252898544073,
-0.013637518510222435,
-0.018529964610934258,
-0.018620215356349945,
-0.021266603842377663,
-0.011775531806051731,
0.014415805228054523,
-0.0732293576002121,
-0.00831255316734314,
0.04304008185863495,
-0.0012048165081068873,
-0.013721968978643417,
0.04837571457028389,
-0.012671826407313347,
0.047508906573057175,
-0.0031836822163313627,
-0.07440363615751266,
-0.04639434814453125,
-0.01958273909986019,
-0.026502862572669983,
-0.04156289994716644,
0.025720862671732903,
-0.012177378870546818,
-0.04286950081586838,
0.04030488058924675,
-0.013507317751646042,
0.05103004723787308,
0.029269054532051086,
-0.010571779683232307,
-0.04207272455096245,
-0.018048930913209915,
-0.005250796675682068,
0.0009491739911027253,
0.017766786739230156,
0.022661790251731873,
-0.000992167042568326,
0.03400703892111778,
0.06820206344127655,
-0.051824770867824554,
0.023967256769537926,
-0.014585568569600582,
0.010150771588087082,
-0.0059894067235291,
0.037477221339941025,
0.04332880303263664,
-0.029865220189094543,
0.0019436932634562254,
0.013883362524211407,
0.0011185735929757357,
-0.0004934886819683015,
-0.05732663720846176,
0.021031489595770836,
0.030426260083913803,
-0.01393778808414936,
0.014790943823754787,
0.04499301314353943,
0.0659949854016304,
-0.038072701543569565,
-0.017798325046896935,
0.046547986567020416,
0.0687405914068222,
0.07116150110960007,
0.02978598140180111,
-0.035454798489809036,
0.01392565667629242,
-0.04932836443185806,
0.004177733790129423,
-0.017664292827248573,
0.02827039547264576,
-0.007727915421128273,
0.07509521394968033,
-0.05092627927660942,
0.017671460285782814,
0.002267960924655199,
-0.004561442881822586,
0.04095567390322685,
0.01282756682485342,
0.031853996217250824,
-0.014500558376312256,
-0.004942816682159901,
-0.015553976409137249,
0.014633390121161938,
-0.02937494032084942,
0.006634849589318037,
0.012266809120774269,
0.035921819508075714,
-0.03325705602765083,
-0.007942866533994675,
0.05992809310555458,
-0.012040926143527031,
0.014775088056921959,
-0.005731217097491026,
-0.009880647994577885,
-0.0486571341753006,
-0.03182592615485191,
0.038655247539281845,
0.019717300310730934,
-0.04636513069272041,
-0.05116695165634155,
0.011364741250872612,
-0.001975476508960128,
0.0060089267790317535,
0.050643544644117355,
0.021706197410821915,
0.06329818069934845,
-0.00361053878441453,
0.039819225668907166,
0.026353934779763222,
-0.006809627637267113,
0.003922917880117893,
0.007129645440727472,
0.007409493904560804,
0.012355889193713665,
-0.026435699313879013,
-0.0013732212828472257,
0.01950768567621708,
0.00873978715389967,
-0.022500423714518547,
-0.013410191982984543,
0.03753788396716118,
-0.006840899586677551,
-0.0003132915298920125,
-0.029438208788633347,
-0.059105370193719864,
-0.013147936202585697,
-0.010222956538200378,
-0.03389456868171692,
0.06734546273946762,
0.06928586959838867,
0.0768488198518753,
-0.009137481451034546,
-0.03876376897096634,
0.00007998749788384885,
0.008973327465355396,
-0.05766797438263893,
0.002995542250573635,
-0.019993020221590996,
-0.012733913026750088,
0.018163079395890236,
0.011418754234910011,
-0.03907092288136482,
0.01284041814506054,
0.06379003822803497,
-0.038290224969387054,
0.029116053134202957,
0.014171713031828403,
0.015568524599075317,
-0.002674597082659602,
-0.0009826577734202147,
-0.02887292392551899,
0.01846829429268837,
-0.02737691067159176,
-0.0682186558842659,
0.002316646743565798,
-0.04363685101270676,
0.02856689691543579,
0.05529852584004402,
0.008274931460618973,
0.028618844226002693,
0.05793754756450653,
0.05217374116182327,
-0.03323226794600487,
-0.06949018687009811,
0.02636454626917839,
0.0012000029673799872,
-0.0672040730714798,
0.045076195150613785,
-0.022586381062865257,
0.029708854854106903,
-0.06662224978208542,
0.03880966082215309,
-0.046896930783987045,
0.05371425673365593,
-0.0271073617041111,
-0.0182513240724802,
-0.009524047374725342,
-0.028770698234438896,
0.006142540369182825,
0.0499148890376091,
0.04378347471356392,
0.03937286511063576,
-0.1101684644818306,
-0.08545590192079544,
0.01654841937124729,
0.03484519198536873,
-0.021356681361794472,
-0.015202238224446774,
-0.020343653857707977,
-0.044976331293582916,
-0.026906462386250496,
0.022241732105612755,
-0.022339507937431335,
0.049257345497608185,
-0.006241988856345415,
-0.00823794025927782,
0.002416527597233653,
-0.045486629009246826,
-0.018247833475470543,
0.026595525443553925,
0.025834431871771812,
-0.061606161296367645,
0.005658287089318037,
0.0257294662296772,
-0.04744909331202507,
0.07796203345060349,
-0.027353400364518166,
0.0034115000162273645,
-0.031183786690235138,
0.023108039051294327,
0.012471185065805912,
-0.021348396316170692,
-0.00007882968202466145,
-0.06850641220808029,
-0.009990308433771133,
-0.03118777833878994,
0.026890253648161888,
0.03406848758459091,
0.07548709958791733,
0.023564906790852547,
-0.024266427382826805,
0.032090336084365845,
0.08545003086328506,
0.0052709924057126045,
0.051917292177677155,
-0.03377220034599304,
0.05929091200232506,
0.03561021387577057,
-0.006967537570744753,
-0.05828209966421127,
-0.07064272463321686,
-0.006365675944834948,
0.01606188900768757,
0.028520889580249786,
-0.05046651512384415,
-0.026501605287194252,
-0.02857087552547455,
0.014982670545578003,
-0.08047943562269211,
-0.003066312987357378,
-0.026142634451389313,
0.00005433833212009631,
0.02700739912688732,
-0.006456326227635145,
-0.005524259991943836,
0.023589499294757843,
0.03659774363040924,
-0.006762894336134195,
0.004742500372231007,
-0.0063634226098656654,
-0.0020364958327263594,
-0.03528442606329918,
0.04437931627035141,
-0.004632845986634493,
0.025498416274785995,
0.0011917040683329105,
0.052373651415109634,
0.04258270189166069,
-0.027700571343302727,
-0.029961438849568367,
0.0019831524696201086,
0.007218539249151945,
0.0423186719417572,
0.037059009075164795,
0.05948914587497711,
0.015682127326726913,
0.03537825495004654,
0.06912054121494293,
0.018178774043917656,
-0.009636118076741695,
0.004434081260114908,
0.002189303282648325,
0.0036254196893423796,
0.0620550774037838,
-0.005230966955423355,
-0.0007813634001649916,
-0.025020916014909744,
0.02594553865492344,
0.024312229827046394,
0.0305069237947464,
0.006847187876701355,
0.03477128595113754,
-0.04070131853222847,
-0.00684666633605957,
-0.05453331395983696,
-0.03812626004219055,
0.02687727101147175,
-0.030011998489499092,
-0.0505923330783844,
-0.06953009963035583,
-0.033527448773384094,
-0.022844482213258743,
0.0014074796345084906,
-0.0009295371128246188,
0.015939684584736824,
-0.0064266338013112545,
-0.021103056147694588,
-0.0249656792730093,
0.009794052690267563,
0.016668960452079773,
0.009635276161134243,
-0.013499920256435871,
0.020183615386486053,
-0.019699325785040855,
-0.02513221465051174,
-0.04611135274171829,
-0.015535950660705566,
0.027959678322076797,
0.021626794710755348,
0.012034491635859013,
-0.021865589544177055,
-0.009426025673747063,
-0.00022185100533533841,
-0.05758780241012573,
-0.039790138602256775,
0.02666090987622738,
-0.0005116835236549377,
-0.0033176876604557037,
0.029921509325504303,
0.01734955422580242,
0.023028003051877022,
-0.06477891653776169,
-0.005163182504475117,
0.006357474718242884,
0.02725820429623127,
0.008866317570209503,
0.008000656962394714,
-0.0017504272982478142,
0.011557877995073795,
0.0754353255033493,
0.033989351242780685,
0.032663434743881226,
-0.004099175333976746,
0.031952153891325,
-0.07061222195625305,
0.02245951257646084,
0.032434068620204926,
0.006416809745132923,
-0.05413960665464401,
-0.05101226642727852,
0.05226878821849823,
0.041702061891555786,
-0.10058367252349854,
0.04312388598918915,
-0.005914662498980761,
0.07399231940507889,
0.018576519563794136,
-0.018217183649539948,
0.03735345974564552,
-0.011620190925896168,
-0.012987714260816574,
-0.053256887942552567,
-0.04545445740222931,
-0.004535560496151447,
-0.0555642731487751,
-0.09402639418840408,
0.0014786716783419251,
0.030848052352666855,
-0.03905569389462471,
0.01033859234303236,
0.010309254750609398,
-0.024367021396756172,
-0.018144933506846428,
-0.036942966282367706,
-0.00863692071288824,
0.06267416477203369,
0.006476125214248896,
0.007211314048618078,
-0.037574343383312225,
0.001923506846651435,
0.06394181400537491,
0.03116467036306858,
0.02855563908815384,
-0.03601754829287529,
0.048383548855781555,
0.027629772201180458,
-0.019391419366002083,
0.02913775108754635,
0.02910410612821579,
0.010617580264806747,
-0.016451798379421234,
0.010967926122248173,
0.00762662710621953,
-0.03116583451628685,
-0.00648995628580451
] |
[
14.931057929992676,
-0.7781991958618164
] |
Nuclear Theory
|
General Physics
|
nucl-th
|
na
|
na
|
2007-03-31T22:45:05
|
Intersection bodies represent a remarkable class of geometric objects
associated with sections of star bodies and invoking
Radon transforms, generalized cosine transforms, and the relevant Fourier
analysis. The main focus of this article is interrelation between generalized
cosine transforms of different kinds in the context of their application to
investigation of a certain family of intersection bodies, which we call
$\lam$-intersection bodies. The latter include $k$-intersection bodies (in the
sense of A. Koldobsky) and unit balls of finite-dimensional subspaces of
$L_p$-spaces. In particular, we show that restrictions onto lower dimensional
subspaces of the spherical Radon transforms and the generalized cosine
transforms preserve their integral-geometric structure. We apply this result to
the study of sections of $\lam$-intersection bodies. New characterizations of
this class of bodies are obtained and examples are given. We also review some
known facts and give them new proofs.
|
Intersection Bodies and Generalized Cosine Transforms
|
math.FA
|
0704.0061
| 2,007
|
[
-0.008401580154895782,
0.007544234860688448,
-0.014059052802622318,
-0.07073020935058594,
0.02718506008386612,
0.013001427054405212,
0.009621737524867058,
-0.009713906794786453,
-0.01831582747399807,
0.0037246132269501686,
-0.03732956573367119,
0.02581404522061348,
0.023277176544070244,
-0.029765721410512924,
-0.010531113483011723,
-0.05582950636744499,
-0.014324749819934368,
-0.0021288481075316668,
-0.037493638694286346,
0.07401608675718307,
-0.015750493854284286,
0.013281391933560371,
-0.007904612459242344,
-0.050335247069597244,
0.1061522513628006,
-0.019857600331306458,
0.002240937203168869,
0.021146446466445923,
-0.058990929275751114,
0.02937226928770542,
0.0729389414191246,
-0.056531086564064026,
0.04108147323131561,
-0.08069876581430435,
-0.06361229717731476,
-0.023747572675347328,
0.07421154528856277,
-0.025029238313436508,
0.051524966955184937,
0.021367555484175682,
0.06869272887706757,
-0.007641151547431946,
0.0462135449051857,
-0.010570980608463287,
0.014527692459523678,
0.0013010326074436307,
0.02949363738298416,
0.037230852991342545,
0.005936106666922569,
0.04649617150425911,
-0.0401410274207592,
0.03302675485610962,
0.009924519807100296,
-0.05368802696466446,
-0.05027006193995476,
-0.009969701059162617,
-0.0034877052530646324,
-0.058933794498443604,
0.06204335018992424,
-0.012520425021648407,
-0.015526454895734787,
0.011344550177454948,
-0.02479705959558487,
-0.007872512564063072,
0.03786301985383034,
-0.07040546834468842,
-0.002741534262895584,
0.02289658971130848,
0.020549733191728592,
-0.03748393803834915,
0.04794309660792351,
0.01365902554243803,
0.08546759188175201,
0.021116387099027634,
-0.052103083580732346,
-0.02684086747467518,
0.024272603914141655,
0.04687878116965294,
-0.045859627425670624,
0.019389772787690163,
0.0003898734867107123,
-0.05031943693757057,
0.04875960573554039,
0.023859579116106033,
0.02516987919807434,
0.0432591512799263,
0.05534224584698677,
0.021348731592297554,
-0.028850436210632324,
0.03265061974525452,
0.07234872877597809,
-0.0024027125909924507,
-0.0046853902749717236,
0.03382954001426697,
-0.060051288455724716,
0.0591609925031662,
0.01048694085329771,
-0.008320489898324013,
-0.009029127657413483,
0.006383000873029232,
-0.027470335364341736,
0.042820002883672714,
-0.006435798481106758,
0.042163748294115067,
0.033494338393211365,
0.014211035333573818,
0.039053164422512054,
0.009105376899242401,
0.02067524939775467,
-0.031907178461551666,
-0.0846373587846756,
-0.03082563355565071,
0.019744984805583954,
-0.03192313387989998,
0.009818676859140396,
-0.04257911443710327,
0.06449958682060242,
-0.07414299994707108,
0.0069595519453287125,
0.0875696912407875,
0.041928816586732864,
-0.02334144525229931,
-0.03529215604066849,
0.04905006289482117,
-0.002427811501547694,
0.01526402123272419,
-0.008052367717027664,
-0.03416043147444725,
0.055341556668281555,
0.0025932458229362965,
0.00941998790949583,
0.0260476004332304,
-0.032972101122140884,
0.02801455557346344,
0.05064084753394127,
0.06042497232556343,
-0.011826480738818645,
-0.05441802740097046,
0.025973135605454445,
-0.039941590279340744,
-0.00035779931931756437,
0.020482834428548813,
0.02127525396645069,
-0.037785112857818604,
0.0019468109821900725,
-0.012388776056468487,
-0.007303483318537474,
-0.0880742147564888,
-0.051147252321243286,
0.014550217427313328,
0.017249271273612976,
0.0662425309419632,
0.05751314386725426,
0.011150403879582882,
-0.05076674744486809,
-0.050007108598947525,
-0.007512120064347982,
0.04234280437231064,
0.08204533159732819,
0.02912347950041294,
-0.012586844153702259,
0.04507269337773323,
-0.06290794909000397,
0.009284273721277714,
-0.08840984851121902,
-0.0009326605941168964,
-0.039470117539167404,
0.012704583816230297,
0.022051595151424408,
-0.004030408337712288,
-0.052855703979730606,
0.0008542644791305065,
0.008989964611828327,
-0.022926438599824905,
-0.014875832945108414,
-0.020078595727682114,
-0.012779978103935719,
-0.07070093601942062,
0.04376037046313286,
0.007883484475314617,
-0.03616314381361008,
-0.025328394025564194,
0.02772057242691517,
0.02774663083255291,
0.048652853816747665,
0.014310838654637337,
-0.03730291873216629,
0.008748284541070461,
-0.004957421217113733,
-0.021873828023672104,
-0.004545862320810556,
0.028976524248719215,
-0.06546904146671295,
-0.0622367188334465,
0.031485047191381454,
-0.0017498355591669679,
0.03893981873989105,
-0.02803325653076172,
-0.05916786193847656,
-0.04754088446497917,
-0.022923538461327553,
0.028388364240527153,
-0.013891864567995071,
0.03492238372564316,
0.001281206146813929,
0.051219064742326736,
0.010037319734692574,
-0.0037804425228387117,
0.026402216404676437,
0.03002576157450676,
0.07313461601734161,
0.013395071029663086,
0.005372425075620413,
-0.030032530426979065,
-0.05017026141285896,
-0.02749994397163391,
0.017599737271666527,
-0.026742413640022278,
-0.0043687582947313786,
-0.0036998954601585865,
0.031810108572244644,
0.0006267391727305949,
0.0035563029814511538,
-0.018445465713739395,
0.063820019364357,
0.019727783277630806,
-0.019925683736801147,
0.026413097977638245,
-0.009462135843932629,
-0.000987821607850492,
-0.06701662391424179,
-0.021083340048789978,
0.048150740563869476,
-0.010213416069746017,
-0.016261285170912743,
-0.001240782206878066,
-0.055587805807590485,
0.04700032249093056,
0.02149963192641735,
0.07677055895328522,
0.046353038400411606,
0.017993034794926643,
-0.013497455045580864,
-0.06532832980155945,
-0.018685223534703255,
0.022640934213995934,
0.008882437832653522,
0.005087521858513355,
-0.07228706032037735,
0.009750879369676113,
-0.053270068019628525,
0.03530214726924896,
0.015294204466044903,
0.010318665765225887,
0.005004342645406723,
-0.042820144444704056,
-0.009614305570721626,
0.026421545073390007,
-0.013977590948343277,
-0.060911767184734344,
0.01400894857943058,
-0.055796995759010315,
-0.020564524456858635,
-0.0019021449843421578,
-0.06432043761014938,
-0.020549828186631203,
-0.017321724444627762,
0.013311699032783508,
-0.01330704428255558,
-0.03167976811528206,
-0.004823184106498957,
0.03189191594719887,
0.06797737628221512,
0.03836614638566971,
-0.033065807074308395,
-0.006020287983119488,
0.0002006208524107933,
-0.06550461798906326,
-0.03506750985980034,
-0.01929946057498455,
-0.006320666521787643,
0.0013394482666626573,
-0.02795720286667347,
-0.054582443088293076,
-0.011404728516936302,
0.023681672289967537,
-0.0016072578728199005,
0.033053670078516006,
0.03188982978463173,
0.045487985014915466,
-0.023169176653027534,
-0.006906063761562109,
0.004778848960995674,
-0.04465264081954956,
0.005887483712285757,
0.05919840559363365,
0.09044122695922852,
0.0029705355409532785,
-0.023972302675247192,
0.00094386882847175,
0.001509706024080515,
0.019268248230218887,
0.0008284929790534079,
-0.02889179065823555,
0.05419798195362091,
-0.007043907884508371,
0.0013176888460293412,
-0.04555793106555939,
-0.0023000703658908606,
-0.026232251897454262,
0.04488363116979599,
0.016112199053168297,
-0.02128789573907852,
0.001048242556862533,
-0.05278301239013672,
0.046523623168468475,
0.021809866651892662,
0.006086541339755058,
0.024834563955664635,
0.04670662432909012,
0.014657573774456978,
-0.020439038053154945,
0.03836114704608917,
-0.1045139729976654,
-0.03690848872065544,
0.01794295385479927,
0.0030227922834455967,
-0.05505310744047165,
0.002125880913808942,
-0.025997361168265343,
-0.02102390117943287,
0.08188797533512115,
0.007964026182889938,
0.01249951682984829,
-0.01582195796072483,
0.01840239204466343,
-0.0398448146879673,
0.02067270688712597,
0.004249311983585358,
-0.026397639885544777,
0.032359231263399124,
-0.04877321422100067,
-0.02738240733742714,
-0.08188612759113312,
0.01079644076526165,
0.07215454429388046,
-0.0027902633883059025,
-0.029539398849010468,
0.02073253132402897,
-0.05672401189804077,
-0.07263771444559097,
-0.0008741237106733024,
0.05469990149140358,
-0.05696900188922882,
-0.0006760178948752582,
0.07414303719997406,
0.07570239156484604,
0.024758387356996536,
0.023662323132157326,
-0.011703433468937874,
0.014273698441684246,
-0.007707527838647366,
0.02068098820745945,
0.03588661178946495,
0.0385286808013916,
0.015478049404919147,
0.03024320863187313,
0.03342641144990921,
0.010176749899983406,
0.012357842177152634,
-0.049437835812568665,
0.005261602811515331,
0.041252318769693375,
0.013048820197582245,
0.0369582436978817,
0.016833167523145676,
-0.06106121838092804,
0.02372005581855774,
-0.006497885566204786,
-0.05850304290652275,
0.07397960871458054,
-0.008563978597521782,
0.03357705473899841,
0.012274053879082203,
0.03175080195069313,
0.031980860978364944,
-0.015793902799487114,
-0.0005354681634344161,
-0.01779642514884472,
-0.022188544273376465,
0.0297154001891613,
-0.006606752518564463,
0.002043947810307145,
-0.01208093948662281,
0.0002969497290905565,
-0.03024241328239441,
0.0002555558457970619,
-0.00683100800961256,
-0.008362969383597374,
-0.015566322021186352,
-0.04895151033997536,
-0.06757542490959167,
-0.017595887184143066,
-0.05214753374457359,
0.006293572951108217,
-0.0068012564443051815,
-0.009565377607941628,
-0.02821594849228859,
0.023501230403780937,
-0.019128672778606415,
0.015228671953082085,
0.0025209339801222086,
0.03562641888856888,
-0.07812807708978653,
0.022685129195451736,
0.043498631566762924,
-0.03261948376893997,
0.021392837166786194,
0.017526617273688316,
0.0081497672945261,
-0.04075484350323677,
0.04057503491640091,
0.005843578837811947,
0.0024263113737106323,
-0.004119574557989836,
0.012349129654467106,
-0.004040189553052187,
0.023302948102355003,
-0.007614615838974714,
-0.04774102568626404,
0.010926373302936554,
0.0291645098477602,
0.014325134456157684,
0.025178469717502594,
-0.08396744728088379,
0.006423127371817827,
-0.07512807846069336,
-0.0016780674923211336,
0.01919306442141533,
0.025807276368141174,
0.065140500664711,
-0.031242165714502335,
0.00942379329353571,
-0.0178814847022295,
0.04633176699280739,
0.03508482128381729,
0.06952765583992004,
-0.01067319791764021,
-0.00953472126275301,
0.0000712719265720807,
-0.0038118106313049793,
-0.03166284039616585,
-0.015628013759851456,
0.03309040144085884,
0.06601845473051071,
-0.0642542913556099,
0.006640133447945118,
-0.05800742655992508,
0.02528686262667179,
0.03297858685255051,
0.045047055929899216,
0.02118837647140026,
-0.0253631342202425,
0.013910185545682907,
0.033662229776382446,
0.002156598959118128,
-0.05435086041688919,
0.010394005104899406,
-0.006564841605722904,
0.05127314105629921,
-0.03433018922805786,
0.0321178175508976,
0.001987364375963807,
-0.0013903804356232285,
-0.043531522154808044,
0.011831233277916908,
-0.004951329901814461,
-0.006035493221133947,
-0.029053552076220512,
0.060831911861896515,
0.025918763130903244,
-0.04377825930714607,
-0.01701919548213482,
-0.020761307328939438,
-0.025180675089359283,
0.07508629560470581,
0.018984682857990265,
-0.009916597977280617,
0.004892877768725157,
-0.009099012240767479,
-0.02265053428709507,
-0.024094706401228905,
0.03210187703371048,
0.029808284714818,
-0.002439158735796809,
0.03395944833755493,
0.034212853759527206,
0.007074370980262756,
-0.014672129414975643,
0.006703680381178856,
-0.055067285895347595,
-0.02604757621884346,
0.06598421931266785,
0.022690799087285995,
0.001564603066071868,
0.054519910365343094,
0.03444492816925049,
-0.04948851093649864,
-0.005223166663199663,
0.010951810516417027,
-0.004191004205495119,
-0.013827359303832054,
0.06718554347753525,
0.10101409256458282,
-0.029345471411943436,
-0.021675022318959236,
0.006908893585205078,
0.032704439014196396,
-0.03788246586918831,
-0.007784563582390547,
-0.0015566902002319694,
0.013970434665679932,
-0.02286379039287567,
0.0047049918211996555,
-0.0362396277487278,
0.05983411520719528,
0.011052394285798073,
-0.0802336111664772,
0.029716171324253082,
0.046386558562517166,
0.045031387358903885,
-0.01911037787795067,
-0.06866798549890518,
-0.04244969040155411,
-0.013604345731437206,
-0.06280547380447388,
-0.046610888093709946,
0.046360574662685394,
0.03662410005927086,
-0.002917313715443015,
-0.0247513297945261,
-0.018566017970442772,
0.008165168575942516,
-0.000561645021662116,
0.03361215069890022,
-0.03772778809070587,
0.01222891453653574,
0.0225459523499012,
-0.01992228627204895,
-0.03953006491065025,
0.03447332605719566,
-0.028358811512589455,
-0.00544722331687808,
-0.11572118103504181,
-0.0017436702037230134,
-0.03454054892063141,
0.02138686180114746,
-0.007726775482296944,
0.024021748453378677,
-0.011269651353359222,
-0.004058409482240677,
-0.022946175187826157,
0.01723545417189598,
0.008968863636255264,
0.022067958489060402,
-0.10936540365219116,
-0.034449148923158646,
-0.0049483757466077805,
0.05249132588505745,
-0.012789364904165268,
-0.01890197955071926,
-0.037982482463121414,
0.00566728925332427,
0.02155289426445961,
-0.0014175642281770706,
-0.04425821080803871,
0.03520384058356285,
-0.028452549129724503,
-0.04132300987839699,
0.036055855453014374,
0.007843074388802052,
-0.009019333869218826,
0.005340381991118193,
-0.03758158162236214,
-0.06861323118209839,
0.045308057218790054,
-0.02423616126179695,
-0.022296585142612457,
0.04289006441831589,
-0.05588836967945099,
-0.029214613139629364,
-0.033522579818964005,
-0.04356188327074051,
0.00018171928240917623,
-0.004279111512005329,
-0.024269282817840576,
-0.00217854673974216,
0.0367623046040535,
-0.05177649110555649,
-0.08204017579555511,
0.025500910356640816,
-0.01293888594955206,
0.06789782643318176,
-0.03941808268427849,
0.012502550147473812,
0.023531412705779076,
-0.052310775965452194,
0.003763261716812849,
-0.009769700467586517,
0.008120307698845863,
0.033099327236413956,
0.008958149701356888,
-0.02160685695707798,
0.040226951241493225,
-0.006217352580279112,
-0.03419847413897514,
0.03479577228426933,
-0.08012888580560684,
-0.0027409978210926056,
-0.03982384502887726,
0.04954291135072708,
-0.025785623118281364,
-0.04034873843193054,
-0.053610771894454956,
-0.007890674285590649,
0.049315765500068665,
-0.02789228968322277,
-0.020646968856453896,
0.0298304483294487,
0.04452819004654884,
-0.02119942009449005,
-0.01778937131166458,
-0.04882252588868141,
-0.03697023168206215,
0.0177107322961092,
0.045702725648880005,
-0.07355238497257233,
0.031104160472750664,
0.01924736239016056,
0.07562444359064102,
0.040615394711494446,
-0.021127445623278618,
0.026212068274617195,
-0.010813985951244831,
0.06372079998254776,
0.022673582658171654,
-0.004014991689473391,
0.007360047195106745,
-0.0058784787543118,
0.021943088620901108,
0.06634586304426193,
0.028135737404227257,
-0.009426099248230457,
0.012120967730879784,
-0.035854026675224304,
-0.007122659124433994,
0.033650510013103485,
-0.0023879841901361942,
-0.03730928525328636,
-0.0003169107949361205,
-0.02407359890639782,
0.04352984577417374,
-0.007631826214492321,
0.006218143738806248,
-0.010544572956860065,
-0.02251213602721691,
-0.011697947978973389,
-0.07378467172384262,
-0.0039050024934113026,
0.014838493429124355,
-0.05319945514202118,
-0.02042897418141365,
-0.06197690963745117,
-0.025801455602049828,
0.004104573745280504,
0.03043820522725582,
-0.0026465740520507097,
0.025911610573530197,
-0.021512934938073158,
-0.013753766193985939,
0.0273501668125391,
0.07823356986045837,
-0.006381502375006676,
0.005411433521658182,
-0.022849366068840027,
0.004781428258866072,
-0.03420208394527435,
-0.04470902681350708,
-0.017925603315234184,
-0.019610410556197166,
0.005075492430478334,
0.04273437336087227,
0.018918326124548912,
0.005480768159031868,
-0.027950327843427658,
-0.05676852539181709,
-0.020571142435073853,
0.049574028700590134,
-0.024028170853853226,
0.02018401212990284,
0.014712505973875523,
0.03894354775547981,
-0.019971415400505066,
0.01817307434976101,
-0.015427179634571075,
-0.028190605342388153,
0.008253948763012886,
0.014088809490203857,
0.010243916884064674,
0.03731153905391693,
-0.010790970176458359,
0.05187353864312172,
0.07357336580753326,
0.009432310238480568,
0.011491186916828156,
0.08123945444822311,
0.019461171701550484,
-0.02769818715751171,
-0.000525682931765914,
0.001490286784246564,
0.03612898662686348,
-0.04362574592232704,
-0.020959969609975815,
-0.0034254391212016344,
0.005182825960218906,
-0.06934337317943573,
0.003183026099577546,
-0.003817496122792363,
0.057918425649404526,
0.017252009361982346,
0.023801233619451523,
0.026378341019153595,
-0.040149934589862823,
0.021748211234807968,
-0.042868033051490784,
0.02391737699508667,
-0.028747500851750374,
-0.04218324273824692,
-0.014388936571776867,
-0.011476379819214344,
0.03161579743027687,
-0.05746562033891678,
0.06341717392206192,
0.013314329087734222,
-0.05244359001517296,
0.007390755228698254,
-0.05106320232152939,
0.04130386933684349,
0.019614538177847862,
0.048068881034851074,
-0.005305346101522446,
0.007248815149068832,
0.014067385345697403,
0.013349952176213264,
-0.01515012327581644,
-0.0017061131075024605,
-0.011020214296877384,
0.09253695607185364,
0.059827983379364014,
0.023320110514760017,
0.05126826465129852,
-0.0020952767226845026,
0.01788528636097908,
0.03188537061214447,
-0.029104407876729965,
-0.00525988545268774,
-0.021162686869502068,
0.0007581370300613344
] |
[
2.0069077014923096,
4.007000923156738
] |
Functional Analysis
|
Mathematics
|
math-FA
|
na
|
na
|
2007-03-31T23:52:33
|
In this paper, we introduce the on-line Viterbi algorithm for decoding hidden
Markov models (HMMs) in much smaller than linear space. Our analysis on
two-state HMMs suggests that the expected maximum memory used to decode
sequence of length $n$ with $m$-state HMM can be as low as $\Theta(m\log n)$,
without a significant slow-down compared to the classical Viterbi algorithm.
Classical Viterbi algorithm requires $O(mn)$ space, which is impractical for
analysis of long DNA sequences (such as complete human genome chromosomes) and
for continuous data streams. We also experimentally demonstrate the performance
of the on-line Viterbi algorithm on a simple HMM for gene finding on both
simulated and real DNA sequences.
|
On-line Viterbi Algorithm and Its Relationship to Random Walks
|
cs.DS
|
0704.0062
| 2,007
|
[
0.026571527123451233,
0.0040105790831148624,
-0.01050800085067749,
0.010377710685133934,
-0.04688633605837822,
-0.01964082010090351,
0.01706888899207115,
0.027185749262571335,
-0.05398869886994362,
-0.002598785562440753,
-0.05931355804204941,
0.02603764273226261,
0.008389584720134735,
0.0032271784730255604,
-0.03677818924188614,
-0.004838596098124981,
0.024419108405709267,
0.023163408041000366,
-0.024768169969320297,
-0.011936075054109097,
0.02648661658167839,
0.006930307485163212,
-0.03129894658923149,
0.04235447198152542,
0.09186810255050659,
0.008256617933511734,
0.023715952411293983,
0.010159069672226906,
-0.014796281233429909,
0.05682801082730293,
0.03858812153339386,
-0.04483066126704216,
-0.022107237949967384,
-0.05091049522161484,
-0.025635333731770515,
0.002872752258554101,
0.013831999152898788,
-0.07280569523572922,
-0.009874777868390083,
0.05983741953969002,
0.04185159131884575,
-0.01578519307076931,
0.020712455734610558,
-0.009138131514191628,
0.02465088665485382,
-0.010068151168525219,
0.031085006892681122,
0.03545943647623062,
0.02530856430530548,
-0.04936840012669563,
0.003930168226361275,
0.008836574852466583,
0.03232763335108757,
-0.03082062490284443,
0.001665104296989739,
0.025584915652871132,
-0.00931409653276205,
0.001062127761542797,
0.07350112497806549,
0.00521650817245245,
0.041858427226543427,
0.0010316213592886925,
-0.06906826049089432,
-0.000027451978894532658,
0.028290051966905594,
-0.010300553403794765,
-0.014746659435331821,
-0.017524991184473038,
0.005173549987375736,
0.010786937549710274,
0.0466124527156353,
-0.020154913887381554,
-0.019085586071014404,
-0.004408644512295723,
-0.019880883395671844,
0.002528140554204583,
0.006257906090468168,
-0.008513448759913445,
0.03882512450218201,
0.0507248230278492,
-0.023104555904865265,
-0.03339669480919838,
0.0024257097393274307,
0.03583688661456108,
0.07807452976703644,
-0.015417742542922497,
-0.001118508051149547,
0.05064766854047775,
-0.02919773943722248,
0.05942395329475403,
-0.02262752130627632,
0.02271655760705471,
0.08151669800281525,
0.0732278898358345,
-0.056518252938985825,
0.0751538798213005,
-0.052362170070409775,
0.028821134939789772,
-0.018636567518115044,
-0.04885223135352135,
0.01546830590814352,
0.06466451287269592,
0.019304530695080757,
0.008178053423762321,
0.04454246535897255,
0.020881332457065582,
0.017107389867305756,
0.027041053399443626,
-0.024414565414190292,
-0.026983650401234627,
-0.0072916909120976925,
-0.009467455558478832,
-0.03440001606941223,
-0.01486530527472496,
-0.020208731293678284,
0.019274912774562836,
0.04688682407140732,
-0.031200340017676353,
0.0015570741379633546,
0.023337597027420998,
-0.023841923102736473,
-0.011215483769774437,
-0.028717990964651108,
0.015410314314067364,
0.007796161342412233,
0.005504916422069073,
-0.06720513850450516,
0.0435955636203289,
0.028453819453716278,
-0.018866194412112236,
0.002204949501901865,
0.055153533816337585,
-0.008738003671169281,
0.03398723527789116,
-0.011929675936698914,
0.02135227620601654,
-0.04977715387940407,
-0.015582765452563763,
0.043214283883571625,
0.01933426223695278,
-0.028179189190268517,
0.026158075779676437,
0.018258918076753616,
-0.022403201088309288,
0.023913957178592682,
-0.05204358696937561,
-0.036954134702682495,
-0.06076134368777275,
-0.003457939252257347,
0.0013026768574491143,
0.015343240462243557,
0.04319716989994049,
0.00919889472424984,
0.04342959076166153,
-0.012021735310554504,
-0.014809058979153633,
0.004672291222959757,
0.0547185093164444,
0.010835816152393818,
0.030985698103904724,
-0.02038966305553913,
0.05320845916867256,
-0.04567999392747879,
0.031000301241874695,
-0.06879419088363647,
-0.0022732021752744913,
0.039504487067461014,
-0.002804342657327652,
-0.003303710138425231,
0.03881165757775307,
-0.0162411667406559,
-0.031765297055244446,
0.0006985205691307783,
-0.013921615667641163,
-0.040992219001054764,
0.011847506277263165,
-0.02845694124698639,
-0.019294248893857002,
0.043739527463912964,
0.028001276776194572,
0.06370808929204941,
-0.04117000102996826,
-0.010714270174503326,
0.03221986070275307,
-0.011592934839427471,
0.029354972764849663,
-0.008395162411034107,
-0.03395751118659973,
-0.007494307588785887,
-0.06821360439062119,
0.005299538839608431,
0.024128127843141556,
-0.04051845148205757,
-0.07551918923854828,
0.041665539145469666,
-0.00013040077465120703,
0.03217745199799538,
-0.06666327267885208,
-0.0006560416077263653,
-0.03436443582177162,
-0.0012424129527062178,
-0.015317263081669807,
-0.03710651025176048,
0.008203147910535336,
-0.02692900225520134,
0.028082024306058884,
0.037353456020355225,
-0.013983567245304585,
0.01678556576371193,
-0.0019465781515464187,
0.07967710494995117,
0.016829682514071465,
-0.036563076078891754,
0.005525386892259121,
0.00981805007904768,
-0.0013466383097693324,
-0.0015998582821339369,
-0.01932181417942047,
-0.006175583694130182,
0.0024661817587912083,
0.09020847827196121,
-0.06395933777093887,
0.01707577146589756,
0.0020337330643087626,
0.027983402833342552,
0.01676744967699051,
-0.009423872455954552,
-0.005034144502133131,
-0.0700145810842514,
0.021938111633062363,
-0.010257184505462646,
-0.024473773315548897,
0.057390712201595306,
-0.015099309384822845,
-0.023151449859142303,
0.020495090633630753,
-0.013271641917526722,
0.0474124401807785,
0.026586055755615234,
0.056765198707580566,
0.046642422676086426,
0.013704841025173664,
0.018657678738236427,
-0.020968375727534294,
-0.045817725360393524,
-0.07232838124036789,
0.010110821574926376,
-0.01769755408167839,
-0.044269487261772156,
0.0025906157679855824,
-0.049425069242715836,
0.013125092722475529,
0.07401657849550247,
0.02218000963330269,
0.024057215079665184,
-0.015367857180535793,
-0.016443826258182526,
0.012999658472836018,
-0.023734424263238907,
-0.031215015798807144,
0.05884135514497757,
-0.01544762123376131,
0.012878467328846455,
0.008051515556871891,
0.0012587382225319743,
0.00862982589751482,
0.021089667454361916,
-0.03968838229775429,
-0.014256862923502922,
-0.0028972153086215258,
-0.0020101710688322783,
0.05410296097397804,
0.060360439121723175,
0.03739917650818825,
-0.007742395158857107,
0.014589902013540268,
0.018215186893939972,
0.006318473722785711,
0.02368416264653206,
-0.033914659172296524,
-0.05823789909482002,
-0.049367647618055344,
-0.07409824430942535,
-0.029831454157829285,
-0.036859046667814255,
0.012882769107818604,
-0.04626215994358063,
0.006309136748313904,
0.025484172627329826,
0.010492012836039066,
-0.06064094603061676,
0.020852694287896156,
0.027549779042601585,
0.05364320054650307,
0.04457902908325195,
0.07129890471696854,
0.03311832249164581,
-0.02815396711230278,
0.0013851579278707504,
0.01578451693058014,
0.003537766868248582,
0.02539960853755474,
0.060071058571338654,
-0.03914330527186394,
0.010961024090647697,
-0.046163491904735565,
0.001404592301696539,
-0.02883477322757244,
-0.011979048140347004,
-0.02828652411699295,
0.0004396555304992944,
0.01309867762029171,
-0.029345378279685974,
0.030524764209985733,
-0.015802452340722084,
-0.014660516753792763,
0.01118930522352457,
0.017698640003800392,
0.05104537680745125,
0.0443747416138649,
0.053619109094142914,
-0.06313041597604752,
-0.020023806020617485,
-0.10594400763511658,
0.03180287033319473,
-0.0036672570277005434,
0.013625884428620338,
0.037000872194767,
-0.04509197548031807,
0.007638107053935528,
0.04175454005599022,
0.07024439424276352,
0.01068359985947609,
-0.0015991699183359742,
-0.02248595654964447,
-0.04216146096587181,
-0.06491324305534363,
0.014384971931576729,
-0.04350331053137779,
-0.051326997578144073,
-0.0314171202480793,
0.024880586192011833,
-0.03355581685900688,
-0.012881126254796982,
0.01937389373779297,
-0.012357451021671295,
0.010822747834026814,
-0.018744172528386116,
0.032727088779211044,
-0.023941770195961,
-0.0674247220158577,
-0.03059624508023262,
-0.01068450603634119,
-0.02125072292983532,
-0.0018446174217388034,
0.012805749662220478,
-0.029400387778878212,
-0.04031892865896225,
0.08507703244686127,
0.01097853109240532,
0.02690831758081913,
-0.018420128151774406,
0.03619055449962616,
-0.0020324804354459047,
0.07099691778421402,
-0.0026969381142407656,
0.009787135757505894,
0.06305015087127686,
0.035992976278066635,
-0.03826238587498665,
-0.03915680572390556,
-0.028714630752801895,
0.07080990821123123,
0.025397157296538353,
0.024235298857092857,
-0.028749700635671616,
-0.052851855754852295,
-0.04889094457030296,
0.019931545481085777,
0.018026474863290787,
0.05857131630182266,
-0.04091548174619675,
0.030194343999028206,
-0.051354579627513885,
0.02218438684940338,
-0.0016707644099369645,
-0.040900398045778275,
0.006186491809785366,
-0.012494643218815327,
-0.018869906663894653,
-0.03681160882115364,
-0.061607811599969864,
-0.03494597226381302,
-0.02327227219939232,
0.014266551472246647,
-0.008892720565199852,
0.03659331426024437,
0.029644565656781197,
-0.009955432265996933,
-0.0015570013783872128,
-0.03362451121211052,
-0.07335913181304932,
-0.010630394332110882,
0.05744415521621704,
-0.043651942163705826,
0.026149524375796318,
-0.042523156851530075,
-0.01903769187629223,
0.07597780227661133,
0.004157510120421648,
0.0004103172104805708,
0.025414608418941498,
-0.01925460435450077,
-0.07979398220777512,
0.00248263543471694,
0.0285224337130785,
0.0506499744951725,
-0.044810812920331955,
-0.019347744062542915,
0.01244670245796442,
-0.04461713135242462,
0.05460740253329277,
-0.04274141788482666,
0.0034115826711058617,
-0.06300553679466248,
0.00909082219004631,
0.018985779955983162,
0.03923705220222473,
0.006800792645663023,
-0.027514494955539703,
0.055996570736169815,
0.02171042561531067,
-0.005005558952689171,
0.08879054337739944,
-0.012966075912117958,
-0.015515591017901897,
0.05659589171409607,
0.021295849233865738,
0.0128928292542696,
-0.0034491948317736387,
-0.00006980543548706919,
-0.053097184747457504,
0.014518000185489655,
0.01768098771572113,
0.01676803268492222,
0.08391401916742325,
0.08206640928983688,
-0.0072714281268417835,
-0.026025086641311646,
-0.002817317843437195,
0.03344422206282616,
0.0019457141170278192,
0.017047468572854996,
0.0015536041464656591,
0.10797740519046783,
-0.021603237837553024,
-0.031146755442023277,
-0.0057101016864180565,
0.06974360346794128,
0.05295059457421303,
0.0413195826113224,
0.05167779326438904,
0.006042589899152517,
0.033761993050575256,
0.01876455545425415,
-0.0208313949406147,
-0.04778033122420311,
-0.03766279295086861,
0.023244090378284454,
0.0754108801484108,
-0.03443881496787071,
-0.00679674930870533,
0.04827146977186203,
0.005420781206339598,
-0.05899716168642044,
0.015337621793150902,
0.012622716836631298,
-0.033219363540410995,
-0.0033973653335124254,
0.056615132838487625,
0.01334010623395443,
0.00467321090400219,
-0.028607115149497986,
0.010620363987982273,
-0.014799337834119797,
0.01214594766497612,
-0.01058794092386961,
-0.003379958448931575,
0.006141464691609144,
0.0210905522108078,
0.017503533512353897,
0.056854307651519775,
0.01062594074755907,
0.017763501033186913,
-0.06523962318897247,
-0.11280671507120132,
0.0005850452580489218,
0.007623030338436365,
-0.04687876999378204,
-0.020389540120959282,
-0.009237795136868954,
-0.033337391912937164,
0.02087346464395523,
-0.009774822741746902,
-0.008364614099264145,
0.030920077115297318,
-0.007443724665790796,
-0.028580229729413986,
-0.03203587979078293,
0.027994994074106216,
-0.03347620740532875,
0.08862398564815521,
0.004545606207102537,
0.01930946856737137,
0.014069129712879658,
-0.029075201600790024,
0.06277315318584442,
0.018482008948922157,
-0.0497199222445488,
0.02376680262386799,
0.0023708415683358908,
0.010232704691588879,
0.02169446460902691,
-0.008222556672990322,
-0.029737038537859917,
0.03550343960523605,
-0.044274844229221344,
-0.0739479511976242,
-0.03605099394917488,
0.00842327531427145,
0.02639586478471756,
0.0022735893726348877,
-0.0043829577043652534,
-0.04685434699058533,
0.00013829994713887572,
0.0015727238496765494,
-0.009619372896850109,
0.01870977319777012,
-0.01967114955186844,
0.04509977623820305,
-0.006545464042574167,
-0.03511393070220947,
0.02869306318461895,
0.04446719214320183,
0.021909980103373528,
-0.07008924335241318,
-0.012628172524273396,
-0.04399121552705765,
-0.03785969316959381,
-0.06501831859350204,
-0.01909257471561432,
-0.03623243048787117,
0.022756274789571762,
-0.046684253960847855,
-0.0011777265463024378,
-0.04225652664899826,
0.02335086278617382,
-0.008947541005909443,
-0.016206689178943634,
0.04067777097225189,
-0.049020566046237946,
0.0016481487546116114,
-0.0005698464810848236,
-0.025608442723751068,
0.01216018944978714,
-0.06360354274511337,
-0.03420967236161232,
-0.02368735708296299,
-0.008341172710061073,
-0.03730679675936699,
0.0011865980923175812,
-0.052012231200933456,
0.0011641962919384241,
0.05132855474948883,
-0.006002289708703756,
-0.013232145458459854,
0.013234945945441723,
-0.02632908709347248,
-0.07249968498945236,
-0.0022178927902132273,
-0.03384528309106827,
-0.05624512955546379,
-0.023857412859797478,
0.047227777540683746,
-0.017169024795293808,
0.04100493714213371,
-0.004152514506131411,
0.018281683325767517,
0.06004834175109863,
-0.004493555519729853,
0.018022075295448303,
0.010321935638785362,
-0.01905900053679943,
-0.06037268042564392,
-0.04861108958721161,
-0.038042452186346054,
-0.0017084686551243067,
-0.041374217718839645,
-0.06312418729066849,
-0.032235220074653625,
0.023804500699043274,
0.040281426161527634,
0.03480403497815132,
-0.0696139857172966,
0.001131668221205473,
0.0383906252682209,
-0.04059174656867981,
0.0626283660531044,
-0.02261519432067871,
-0.03851179778575897,
-0.018781889230012894,
-0.029329780489206314,
-0.061895862221717834,
-0.031901054084300995,
0.021536312997341156,
-0.04539255425333977,
0.03982994332909584,
-0.005541006103157997,
-0.01682237721979618,
-0.03265906125307083,
-0.02645069546997547,
-0.034912966191768646,
0.02193986065685749,
-0.06802424788475037,
0.037803810089826584,
0.011785916984081268,
0.012866233475506306,
-0.031487733125686646,
0.016489233821630478,
0.0257125087082386,
0.022475983947515488,
-0.0691736564040184,
-0.0003728859592229128,
0.015370486304163933,
0.008994865231215954,
-0.015833720564842224,
-0.04954893887042999,
0.012783129699528217,
-0.011065616272389889,
0.11013326793909073,
0.04633687064051628,
-0.03896264359354973,
-0.0287693552672863,
-0.011397510766983032,
0.06186689808964729,
-0.012753504328429699,
0.0362606979906559,
0.08477579802274704,
0.01935685984790325,
-0.025368042290210724,
0.064753957092762,
0.08102105557918549,
-0.046168383210897446,
-0.004090298432856798,
-0.010363874956965446,
0.027736278250813484,
0.014548626728355885,
-0.007220197003334761,
0.025938453152775764,
-0.04905320703983307,
-0.015317175537347794,
-0.0038207487668842077,
0.0351373553276062,
-0.05055902525782585,
0.06805010885000229,
-0.0019096587784588337,
-0.03544582054018974,
-0.005553785711526871,
-0.029985619708895683,
0.012822097167372704,
-0.037730760872364044,
-0.03807820379734039,
-0.03220248222351074,
-0.007397524081170559,
0.04155273362994194,
-0.013671415857970715,
-0.019043300300836563,
0.021006012335419655,
-0.0688156932592392,
-0.032748449593782425,
0.037340231239795685,
0.010179851204156876,
-0.007861562073230743,
0.00877889059484005,
0.031438808888196945,
-0.0316186286509037,
-0.04484818875789642,
-0.03388422727584839,
-0.06006940081715584,
-0.06935352832078934,
0.013706494122743607,
0.011076299473643303,
-0.005691123194992542,
-0.04335501790046692,
0.015435092151165009,
0.048009343445301056,
-0.0637449249625206,
0.020768670365214348,
0.029748596251010895,
0.062499187886714935,
-0.033887434750795364,
0.060600847005844116,
0.01891636662185192,
0.07648860663175583,
0.00818304531276226,
-0.01626954786479473,
-0.013760694302618504,
0.03410670906305313,
0.013411288149654865,
-0.02380249835550785,
-0.06511039286851883,
0.030912257730960846,
0.029330631718039513,
0.0276830792427063,
-0.014299645088613033,
-0.042196523398160934,
-0.012636207975447178,
-0.004434539936482906,
0.0172605998814106,
-0.02837713621556759,
0.02623467892408371,
-0.05337723344564438,
-0.01654035411775112,
0.09476718306541443,
0.03444140404462814,
-0.07238352298736572,
0.009811420924961567,
0.04544960707426071,
0.06728118658065796,
0.008035559207201004,
-0.009613530710339546,
-0.012324868701398373,
-0.008063709363341331,
0.005055513232946396,
-0.0546831414103508,
0.004995862487703562,
-0.03562583401799202,
0.033202726393938065,
-0.07222822308540344,
-0.026779819279909134,
0.00027352251345291734,
-0.018861688673496246,
0.0531136728823185,
0.005447058472782373,
0.04803880304098129,
-0.02066737599670887,
-0.05468929186463356,
-0.012084756046533585,
0.048609714955091476,
0.008266896940767765,
0.002759371418505907,
-0.04117638245224953,
-0.026994844898581505,
0.018234286457300186,
0.022121205925941467,
0.03592764958739281,
0.023482657968997955,
0.039299219846725464,
0.07392444461584091,
-0.0575842447578907,
0.05368100479245186,
-0.029986383393406868,
-0.045616816729307175,
0.04996095597743988,
0.02095947042107582,
0.0021289160940796137,
-0.020030053332448006,
0.03602422773838043
] |
[
4.347805976867676,
6.8107428550720215
] |
Data Structures and Algorithms
|
Computer Science
|
cs-DS
|
na
|
na
|
2007-04-01T00:15:54
|
Neutrinoless double beta decay is one of the most sensitive approaches in
non-accelerator particle physics to take us into a regime of physics beyond the
standard model. This article is a brief review of the experiments in search of
neutrinoless double beta decay from 76Ge. Following a brief introduction of the
process of double beta decay from 76Ge, the results of the very first
experiments IGEX and Heidelberg-Moscow which give indications of the existence
of possible neutrinoless double beta decay mode has been reviewed. Then ongoing
efforts to substantiate the early findings are presented and the Majorana
experiment as a future experimental approach which will allow a very detailed
study of the neutrinoless decay mode is discussed.
|
Experimental efforts in search of 76Ge Neutrinoless Double Beta Decay
|
hep-ph
|
0704.0063
| 2,007
|
[
-0.007545949425548315,
0.01866515725851059,
0.00884438119828701,
0.0064313062466681,
-0.022281575947999954,
0.041307173669338226,
0.012286866083741188,
0.005148317199200392,
-0.03639855980873108,
-0.05561613291501999,
-0.03583114221692085,
0.09789598733186722,
0.038959112018346786,
0.01656309701502323,
0.027312787249684334,
-0.019174646586179733,
0.045702386647462845,
0.00994909554719925,
0.009451406076550484,
0.0032102130353450775,
-0.010307587683200836,
-0.022715559229254723,
-0.008340096101164818,
-0.04273327812552452,
0.05174527317285538,
-0.0038939653895795345,
0.018875647336244583,
0.048264116048812866,
-0.028622029349207878,
0.007674584165215492,
0.02385902777314186,
-0.11005492508411407,
0.06695117056369781,
-0.0017770263366401196,
-0.008968579582870007,
-0.011488061398267746,
0.053238529711961746,
0.015026425011456013,
-0.01311890222132206,
0.009372257627546787,
0.03695936128497124,
-0.030528051778674126,
-0.038924690335989,
-0.03654586523771286,
0.06501420587301254,
0.06809024512767792,
0.011051802895963192,
-0.019427375867962837,
0.03804226219654083,
-0.0299821887165308,
0.00742693804204464,
0.01942712441086769,
0.0014181678416207433,
-0.025943344458937645,
-0.01439653243869543,
-0.007573145907372236,
-0.010010682046413422,
-0.0044901673682034016,
0.07667724788188934,
-0.04535532370209694,
0.02105281688272953,
0.06978610903024673,
-0.014079265296459198,
0.0020963281858712435,
0.02390170656144619,
-0.09170439094305038,
-0.05926593765616417,
-0.0006527364603243768,
-0.010929428040981293,
-0.03769508749246597,
0.03492037206888199,
-0.014672345481812954,
-0.01758781261742115,
0.004657925572246313,
0.027309680357575417,
0.012350606732070446,
0.0016264633741229773,
-0.022526925429701805,
0.00654061371460557,
-0.011678550392389297,
0.011895464733242989,
-0.03725345432758331,
0.04670615494251251,
0.06324684619903564,
0.08933104574680328,
-0.03514011576771736,
-0.039675891399383545,
0.016843780875205994,
-0.04256776347756386,
0.020260678604245186,
0.05403822287917137,
0.0016759077552706003,
0.03624778240919113,
0.0013798469444736838,
-0.012700877152383327,
0.04914303496479988,
-0.05450587719678879,
0.07233414798974991,
-0.006278958637267351,
-0.03540361300110817,
0.00651041604578495,
0.03728511929512024,
0.009755200706422329,
-0.0010237966198474169,
0.07799463719129562,
0.022202657535672188,
0.009268153458833694,
0.01718864031136036,
0.02095137909054756,
-0.052423592656850815,
-0.039695028215646744,
0.01940936967730522,
-0.0019542882218956947,
-0.011419656686484814,
-0.011509645730257034,
0.021382244303822517,
0.03769005089998245,
-0.09720741212368011,
0.0327502116560936,
0.02262088470160961,
-0.012114070355892181,
0.030979350209236145,
-0.026406602934002876,
0.025520561262965202,
-0.004963697865605354,
-0.030007418245077133,
-0.05329940840601921,
0.037807196378707886,
0.024729378521442413,
-0.011444025672972202,
-0.05043581500649452,
-0.01850791648030281,
-0.03302398696541786,
-0.006480760872364044,
0.06883129477500916,
0.03326641023159027,
-0.05494999140501022,
-0.03771372511982918,
0.02242371253669262,
-0.052589111030101776,
-0.006783865392208099,
-0.00031826819758862257,
0.04028359428048134,
-0.0033493146765977144,
0.06106755882501602,
-0.05287783965468407,
-0.009420277550816536,
0.010873057879507542,
-0.07998073846101761,
0.028600208461284637,
-0.03131052479147911,
0.027495969086885452,
0.053667739033699036,
0.029479632154107094,
-0.07068457454442978,
-0.05207672342658043,
-0.032366275787353516,
0.010297381319105625,
-0.00232970854267478,
0.020702142268419266,
0.012077097781002522,
0.002061443403363228,
-0.03735322132706642,
0.03250052407383919,
0.0022255918011069298,
0.04373945668339729,
-0.008296730928122997,
-0.004648670554161072,
0.04779583960771561,
0.0025705958250910044,
-0.04100876674056053,
-0.04290686920285225,
-0.0198641587048769,
0.03275929391384125,
0.007145187351852655,
0.012677359394729137,
0.01781233213841915,
-0.024815572425723076,
0.03593292087316513,
-0.012336647137999535,
0.027248511090874672,
-0.01863730326294899,
0.02946929633617401,
0.058963414281606674,
-0.004370038863271475,
0.003604306373745203,
0.04351765662431717,
0.032793592661619186,
0.048090532422065735,
-0.05728599801659584,
-0.004533662460744381,
-0.01689871959388256,
-0.026306694373488426,
-0.04448310658335686,
0.024395983666181564,
-0.008005520328879356,
0.08239836245775223,
-0.025621144101023674,
0.023386934772133827,
-0.018661873415112495,
-0.03317655622959137,
-0.011483797803521156,
-0.0645756870508194,
-0.01993253454566002,
0.03321691229939461,
0.005096587352454662,
0.025216614827513695,
-0.006427745800465345,
0.017922868952155113,
-0.007207253482192755,
0.041539836674928665,
0.035920701920986176,
-0.002775347325950861,
0.021862665191292763,
-0.005826733075082302,
-0.026277637109160423,
0.026815379038453102,
-0.010176325216889381,
-0.04550911858677864,
0.056157033890485764,
0.03117886185646057,
-0.01580667309463024,
-0.02256879210472107,
-0.009604447521269321,
0.04024567827582359,
0.029842618852853775,
-0.03276525437831879,
0.0015479588182643056,
-0.06572753190994263,
-0.018337178975343704,
-0.05694675073027611,
-0.05378420650959015,
0.016295621171593666,
-0.03333388641476631,
-0.0474419891834259,
0.010094720870256424,
-0.020283041521906853,
-0.00019069730478804559,
0.04868024215102196,
0.049807000905275345,
0.012337992899119854,
0.0037230760790407658,
-0.07355089485645294,
0.012443768791854382,
-0.028394702821969986,
-0.02063445746898651,
-0.01665310561656952,
0.03937114402651787,
-0.01024597231298685,
0.0034995852038264275,
-0.01355352345854044,
0.03488888964056969,
-0.0041487328708171844,
0.033490490168333054,
0.07097987830638885,
-0.005723936017602682,
-0.030395526438951492,
0.04125206544995308,
-0.0559324212372303,
-0.0517495833337307,
0.05224986746907234,
-0.040503665804862976,
-0.0057509965263307095,
-0.01613110490143299,
0.002206229604780674,
0.0169026218354702,
0.0019561934750527143,
-0.039606206119060516,
-0.02654259093105793,
-0.021469596773386,
-0.020998893305659294,
0.00869702361524105,
0.03496586158871651,
0.08004256337881088,
-0.012152299284934998,
0.05678066238760948,
0.07862849533557892,
0.03558952361345291,
0.020105477422475815,
-0.004647471010684967,
-0.08499423414468765,
-0.0016094337916001678,
-0.0060926880687475204,
-0.07627247273921967,
-0.0006705237901769578,
0.026510506868362427,
0.016335058957338333,
-0.03040550835430622,
0.032742951065301895,
0.03237798810005188,
-0.037036217749118805,
-0.04674224928021431,
0.06536252051591873,
0.021278604865074158,
0.034773215651512146,
0.0592760294675827,
0.044690050184726715,
0.006914949510246515,
-0.009239865466952324,
0.05343926325440407,
0.01692056469619274,
-0.046777985990047455,
-0.06363166123628616,
0.0005199037841521204,
0.041292570531368256,
-0.02669598162174225,
-0.011642346158623695,
0.0316542387008667,
-0.010813707485795021,
0.019097762182354927,
-0.006596481893211603,
0.038740113377571106,
0.023122377693653107,
-0.018408726900815964,
-0.011438737623393536,
0.07778923213481903,
0.007752926088869572,
0.04642422869801521,
0.11448851227760315,
0.041509389877319336,
0.04332305118441582,
-0.02938600815832615,
0.035826630890369415,
-0.03649089112877846,
0.025053324177861214,
0.006346719805151224,
0.02440395951271057,
0.04345448687672615,
-0.0273969117552042,
0.036849088966846466,
0.022535305470228195,
0.05857120081782341,
-0.030636632815003395,
-0.032606180757284164,
-0.053965017199516296,
0.02787921018898487,
-0.042180385440588,
0.05649719759821892,
-0.02966700680553913,
-0.010451383888721466,
-0.012634284794330597,
-0.054397597908973694,
-0.05514303967356682,
-0.03884078934788704,
0.0008401406230404973,
-0.02560059167444706,
-0.02388722263276577,
-0.008610778488218784,
0.031590111553668976,
0.03438744321465492,
0.004965573083609343,
0.013737655244767666,
-0.047997135668992996,
0.011381031945347786,
-0.015014104545116425,
0.015245790593326092,
0.02931816130876541,
-0.027024023234844208,
0.05223928019404411,
0.008630011230707169,
0.00013449085236061364,
-0.022195039317011833,
0.025492079555988312,
-0.017024295404553413,
0.013082616962492466,
0.0016347416676580906,
0.02329021319746971,
0.021180789917707443,
0.03288014605641365,
-0.06637296825647354,
-0.05685977637767792,
-0.06053781881928444,
0.013663046061992645,
-0.0007710058707743883,
-0.0008326780516654253,
0.014041449874639511,
-0.04682542756199837,
0.03765822947025299,
-0.056601498275995255,
0.05047746002674103,
0.024743229150772095,
-0.013521667569875717,
0.05042140558362007,
0.038785770535469055,
0.007829585112631321,
-0.057180002331733704,
-0.059230346232652664,
0.040602054446935654,
-0.0296537633985281,
-0.05587887763977051,
-0.01588873192667961,
-0.037271950393915176,
-0.02956222929060459,
0.047624219208955765,
-0.01624823547899723,
-0.018761862069368362,
0.05335160344839096,
-0.022387487813830376,
0.02346205711364746,
-0.021936412900686264,
-0.06636466085910797,
-0.026028163731098175,
0.05140744149684906,
-0.011881374754011631,
-0.025610946118831635,
0.03167751431465149,
-0.08900594711303711,
-0.04161731153726578,
0.037990689277648926,
-0.025508027523756027,
-0.0094596017152071,
0.016050374135375023,
-0.05959039181470871,
-0.05933862552046776,
0.02200642041862011,
0.008551347069442272,
0.01576535589993,
-0.01484169252216816,
0.010305928066372871,
-0.04526693373918533,
0.030581627041101456,
0.06680236756801605,
-0.053001224994659424,
0.01564636453986168,
-0.012409205548465252,
0.02669542282819748,
-0.016615107655525208,
0.0049043395556509495,
0.037021324038505554,
-0.03088744543492794,
0.03678188845515251,
-0.01980566792190075,
-0.037020668387413025,
0.061461836099624634,
-0.06247241050004959,
0.015730032697319984,
0.05018549785017967,
0.020413720980286598,
-0.015875520184636116,
0.06484724581241608,
0.06819894909858704,
-0.07554753124713898,
0.031692132353782654,
0.006934930570423603,
0.01759151928126812,
0.09694693982601166,
0.04275491088628769,
-0.036959681659936905,
0.002046278677880764,
0.022539429366588593,
0.03615438565611839,
-0.007281971164047718,
0.009242664091289043,
0.04107685759663582,
0.08033132553100586,
-0.014546336606144905,
0.048678748309612274,
0.013699269853532314,
-0.006083786953240633,
0.11440326273441315,
0.016525540500879288,
-0.005734544713050127,
-0.003674672218039632,
0.00727731641381979,
0.016849374398589134,
-0.022872699424624443,
-0.02715526707470417,
-0.022866329178214073,
0.005438338033854961,
0.004599032923579216,
-0.041384704411029816,
-0.00506671704351902,
0.0563901923596859,
-0.024329233914613724,
-0.0482710562646389,
-0.024024685844779015,
-0.04053546115756035,
-0.006139448378235102,
0.04148909077048302,
0.04605235531926155,
-0.02598913386464119,
-0.025108037516474724,
-0.049786292016506195,
-0.022875970229506493,
-0.024917121976614,
-0.026892393827438354,
-0.014355465769767761,
0.01781127229332924,
0.05524618923664093,
-0.032347582280635834,
0.02565428800880909,
0.05416452884674072,
0.039285413920879364,
-0.030567893758416176,
-0.000744420918636024,
-0.026048479601740837,
0.012843121774494648,
0.02336830087006092,
0.01741836778819561,
-0.01419319212436676,
-0.004288686905056238,
-0.017872758209705353,
0.015595466829836369,
0.022057345137000084,
0.014122250489890575,
0.012726855464279652,
-0.049049220979213715,
-0.04881454259157181,
-0.0471319742500782,
-0.013101588003337383,
-0.020067956298589706,
0.03938031941652298,
0.017834234982728958,
0.05336550995707512,
-0.031462300568819046,
-0.02299015037715435,
0.030694421380758286,
0.009046891704201698,
-0.04145960882306099,
-0.0015899169957265258,
-0.023520400747656822,
-0.0296196099370718,
0.028519801795482635,
-0.006233166437596083,
-0.05490925535559654,
-0.0035508719738572836,
-0.040325671434402466,
-0.031213851645588875,
0.09417153149843216,
-0.01927880384027958,
-0.010897991247475147,
-0.002120279474183917,
0.05388407036662102,
0.049173709005117416,
-0.047635518014431,
-0.05271196737885475,
-0.025481494143605232,
0.004360082093626261,
0.0073715075850486755,
0.0036695534363389015,
-0.025766298174858093,
0.025131555274128914,
0.010078041814267635,
0.009918301366269588,
0.022464439272880554,
-0.012120140716433525,
-0.0689082071185112,
0.023379839956760406,
-0.009458601474761963,
-0.009792448952794075,
-0.001953032915480435,
-0.05346101149916649,
0.02201809547841549,
-0.06619754433631897,
-0.003742138622328639,
-0.04990348964929581,
0.013367709703743458,
-0.009983902797102928,
-0.034361567348241806,
0.021356159821152687,
0.020677806809544563,
-0.047632768750190735,
0.02742771804332733,
0.02041444554924965,
0.0004926823312416673,
-0.08512340486049652,
-0.0037213610485196114,
-0.07836992293596268,
0.025588976219296455,
0.016973985359072685,
-0.0291203074157238,
-0.026455743238329887,
-0.05317961797118187,
0.03706471621990204,
-0.011158342473208904,
-0.027889303863048553,
0.03268340975046158,
0.0274606104940176,
-0.04413954168558121,
-0.004386525135487318,
0.004866622854024172,
-0.0006676203338429332,
0.013553212396800518,
0.02021321840584278,
-0.012209814973175526,
0.037174075841903687,
-0.014315142296254635,
-0.0351007841527462,
0.004388670902699232,
-0.0036571475211530924,
0.07800223678350449,
-0.040389277040958405,
-0.00012167428212706,
-0.01969902776181698,
-0.047240741550922394,
-0.036672141402959824,
0.0217508003115654,
-0.057477179914712906,
-0.04261726140975952,
-0.010802306234836578,
-0.024460481479763985,
-0.002684853971004486,
0.017789101228117943,
0.023315399885177612,
0.05233348160982132,
0.029474161565303802,
0.003880701493471861,
0.040139779448509216,
-0.029054692015051842,
-0.023919671773910522,
0.0021267258562147617,
0.012873454950749874,
-0.053814828395843506,
-0.10536574572324753,
-0.05935421213507652,
-0.0850701704621315,
0.0919373631477356,
-0.0407368503510952,
0.02690698951482773,
-0.02227342687547207,
0.016024041920900345,
-0.06185026839375496,
-0.012000253424048424,
0.0018608862301334739,
-0.0031139468774199486,
0.053980741649866104,
-0.027499942108988762,
-0.08091486245393753,
0.042584992945194244,
0.025682685896754265,
-0.0069955685175955296,
-0.023823799565434456,
-0.015170469880104065,
-0.003973911516368389,
-0.056416645646095276,
-0.023689627647399902,
-0.004627510905265808,
0.023931359872221947,
0.0073598953895270824,
0.006842658389359713,
0.03481636196374893,
-0.014040696434676647,
-0.011009858921170235,
0.010792315937578678,
0.037059664726257324,
0.017001785337924957,
0.003954945132136345,
0.048196665942668915,
0.0398012138903141,
-0.03489388898015022,
0.028040515258908272,
0.04028443619608879,
-0.0016966911498457193,
0.0006426008767448366,
0.02322075329720974,
0.006095599848777056,
0.06702817231416702,
0.013553574681282043,
-0.0355854332447052,
-0.033502016216516495,
-0.041212938725948334,
-0.026734620332717896,
0.012542914599180222,
0.014405046589672565,
0.028928332030773163,
-0.0073592085391283035,
-0.03320130705833435,
-0.04950505867600441,
-0.016530226916074753,
0.0013898111646994948,
-0.04202650859951973,
-0.023646382614970207,
-0.0474993921816349,
-0.00127797934692353,
-0.04864535108208656,
-0.011702935211360455,
0.03095974028110504,
-0.015884241089224815,
-0.012431897222995758,
-0.015413728542625904,
0.009070967324078083,
0.037756506353616714,
-0.0219273641705513,
0.013827810063958168,
-0.02311382070183754,
0.007164804730564356,
-0.037827812135219574,
0.03765033930540085,
-0.05328650400042534,
0.01623644307255745,
-0.00527903763577342,
0.02269745245575905,
0.05665907636284828,
-0.08354045450687408,
-0.0212856512516737,
0.004926222376525402,
-0.0725882351398468,
-0.019524378702044487,
-0.02155202254652977,
0.032285869121551514,
0.0165620855987072,
0.052055008709430695,
-0.04917237162590027,
0.052463680505752563,
-0.026514336466789246,
0.012593611143529415,
0.038693275302648544,
-0.006444806698709726,
0.008217733353376389,
0.05272612348198891,
-0.022910665720701218,
0.029641132801771164,
-0.0017333299620077014,
0.06264674663543701,
0.023089099675416946,
0.03339405357837677,
-0.01977146416902542,
-0.04188203066587448,
0.06168321147561073,
-0.03219340369105339,
0.00252929818816483,
-0.00926143117249012,
-0.02347606047987938,
0.0074946279637515545,
-0.06309270858764648,
-0.043418098241090775,
-0.04774075001478195,
0.012835505418479443,
0.1000511571764946,
0.00770249729976058,
0.030509060248732567,
-0.04470690339803696,
-0.04022734984755516,
0.026433592662215233,
-0.04452304169535637,
-0.0017606070032343268,
0.00948598887771368,
0.061567582190036774,
-0.04471462592482567,
0.005373888649046421,
0.00856377836316824,
-0.004971576854586601,
0.019083309918642044,
0.013434398919343948,
0.02248070389032364,
0.011730620637536049,
-0.035413019359111786,
0.05249888822436333,
0.038915522396564484,
-0.06314016133546829,
0.0179736390709877,
-0.00482167536392808,
-0.007254287600517273,
0.04777073860168457,
-0.025691727176308632,
0.010274183005094528,
-0.007256318815052509,
0.028182268142700195,
0.03971197083592415,
-0.02907002903521061,
0.021439535543322563,
0.0007286996697075665,
0.00529896467924118,
0.05791645497083664,
-0.010514329187572002,
-0.008574500679969788,
-0.02542836032807827,
0.017619237303733826
] |
[
16.618389129638672,
1.1276811361312866
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
na
|
na
|
2007-04-01T13:32:15
|
We capture the off-shell as well as the on-shell nilpotent
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the
Lagrangian densities of the four (3 + 1)-dimensional (4D) (non-)Abelian 1-form
gauge theories within the framework of the superfield formalism. In particular,
we provide the geometrical interpretations for (i) the above nilpotent symmetry
invariance, and (ii) the above Lagrangian densities, in the language of the
specific quantities defined in the domain of the above superfield formalism.
Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge
theories, are clarified within the framework of the above superfield formalism
where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional
supermanifold parametrized by the four spacetime coordinates x^\mu (with \mu =
0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta. One of
the key results of our present investigation is a great deal of simplification
in the geometrical understanding of the nilpotent (anti-)BRST symmetry
invariance.
|
Nilpotent symmetry invariance in the superfield formulation: the
(non-)Abelian 1-form gauge theories
|
hep-th
|
0704.0064
| 2,007
|
[
0.02030588500201702,
0.036730799823999405,
-0.020741499960422516,
-0.030712084844708443,
0.018591012805700302,
0.06848767399787903,
0.06870343536138535,
0.0305954497307539,
-0.05268169939517975,
-0.005143221002072096,
-0.058519382029771805,
-0.007200361229479313,
0.020648859441280365,
0.0006932853139005601,
0.0010312868980690837,
-0.027172796428203583,
0.04140227288007736,
0.006929006893187761,
0.04572899267077446,
-0.06447753310203552,
-0.058168601244688034,
-0.02579353004693985,
-0.01123484130948782,
-0.05137626826763153,
0.07684153318405151,
0.05742553249001503,
0.013198667205870152,
-0.014533285051584244,
-0.012555424124002457,
-0.017574895173311234,
0.05076541751623154,
-0.035316914319992065,
0.043971046805381775,
-0.05889245495200157,
-0.030398044735193253,
-0.027753515169024467,
0.08015403151512146,
0.01650146022439003,
-0.01926557905972004,
0.02312852069735527,
0.04494912549853325,
-0.02702328749001026,
0.003111649304628372,
-0.018601130694150925,
-0.01882460154592991,
0.03235303983092308,
0.015853654593229294,
0.005682913586497307,
-0.0016010493272915483,
-0.023988870903849602,
0.03653602674603462,
0.03532223403453827,
0.023192409425973892,
-0.07235093414783478,
-0.06180889531970024,
0.02352372370660305,
0.024319855496287346,
-0.021711526438593864,
-0.007845970802009106,
-0.007349911145865917,
0.003083231393247843,
0.01135256327688694,
-0.02380976639688015,
0.034644924104213715,
0.040509920567274094,
-0.02778240479528904,
-0.06117749959230423,
-0.041769254952669144,
-0.004106538370251656,
-0.07449738681316376,
0.04215775430202484,
0.030019326135516167,
-0.00040484682540409267,
0.02751205861568451,
-0.03691581264138222,
0.011823911219835281,
-0.00939998496323824,
0.00190318888053298,
-0.02062838152050972,
-0.0009057681891135871,
0.03402616083621979,
-0.011011986061930656,
0.02171114832162857,
0.044636793434619904,
0.09494949877262115,
-0.025257352739572525,
0.04223507270216942,
0.01719558797776699,
-0.02865809015929699,
0.015083203092217445,
-0.005055525805801153,
0.026668371632695198,
0.024153951555490494,
0.03211827203631401,
-0.04577977955341339,
0.04507824778556824,
0.01083064079284668,
0.03311515599489212,
-0.07110320031642914,
-0.046351365745067596,
-0.009092066437005997,
0.11291836202144623,
-0.007374316453933716,
0.015734544023871422,
0.06570504605770111,
0.016185550019145012,
0.054811760783195496,
0.007779758423566818,
0.018768001347780228,
-0.043984461575746536,
-0.10029435902833939,
-0.046370673924684525,
0.03198467195034027,
0.04013580083847046,
-0.09531321376562119,
-0.02866511233150959,
0.038630347698926926,
-0.10303182899951935,
0.010476483963429928,
0.061451058834791183,
-0.0047125560231506824,
-0.008254614658653736,
0.03816448897123337,
0.037960443645715714,
0.012300937436521053,
0.01613592728972435,
-0.08368821442127228,
0.03575834259390831,
0.042443566024303436,
-0.018971716985106468,
0.02567206881940365,
0.03751310706138611,
-0.034403275698423386,
-0.004683190491050482,
0.025179406628012657,
0.04481156915426254,
-0.03209337964653969,
-0.020324155688285828,
0.04118857532739639,
-0.019605841487646103,
0.00547552015632391,
0.02245737612247467,
0.024199020117521286,
-0.01367710717022419,
0.04700806736946106,
-0.06692678481340408,
-0.02085007168352604,
-0.06601688265800476,
-0.04162902384996414,
-0.0007681942661292851,
0.04882553964853287,
0.038065411150455475,
-0.0061295428313314915,
0.04913606494665146,
-0.0407051220536232,
-0.041743576526641846,
-0.0036568816285580397,
0.027812758460640907,
0.02374507300555706,
-0.007908227853477001,
0.011160914786159992,
0.01897202804684639,
-0.029984362423419952,
0.051556795835494995,
-0.04529959335923195,
0.026417208835482597,
0.04197430610656738,
0.010780745185911655,
0.01332459133118391,
-0.004423420876264572,
-0.03210088983178139,
-0.00993445236235857,
-0.03075067140161991,
-0.0488099530339241,
-0.010574066080152988,
0.014417731203138828,
-0.028210630640387535,
-0.06805238127708435,
0.02460937201976776,
-0.004737867973744869,
0.04379138723015785,
0.0020670839585363865,
0.03523055464029312,
0.03315337374806404,
0.013447688892483711,
0.006962305400520563,
-0.008890236727893353,
-0.034089796245098114,
-0.029038192704319954,
-0.0007373152184300125,
0.016599126160144806,
0.04279177263379097,
-0.022613778710365295,
0.010944880545139313,
0.013348096050322056,
-0.004118992481380701,
0.04050964489579201,
-0.016512449830770493,
0.01192539557814598,
-0.012035063467919827,
-0.011404911056160927,
0.011807349510490894,
-0.04574541747570038,
0.018400197848677635,
0.014259617775678635,
0.032279446721076965,
-0.04168647155165672,
0.028523679822683334,
0.06514526903629303,
-0.023708436638116837,
0.015326653607189655,
-0.022362178191542625,
-0.0345565490424633,
-0.025945834815502167,
-0.029970213770866394,
0.02249898947775364,
0.018926875665783882,
-0.03879309818148613,
-0.09418236464262009,
0.05678801238536835,
0.050651680678129196,
-0.04540649801492691,
0.03839145600795746,
0.021690167486667633,
0.002626554574817419,
0.03561215102672577,
-0.016920706257224083,
-0.026522081345319748,
0.012370070442557335,
-0.051031872630119324,
-0.04229980334639549,
-0.03632352873682976,
0.03169836476445198,
-0.015855509787797928,
-0.05085239186882973,
0.043654169887304306,
-0.00812109000980854,
0.012855401262640953,
0.08276333659887314,
0.06083652004599571,
0.0367179773747921,
0.0561852753162384,
0.0016029335092753172,
-0.001806013286113739,
0.008382531814277172,
0.014822564087808132,
0.011468281038105488,
-0.016785841435194016,
-0.024269653484225273,
0.036267854273319244,
-0.01991790533065796,
0.008304283954203129,
0.005254730582237244,
-0.010124647058546543,
0.056031618267297745,
-0.022172247990965843,
0.015790557488799095,
0.026694800704717636,
-0.06561198830604553,
-0.06910409778356552,
0.03238054737448692,
-0.06312860548496246,
0.024761971086263657,
-0.013089567422866821,
-0.040059685707092285,
0.010031481273472309,
0.03978075087070465,
-0.04531291127204895,
-0.008029620163142681,
-0.009625007398426533,
-0.016155224293470383,
0.03272158280014992,
0.041831016540527344,
0.05966970697045326,
-0.042359571903944016,
0.024586839601397514,
0.02003333903849125,
-0.006392099428921938,
0.01163620874285698,
-0.030507851392030716,
-0.06873493641614914,
-0.006687451153993607,
-0.03440316021442413,
-0.029363350942730904,
0.04743805155158043,
0.0014437463833019137,
0.009233633056282997,
-0.05103142559528351,
-0.01739647425711155,
0.023010501638054848,
-0.006878315471112728,
-0.009541498497128487,
0.021170539781451225,
0.04795203357934952,
-0.011282001622021198,
0.02590348571538925,
0.044155530631542206,
-0.02035105600953102,
-0.011200129985809326,
0.012863569892942905,
-0.03251545503735542,
0.03496955707669258,
0.005090594757348299,
0.009330562315881252,
0.04474658519029617,
-0.0016864610370248556,
-0.02625267393887043,
0.003762333421036601,
0.05595504865050316,
-0.02976783737540245,
-0.03388083353638649,
0.007811673916876316,
0.013241139240562916,
-0.022917406633496284,
-0.07417276501655579,
0.011390520259737968,
0.015855537727475166,
0.01535059791058302,
0.12780141830444336,
0.039914656430482864,
-0.005657361354678869,
-0.010420397855341434,
0.01187848299741745,
-0.02415877766907215,
0.019371941685676575,
0.05830226466059685,
-0.01855836622416973,
0.030072491616010666,
-0.03719323128461838,
-0.021918701007962227,
-0.043300483375787735,
0.05490262061357498,
-0.006042122840881348,
-0.007746519986540079,
-0.014314835891127586,
0.02039283514022827,
-0.0783129408955574,
0.02221873216331005,
-0.04879477992653847,
-0.015344755724072456,
0.017561133950948715,
-0.06141110509634018,
-0.02854539081454277,
-0.0118754543364048,
0.005779342260211706,
0.009576240554451942,
-0.0038734073750674725,
-0.04356389865279198,
0.029769843444228172,
0.026554441079497337,
-0.04849746823310852,
0.02107417769730091,
0.05995960161089897,
0.01855248026549816,
-0.0064639137126505375,
0.0441170260310173,
0.07695967704057693,
-0.02889053337275982,
0.05597143620252609,
0.029818011447787285,
0.03077712282538414,
-0.026966333389282227,
-0.007087353616952896,
0.009992970153689384,
0.03365182504057884,
0.059183426201343536,
-0.019969437271356583,
-0.011786187067627907,
0.007530299946665764,
0.007572579197585583,
-0.00017402810044586658,
-0.05188876762986183,
0.052716970443725586,
0.024968396872282028,
0.035764556378126144,
-0.02124033123254776,
-0.06554075330495834,
-0.008104833774268627,
0.00996975414454937,
-0.04680842533707619,
0.08507563173770905,
-0.017452409490942955,
0.01224252674728632,
-0.03279896080493927,
-0.004266845062375069,
0.008619590662419796,
-0.04734799265861511,
0.014968568459153175,
-0.028029758483171463,
-0.02720900997519493,
0.0048610433004796505,
-0.035748451948165894,
-0.05057355761528015,
-0.004964995197951794,
-0.017658958211541176,
0.0019571196753531694,
0.04708729311823845,
-0.033943288028240204,
-0.010927790775895119,
-0.05438295006752014,
-0.017466509714722633,
-0.037814658135175705,
-0.015390859916806221,
-0.04945427179336548,
-0.016123080626130104,
0.004318020306527615,
-0.012781668454408646,
-0.05683941766619682,
0.030221791937947273,
0.015195660293102264,
-0.002148647094145417,
0.03563547506928444,
0.030121853575110435,
-0.1098632737994194,
0.07324112206697464,
0.004691201262176037,
0.028602827340364456,
-0.03323686867952347,
-0.0037541957572102547,
-0.017758196219801903,
0.039546795189380646,
0.04580420255661011,
0.028370467945933342,
-0.029438503086566925,
0.026449086144566536,
-0.010897370986640453,
-0.022417010739445686,
0.004151942674070597,
-0.011809222400188446,
-0.00858652126044035,
0.018727758899331093,
0.00273352162912488,
0.03658917918801308,
0.029141927137970924,
-0.10768838226795197,
0.004980532452464104,
-0.011498643085360527,
0.017077604308724403,
0.020573662593960762,
0.026320666074752808,
0.04807201772928238,
-0.03245634213089943,
0.03666224703192711,
-0.029732858762145042,
0.003534202929586172,
0.0594605915248394,
0.014471510425209999,
-0.03695552051067352,
-0.037088654935359955,
-0.007946189492940903,
0.021180985495448112,
-0.0031444747000932693,
-0.03183399513363838,
0.010742449201643467,
0.05488945543766022,
-0.030940357595682144,
0.0202043317258358,
0.024062752723693848,
0.07592836022377014,
0.024442140012979507,
-0.026282813400030136,
-0.026832913979887962,
-0.03951442614197731,
-0.0004310255462769419,
0.04520223289728165,
-0.002348900306969881,
-0.029823848977684975,
0.007851495407521725,
0.011681271716952324,
0.02923434041440487,
0.019633810967206955,
-0.047060757875442505,
-0.0010313845705240965,
-0.05173613131046295,
-0.028378669172525406,
0.00720046553760767,
0.0466189980506897,
-0.01419130340218544,
-0.015025530010461807,
0.02650384232401848,
0.026973906904459,
0.00045764161041006446,
0.005084961652755737,
-0.021683156490325928,
-0.003897635266184807,
0.025089068338274956,
0.046601176261901855,
0.00854311604052782,
-0.024922730401158333,
-0.042084697633981705,
-0.04187918081879616,
0.0030149929225444794,
0.015248317271471024,
0.02235831692814827,
-0.03861301764845848,
-0.012116369791328907,
0.02506934106349945,
0.009411563165485859,
-0.026526106521487236,
-0.011423230171203613,
-0.07646143436431885,
0.06114766374230385,
0.015538186766207218,
0.0320245623588562,
-0.005244503263384104,
0.06702083349227905,
0.013398252427577972,
-0.050045933574438095,
-0.0250055193901062,
0.02510281279683113,
-0.0023898566141724586,
0.03625758737325668,
-0.00568693783134222,
0.02935469150543213,
0.04017225652933121,
-0.04538315162062645,
0.03503996506333351,
-0.02151678130030632,
-0.0076519339345395565,
-0.051248665899038315,
-0.010406129993498325,
0.03708392754197121,
-0.014963037334382534,
-0.027290232479572296,
-0.04304840415716171,
0.05250631645321846,
-0.05581377446651459,
-0.0751756951212883,
0.07322649657726288,
0.009822949767112732,
0.002511761151254177,
0.07168392837047577,
0.0497576966881752,
-0.01196762453764677,
0.05000219866633415,
-0.02539719082415104,
0.01325297262519598,
0.009689622558653355,
0.01474639493972063,
0.007973240688443184,
0.02656657062470913,
0.03552042320370674,
0.01799609698355198,
-0.04313778877258301,
-0.021089475601911545,
-0.023408470675349236,
-0.07871841639280319,
0.022545166313648224,
-0.03881051018834114,
-0.046960894018411636,
-0.005019288044422865,
0.0017885485431179404,
0.03285740315914154,
-0.0826263502240181,
-0.022400131449103355,
-0.03894103318452835,
-0.025237761437892914,
-0.03792959824204445,
-0.06443272531032562,
-0.019815435633063316,
0.021914362907409668,
0.018198110163211823,
0.049724068492650986,
0.010405080392956734,
-0.02582441084086895,
-0.021346217021346092,
-0.037973802536726,
-0.04854203760623932,
0.05732027068734169,
0.03248170018196106,
-0.009272754192352295,
-0.0004308974021114409,
0.022756842896342278,
0.048824287950992584,
-0.0004972090828232467,
-0.0527019239962101,
0.037125106900930405,
-0.04855675622820854,
-0.03614838421344757,
-0.02618028037250042,
-0.010670448653399944,
-0.017722545191645622,
0.0027029095217585564,
-0.04117526486515999,
-0.03610948473215103,
0.026557082310318947,
-0.02794521115720272,
-0.07091449201107025,
0.062253255397081375,
0.01277051493525505,
0.016780348494648933,
-0.04127569496631622,
0.017630035057663918,
0.010017056949436665,
-0.05096760764718056,
0.024173177778720856,
-0.023056339472532272,
0.018081344664096832,
-0.013358320109546185,
-0.04318147897720337,
-0.0076185730285942554,
0.007251854985952377,
0.03469185531139374,
-0.04373190179467201,
0.10124935954809189,
0.07653804868459702,
0.0022116785403341055,
-0.0023027758579701185,
0.0042666057124733925,
-0.05352752283215523,
0.06940514594316483,
0.04967457056045532,
-0.05090712383389473,
0.004671019036322832,
0.021902140229940414,
-0.012831068597733974,
0.02711530774831772,
-0.02356112375855446,
0.04054216295480728,
-0.04988318681716919,
0.019031034782528877,
-0.0666876807808876,
-0.03480534255504608,
-0.03758518397808075,
0.028375471010804176,
0.03429035097360611,
-0.03245478495955467,
-0.02598089724779129,
0.009533527307212353,
0.043694522231817245,
-0.0054586511105299,
-0.005267350468784571,
-0.018771186470985413,
-0.0003472304088063538,
-0.025945158675312996,
0.03738032653927803,
-0.021519219502806664,
0.03523886203765869,
0.007872437126934528,
0.06312579661607742,
0.0006362076965160668,
-0.022893410176038742,
0.03776790201663971,
-0.008679166436195374,
0.013242258690297604,
0.019354209303855896,
-0.030610188841819763,
-0.009081827476620674,
-0.014634723775088787,
-0.0077912164852023125,
0.07339135557413101,
0.06466727703809738,
-0.020997293293476105,
0.038194093853235245,
-0.013496574945747852,
-0.04683826118707657,
-0.03496059402823448,
0.0032888399437069893,
-0.03731604665517807,
0.00373939354903996,
-0.023049246519804,
0.014317214488983154,
-0.008179218508303165,
-0.011175858788192272,
-0.017703067511320114,
-0.0327642597258091,
0.023449905216693878,
-0.04582780972123146,
-0.04534383490681648,
0.042755063623189926,
-0.03256703168153763,
-0.03802542760968208,
-0.028810037299990654,
0.03251519799232483,
-0.06574525684118271,
-0.008086860179901123,
0.02824678272008896,
0.05627615749835968,
-0.01297727506607771,
-0.038207199424505234,
0.015766369178891182,
0.027430439367890358,
0.03163524344563484,
0.04119936004281044,
-0.031088847666978836,
-0.04003329947590828,
0.012139600701630116,
-0.021050402894616127,
-0.04227554425597191,
-0.016633566468954086,
0.03859024494886398,
-0.017476489767432213,
0.005031707230955362,
-0.04355769231915474,
-0.0405428372323513,
0.0041517834179103374,
-0.019965674728155136,
0.018893497064709663,
-0.01186605729162693,
0.0428888238966465,
0.010629694908857346,
0.00460720295086503,
-0.08575285971164703,
0.0625172108411789,
-0.011125058867037296,
-0.03751738741993904,
-0.006399228237569332,
0.03188839554786682,
-0.040778033435344696,
0.001680706162005663,
-0.05679978430271149,
0.049977779388427734,
0.05900135263800621,
-0.003205588785931468,
0.09802144020795822,
-0.01611841656267643,
0.018613208085298538,
-0.031944792717695236,
-0.01824834942817688,
0.009167015552520752,
0.02195490337908268,
0.05498059466481209,
-0.014016998931765556,
0.011867623776197433,
-0.03788642957806587,
-0.055707644671201706,
-0.020558947697281837,
-0.030429190024733543,
0.06368722766637802,
0.017241492867469788,
-0.0521736778318882,
0.00011065085709560663,
-0.059329207986593246,
0.07430857419967651,
-0.038675837218761444,
0.03520707041025162,
0.002644734922796488,
-0.005013186950236559,
-0.0019868947565555573,
0.005224434193223715,
0.01999453641474247,
-0.05162743851542473,
0.02971351146697998,
0.002824642928317189,
-0.045740071684122086,
-0.007305764127522707,
-0.015901779755949974,
0.058560751378536224,
-0.005611920729279518,
-0.0038552985060960054,
-0.0029286211356520653,
0.020794671028852463,
-0.023413827642798424,
-0.013157487846910954,
0.024229032918810844,
0.02133931592106819,
-0.006448001135140657,
-0.016511790454387665,
0.08776017278432846,
0.007042646408081055,
0.027289239689707756,
-0.03983611613512039,
0.05363509804010391,
0.0646483302116394,
-0.03972205892205238,
-0.009686608798801899,
-0.02865763008594513,
0.017200756818056107
] |
[
12.300353050231934,
0.4770188629627228
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-04-02T01:14:48
|
We introduce a family of rings of symmetric functions depending on an
infinite sequence of parameters. A distinguished basis of such a ring is
comprised by analogues of the Schur functions. The corresponding structure
coefficients are polynomials in the parameters which we call the
Littlewood-Richardson polynomials. We give a combinatorial rule for their
calculation by modifying an earlier result of B. Sagan and the author. The new
rule provides a formula for these polynomials which is manifestly positive in
the sense of W. Graham. We apply this formula for the calculation of the
product of equivariant Schubert classes on Grassmannians which implies a
stability property of the structure coefficients. The first manifestly positive
formula for such an expansion was given by A. Knutson and T. Tao by using
combinatorics of puzzles while the stability property was not apparent from
that formula. We also use the Littlewood-Richardson polynomials to describe the
multiplication rule in the algebra of the Casimir elements for the general
linear Lie algebra in the basis of the quantum immanants constructed by A.
Okounkov and G. Olshanski.
|
Littlewood-Richardson polynomials
|
math.AG math.CO
|
0704.0065
| 2,007
|
[
0.0033880616538226604,
0.01037617027759552,
-0.00844908319413662,
-0.08796031773090363,
-0.013371569104492664,
-0.020954426378011703,
0.030144786462187767,
-0.010115223936736584,
-0.03138924017548561,
0.03088155947625637,
-0.11196225136518478,
0.04866791516542435,
0.007029972039163113,
-0.015227386727929115,
0.018035495653748512,
-0.009830877184867859,
0.013341107405722141,
0.012875057756900787,
-0.03192092478275299,
-0.00678298668935895,
-0.055654797703027725,
0.025859801098704338,
-0.037707649171352386,
-0.018581710755825043,
0.11197765171527863,
-0.022470325231552124,
0.014955406077206135,
-0.00674011604860425,
-0.060957249253988266,
0.03502008691430092,
0.043335460126399994,
-0.05123848468065262,
0.0024754961486905813,
-0.03459713235497475,
-0.04746619984507561,
-0.022130832076072693,
0.0751931220293045,
0.000007193567853391869,
0.020723789930343628,
0.026832634583115578,
0.029962603002786636,
-0.03490595147013664,
0.028175143525004387,
-0.0029155327938497066,
0.002975692041218281,
0.011942828074097633,
0.0253430288285017,
0.003932042978703976,
0.04556938633322716,
-0.030917009338736534,
-0.0006538335001096129,
0.005725023802369833,
0.02036965638399124,
-0.06493066251277924,
-0.02919922210276127,
0.05914278328418732,
0.0040589990094304085,
-0.04697937145829201,
0.032563310116529465,
0.04209285229444504,
0.007926087826490402,
0.03346460685133934,
-0.03308600187301636,
0.007652937434613705,
0.028637802228331566,
-0.06221231445670128,
-0.02957986295223236,
-0.005625708028674126,
-0.016226915642619133,
0.027266304939985275,
0.0470803864300251,
-0.013223678804934025,
0.04891134425997734,
0.016803231090307236,
0.012267102487385273,
0.017641251906752586,
0.016465140506625175,
0.04232628643512726,
0.0010416785953566432,
-0.00038433587178587914,
0.027007626369595528,
-0.05147610604763031,
0.02260418049991131,
0.044961653649806976,
0.016092123463749886,
-0.02245466783642769,
0.04270298033952713,
0.020468557253479958,
-0.0431705042719841,
0.029613537713885307,
-0.003447385272011161,
0.034424085170030594,
0.026286112144589424,
0.05554952099919319,
-0.010971133597195148,
-0.00011525850277394056,
-0.01471000351011753,
0.0038890899159014225,
-0.034840039908885956,
-0.03441125154495239,
-0.010887510143220425,
0.04406438395380974,
0.007431056350469589,
0.011681362986564636,
0.04475724324584007,
0.029390044510364532,
0.038631077855825424,
-0.0038933721370995045,
0.015744345262646675,
-0.026575187221169472,
-0.07219034433364868,
0.014796234667301178,
-0.03680288419127464,
-0.03179018199443817,
-0.05756356567144394,
0.00532190129160881,
0.030184432864189148,
-0.09885254502296448,
0.016445957124233246,
0.05818590149283409,
-0.035977065563201904,
-0.06036592647433281,
0.017548365518450737,
0.033240191638469696,
0.024906449019908905,
0.019910195842385292,
-0.038346175104379654,
0.02124117687344551,
0.050109151750802994,
-0.0648355484008789,
-0.001502889208495617,
0.00008844473632052541,
-0.025657393038272858,
-0.00668266462162137,
0.04219699651002884,
0.04348181188106537,
-0.012639527209103107,
-0.004569308366626501,
0.020754503086209297,
0.022952772676944733,
-0.011426020413637161,
-0.015312223695218563,
-0.04722457006573677,
-0.016163239255547523,
0.029477771371603012,
-0.033619239926338196,
0.020391354337334633,
-0.07900518923997879,
-0.046519920229911804,
-0.025986818596720695,
0.022552167996764183,
0.04880159720778465,
0.015868792310357094,
0.051360249519348145,
-0.05499916151165962,
-0.03350815549492836,
0.019218670204281807,
-0.003963030409067869,
0.0052425493486225605,
0.022249160334467888,
0.005334520246833563,
0.03575076162815094,
-0.030845260247588158,
0.0555100217461586,
-0.08378475159406662,
0.0418451651930809,
0.020151561126112938,
0.0360562689602375,
-0.00145665742456913,
0.028614845126867294,
-0.008187299594283104,
0.010162699967622757,
-0.022155480459332466,
-0.03407464921474457,
0.0667731910943985,
-0.009989061392843723,
-0.0033566418569535017,
-0.02563604712486267,
0.03977399319410324,
0.03471418842673302,
0.036345575004816055,
0.012490084394812584,
0.038042884320020676,
0.025424089282751083,
-0.020704885944724083,
0.04435725510120392,
0.034301042556762695,
-0.024096060544252396,
-0.03550007566809654,
-0.04790017753839493,
0.03585467487573624,
0.0691467747092247,
-0.03901094198226929,
-0.02098790369927883,
-0.003996151965111494,
-0.008863108232617378,
0.02954910509288311,
-0.03139311820268631,
0.01596888154745102,
-0.04331737384200096,
-0.012997729703783989,
0.026907505467534065,
-0.04756927490234375,
0.0011188804637640715,
-0.02935236506164074,
0.04119325429201126,
0.031118003651499748,
-0.003376907901838422,
0.03311184421181679,
-0.04829993471503258,
0.03553410619497299,
-0.04440021887421608,
0.004243985749781132,
0.03791498392820358,
-0.024977298453450203,
0.013414561748504639,
0.017533548176288605,
-0.05601369962096214,
-0.029092170298099518,
0.0403914637863636,
0.07907360047101974,
-0.02910435013473034,
-0.006966543849557638,
0.02676030993461609,
0.0019115739269182086,
0.016542106866836548,
-0.01398277934640646,
-0.00809583067893982,
-0.028915926814079285,
-0.04599212855100632,
-0.03931248188018799,
-0.06049508973956108,
-0.00542069785296917,
-0.01834355667233467,
0.021660959348082542,
-0.0163239948451519,
-0.009486810304224491,
0.03541713207960129,
0.04057715833187103,
0.13738033175468445,
0.04017002880573273,
0.006966697983443737,
0.04342162236571312,
-0.01120973750948906,
-0.045323461294174194,
-0.013385741971433163,
-0.010521200485527515,
-0.0025167022831737995,
-0.05894576385617256,
0.015866003930568695,
0.009561811573803425,
-0.01571895368397236,
0.035407453775405884,
0.054569993168115616,
-0.041558392345905304,
-0.04078999161720276,
-0.08111465722322464,
0.011228682473301888,
0.01686732843518257,
-0.021441355347633362,
0.054357923567295074,
-0.03370749205350876,
0.001955202780663967,
-0.017588812857866287,
-0.05474863946437836,
-0.005109735764563084,
-0.006832602899521589,
-0.04892617464065552,
-0.010863573290407658,
-0.029002487659454346,
-0.036011405289173126,
0.018476663157343864,
0.07770563662052155,
0.06744975596666336,
-0.01509944349527359,
-0.008117498829960823,
0.01597680151462555,
0.009926220402121544,
0.01909060962498188,
-0.03501651808619499,
-0.0609084777534008,
0.004090878181159496,
-0.05761559680104256,
-0.020035548135638237,
0.047813672572374344,
0.08297894150018692,
0.01420926209539175,
0.007705477066338062,
-0.0027197187300771475,
0.07774922996759415,
-0.024526558816432953,
0.011831407435238361,
0.02633497305214405,
0.03622925654053688,
0.017524221912026405,
0.07055886089801788,
0.07454279065132141,
-0.0124312499538064,
-0.03983362391591072,
0.033652447164058685,
0.03547453135251999,
0.001716600963845849,
-0.014899425208568573,
-0.016657324507832527,
-0.005660959519445896,
-0.009026496671140194,
0.0038481703959405422,
0.04246331751346588,
0.0466097816824913,
0.0022772331722080708,
-0.06280087679624557,
0.011639426462352276,
-0.007541321683675051,
-0.049098093062639236,
-0.03264079615473747,
0.08345349878072739,
0.024151017889380455,
0.03358288109302521,
0.07583735138177872,
-0.02377111092209816,
-0.018288899213075638,
-0.05796413496136665,
-0.003261617384850979,
-0.09473657608032227,
0.023072900250554085,
-0.017174892127513885,
-0.041741520166397095,
-0.0072110197506845,
-0.010356433689594269,
-0.05133560299873352,
-0.021481623873114586,
0.07141678780317307,
-0.0019333182135596871,
0.005409969482570887,
-0.021145114675164223,
-0.019058117642998695,
-0.030027752742171288,
-0.006471505854278803,
-0.05737103521823883,
-0.0206052977591753,
0.05354885384440422,
-0.03140624240040779,
-0.0029528045561164618,
-0.005137624219059944,
-0.05892138555645943,
0.038924336433410645,
-0.04943959787487984,
0.0186606477946043,
0.035081714391708374,
0.029937785118818283,
-0.015319199301302433,
-0.0022091304417699575,
0.033098820596933365,
0.0062277186661958694,
0.017452988773584366,
0.03978455066680908,
0.016222747042775154,
-0.010130658745765686,
0.03662683814764023,
0.008570007048547268,
0.027293266728520393,
-0.01862393692135811,
0.025516416877508163,
-0.034267276525497437,
0.021854888647794724,
0.01666918583214283,
0.01708996295928955,
0.01980193518102169,
0.05360835790634155,
-0.028072040528059006,
-0.022066665813326836,
-0.016653243452310562,
0.0831679105758667,
-0.007152550853788853,
0.014504176564514637,
0.005431605968624353,
-0.08975014835596085,
-0.030278902500867844,
-0.05266299843788147,
0.001992604462429881,
0.03791114687919617,
0.007263693958520889,
0.040218476206064224,
0.008537054993212223,
-0.007767491973936558,
0.041401807218790054,
-0.01871170476078987,
0.014548344537615776,
-0.0003830059140454978,
-0.013153423555195332,
-0.021846946328878403,
-0.016432063654065132,
-0.027592597529292107,
0.02755628153681755,
0.04071856662631035,
-0.042314328253269196,
-0.005876433104276657,
0.03339588642120361,
-0.020127778872847557,
0.035465069115161896,
0.004650721792131662,
-0.0686480700969696,
-0.0015887761255726218,
-0.01300755050033331,
-0.033844880759716034,
0.041473355144262314,
0.011148106306791306,
-0.0449698381125927,
0.04393279552459717,
-0.0200070571154356,
-0.014436355791985989,
0.018269583582878113,
-0.010810473933815956,
-0.0516301691532135,
0.06563044339418411,
0.020182689651846886,
0.06324615329504013,
-0.04756563529372215,
0.008269120939075947,
-0.013599229045212269,
-0.03629814460873604,
0.05020255222916603,
0.00770929642021656,
0.004488438833504915,
-0.005947625730186701,
-0.02558067999780178,
0.02059747278690338,
0.0020384532399475574,
-0.017025208100676537,
-0.07990152388811111,
0.05758092179894447,
0.042866628617048264,
0.04232821613550186,
-0.013596988283097744,
-0.04377810284495354,
-0.005396517459303141,
0.02697434090077877,
-0.01854044385254383,
0.022526225075125694,
0.05450290068984032,
0.042248886078596115,
0.009984412230551243,
0.01747097633779049,
0.0038677954580634832,
0.04978133738040924,
0.05674230307340622,
-0.011893035843968391,
-0.0491885207593441,
0.001088094781152904,
-0.017969729378819466,
0.026539405807852745,
0.001234514289535582,
0.059538789093494415,
-0.014293978922069073,
0.07971953600645065,
-0.011783132329583168,
-0.06162184476852417,
0.0018605777295306325,
0.0726434737443924,
0.04503908380866051,
0.04356564208865166,
-0.038407959043979645,
-0.030360326170921326,
0.023645369336009026,
0.013004436157643795,
0.026839112862944603,
-0.006806198973208666,
0.014254875481128693,
0.0047501311637461185,
0.020991602912545204,
0.021583316847682,
0.011741709895431995,
0.016666216775774956,
-0.023499932140111923,
-0.017673250287771225,
-0.05929002910852432,
0.02585023269057274,
-0.045717716217041016,
-0.0013206833973526955,
0.04770870879292488,
0.007862524129450321,
-0.007212425582110882,
-0.03080974891781807,
-0.03133676201105118,
0.04371935874223709,
0.035914745181798935,
0.013375917449593544,
-0.0037429952062666416,
0.01089023519307375,
0.011989621445536613,
-0.02771240472793579,
0.020274583250284195,
0.023952901363372803,
0.01269233226776123,
-0.019152384251356125,
-0.07115045189857483,
0.011501464992761612,
-0.007393885403871536,
0.03314080461859703,
-0.010391633957624435,
-0.01725507527589798,
0.02217807248234749,
0.01708686165511608,
0.0060837301425635815,
0.007221913430839777,
0.008313595317304134,
0.011923466809093952,
-0.042839787900447845,
-0.01715284027159214,
-0.011599565856158733,
0.016437293961644173,
0.02552151493728161,
0.06125480309128761,
0.035551950335502625,
0.022967465221881866,
-0.02964823506772518,
-0.001604726305231452,
-0.00939091108739376,
-0.10918359458446503,
0.03196302801370621,
0.003107552882283926,
-0.02610183320939541,
0.023647993803024292,
-0.017376232892274857,
-0.06343946605920792,
0.07736674696207047,
-0.02985839918255806,
-0.07337832450866699,
0.03191635385155678,
-0.029074573889374733,
0.00576033117249608,
-0.012859608978033066,
-0.04553094506263733,
-0.021122602745890617,
0.019934052601456642,
-0.03744062781333923,
-0.03733519837260246,
0.007055947091430426,
-0.014681771397590637,
0.03818371146917343,
-0.03477100655436516,
-0.003353774780407548,
0.025130700320005417,
0.013313994742929935,
0.011077499948441982,
-0.03952837362885475,
-0.12017040699720383,
0.023462528362870216,
-0.012964845634996891,
-0.028558576479554176,
0.004483239725232124,
0.012800960801541805,
0.010641119442880154,
-0.08599452674388885,
0.018530331552028656,
0.009313981048762798,
0.019438713788986206,
-0.052945300936698914,
-0.038525182753801346,
0.016180753707885742,
0.04226987063884735,
0.03446570038795471,
-0.05040033161640167,
-0.013985758647322655,
0.02206340804696083,
-0.07399759441614151,
-0.033301327377557755,
-0.013237394392490387,
-0.0016921429196372628,
0.021212883293628693,
0.0024714567698538303,
-0.018452223390340805,
-0.02444359101355076,
0.04488004371523857,
-0.020120088011026382,
-0.031182534992694855,
0.017861375585198402,
-0.06726675480604172,
-0.011632198467850685,
-0.05214262753725052,
0.0165850892663002,
0.026855280622839928,
-0.036712463945150375,
-0.02257860079407692,
-0.024731826037168503,
0.02056899294257164,
0.006679442711174488,
-0.02205314114689827,
0.08425795286893845,
0.03900984674692154,
-0.026863738894462585,
0.00522649148479104,
-0.025231139734387398,
-0.04780299589037895,
-0.024176403880119324,
-0.008548206649720669,
0.02542852982878685,
0.011705386452376842,
-0.0008534492226317525,
-0.07406982779502869,
0.060440316796302795,
-0.027213601395487785,
0.06269606947898865,
-0.005098891910165548,
0.01992020756006241,
0.04858466610312462,
0.04068954288959503,
-0.0027245215605944395,
0.03213170915842056,
0.022478608414530754,
0.015718912705779076,
0.0074298628605902195,
-0.02302704006433487,
0.0014013281324878335,
-0.015242057852447033,
-0.07122091948986053,
0.09581449627876282,
-0.04558780789375305,
0.020183702930808067,
-0.0767025426030159,
-0.018943220376968384,
-0.05318967625498772,
-0.0011920960387215018,
-0.023772677406668663,
-0.0031458756420761347,
0.05025814101099968,
-0.02304130233824253,
-0.03881552442908287,
0.015287416987121105,
0.07748894393444061,
-0.02257309854030609,
-0.011959617026150227,
-0.04287384822964668,
-0.008377127349376678,
-0.018345437943935394,
-0.017368441447615623,
-0.05792735517024994,
0.02786852791905403,
-0.010177802294492722,
0.08116460591554642,
0.009935062378644943,
-0.0029127171728760004,
-0.026327265426516533,
0.010555441491305828,
0.04291417822241783,
0.03449827432632446,
0.019931789487600327,
0.005712053272873163,
-0.03314013034105301,
0.05233430862426758,
0.10783855617046356,
0.041002970188856125,
-0.012874999083578587,
0.08159559220075607,
-0.021380307152867317,
-0.05636211484670639,
0.05218552052974701,
-0.07422053068876266,
0.018940087407827377,
0.014908796176314354,
0.00135632767342031,
0.030563851818442345,
0.015208748169243336,
-0.01771395653486252,
-0.023397665470838547,
-0.00032906667911447585,
0.019338764250278473,
-0.0017971994820982218,
0.015405520796775818,
0.0689866691827774,
-0.02236894518136978,
0.011230423115193844,
0.0014075968647375703,
-0.04092225804924965,
-0.012133807875216007,
0.0052278367802500725,
-0.024415982887148857,
0.005836617201566696,
-0.024771368131041527,
-0.04441647231578827,
-0.022967075929045677,
-0.007719007320702076,
-0.01927686110138893,
-0.035778868943452835,
-0.0012333247577771544,
0.020299402996897697,
0.0072034988552331924,
-0.002402054611593485,
0.0048338850028812885,
-0.0405799001455307,
0.016244761645793915,
0.008456184528768063,
-0.0019180208910256624,
-0.06776386499404907,
0.022556275129318237,
0.002739415504038334,
-0.04850006476044655,
0.010924427770078182,
-0.0006257938221096992,
0.03802740201354027,
-0.024743586778640747,
-0.006013594102114439,
-0.03889288008213043,
0.020087014883756638,
-0.0015454578679054976,
-0.0370648130774498,
0.007875721901655197,
0.06244895979762077,
-0.019600605592131615,
-0.017320619896054268,
0.017811080440878868,
0.0015648831613361835,
0.021047579124569893,
0.003521277802065015,
0.05435718223452568,
-0.000923687475733459,
-0.0015014978125691414,
-0.05225663632154465,
0.01726982742547989,
-0.0011623003520071507,
0.05756378918886185,
0.00927466806024313,
-0.04292968660593033,
0.014817719347774982,
-0.04017457365989685,
-0.043151941150426865,
-0.025995537638664246,
-0.03293823078274727,
-0.00551991444081068,
0.0327787809073925,
-0.01810598559677601,
-0.023830659687519073,
-0.05739325284957886,
0.04394400492310524,
-0.03366503864526749,
-0.016636217013001442,
-0.05880797281861305,
-0.029232781380414963,
0.008260061033070087,
0.06165708974003792,
-0.00632871501147747,
-0.1294761598110199,
-0.011695604771375656,
-0.022999649867415428,
-0.0119343725964427,
-0.041779305785894394,
-0.058871299028396606,
0.021249912679195404,
0.027961477637290955,
0.014395018108189106,
-0.01901102438569069,
-0.0026024563703686,
0.0017585711320862174,
0.0004616566584445536,
0.027137579396367073,
0.026069462299346924,
0.02642633207142353,
0.076115682721138,
0.07491160929203033,
-0.03294694796204567,
0.022237127646803856,
0.0068063884973526,
-0.024640876799821854,
0.07677855342626572,
-0.03287153318524361,
0.014138130471110344,
-0.050985466688871384,
0.013200162909924984
] |
[
0.7816035747528076,
2.2413766384124756
] |
Algebraic Geometry
|
Mathematics
|
math-AG
|
math-CO
|
na
|
2007-04-01T06:22:38
|
Possible (algebraic) commutation relations in the Lagrangian quantum theory
of free (scalar, spinor and vector) fields are considered from mathematical
view-point. As sources of these relations are employed the Heisenberg
equations/relations for the dynamical variables and a specific condition for
uniqueness of the operators of the dynamical variables (with respect to some
class of Lagrangians). The paracommutation relations or some their
generalizations are pointed as the most general ones that entail the validity
of all Heisenberg equations. The simultaneous fulfillment of the Heisenberg
equations and the uniqueness requirement turn to be impossible. This problem is
solved via a redefinition of the dynamical variables, similar to the normal
ordering procedure and containing it as a special case. That implies
corresponding changes in the admissible commutation relations. The introduction
of the concept of the vacuum makes narrow the class of the possible commutation
relations; in particular, the mentioned redefinition of the dynamical variables
is reduced to normal ordering. As a last restriction on that class is imposed
the requirement for existing of an effective procedure for calculating vacuum
mean values. The standard bilinear commutation relations are pointed as the
only known ones that satisfy all of the mentioned conditions and do not
contradict to the existing data.
|
Lagrangian quantum field theory in momentum picture. IV. Commutation
relations for free fields
|
hep-th
|
0704.0066
| 2,007
|
[
-0.0022582404781132936,
0.02178623154759407,
-0.004517121706157923,
-0.011732121929526329,
0.007713682949542999,
0.03812112286686897,
0.04184554144740105,
0.026831315830349922,
-0.0300617516040802,
0.015607239678502083,
-0.06080746650695801,
0.02175785042345524,
0.015991711989045143,
0.016387764364480972,
-0.0034588235430419445,
-0.01940062642097473,
0.042159922420978546,
0.007801203988492489,
-0.0038827008102089167,
-0.060138046741485596,
0.0032471015583723783,
-0.028574157506227493,
-0.016765620559453964,
-0.027096007019281387,
0.06848908960819244,
-0.010667350143194199,
0.018492693081498146,
-0.02098674885928631,
-0.020624741911888123,
-0.021021418273448944,
0.05616235360503197,
0.015659375116229057,
0.011052188463509083,
-0.0545232854783535,
-0.052516594529151917,
-0.06307800859212875,
0.0831056758761406,
0.04611498489975929,
0.01959429308772087,
0.052886974066495895,
0.016089539974927902,
-0.023863015696406364,
0.016022058203816414,
-0.011014144867658615,
0.010347627103328705,
0.020104484632611275,
0.016123108565807343,
-0.041897039860486984,
0.02365848235785961,
-0.02662908099591732,
0.020879622548818588,
0.025208719074726105,
-0.00791084673255682,
-0.05117078870534897,
-0.016977723687887192,
0.06200714036822319,
0.03246891498565674,
-0.01661982201039791,
0.04114476591348648,
0.014278768561780453,
-0.005351080093532801,
0.004888130817562342,
-0.017176588997244835,
0.014392262324690819,
0.03764442726969719,
-0.07062340527772903,
-0.04064061865210533,
0.020425401628017426,
-0.04848771542310715,
-0.022711284458637238,
0.03062029741704464,
-0.04364722594618797,
0.03318490460515022,
0.016795465722680092,
-0.01273793913424015,
0.0014395227190107107,
-0.009827892296016216,
-0.012195871211588383,
0.04290338233113289,
-0.05859073996543884,
-0.02821185812354088,
-0.03205093368887901,
0.06679132580757141,
0.02858828939497471,
0.0921579897403717,
-0.05270487442612648,
0.01822737045586109,
0.028258811682462692,
-0.02281372621655464,
0.03047695942223072,
0.009288405999541283,
0.0054038288071751595,
0.08252748847007751,
0.07665146142244339,
-0.06710202991962433,
0.02258438430726528,
0.009378468617796898,
0.04652296006679535,
-0.022784972563385963,
-0.05513797700405121,
-0.03678502142429352,
0.09671390056610107,
0.05791522562503815,
0.008929544128477573,
0.05061119422316551,
-0.0035336001310497522,
0.03406444936990738,
-0.0021953785326331854,
-0.043206892907619476,
-0.022372093051671982,
-0.08287177234888077,
0.020793644711375237,
-0.012442553415894508,
-0.004466302692890167,
-0.05606413260102272,
-0.02728566899895668,
0.055025212466716766,
-0.09022083878517151,
0.0009474524995312095,
0.038193441927433014,
0.0014831898733973503,
0.006683101411908865,
-0.003708023577928543,
0.01427215151488781,
0.010051034390926361,
0.027843955904245377,
-0.08121182024478912,
-0.04427149146795273,
0.02663911134004593,
-0.006415579933673143,
0.02109852060675621,
-0.011131097562611103,
-0.049299221485853195,
0.05857330560684204,
0.004872323479503393,
0.008360322564840317,
0.007513626012951136,
-0.0395471528172493,
0.051758360117673874,
-0.055149391293525696,
0.061755962669849396,
-0.00969616323709488,
0.010296272113919258,
-0.0374111644923687,
0.03413502126932144,
-0.06765186041593552,
0.07996294647455215,
-0.08765572309494019,
-0.0056594368070364,
-0.02086728997528553,
0.04793150722980499,
0.0374823734164238,
-0.005643943790346384,
0.03290379047393799,
-0.023619620129466057,
-0.04272254928946495,
-0.03016897477209568,
0.01322153303772211,
0.07038979232311249,
-0.004713104572147131,
0.012673464603722095,
-0.025969017297029495,
0.0004598592931870371,
0.02777940034866333,
-0.01981421932578087,
0.0022179889492690563,
0.060520801693201065,
0.005865020677447319,
-0.01323046162724495,
0.007787235081195831,
-0.05827973783016205,
-0.02574726566672325,
-0.038690295070409775,
-0.029581474140286446,
0.041868507862091064,
0.02063404768705368,
-0.023974671959877014,
-0.05713093280792236,
-0.02221319079399109,
0.05486554279923439,
0.006460804492235184,
-0.03733297809958458,
0.048899341374635696,
0.00792550016194582,
0.01108976174145937,
0.03389233723282814,
0.017650717869400978,
0.02802031859755516,
-0.06268315017223358,
-0.03330443426966667,
0.01394506823271513,
0.046919647604227066,
-0.06343147903680801,
-0.042766157537698746,
-0.05777939409017563,
0.007065112702548504,
0.057133615016937256,
0.004016906023025513,
-0.0249234139919281,
-0.0426771305501461,
-0.02032540924847126,
0.006203656084835529,
-0.081610307097435,
0.04746553674340248,
-0.01977529004216194,
0.04323798790574074,
0.03405221924185753,
0.04459724202752113,
0.03754608333110809,
-0.011395040899515152,
0.06759632378816605,
-0.010357623919844627,
0.018125014379620552,
0.06753650307655334,
-0.030644241720438004,
-0.010716783814132214,
0.025409819558262825,
-0.022645359858870506,
-0.021348025649785995,
0.06163027137517929,
0.011449490673840046,
-0.018419204279780388,
0.03829032927751541,
-0.011941961944103241,
0.06442088633775711,
0.03641713783144951,
-0.00660666823387146,
-0.03212444856762886,
-0.03726082667708397,
-0.016690898686647415,
-0.006025355309247971,
-0.06419436633586884,
0.024314777925610542,
0.0007510629366151989,
0.023688919842243195,
0.005447664763778448,
0.019608469679951668,
0.05099499225616455,
0.08523476868867874,
0.07789839059114456,
0.0594642199575901,
0.020329540595412254,
0.051736459136009216,
-0.01755201257765293,
-0.012104359455406666,
0.01889720931649208,
0.041699182242155075,
-0.01645348034799099,
-0.03614462539553642,
0.023210864514112473,
-0.0007653625216335058,
-0.015724636614322662,
-0.0035905989352613688,
0.047740545123815536,
-0.004790195729583502,
-0.04142706096172333,
-0.03376295790076256,
0.01969677209854126,
-0.020857805386185646,
-0.03735161945223808,
0.04990505427122116,
-0.06055459752678871,
-0.023685449734330177,
0.03136841580271721,
-0.07108866423368454,
-0.0014629393117502332,
-0.008124168962240219,
-0.0249667726457119,
0.0019589087460190058,
-0.04481583833694458,
-0.05210816115140915,
0.038279760628938675,
0.038700126111507416,
0.06080414354801178,
0.0036882224958389997,
-0.054355982691049576,
0.017015976831316948,
-0.0689675360918045,
-0.023371880874037743,
-0.05011904239654541,
-0.03837403655052185,
-0.002346581779420376,
-0.04958194121718407,
0.009876301512122154,
0.004832449369132519,
0.017926901578903198,
0.034908633679151535,
-0.025168590247631073,
-0.0004538575012702495,
0.04715712368488312,
0.015838978812098503,
0.02724490314722061,
0.001966472715139389,
0.03430892154574394,
0.0018634697189554572,
0.07319612801074982,
0.055992163717746735,
-0.027184192091226578,
-0.02150104194879532,
0.038487330079078674,
-0.011022687889635563,
0.011958564631640911,
0.015674762427806854,
0.03652072325348854,
0.02416820079088211,
0.001645954791456461,
-0.009275354444980621,
0.019375627860426903,
0.02981990948319435,
-0.005905108526349068,
-0.03987272456288338,
0.012705596163868904,
-0.025332769379019737,
-0.04408160597085953,
-0.0252432469278574,
-0.002082036342471838,
0.011906662955880165,
0.010200245305895805,
0.0792073979973793,
-0.015850625932216644,
-0.025490254163742065,
-0.05377773568034172,
0.017910588532686234,
-0.07058898359537125,
0.023685922846198082,
0.07056843489408493,
-0.019376635551452637,
0.026561154052615166,
-0.04721829295158386,
-0.013928334228694439,
-0.022008782252669334,
0.0524069182574749,
-0.016435150057077408,
-0.021730808541178703,
-0.027465470135211945,
-0.007467327639460564,
-0.00579298147931695,
0.021838484331965446,
-0.014018206857144833,
-0.04195060580968857,
0.03941531479358673,
-0.03464299440383911,
-0.07350622117519379,
0.01008624117821455,
-0.017828408628702164,
-0.011859248392283916,
-0.0336388424038887,
-0.011091799475252628,
0.0335017591714859,
0.005871984176337719,
-0.06906019151210785,
0.0010878096800297499,
0.02604086510837078,
0.0012315759668126702,
-0.030718453228473663,
0.04127312824130058,
0.05331381410360336,
-0.013700755313038826,
0.048545289784669876,
0.02441781759262085,
-0.00261335214599967,
-0.03677257150411606,
0.04583941400051117,
0.00880703330039978,
0.0010103312088176608,
0.025922739878296852,
-0.0043931566178798676,
0.011658117175102234,
0.008226613514125347,
-0.0651089996099472,
-0.05366945266723633,
-0.06536270678043365,
0.015619112178683281,
0.009657096117734909,
0.01453128457069397,
0.0052644358947873116,
0.007462468463927507,
0.032825008034706116,
-0.03394043445587158,
-0.0001710138749331236,
0.09074463695287704,
0.035178638994693756,
0.027423573657870293,
0.026471327990293503,
0.016974564641714096,
0.027379103004932404,
-0.03907652944326401,
0.059269726276397705,
-0.0585138201713562,
-0.04115445166826248,
-0.010229486972093582,
-0.03537885844707489,
-0.040396902710199356,
0.029053065925836563,
0.030679330229759216,
-0.010402093641459942,
0.03642470762133598,
-0.004078209400177002,
0.017174871638417244,
-0.0045066880993545055,
-0.034538283944129944,
-0.07773089408874512,
0.03758268430829048,
0.006165749859064817,
-0.026102472096681595,
0.022609060630202293,
0.01319513376802206,
-0.021379034966230392,
0.04515808820724487,
-0.011053934693336487,
-0.03244746848940849,
0.028929250314831734,
-0.020442362874746323,
-0.06626013666391373,
0.02373836375772953,
-0.020447595044970512,
-0.013304096646606922,
-0.025214340537786484,
0.007398328278213739,
-0.03114546462893486,
0.01647571474313736,
0.00704504270106554,
0.06958253681659698,
-0.0143943065777421,
-0.001194202690385282,
0.008982460014522076,
0.0153929702937603,
0.02525518834590912,
-0.020947162061929703,
-0.09292512387037277,
-0.0026143596041947603,
0.02246478758752346,
0.00646505830809474,
0.018921032547950745,
-0.06861108541488647,
-0.016297467052936554,
-0.023238973692059517,
0.01044019777327776,
0.011789077892899513,
0.028607742860913277,
0.06564817577600479,
-0.007887516170740128,
0.05002550780773163,
-0.03190188109874725,
0.011087330989539623,
0.07917184382677078,
0.07557225972414017,
-0.019873909652233124,
-0.013400916010141373,
-0.02180297113955021,
0.06851181387901306,
0.049382735043764114,
-0.003137056017294526,
0.01804359443485737,
0.06449718028306961,
-0.04783586785197258,
-0.009896357543766499,
-0.002253746846690774,
0.028347693383693695,
0.0444800890982151,
-0.008707545697689056,
0.01721404865384102,
-0.005145134404301643,
0.01233973354101181,
0.02359342761337757,
-0.006836341228336096,
-0.05972066894173622,
0.03791302442550659,
-0.03541618585586548,
0.02541642263531685,
0.02630210854113102,
-0.009550836868584156,
0.003816568059846759,
0.007336036302149296,
-0.06363500654697418,
-0.010825690813362598,
0.008154959417879581,
-0.03633573278784752,
-0.009717924520373344,
0.00971964467316866,
-0.010403517633676529,
-0.012227234430611134,
-0.004303457215428352,
0.008421056903898716,
-0.014438501559197903,
0.05011497437953949,
0.011780830100178719,
-0.004851372912526131,
-0.004219758789986372,
-0.0163874551653862,
0.02390941046178341,
0.03643416613340378,
-0.012975367717444897,
0.025464704260230064,
-0.05478055030107498,
-0.03364001214504242,
-0.025377973914146423,
-0.02083437889814377,
0.032807063311338425,
-0.014639084227383137,
-0.0454762764275074,
0.034538235515356064,
0.04291822016239166,
-0.0017720791511237621,
-0.023139646276831627,
0.012253697030246258,
-0.0006224686512723565,
-0.03706187382340431,
-0.02099408209323883,
0.0030632170382887125,
0.014570750296115875,
0.025040116161108017,
0.06356775760650635,
0.07806038856506348,
0.025022119283676147,
-0.051446475088596344,
0.05482938513159752,
-0.04798746481537819,
-0.05888332799077034,
-0.036068737506866455,
0.00725457351654768,
-0.02384021133184433,
0.05641189217567444,
-0.015837399289011955,
-0.0881119892001152,
0.0335875079035759,
-0.04208468273282051,
-0.05645035207271576,
0.028059860691428185,
-0.028957759961485863,
-0.026791298761963844,
0.02842043898999691,
0.015919478610157967,
-0.03794905170798302,
0.008332408964633942,
-0.07599854469299316,
-0.02018369734287262,
0.033745069056749344,
-0.00881124846637249,
0.06897002458572388,
-0.019804809242486954,
-0.019015280529856682,
-0.010409004054963589,
-0.008380720391869545,
0.07379157841205597,
-0.009188749827444553,
-0.07560911029577255,
0.019268780946731567,
-0.020226098597049713,
-0.06298956274986267,
-0.021612195298075676,
-0.039204396307468414,
-0.005474041681736708,
-0.0607379786670208,
0.022968683391809464,
-0.03562942519783974,
-0.020713936537504196,
-0.017231393605470657,
-0.06302656978368759,
0.04249336197972298,
0.018339848145842552,
0.01783173717558384,
0.03937593102455139,
-0.0318157784640789,
-0.025764426216483116,
-0.033722173422575,
-0.005157043691724539,
-0.03036319464445114,
0.025647832080721855,
0.006742970552295446,
-0.014137172140181065,
-0.01325950212776661,
-0.05217021331191063,
0.04427339881658554,
0.018209360539913177,
-0.035202447324991226,
0.044907066971063614,
-0.028162581846117973,
-0.08546414971351624,
-0.00825560837984085,
-0.043104011565446854,
-0.04611871391534805,
-0.010777946561574936,
-0.08115338534116745,
-0.0727018490433693,
0.026397382840514183,
-0.0005496456287801266,
-0.030459659174084663,
0.020484551787376404,
0.02605578675866127,
-0.003928782884031534,
0.011562648229300976,
-0.010082979686558247,
-0.009535020217299461,
0.009226914495229721,
0.04137909412384033,
0.0035901169758290052,
-0.03009745478630066,
-0.035842590034008026,
-0.025623690336942673,
0.04965507611632347,
-0.006607167888432741,
0.054811615496873856,
-0.013340207748115063,
0.0063812825828790665,
0.11408243328332901,
-0.017140647396445274,
0.07044797390699387,
-0.04655740037560463,
-0.019460882991552353,
-0.0021814315114170313,
-0.016355836763978004,
-0.03443651646375656,
-0.011642398312687874,
0.0066281938925385475,
-0.016132516786456108,
0.06934009492397308,
0.023385871201753616,
-0.0035516968928277493,
0.011330471374094486,
-0.001522905775345862,
-0.04941399767994881,
-0.024857789278030396,
-0.013180875219404697,
-0.015624966472387314,
0.0498369000852108,
-0.01205324474722147,
-0.017886528745293617,
0.034370921552181244,
0.05198533087968826,
0.02505396492779255,
-0.004720405209809542,
-0.024309171363711357,
-0.040940333157777786,
0.014370481483638287,
0.005607077851891518,
-0.04343096539378166,
0.028680358082056046,
0.004644280765205622,
0.05416765436530113,
0.02489158697426319,
-0.008744543418288231,
0.011472655460238457,
-0.033988192677497864,
0.005015021190047264,
0.053379323333501816,
0.020453518256545067,
-0.028565380722284317,
0.007900253869593143,
-0.005593876354396343,
0.0516183078289032,
0.07629550248384476,
0.006359415594488382,
0.06022479385137558,
-0.009826715104281902,
-0.007866468280553818,
0.06293990463018417,
-0.022214049473404884,
0.004030879121273756,
0.004653014242649078,
-0.01634128764271736,
0.008382764644920826,
-0.0070396605879068375,
-0.018431998789310455,
0.011376997455954552,
0.007969483733177185,
0.019972290843725204,
-0.03980640694499016,
0.04563866928219795,
0.0751020684838295,
-0.03651461750268936,
-0.05240297690033913,
-0.04479463770985603,
-0.033736806362867355,
-0.07666744291782379,
0.015255134552717209,
0.031031370162963867,
0.04667142406105995,
-0.03186478838324547,
-0.015736963599920273,
-0.003898759139701724,
0.042398370802402496,
0.003881205106154084,
0.018666254356503487,
-0.04220346361398697,
0.025351418182253838,
0.008144448511302471,
-0.0014331740094348788,
-0.011662294156849384,
-0.022113438695669174,
0.0035254028625786304,
-0.014777787029743195,
0.03397388383746147,
-0.0799131765961647,
0.0010823473567143083,
-0.005978166125714779,
-0.03497208282351494,
0.007056831382215023,
0.03730328753590584,
0.020276732742786407,
-0.025444727391004562,
-0.026371056213974953,
-0.08915317803621292,
0.010801771655678749,
-0.017541050910949707,
-0.05822475254535675,
0.029043160378932953,
0.03355356305837631,
-0.05137136951088905,
0.019020121544599533,
-0.014595805667340755,
-0.001033189008012414,
0.010745406150817871,
0.009069194085896015,
0.04189617559313774,
-0.006336380261927843,
-0.0069618383422493935,
-0.02584659866988659,
0.0015372256748378277,
-0.03631528466939926,
0.07221062481403351,
-0.010718033649027348,
-0.05319700762629509,
0.004709856119006872,
0.022172318771481514,
-0.050819285213947296,
0.008641041815280914,
-0.015830079093575478,
0.03635033220052719,
0.027618408203125,
-0.005535405594855547,
-0.03879980742931366,
-0.053096622228622437,
0.05341118201613426,
-0.019072387367486954,
0.00285927252843976,
-0.026775725185871124,
-0.004119975958019495,
-0.006003823131322861,
-0.011642491444945335,
-0.0007488919072784483,
-0.05548814311623573,
0.039384063333272934,
0.0034127256367355585,
0.0004804999043699354,
-0.022099360823631287,
-0.052894312888383865,
0.008358924649655819,
0.036454129964113235,
-0.02267785370349884,
-0.019703196361660957,
0.0018223318038508296,
-0.010580426082015038,
0.003585346043109894,
0.011034581810235977,
-0.0005798431811854243,
-0.014861016534268856,
0.04514575004577637,
0.09723378717899323,
-0.005138085223734379,
0.039759788662195206,
0.01794973760843277,
0.013911220245063305,
0.049117203801870346,
-0.02490612305700779,
-0.0018561589531600475,
-0.05743426829576492,
0.06396785378456116
] |
[
11.615487098693848,
1.0792583227157593
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-04-01T05:30:59
|
Epitaxial self-assembled quantum dots (SAQDs) are of interest for
nanostructured optoelectronic and electronic devices such as lasers,
photodetectors and nanoscale logic. Spatial order and size order of SAQDs are
important to the development of usable devices. It is likely that these two
types of order are strongly linked; thus, a study of spatial order will also
have strong implications for size order. Here a study of spatial order is
undertaken using a linear analysis of a commonly used model of SAQD formation
based on surface diffusion. Analytic formulas for film-height correlation
functions are found that characterize quantum dot spatial order and
corresponding correlation lengths that quantify order. Initial atomic-scale
random fluctuations result in relatively small correlation lengths (about two
dots) when the effect of a wetting potential is negligible; however, the
correlation lengths diverge when SAQDs are allowed to form at a near-critical
film height. The present work reinforces previous findings about anisotropy and
SAQD order and presents as explicit and transparent mechanism for ordering with
corresponding analytic equations. In addition, SAQD formation is by its nature
a stochastic process, and various mathematical aspects regarding statistical
analysis of SAQD formation and order are presented.
|
Order of Epitaxial Self-Assembled Quantum Dots: Linear Analysis
|
cond-mat.mtrl-sci
|
0704.0067
| 2,007
|
[
0.01452892180532217,
0.027363214641809464,
-0.01534523069858551,
-0.06599045544862747,
-0.0006083791377022862,
0.062323927879333496,
0.04860002547502518,
-0.01715284027159214,
-0.01017696037888527,
0.015555688180029392,
-0.029094718396663666,
0.047210972756147385,
0.05591721087694168,
0.007563343737274408,
-0.016397573053836823,
-0.02142729051411152,
0.009782503359019756,
0.0047212522476911545,
-0.005621735006570816,
0.01669815182685852,
-0.03121122345328331,
-0.01712753251194954,
-0.06429627537727356,
-0.04332086816430092,
0.07118582725524902,
0.00431825453415513,
-0.013602259568870068,
0.0009294286137446761,
-0.006300617009401321,
0.015269402414560318,
0.06368895620107651,
-0.017894668504595757,
0.01852700114250183,
-0.043777357786893845,
-0.043065350502729416,
-0.024089785292744637,
0.03950022906064987,
-0.029165754094719887,
-0.0013478242326527834,
0.045255132019519806,
0.023914193734526634,
-0.05622848495841026,
0.019676096737384796,
-0.08473068475723267,
0.01973426714539528,
-0.02586974762380123,
0.018270576372742653,
-0.004068530164659023,
0.07141122967004776,
-0.01560844387859106,
0.0043134684674441814,
0.10757462680339813,
0.019039276987314224,
-0.03764485940337181,
0.04722849279642105,
0.05146818980574608,
-0.0134506244212389,
0.008604202419519424,
0.07124977558851242,
0.03752250224351883,
0.026554370298981667,
0.0313941054046154,
-0.019077003002166748,
-0.0375247485935688,
0.05859658494591713,
-0.060421690344810486,
-0.00011868956789840013,
-0.001052031060680747,
-0.02610296569764614,
-0.01559032779186964,
0.014508718624711037,
-0.04944003000855446,
0.05271022021770477,
0.055961813777685165,
-0.006349417380988598,
0.012167342938482761,
-0.021410182118415833,
-0.015886984765529633,
-0.05238126963376999,
0.022119835019111633,
-0.013206487521529198,
-0.046917226165533066,
0.020112203434109688,
0.0484837107360363,
0.0654168576002121,
-0.004644848871976137,
0.03182532638311386,
-0.00043638964416459203,
-0.04834740236401558,
0.042227309197187424,
0.013837279751896858,
0.022586507722735405,
0.02879541739821434,
0.07358448952436447,
-0.03564777225255966,
0.025041133165359497,
-0.014849687926471233,
0.03527849167585373,
-0.02110813558101654,
-0.05471385642886162,
-0.010859918780624866,
0.02764289267361164,
0.013815968297421932,
0.001977951033040881,
0.003314197761937976,
0.0393143929541111,
-0.03836648538708687,
0.03949468210339546,
0.010617130436003208,
-0.016379429027438164,
-0.10958509892225266,
0.007305094040930271,
-0.015183879993855953,
0.008980721235275269,
0.03538253903388977,
-0.012144166976213455,
0.05710187554359436,
-0.05507199093699455,
-0.013193914666771889,
0.04661661759018898,
0.05099378898739815,
-0.002886628732085228,
-0.002070216229185462,
0.01747754216194153,
0.0033636747393757105,
0.03273394703865051,
-0.019595395773649216,
-0.011882530525326729,
0.0294359028339386,
0.04478210583329201,
0.02758602611720562,
0.008052993565797806,
-0.052316997200250626,
0.027815425768494606,
-0.014933096244931221,
0.05374690517783165,
-0.034436166286468506,
-0.05590081587433815,
0.022089708596467972,
-0.010925463400781155,
0.004201083909720182,
-0.016465675085783005,
-0.003935216926038265,
0.01035034004598856,
0.011894037015736103,
-0.06835662573575974,
0.05850512906908989,
-0.03787791356444359,
-0.039287541061639786,
-0.02986256405711174,
-0.006346804089844227,
-0.02681940235197544,
-0.04316458851099014,
-0.00854487530887127,
-0.025945909321308136,
-0.005971480160951614,
0.009314334951341152,
-0.020616566762328148,
0.07154092192649841,
-0.0163564532995224,
0.010659260675311089,
0.013619166798889637,
-0.024082379415631294,
0.05446173623204231,
-0.021467989310622215,
-0.030557308346033096,
0.05104183778166771,
0.015137006528675556,
0.019876716658473015,
0.02533579058945179,
-0.015375356189906597,
-0.025747325271368027,
-0.04029340669512749,
-0.01526925340294838,
-0.027725795283913612,
0.03076230362057686,
-0.0046882168389856815,
-0.0353400856256485,
0.031333062797784805,
0.0059997886419296265,
0.06810310482978821,
0.02461658976972103,
0.012740151956677437,
0.008024136535823345,
0.02610771730542183,
-0.036021724343299866,
0.03393039107322693,
-0.028096426278352737,
-0.014757531695067883,
0.008540223352611065,
0.025300495326519012,
-0.008154981769621372,
-0.08525211364030838,
-0.03607926145195961,
-0.021473873406648636,
-0.03349980339407921,
0.06815442442893982,
-0.013299655169248581,
0.0062992144376039505,
-0.0624566525220871,
-0.04841738939285278,
-0.004714459180831909,
-0.07025161385536194,
0.03353237733244896,
-0.0028094628360122442,
0.0395536869764328,
-0.0017522737616673112,
0.06346603482961655,
0.00752872321754694,
0.020683133974671364,
0.034891292452812195,
0.014925931580364704,
-0.008037214167416096,
-0.0005071945488452911,
0.019768111407756805,
-0.0013586304849013686,
0.03796359896659851,
-0.025235608220100403,
-0.048963721841573715,
0.040001433342695236,
0.019382916390895844,
-0.029312454164028168,
-0.003167808288708329,
-0.005881038494408131,
0.04807639867067337,
0.04700741916894913,
-0.02201765589416027,
0.0058166952803730965,
-0.03976457938551903,
-0.014031773433089256,
-0.05313410609960556,
-0.0519326776266098,
-0.016498496755957603,
0.011652907356619835,
-0.0140590975061059,
0.06050405278801918,
-0.05082429200410843,
0.013482527807354927,
0.038986798375844955,
0.04220603406429291,
0.021845625713467598,
0.014599629677832127,
0.016833482310175896,
0.00412916112691164,
-0.06299365311861038,
-0.013460667803883553,
-0.005063120741397142,
0.023228727281093597,
-0.05984409898519516,
0.05857197195291519,
0.03402230888605118,
-0.0004539154178928584,
0.026138603687286377,
0.027169207111001015,
0.02173789218068123,
-0.06262260675430298,
-0.06021350622177124,
0.04222308471798897,
-0.017501721158623695,
-0.07049176096916199,
0.002052594907581806,
-0.025143494829535484,
0.012962360866367817,
-0.0551493763923645,
-0.02945350669324398,
0.009533196687698364,
-0.025322871282696724,
-0.019914252683520317,
0.03579263389110565,
-0.04020411893725395,
0.028319967910647392,
0.03747165575623512,
0.07381241023540497,
0.06848354637622833,
0.016207527369260788,
0.0268106572329998,
0.037456437945365906,
-0.01461876928806305,
-0.030174465849995613,
0.012660704553127289,
-0.05558903142809868,
0.026072589680552483,
-0.06012700870633125,
0.024933943524956703,
0.013446095399558544,
-0.003771458985283971,
0.11279306560754776,
-0.012733515352010727,
0.0026041059754788876,
0.039014700800180435,
-0.02338588424026966,
-0.021396616473793983,
-0.005698604974895716,
0.06197395175695419,
0.024076921865344048,
0.04725288972258568,
0.044591255486011505,
-0.03680982440710068,
-0.006253351923078299,
0.04460659250617027,
-0.017205860465765,
0.016702471300959587,
0.027953336015343666,
-0.01979735866189003,
0.02645043283700943,
0.05163569375872612,
0.01874304562807083,
-0.011293675750494003,
0.01025119423866272,
0.010247524827718735,
-0.041020456701517105,
0.0679096207022667,
0.012711556628346443,
-0.019180234521627426,
-0.009342726320028305,
0.025098681449890137,
0.03365828096866608,
0.006124814972281456,
0.08860456943511963,
0.033714909106492996,
-0.000247395655605942,
-0.019303755834698677,
-0.030084308236837387,
-0.04561135172843933,
0.005067832302302122,
0.020370032638311386,
0.026606038212776184,
0.04019377753138542,
0.008482709527015686,
0.025151198729872704,
0.02266230247914791,
0.0250275656580925,
0.0015817014500498772,
-0.02065119333565235,
-0.0005351189756765962,
-0.05071628838777542,
-0.04861054942011833,
0.01892298460006714,
-0.059423450380563736,
0.02320733107626438,
-0.0032100938260555267,
-0.023304862901568413,
-0.032841868698596954,
-0.04582864046096802,
-0.05282524973154068,
0.018471555784344673,
-0.004673896357417107,
0.011281255632638931,
0.016318943351507187,
-0.010717207565903664,
-0.058469850569963455,
-0.021030951291322708,
0.043964892625808716,
0.0025008555967360735,
-0.029746169224381447,
0.09348111599683762,
0.031664103269577026,
-0.028537265956401825,
0.09346288442611694,
-0.03392590954899788,
0.037995003163814545,
-0.03533201292157173,
0.041961148381233215,
-0.028804073110222816,
0.023881105706095695,
0.01794927380979061,
-0.0301181823015213,
0.028027886524796486,
0.03916328772902489,
-0.018390314653515816,
-0.08572643250226974,
-0.01975115016102791,
-0.03316868469119072,
0.00171181233599782,
0.03363348916172981,
0.0919310599565506,
-0.07054828107357025,
-0.005281355232000351,
-0.009143248200416565,
-0.030307089909911156,
0.04473130404949188,
0.012504521757364273,
0.014729290269315243,
-0.037711724638938904,
-0.006959178484976292,
0.03941544517874718,
-0.08373897522687912,
-0.05360668897628784,
-0.03535837680101395,
-0.0419389083981514,
-0.0287611223757267,
-0.06663738191127777,
-0.02247794345021248,
-0.026604564860463142,
-0.022812742739915848,
-0.050068967044353485,
0.08875676244497299,
0.03560028597712517,
0.062209516763687134,
-0.050094857811927795,
-0.04058941453695297,
-0.09841360151767731,
-0.015134960412979126,
-0.018122950568795204,
-0.00935445073992014,
-0.02836986817419529,
-0.016321972012519836,
-0.05533831566572189,
0.020467447116971016,
-0.029620304703712463,
-0.016313564032316208,
0.03610625118017197,
-0.028158504515886307,
-0.0608588270843029,
0.03166744112968445,
0.01506005134433508,
0.007701341062784195,
-0.009941404685378075,
-0.01941588707268238,
-0.0016489841509610415,
-0.0037662361282855272,
0.015632199123501778,
0.0787079781293869,
-0.013667243532836437,
-0.046441029757261276,
-0.005095131229609251,
0.009403442032635212,
0.05001826956868172,
-0.026127725839614868,
-0.03838037699460983,
-0.0044919876381754875,
0.009384975768625736,
0.02164517529308796,
0.020882150158286095,
-0.03238251805305481,
-0.02686433121562004,
0.03199794143438339,
0.03630563244223595,
0.004657546058297157,
0.015954675152897835,
0.03822772577404976,
-0.025875572115182877,
0.01614607870578766,
0.027018042281270027,
0.012778889387845993,
0.06762748956680298,
0.03102746792137623,
0.004551420919597149,
-0.06309835612773895,
-0.010494495742022991,
0.00964389555156231,
0.009730445221066475,
-0.0021183050703257322,
-0.04126329347491264,
0.07198615372180939,
-0.04719778522849083,
-0.02187405154109001,
0.016520626842975616,
0.06466946005821228,
0.040725983679294586,
-0.01694210059940815,
0.05181535705924034,
-0.05354695022106171,
0.03946729749441147,
0.023732485249638557,
-0.0354439951479435,
0.004952380899339914,
-0.019066210836172104,
0.0007709414348937571,
0.050814807415008545,
-0.03857874125242233,
0.008987145498394966,
0.05776860937476158,
0.03427927568554878,
-0.0319468230009079,
-0.025059368461370468,
0.0423043891787529,
-0.03080686926841736,
-0.026396891102194786,
-0.001713628531433642,
-0.006073209922760725,
-0.021853141486644745,
0.02781318500638008,
-0.02686752937734127,
0.035862334072589874,
0.029317671433091164,
0.006996606010943651,
0.016284452751278877,
0.0013867662055417895,
-0.008308345451951027,
-0.019169896841049194,
-0.011653413996100426,
-0.016287827864289284,
0.016568312421441078,
-0.04135197028517723,
-0.056814614683389664,
0.019426792860031128,
-0.013482270762324333,
0.043811772018671036,
0.0004661178681999445,
-0.01931515894830227,
0.030675632879137993,
-0.02919173613190651,
-0.02134193480014801,
0.010360786691308022,
0.027500411495566368,
-0.023854201659560204,
-0.07677419483661652,
0.02476334013044834,
-0.0032995562069118023,
-0.04837290942668915,
0.057094693183898926,
0.032966386526823044,
0.0030674173031002283,
0.0014678521547466516,
-0.02860247902572155,
0.040052369236946106,
-0.0005704424693249166,
-0.056079354137182236,
0.030056597664952278,
-0.01269592996686697,
-0.010473762638866901,
-0.039220910519361496,
0.004931410774588585,
-0.048651669174432755,
0.04897485300898552,
-0.0297146737575531,
-0.06626000255346298,
0.03396941348910332,
-0.027390332892537117,
-0.020198270678520203,
0.09997649490833282,
-0.041645485907793045,
-0.030995268374681473,
-0.014675582759082317,
-0.04932725802063942,
-0.00008048326708376408,
0.07266663759946823,
0.013626360334455967,
-0.00013242939894553274,
-0.00511166313663125,
0.023860109969973564,
-0.011935240589082241,
0.03049147129058838,
0.048636846244335175,
-0.058921489864587784,
-0.031014133244752884,
0.006105841137468815,
-0.011130665428936481,
-0.0523456372320652,
0.04420199617743492,
0.0000593001714150887,
0.014024296775460243,
-0.060330551117658615,
-0.0029645913746207952,
-0.011764287948608398,
-0.02232000045478344,
-0.05308254808187485,
-0.05667640641331673,
-0.032210782170295715,
0.042485736310482025,
0.026266325265169144,
0.031197501346468925,
0.010668321512639523,
-0.024948257952928543,
-0.06750546395778656,
0.01423380896449089,
0.027596302330493927,
-0.0011597078992053866,
0.030666707083582878,
0.020018063485622406,
-0.020552940666675568,
0.012748265638947487,
0.04330812394618988,
-0.01614377647638321,
-0.04668978974223137,
0.04279221594333649,
-0.0035866270773112774,
-0.0357799232006073,
-0.021362684667110443,
-0.04274902120232582,
0.08908654749393463,
-0.014935657382011414,
0.03221190720796585,
-0.044596023857593536,
-0.00695748720318079,
0.010752915404736996,
-0.03914343938231468,
0.05380561947822571,
-0.039334487169981,
-0.046459272503852844,
-0.027988867834210396,
0.020940573886036873,
-0.04861811175942421,
-0.01930452138185501,
-0.001167926238849759,
0.04628859832882881,
-0.021557478234171867,
-0.020331483334302902,
-0.011286566033959389,
-0.008301048539578915,
0.014466313645243645,
0.031519483774900436,
0.02495681308209896,
0.04876945540308952,
0.02344810590147972,
0.01583029516041279,
0.0550084263086319,
-0.04467366635799408,
0.015519173815846443,
0.027776651084423065,
0.005069454200565815,
-0.04913237318396568,
-0.0247164499014616,
0.019122090190649033,
-0.06173529848456383,
0.03678491711616516,
0.018704863265156746,
-0.0011064383434131742,
-0.01336025819182396,
0.001512901741079986,
-0.02584531530737877,
-0.06802642345428467,
-0.03719917684793472,
0.018285058438777924,
0.02153891697525978,
0.018732907250523567,
-0.08084462583065033,
0.010412936098873615,
0.06464026868343353,
-0.025858260691165924,
0.0182378888130188,
-0.014604303054511547,
0.013925516046583652,
0.02155935950577259,
0.030412688851356506,
-0.05869211256504059,
-0.01084810309112072,
0.0023835869506001472,
0.047775059938430786,
0.03882722184062004,
-0.01876898668706417,
0.03772900998592377,
0.005214901641011238,
0.050087008625268936,
0.057265955954790115,
0.009091823361814022,
0.04338601976633072,
0.020874211564660072,
-0.0037762760184705257,
0.05992242321372032,
0.0647115632891655,
-0.04561689868569374,
0.03795978054404259,
0.06911128759384155,
0.04363458603620529,
0.028967680409550667,
0.020377565175294876,
-0.028986841440200806,
-0.009076975286006927,
-0.04393329098820686,
-0.006448627449572086,
-0.015434772707521915,
-0.047758523374795914,
0.005010759457945824,
0.0018037937115877867,
-0.0060983686707913876,
-0.0054766652174293995,
-0.04229162260890007,
0.005743343383073807,
-0.0029476077761501074,
-0.03452789783477783,
-0.045873839408159256,
-0.01996771991252899,
-0.03888925909996033,
0.0394815094769001,
-0.004843368660658598,
0.020808907225728035,
-0.011380747891962528,
-0.018830595538020134,
-0.007347566541284323,
-0.009332501329481602,
-0.0008721209596842527,
-0.030875040218234062,
-0.030814187601208687,
0.04736108332872391,
-0.0600033737719059,
-0.000789688725490123,
-0.01421330589801073,
-0.050902411341667175,
0.02616928145289421,
-0.008024179376661777,
-0.08319730311632156,
-0.02874017134308815,
0.03831665962934494,
0.014203987084329128,
-0.06810657680034637,
-0.010462618432939053,
-0.0004387642547953874,
0.052457455545663834,
0.0382160060107708,
0.028360920026898384,
-0.038372330367565155,
0.0003624678065534681,
-0.0043546524830162525,
-0.034657660871744156,
0.024776309728622437,
0.030233316123485565,
-0.017315585166215897,
0.01224181242287159,
-0.012600049376487732,
-0.02007652446627617,
0.0703631266951561,
-0.004524714779108763,
0.042649559676647186,
-0.026952149346470833,
-0.0255906842648983,
-0.039322346448898315,
-0.016174880787730217,
-0.029614930972456932,
0.031090475618839264,
0.01755315251648426,
-0.0652063861489296,
0.025917556136846542,
-0.013778711669147015,
-0.02788892760872841,
0.007376769557595253,
0.04234204441308975,
0.04654546082019806,
0.001895145163871348,
-0.015200212597846985,
0.020351577550172806,
-0.06927935034036636,
0.04369289055466652,
-0.001412938698194921,
0.03373071551322937,
0.028169896453619003,
-0.013106468133628368,
-0.06268832832574844,
-0.005363153759390116,
-0.002111380221322179,
-0.07736871391534805,
0.058508094400167465,
-0.04700564965605736,
-0.017530828714370728,
-0.006874212063848972,
-0.06247603893280029,
0.001514769741334021,
0.022419411689043045,
0.00030154065461829305,
-0.030764907598495483,
-0.018690960481762886,
-0.0072365510277450085,
0.017163822427392006,
0.03266145661473274,
0.027006899937987328,
0.021035492420196533,
0.03542466089129448,
0.09633281081914902,
-0.040296267718076706,
0.007189854979515076,
-0.04950495436787605,
-0.03260176628828049,
0.05836053565144539,
-0.013100729323923588,
-0.009844601154327393,
-0.08462747186422348,
0.010637136176228523
] |
[
9.327493667602539,
-1.0916602611541748
] |
Materials Science
|
Condensed-Matter Physics
|
cond-mat-mtrl-sci
|
na
|
na
|
2007-04-01T05:42:28
|
In the article [Petojevic 2006], A. Petojevi\' c verified useful properties
of the $K_{i}(z)$ functions which generalize Kurepa's [Kurepa 1971] left
factorial function. In this note, we present simplified proofs of two of these
results and we answer the open question stated in [Petojevic 2006]. Finally, we
discuss the differential transcendency of the $K_{i}(z)$ functions.
|
A Note About the {Ki(z)} Functions
|
math.NT math.CV
|
0704.0068
| 2,007
|
[
-0.0013219171669334173,
0.037269074469804764,
0.01026721391826868,
0.019016068428754807,
0.021732810884714127,
0.0034672750625759363,
0.07373419404029846,
-0.028875697404146194,
-0.03720541670918465,
0.02607213705778122,
-0.08449050784111023,
0.05528198555111885,
0.013929820619523525,
0.02341974899172783,
0.027417244389653206,
-0.06429461389780045,
0.038174211978912354,
-0.008016432635486126,
0.02161160297691822,
0.032651402056217194,
-0.02291865274310112,
0.024854514747858047,
-0.05108679458498955,
-0.005810752976685762,
0.10190585255622864,
-0.035443153232336044,
0.000695473630912602,
0.02491796389222145,
-0.0626855120062828,
0.047254715114831924,
0.04203271493315697,
-0.051077403128147125,
0.0016677689272910357,
-0.03156823664903641,
0.026569580659270287,
-0.016546305269002914,
0.10021473467350006,
-0.00315991323441267,
-0.005394853185862303,
-0.012192187830805779,
-0.001991392346099019,
0.04361787065863609,
0.01913144439458847,
-0.013552590273320675,
0.02486717700958252,
0.013782830908894539,
-0.0191305261105299,
-0.028692523017525673,
0.01755600981414318,
-0.06313888728618622,
0.016748487949371338,
0.02075025998055935,
0.02811005711555481,
-0.0319492481648922,
-0.03914956375956535,
0.002676930045709014,
-0.0012842215364798903,
-0.03505750000476837,
0.010695195756852627,
0.006213544402271509,
0.016464997082948685,
0.05427421256899834,
-0.0355316586792469,
-0.038140133023262024,
0.009247361682355404,
-0.07923118770122528,
-0.031154833734035492,
0.035828858613967896,
-0.026048270985484123,
-0.03749004006385803,
0.03022776171565056,
-0.003827075706794858,
0.08282111585140228,
0.00010798690345836803,
-0.021304555237293243,
0.029788337647914886,
0.050860002636909485,
-0.02784845605492592,
0.03168199211359024,
0.016258524730801582,
-0.015102574601769447,
-0.01955992542207241,
0.02325812168419361,
-0.00570263434201479,
0.044275134801864624,
0.027700895443558693,
0.026737291365861893,
0.014065345749258995,
-0.01540356408804655,
0.04972856119275093,
0.025342868641018867,
0.03592745587229729,
0.047436561435461044,
0.06031215935945511,
-0.038366012275218964,
0.04852699860930443,
-0.007144014351069927,
0.012939875945448875,
-0.0224139504134655,
-0.010602079331874847,
-0.007774443831294775,
0.053071364760398865,
0.03921138495206833,
0.01295273657888174,
0.020012415945529938,
-0.030043037608265877,
0.01794498600065708,
-0.00904123205691576,
-0.013241412118077278,
-0.012740397825837135,
-0.04256504401564598,
0.017675327137112617,
0.011919034644961357,
0.0012024083407595754,
-0.03470521792769432,
-0.016656087711453438,
-0.012526352889835835,
-0.04729372262954712,
-0.04835286736488342,
0.02500801347196102,
-0.03000488504767418,
0.005502189509570599,
0.01952519081532955,
0.010218323208391666,
0.02557121217250824,
0.03569026291370392,
-0.05273888632655144,
-0.02855370193719864,
0.004673921037465334,
-0.02881929837167263,
0.0038341484032571316,
0.021725410595536232,
-0.04618507996201515,
-0.024028001353144646,
0.03804939240217209,
0.02269321121275425,
-0.05540386587381363,
-0.0023324782960116863,
-0.038741134107112885,
-0.002628196030855179,
0.027835365384817123,
-0.029590006917715073,
0.004418876953423023,
-0.023380400612950325,
-0.005550069268792868,
-0.02305781841278076,
-0.006293442565947771,
0.0012597286840900779,
-0.060896482318639755,
-0.025019511580467224,
0.014343678951263428,
0.0456547886133194,
0.009587106294929981,
0.028670310974121094,
-0.05303381383419037,
-0.05269986391067505,
-0.011205690912902355,
0.03621165454387665,
0.037567149847745895,
0.010694779455661774,
-0.017917633056640625,
0.0426483117043972,
-0.0009014007518999279,
0.05603358522057533,
-0.005244384054094553,
-0.007860353216528893,
0.03714609518647194,
0.017594804987311363,
-0.054328542202711105,
0.07555857300758362,
-0.04947487637400627,
0.018943071365356445,
0.0003924130869563669,
-0.03677237778902054,
0.011852548457682133,
-0.0158589668571949,
-0.020934080705046654,
-0.008422723971307278,
0.01018124632537365,
0.002612570533528924,
-0.01857643388211727,
-0.025716809555888176,
-0.00022870529210194945,
0.025482282042503357,
-0.04144363850355148,
0.0004987693391740322,
-0.020919637754559517,
0.0003392842772882432,
-0.07160758227109909,
-0.0236150324344635,
-0.006946929730474949,
0.021914944052696228,
-0.019506407901644707,
0.0038559292443096638,
0.007035077083855867,
-0.009525573812425137,
0.050928596407175064,
-0.014661763794720173,
0.0097207585349679,
0.02042166329920292,
0.027271747589111328,
-0.009747796691954136,
-0.03206375613808632,
-0.03162376582622528,
-0.022806813940405846,
0.05722907930612564,
0.017197877168655396,
0.026060186326503754,
0.059085723012685776,
-0.026397619396448135,
0.058122120797634125,
-0.014254380948841572,
0.03309343755245209,
0.008680610917508602,
-0.005063620395958424,
-0.038754407316446304,
-0.023587986826896667,
0.0028102570213377476,
-0.03282153606414795,
-0.050879254937171936,
-0.025383727625012398,
-0.00736955227330327,
-0.0015561003237962723,
0.017575161531567574,
-0.00880866963416338,
0.013060245662927628,
-0.013331040740013123,
-0.0340394489467144,
-0.03290374204516411,
-0.007245862856507301,
-0.06097397580742836,
-0.044194452464580536,
0.026255695149302483,
0.012945889495313168,
-0.011506353504955769,
0.023443087935447693,
-0.008747747167944908,
0.04505980387330055,
0.06771736592054367,
0.06960265338420868,
0.035413958132267,
-0.024282915517687798,
0.023842744529247284,
0.008468685671687126,
-0.07123533636331558,
-0.011642816476523876,
-0.04817526787519455,
-0.031730182468891144,
-0.021262796595692635,
0.012657332234084606,
-0.007104118820279837,
0.044932421296834946,
0.004417784512042999,
0.06715366989374161,
-0.013980929739773273,
-0.07944512367248535,
-0.0614219605922699,
0.04298977553844452,
0.022888535633683205,
-0.0027568337973207235,
0.10860460996627808,
-0.029295828193426132,
0.02892465889453888,
-0.008159182965755463,
-0.06256628781557083,
0.024161959066987038,
0.008236183784902096,
0.01849902607500553,
-0.001782106002792716,
-0.02063133381307125,
-0.015226837247610092,
0.04653370380401611,
0.1012553870677948,
0.08290910720825195,
-0.02054164744913578,
-0.016341334208846092,
-0.0015482952585443854,
-0.03293398767709732,
-0.03037804737687111,
-0.034899864345788956,
-0.01706605777144432,
0.0018584902863949537,
-0.046950437128543854,
0.01620084047317505,
0.014378714375197887,
0.05133804678916931,
0.003954310901463032,
0.00788850337266922,
0.007198484614491463,
0.004541435744613409,
-0.028105957433581352,
0.03062186948955059,
0.03250228613615036,
0.051428843289613724,
0.015954991802573204,
0.05840643122792244,
0.01902991533279419,
-0.06780875474214554,
0.028645891696214676,
0.016637973487377167,
0.0571330189704895,
-0.02738071419298649,
0.0197445061057806,
-0.02039240673184395,
0.048430755734443665,
0.005889337509870529,
0.020622631534934044,
-0.023348161950707436,
-0.03495736047625542,
0.03257611021399498,
-0.01667802408337593,
0.04028918221592903,
-0.011549662798643112,
-0.01956932805478573,
-0.031384341418743134,
0.041558630764484406,
0.031768035143613815,
-0.0002827197895385325,
0.08583810180425644,
0.03688622638583183,
0.04324985295534134,
-0.041883643716573715,
-0.011283527128398418,
-0.024543127045035362,
0.025424811989068985,
0.008499414660036564,
-0.0565669871866703,
0.0292196162045002,
0.019301893189549446,
0.02480604499578476,
-0.042657677084207535,
0.08217864483594894,
-0.06164056435227394,
-0.04919804260134697,
-0.028099767863750458,
0.05041766166687012,
-0.02103044092655182,
0.04520749673247337,
-0.030717140063643456,
0.007613013964146376,
0.06108533963561058,
-0.014168198220431805,
-0.03081926330924034,
-0.031136980280280113,
-0.037675101310014725,
0.020043514668941498,
0.0013173599727451801,
0.042086709290742874,
-0.004650375805795193,
0.007675692439079285,
-0.07515323907136917,
-0.014658970758318901,
0.04852798953652382,
-0.02899559587240219,
0.0017350466223433614,
0.04387025907635689,
0.05333281680941582,
0.0007051092106848955,
0.014636857435107231,
0.026551181450486183,
0.06888407468795776,
-0.013101031072437763,
0.07185979187488556,
0.008446432650089264,
0.05440942943096161,
0.03694358095526695,
0.036308836191892624,
0.008606461808085442,
-0.041860513389110565,
-0.023115500807762146,
-0.04074479639530182,
-0.05564586818218231,
0.055930282920598984,
-0.0180206261575222,
0.06623224914073944,
-0.03983607143163681,
-0.06901134550571442,
0.005583213642239571,
-0.04036384075880051,
-0.007118490990251303,
0.056979261338710785,
0.01848722994327545,
0.06746497005224228,
0.0496256947517395,
0.057237572968006134,
0.013130237348377705,
-0.0540737509727478,
0.010995217598974705,
0.01417828630656004,
-0.022767843678593636,
-0.0018699103966355324,
-0.02467617765069008,
-0.011551527306437492,
0.04366491362452507,
0.011398577131330967,
-0.00878110621124506,
-0.017858145758509636,
0.013619930483400822,
-0.005337094888091087,
-0.015099138021469116,
-0.0771411582827568,
-0.0947650894522667,
0.03798973560333252,
-0.03199087828397751,
0.001686549512669444,
0.03977566212415695,
0.018531139940023422,
-0.02501824125647545,
0.06132037192583084,
-0.0768929198384285,
-0.0032496382482349873,
0.035011112689971924,
-0.027727169916033745,
-0.03999989479780197,
0.01889084465801716,
-0.011125190183520317,
0.03345643728971481,
-0.014335090294480324,
0.034762341529130936,
-0.042275331914424896,
0.010462339036166668,
0.004177694208920002,
-0.011694357730448246,
-0.020178956910967827,
0.0006497644353657961,
0.03492739051580429,
0.010036541149020195,
0.020032979547977448,
-0.01929347775876522,
-0.07341248542070389,
0.0006453386740759015,
0.04977031424641609,
0.033985067158937454,
-0.012338260188698769,
-0.012313435785472393,
-0.03258549049496651,
0.028555503115057945,
0.04867405444383621,
-0.017314499244093895,
0.0701812133193016,
0.04449580982327461,
0.000013739443602389656,
-0.021830426529049873,
0.03671160340309143,
0.06875445693731308,
0.010492530651390553,
-0.0036286553367972374,
-0.00031153581221587956,
-0.015197870321571827,
-0.03291654214262962,
0.033863432705402374,
0.035842277109622955,
-0.006115742959082127,
0.046683795750141144,
0.0556173175573349,
-0.030077490955591202,
0.00959331076592207,
-0.062262993305921555,
0.051433514803647995,
0.015088126994669437,
0.023273933678865433,
0.008858725428581238,
-0.03195240721106529,
0.014426507987082005,
0.058250874280929565,
-0.01089517492800951,
-0.03153718262910843,
0.03416478633880615,
-0.00898066721856594,
0.0747920423746109,
0.023754654452204704,
0.013599595054984093,
0.01319512352347374,
-0.017074022442102432,
-0.05418429896235466,
-0.030987106263637543,
-0.020542917773127556,
-0.011844848282635212,
-0.044459711760282516,
0.06208633631467819,
0.012579795904457569,
-0.07798738032579422,
-0.06765555590391159,
-0.03647006303071976,
-0.030542759224772453,
0.02654315158724785,
0.003952571656554937,
-0.07669516652822495,
-0.02814318798482418,
-0.03077036328613758,
0.019893692806363106,
-0.016902372241020203,
0.013586485758423805,
0.024502817541360855,
-0.07637201249599457,
-0.007412222679704428,
0.037176672369241714,
0.007435454986989498,
0.026469215750694275,
-0.012203517369925976,
-0.03857127204537392,
-0.015385463833808899,
0.041575826704502106,
0.0418461337685585,
-0.011615991592407227,
-0.01634795404970646,
-0.03617537021636963,
-0.056998927146196365,
-0.0148743512108922,
0.06020139902830124,
-0.005866705439984798,
0.006536864675581455,
0.038283947855234146,
0.06405899673700333,
-0.004480239003896713,
-0.03251268342137337,
-0.02284584753215313,
0.008048927411437035,
-0.09211830794811249,
-0.019111119210720062,
0.0030181535985320807,
-0.01663408800959587,
0.019353721290826797,
-0.00779148330911994,
-0.054030124098062515,
0.03598612919449806,
-0.07436865568161011,
-0.09242914617061615,
0.045721132308244705,
-0.03374883532524109,
0.004282962065190077,
-0.01530019287019968,
0.005954117514193058,
-0.004009081516414881,
-0.01868067868053913,
-0.00997290387749672,
-0.016135456040501595,
0.03353035822510719,
-0.0018778169760480523,
0.02934201806783676,
0.05923127010464668,
0.035907384008169174,
0.012533517554402351,
-0.005921205505728722,
-0.013609245419502258,
-0.025665491819381714,
-0.022134555503726006,
0.05454128980636597,
-0.015466563403606415,
-0.06479974091053009,
0.012520662508904934,
-0.031232092529535294,
0.014062811620533466,
-0.09223129600286484,
0.006683260202407837,
-0.0221824049949646,
0.03816678747534752,
0.008969170041382313,
-0.04263448715209961,
-0.06736989319324493,
-0.018657086417078972,
0.00963520910590887,
-0.016779864206910133,
-0.03525940328836441,
-0.009452746249735355,
-0.1415039747953415,
-0.03589276969432831,
-0.005949009675532579,
0.03543699160218239,
0.0036034518852829933,
0.007337961811572313,
-0.05588414520025253,
-0.0038546142168343067,
0.04640510678291321,
0.004374624229967594,
-0.015701662749052048,
0.01958598382771015,
0.027346141636371613,
-0.008632243610918522,
-0.0029236588161438704,
-0.006084351800382137,
-0.0010402211919426918,
-0.016640765592455864,
-0.025275135412812233,
-0.07873464375734329,
-0.017310278490185738,
-0.028167543932795525,
-0.0188785158097744,
0.015077173709869385,
-0.029428772628307343,
-0.03324410319328308,
-0.027512602508068085,
-0.0531095415353775,
-0.022345121949911118,
0.013414028100669384,
-0.02869064174592495,
0.014016829431056976,
0.06633487343788147,
-0.005826291628181934,
-0.04513504356145859,
0.011090952903032303,
-0.004517028108239174,
0.06993068754673004,
-0.06083468720316887,
-0.0003552564012352377,
0.03277040645480156,
-0.022845901548862457,
0.03788471594452858,
0.03367731347680092,
0.005862771533429623,
0.03223583102226257,
-0.005443257745355368,
0.008633875288069248,
0.0005551684880629182,
0.014331642538309097,
-0.05156879872083664,
0.07214214652776718,
-0.024207407608628273,
0.026204029098153114,
-0.053647905588150024,
0.019106561318039894,
-0.029521048069000244,
0.023224888369441032,
-0.09115922451019287,
-0.014714185148477554,
0.009161618538200855,
-0.02695358917117119,
-0.02433224394917488,
0.0035303940530866385,
0.11145789176225662,
0.008239058777689934,
0.011465347371995449,
-0.0568421334028244,
-0.029863351956009865,
-0.021139735355973244,
-0.032243289053440094,
-0.006804898846894503,
0.03787275403738022,
-0.010729070752859116,
0.04074234515428543,
0.002952939597889781,
-0.01033938117325306,
-0.020932674407958984,
0.0026262884493917227,
0.033847030252218246,
-0.009407821111381054,
0.06669024378061295,
0.05215848982334137,
-0.03193286433815956,
0.026081141084432602,
0.061486147344112396,
0.06647082418203354,
-0.008365939371287823,
-0.01176454871892929,
0.015152948908507824,
-0.01846703700721264,
0.03311216086149216,
-0.05292124301195145,
0.0218721404671669,
0.010501584969460964,
0.00513438368216157,
-0.033474382013082504,
0.01631634123623371,
0.01501508615911007,
-0.040136516094207764,
-0.01171805988997221,
-0.03522076457738876,
0.005005895160138607,
-0.028440209105610847,
0.03799691051244736,
-0.013909835368394852,
-0.018866579979658127,
-0.020678499713540077,
-0.06414145976305008,
-0.07535573840141296,
0.029699081555008888,
-0.052220966666936874,
0.010730880312621593,
-0.022203324362635612,
0.0160038024187088,
-0.01723414659500122,
-0.013302508741617203,
0.027191156521439552,
-0.04322730377316475,
-0.043874673545360565,
-0.060152627527713776,
0.033228740096092224,
-0.05500263720750809,
-0.04419933632016182,
-0.012751447036862373,
0.009494425728917122,
0.018868323415517807,
0.04223236069083214,
-0.033265627920627594,
0.03274784982204437,
0.022945595905184746,
-0.02100622095167637,
0.017022397369146347,
0.0040476578287780285,
0.054489776492118835,
0.026778792962431908,
0.043339312076568604,
-0.02580331452190876,
-0.00048522575525566936,
-0.031796734780073166,
-0.012913734652101994,
0.029865359887480736,
0.04275328665971756,
0.011513681150972843,
0.030836675316095352,
0.02479110099375248,
-0.0058477893471717834,
0.007219731342047453,
0.017403706908226013,
0.016370553523302078,
0.034700654447078705,
-0.006812725216150284,
-0.06879901885986328,
-0.040071722120046616,
-0.044018037617206573,
0.07231899350881577,
-0.05611969158053398,
-0.014290537685155869,
-0.034983597695827484,
-0.04628201946616173,
-0.025331614539027214,
0.009170240722596645,
-0.03462245315313339,
0.00630769832059741,
0.018760675564408302,
0.02236761525273323,
0.011302275583148003,
-0.041816242039203644,
-0.004139754455536604,
-0.03611407428979874,
0.000034821834560716525,
-0.03748646378517151,
0.01260552927851677,
-0.015153652057051659,
0.05216831713914871,
-0.058260779827833176,
-0.0499131865799427,
0.00002498273715900723,
0.06601452082395554,
-0.01457275915890932,
-0.010212850756943226,
-0.052227769047021866,
0.019839728251099586,
0.05504389852285385,
0.027210557833313942,
-0.06183919683098793,
-0.01750200055539608,
-0.030382046476006508,
0.06266141682863235,
0.03604207932949066,
0.044148415327072144,
0.012663695961236954,
0.03607557713985443,
0.03279291093349457,
-0.0001060333161149174,
-0.015221204608678818,
0.005806130822747946,
-0.009588957764208317,
0.06254879385232925,
-0.03288311883807182,
0.03249344229698181,
-0.06242234632372856,
0.06292730569839478
] |
[
0.1922001987695694,
2.9992806911468506
] |
Number Theory
|
Mathematics
|
math-NT
|
math-CV
|
na
|
2007-04-01T06:48:47
|
The goal of this paper is to construct invariant dynamical objects for a (not
necessarily invertible) smooth self map of a compact manifold. We prove a
result that takes advantage of differences in rates of expansion in the terms
of a sheaf cohomological long exact sequence to create unique lifts of finite
dimensional invariant subspaces of one term of the sequence to invariant
subspaces of the preceding term. This allows us to take invariant cohomological
classes and under the right circumstances construct unique currents of a given
type, including unique measures of a given type, that represent those classes
and are invariant under pullback. A dynamically interesting self map may have a
plethora of invariant measures, so the uniquess of the constructed currents is
important. It means that if local growth is not too big compared to the growth
rate of the cohomological class then the expanding cohomological class gives
sufficient "marching orders" to the system to prohibit the formation of any
other such invariant current of the same type (say from some local dynamical
subsystem). Because we use subsheaves of the sheaf of currents we give
conditions under which a subsheaf will have the same cohomology as the sheaf
containing it. Using a smoothing argument this allows us to show that the sheaf
cohomology of the currents under consideration can be canonically identified
with the deRham cohomology groups. Our main theorem can be applied in both the
smooth and holomorphic setting.
|
Dynamical Objects for Cohomologically Expanding Maps
|
math.DS
|
0704.0069
| 2,007
|
[
0.029376324266195297,
0.027559254318475723,
0.005329478066414595,
-0.026656750589609146,
-0.0057089077308773994,
0.007753085810691118,
0.07579300552606583,
0.005458212457597256,
-0.04900466650724411,
0.03102255053818226,
-0.04819362238049507,
0.04532291740179062,
0.024557823315262794,
0.015080911107361317,
0.0038240747526288033,
-0.025823207572102547,
-0.0202719047665596,
-0.006393888499587774,
0.012754395604133606,
0.00016804083134047687,
0.027360210195183754,
0.0052446601912379265,
0.07022518664598465,
-0.01665641739964485,
0.09013331681489944,
-0.03567592054605484,
0.053181279450654984,
0.0002765878743957728,
-0.04677227512001991,
0.00745094520971179,
0.10942437499761581,
-0.053630903363227844,
0.028855977579951286,
-0.01845931075513363,
-0.03740639239549637,
-0.028671130537986755,
0.03702297434210777,
0.009204079397022724,
0.042366545647382736,
0.049997054040431976,
0.057951420545578,
-0.009674366563558578,
0.05054045841097832,
-0.006892316043376923,
0.029249900951981544,
-0.010071920230984688,
0.006587824784219265,
-0.028868116438388824,
0.051600243896245956,
-0.0246084276586771,
-0.010804807767271996,
0.03231136128306389,
0.011297689750790596,
-0.030050834640860558,
-0.05601518973708153,
0.04283268004655838,
0.023973068222403526,
-0.049805283546447754,
0.02367367036640644,
-0.0022528788540512323,
-0.023201072588562965,
0.01710347831249237,
-0.0037064366042613983,
-0.012387738563120365,
0.005447776522487402,
-0.03614489361643791,
-0.009310903027653694,
0.009378524497151375,
-0.022090837359428406,
-0.00008028176671359688,
-0.026528727263212204,
-0.026819173246622086,
0.0439898855984211,
0.004987352527678013,
-0.04802010580897331,
0.02999034896492958,
0.0572824589908123,
-0.037378862500190735,
-0.019957512617111206,
-0.023802900686860085,
-0.03311322629451752,
-0.016389524564146996,
0.06143264099955559,
0.007630916312336922,
0.07122684270143509,
0.012769343331456184,
0.02475571073591709,
0.05769046023488045,
-0.06719762831926346,
0.020506594330072403,
0.0240606851875782,
-0.03025839664041996,
0.053044021129608154,
0.08078872412443161,
-0.03131856024265289,
0.024121949449181557,
-0.02497980184853077,
0.024844659492373466,
-0.04283994808793068,
-0.04648401960730553,
0.002291159238666296,
0.0270434208214283,
-0.013217353262007236,
-0.002343457192182541,
0.06803164631128311,
-0.011839598417282104,
0.0264116283506155,
0.004159985575824976,
0.01099324319511652,
-0.029148997738957405,
-0.05046512186527252,
-0.026573294773697853,
0.02329534851014614,
-0.005530558992177248,
-0.0016301691066473722,
-0.014250817708671093,
0.04470989853143692,
-0.010216940194368362,
-0.019313238561153412,
0.03905327245593071,
-0.0029195440001785755,
-0.039604801684617996,
-0.007529322523623705,
0.03965427726507187,
0.03431325405836105,
0.0789162740111351,
-0.055207259953022,
-0.03162650018930435,
0.0491921529173851,
-0.016409756615757942,
0.016386665403842926,
0.00620108051225543,
-0.027782529592514038,
0.005606634076684713,
0.044819608330726624,
-0.012759871780872345,
-0.030169544741511345,
-0.04815453663468361,
0.0718287006020546,
0.0031322843860834837,
0.04765792191028595,
-0.033976562321186066,
0.03657777979969978,
-0.004712332971394062,
0.0007336831768043339,
-0.04993473365902901,
0.0841749757528305,
-0.08346808701753616,
0.004615188110619783,
0.006059794221073389,
-0.01573246717453003,
0.09188661724328995,
-0.01765681803226471,
0.023382268846035004,
-0.006847509182989597,
0.005226637702435255,
-0.020018868148326874,
0.01960507035255432,
0.04677356779575348,
0.027213508263230324,
0.0043313708156347275,
0.02009793370962143,
-0.002761026844382286,
0.050630271434783936,
-0.057943303138017654,
-0.012764235027134418,
0.04951910302042961,
0.03518644720315933,
-0.022019725292921066,
0.043492987751960754,
-0.038200169801712036,
0.024053003638982773,
0.018946919590234756,
-0.03363930061459541,
-0.0037071031983941793,
-0.026368405669927597,
0.011213958263397217,
-0.0767677053809166,
0.04561697319149971,
-0.023325417190790176,
0.011826623231172562,
-0.0855589509010315,
0.05399731919169426,
0.01596738025546074,
0.023544596508145332,
0.042855825275182724,
-0.0011673315893858671,
-0.01960231177508831,
-0.049078259617090225,
-0.0555601604282856,
0.06132157891988754,
0.0018936091801151633,
-0.06770377606153488,
-0.02467695064842701,
-0.010713743977248669,
-0.037939827889204025,
0.06953077018260956,
0.005174130201339722,
-0.01243139524012804,
-0.04106435552239418,
-0.005094632972031832,
-0.000565590220503509,
-0.02077268250286579,
0.002116905990988016,
-0.03521987795829773,
0.05198206380009651,
0.04093843325972557,
-0.032594479620456696,
0.0426766499876976,
-0.001454424113035202,
0.09756315499544144,
-0.01808743178844452,
-0.05672172084450722,
0.018925579264760017,
-0.009792422875761986,
-0.0003784230211749673,
-0.017605554312467575,
-0.025845864787697792,
-0.026177221909165382,
-0.01603793166577816,
0.012826391495764256,
-0.01944907009601593,
-0.01010833028703928,
-0.013875192031264305,
0.01943744532763958,
0.012174607254564762,
-0.01453178096562624,
-0.03837025538086891,
-0.02825837954878807,
-0.014349830336868763,
-0.0541781522333622,
-0.07510814070701599,
0.05503232777118683,
0.010038438253104687,
-0.023201869800686836,
0.012519809417426586,
-0.007547293324023485,
0.06549341976642609,
0.01363900676369667,
0.05549120157957077,
0.025461770594120026,
-0.022371016442775726,
0.061986636370420456,
-0.060513366013765335,
-0.02791644260287285,
-0.0006131389527581632,
0.02994985692203045,
0.0303481612354517,
-0.05364731326699257,
0.06782162189483643,
0.03830164298415184,
-0.0470399335026741,
0.04416913166642189,
0.019763445481657982,
0.02050355263054371,
-0.060957472771406174,
-0.015171834267675877,
0.0555570013821125,
0.000861702486872673,
-0.027798723429441452,
0.020535217598080635,
-0.02111329883337021,
0.03311944007873535,
-0.0059318640269339085,
-0.03489664942026138,
-0.019612738862633705,
0.03329218551516533,
-0.06976188719272614,
-0.0023894761689007282,
-0.015035474672913551,
-0.006399447564035654,
-0.0024735387414693832,
0.07476011663675308,
0.05095754563808441,
-0.059905972331762314,
0.021270817145705223,
0.013880672864615917,
-0.011321429163217545,
-0.055523063987493515,
-0.0392121896147728,
-0.047151725739240646,
-0.03199180215597153,
-0.04597342759370804,
0.00840528029948473,
-0.03686128929257393,
0.009017407894134521,
0.02867402322590351,
-0.03015543706715107,
-0.03986093029379845,
0.01205384824424982,
-0.016148697584867477,
-0.004466160666197538,
0.026393435895442963,
0.062416646629571915,
0.01762297749519348,
0.04969452694058418,
0.033016934990882874,
-0.03048226237297058,
-0.02002951316535473,
0.03341212123632431,
-0.014933543279767036,
-0.006478053983300924,
0.0237226951867342,
-0.0186791829764843,
0.056034721434116364,
-0.015985412523150444,
0.02538250759243965,
-0.046079427003860474,
0.04197036102414131,
-0.004647943656891584,
-0.02327507920563221,
-0.008924189954996109,
-0.046325795352458954,
-0.016322556883096695,
-0.019039053469896317,
0.015890270471572876,
0.054561469703912735,
0.008723832666873932,
0.0456739217042923,
-0.02441934496164322,
0.03851010277867317,
-0.04556531086564064,
-0.0007206745794974267,
-0.05012742802500725,
0.01867869310081005,
-0.014460845850408077,
-0.0033318474888801575,
0.02162349782884121,
-0.016170257702469826,
-0.03045964241027832,
-0.015201392583549023,
0.03425806388258934,
-0.014186708256602287,
-0.022917941212654114,
0.01444721594452858,
0.0010398859158158302,
-0.0541154220700264,
0.039917223155498505,
-0.01036441046744585,
0.006486783269792795,
0.009324581362307072,
-0.04989288002252579,
-0.06631770730018616,
-0.061714500188827515,
-0.062234267592430115,
0.006244218908250332,
-0.0332646407186985,
-0.0172234158962965,
0.03678091987967491,
-0.023914692923426628,
-0.054995324462652206,
-0.026849959045648575,
0.04415158927440643,
-0.025778500363230705,
-0.028160445392131805,
0.025514336302876472,
0.08630621433258057,
-0.04493607208132744,
0.0241798534989357,
0.026705864816904068,
0.052429623901844025,
-0.014968504197895527,
-0.02357962727546692,
0.012160149402916431,
0.05176800116896629,
0.055704791098833084,
0.00014081889821682125,
0.06699933111667633,
0.01737922802567482,
-0.01979890652000904,
-0.0073290662840008736,
-0.008838430978357792,
0.006775500252842903,
0.011795779690146446,
-0.0045105889439582825,
-0.019961530342698097,
-0.0483667254447937,
0.03765327110886574,
-0.0071705603040754795,
-0.03762752190232277,
0.0847354605793953,
-0.006895005702972412,
0.015412445180118084,
-0.03807062283158302,
-0.03161473572254181,
0.062040336430072784,
-0.05209694802761078,
0.007533238269388676,
-0.008583246730268002,
0.018916556611657143,
0.032524701207876205,
-0.019550669938325882,
-0.00940531212836504,
0.030617862939834595,
-0.029888425022363663,
-0.02062891237437725,
0.031461313366889954,
0.03528987988829613,
0.011668889783322811,
-0.00974217988550663,
-0.052725426852703094,
-0.07586601376533508,
-0.005666361656039953,
-0.03065253421664238,
-0.026221608743071556,
0.01122030895203352,
0.021039331331849098,
-0.02701442874968052,
0.04077334329485893,
-0.03532101958990097,
0.0019316766411066055,
-0.023183446377515793,
0.005615991074591875,
-0.0650230348110199,
0.0317767970263958,
0.02129364386200905,
0.06007671728730202,
-0.0038925535045564175,
0.02381136268377304,
-0.0008475290378555655,
-0.028802134096622467,
0.03345835953950882,
0.009018156677484512,
-0.03244208171963692,
-0.0750684067606926,
0.007379407528787851,
0.026791784912347794,
0.01712498441338539,
-0.024085775017738342,
-0.0488317608833313,
0.01875133067369461,
0.01195493433624506,
0.03741230070590973,
0.01519202534109354,
-0.03375808522105217,
0.03212719038128853,
0.010033592581748962,
0.002608121372759342,
-0.031287867575883865,
0.02909676544368267,
0.051082368940114975,
-0.0034479214809834957,
0.021532703191041946,
-0.04441916197538376,
0.035782743245363235,
0.08241865783929825,
0.11000509560108185,
-0.03106890432536602,
-0.03783407062292099,
0.03273807838559151,
0.04573050141334534,
0.03632790967822075,
0.026477377861738205,
0.03213418275117874,
0.06957519054412842,
-0.03348218649625778,
-0.03668802231550217,
-0.032905202358961105,
0.01531748566776514,
0.028448054566979408,
0.029320601373910904,
0.0357663631439209,
-0.026049062609672546,
0.013454773463308811,
-0.03433099761605263,
-0.011297394521534443,
-0.01802234724164009,
0.022993871942162514,
-0.0008586797048337758,
0.09045080095529556,
0.007184168789535761,
0.0018462111474946141,
-0.041785113513469696,
-0.000018899667338700965,
-0.06196006387472153,
-0.00478689419105649,
0.06661833077669144,
-0.05486671254038811,
0.035189349204301834,
-0.01181610394269228,
0.002166099613532424,
-0.0239615086466074,
-0.01883949525654316,
-0.02786393091082573,
-0.00207092659547925,
0.03292004019021988,
-0.003183684078976512,
0.02142992615699768,
-0.0072177560068666935,
0.007397945504635572,
0.021447360515594482,
0.03680549934506416,
-0.020843254402279854,
0.05260389298200607,
-0.04521296173334122,
-0.04770191013813019,
0.033923156559467316,
-0.011806299909949303,
-0.010501180775463581,
-0.03030792996287346,
0.01218345109373331,
0.004844673443585634,
0.009413624182343483,
0.04856665059924126,
0.031818341463804245,
0.047138188034296036,
0.010480403900146484,
-0.0380123034119606,
-0.00781986303627491,
-0.012677004560828209,
-0.016068942844867706,
0.08391579240560532,
0.0551731176674366,
0.061096616089344025,
0.06370040774345398,
-0.04141228273510933,
0.04873422533273697,
-0.018317606300115585,
-0.050782687962055206,
-0.021376945078372955,
-0.0071012964472174644,
-0.010952633805572987,
0.03391677513718605,
-0.004953436553478241,
-0.04151016101241112,
0.07956814765930176,
-0.038441453129053116,
-0.08066869527101517,
0.050712455064058304,
-0.011913960799574852,
0.05745183676481247,
-0.013682546094059944,
-0.03562973067164421,
-0.08242712169885635,
0.005277317948639393,
0.004647708497941494,
-0.02556442655622959,
0.019962860271334648,
-0.021603457629680634,
0.022900981828570366,
-0.043278735131025314,
-0.00318750087171793,
0.011397739872336388,
0.00786591973155737,
-0.008691469207406044,
-0.020229075103998184,
-0.09676811844110489,
0.011452642269432545,
0.00831280741840601,
-0.03495689481496811,
-0.03647185117006302,
-0.03656025230884552,
0.017187556251883507,
-0.07263683527708054,
-0.008930126205086708,
-0.015809670090675354,
0.014504324644804,
-0.033057987689971924,
-0.046476177871227264,
-0.04094645753502846,
-0.005096521228551865,
0.01927979104220867,
0.06174613907933235,
-0.020566793158650398,
-0.024974152445793152,
-0.0678204819560051,
0.024503376334905624,
0.032922472804784775,
0.05146413668990135,
-0.0001322533207712695,
0.0025313771329820156,
0.016230395063757896,
-0.008131308481097221,
0.022186145186424255,
-0.006419266574084759,
-0.0565224327147007,
0.022055258974432945,
0.009756108745932579,
-0.03561568260192871,
0.004124517552554607,
-0.0544944629073143,
-0.010188223794102669,
0.06670679152011871,
-0.034718096256256104,
-0.046320296823978424,
-0.013966560363769531,
0.003809616668149829,
-0.04128429666161537,
0.051950156688690186,
0.06215907633304596,
-0.027914192527532578,
-0.00186180230230093,
-0.03365236520767212,
-0.04195189103484154,
-0.01623428985476494,
0.002486063167452812,
0.018796294927597046,
-0.0015176254091784358,
-0.0024895258247852325,
-0.039748311042785645,
0.015737591311335564,
0.02486526034772396,
0.11825141310691833,
-0.058728113770484924,
0.02226373180747032,
0.08603107184171677,
-0.029367312788963318,
0.07181116938591003,
-0.010895459912717342,
0.02364070527255535,
-0.010857726447284222,
-0.03995198756456375,
-0.006858292501419783,
-0.01428843755275011,
-0.002733069472014904,
-0.005596610251814127,
0.025601519271731377,
-0.03533097729086876,
0.01581609435379505,
-0.028035325929522514,
-0.01202353835105896,
-0.04342236369848251,
-0.010734272189438343,
-0.039964862167835236,
0.010575413703918457,
0.00032644462771713734,
-0.022922441363334656,
-0.03864569962024689,
-0.005968404933810234,
0.07029188424348831,
-0.027695531025528908,
0.007117938715964556,
-0.1271233856678009,
-0.0540919154882431,
-0.011383643373847008,
0.031101975589990616,
-0.027790553867816925,
0.04059933125972748,
-0.01736832782626152,
0.027321821078658104,
0.07341718673706055,
-0.003844016930088401,
-0.006935592740774155,
-0.030024375766515732,
0.05573683977127075,
-0.03617636486887932,
-0.031471509486436844,
0.030761893838644028,
0.0030317327473312616,
0.027952900156378746,
0.061342086642980576,
0.06066516414284706,
-0.0330396331846714,
0.0033107236959040165,
-0.013073394075036049,
-0.023116130381822586,
0.05101807788014412,
-0.05744567885994911,
0.03548987954854965,
0.0801994800567627,
0.0017215923871845007,
-0.0023231152445077896,
0.051078345626592636,
-0.05281881242990494,
-0.006707059685140848,
-0.015637168660759926,
-0.023473450914025307,
-0.05556207895278931,
0.000252689904300496,
0.04342653229832649,
-0.01782136969268322,
0.005116188898682594,
-0.019291460514068604,
0.004328958690166473,
-0.03087887167930603,
-0.018219998106360435,
-0.04015626758337021,
0.034789882600307465,
-0.00993727520108223,
-0.017521539703011513,
0.027932429686188698,
-0.03310021385550499,
0.07500400394201279,
0.03550240769982338,
-0.011270060203969479,
0.04221391677856445,
-0.05452009662985802,
-0.018805207684636116,
-0.016203364357352257,
-0.03392946720123291,
0.016029248014092445,
0.015720775350928307,
-0.02504453808069229,
-0.033926304429769516,
-0.013898571953177452,
-0.00585189601406455,
-0.02500995062291622,
-0.005700834095478058,
-0.024935487657785416,
-0.000579608604311943,
0.009762045927345753,
0.04743124917149544,
-0.019745007157325745,
-0.0000811555510153994,
-0.016536012291908264,
-0.013760299421846867,
-0.014626714400947094,
0.020575057715177536,
-0.04288869723677635,
-0.0113890515640378,
-0.025376850739121437,
0.017686817795038223,
0.03066684678196907,
-0.03324136883020401,
0.027485650032758713,
0.012102288194000721,
-0.017657877877354622,
-0.06313692033290863,
-0.018290001899003983,
-0.01483987644314766,
0.018675364553928375,
-0.04905950278043747,
-0.07173402607440948,
-0.0035759895108640194,
0.023339981213212013,
-0.06249304860830307,
0.015885667875409126,
-0.012144421227276325,
0.0207146555185318,
0.03238304704427719,
0.01211456023156643,
-0.031477730721235275,
-0.009777440689504147,
0.024441562592983246,
-0.044649992138147354,
-0.013433409854769707,
-0.01427718810737133,
-0.01730315387248993,
-0.04023472219705582,
-0.010958234779536724,
0.01422351598739624,
-0.0746540054678917,
0.027574708685278893,
0.0410444512963295,
-0.005995289422571659,
-0.0026188804768025875,
-0.004055155906826258,
0.008755295537412167,
0.0372183732688427,
0.03981891646981239,
-0.02178035117685795,
0.018185611814260483,
0.000022471946067526005,
-0.02582196146249771,
-0.014826337806880474,
0.057610440999269485,
-0.03387710452079773,
0.012170806527137756,
0.022484635934233665,
-0.02301524579524994,
0.04199346527457237,
0.007104536984115839,
0.05265587195754051,
0.047562453895807266,
-0.025625722482800484,
-0.021576059982180595,
-0.039178188890218735,
-0.025071244686841965
] |
[
1.7851459980010986,
2.7222900390625
] |
Dynamical Systems
|
Mathematics
|
math-DS
|
na
|
na
|
2007-04-01T06:49:32
|
The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings with
two electrons has been studied and has been explained in an analytical way, the
evolution of the period and amplitudes against the magnetic field can be
exactly described. Furthermore, the dipole transition of the ground state was
found to have essentially two frequencies, their difference appears as an
oscillation matching the oscillation of the persistent current exactly. A
number of equalities relating the observables and dynamical parameters have
been found.
|
Coincidence of the oscillations in the dipole transition and in the
persistent current of narrow quantum rings with two electrons
|
cond-mat.mes-hall
|
0704.0070
| 2,007
|
[
0.055800724774599075,
0.028255119919776917,
0.0031005151104182005,
-0.0068767257034778595,
0.0474705807864666,
0.04047628864645958,
0.0416329987347126,
0.027709780260920525,
-0.010085547342896461,
-0.004986798390746117,
-0.08415042608976364,
0.04880648851394653,
0.011644147336483002,
0.0013196044601500034,
0.048246629536151886,
-0.018801305443048477,
-0.02598523162305355,
-0.01847792975604534,
0.008330749347805977,
0.021680651232600212,
-0.030265428125858307,
0.012482335790991783,
-0.016613606363534927,
-0.01995752938091755,
0.10577209293842316,
0.023890752345323563,
0.04343795031309128,
0.025687288492918015,
-0.025980424135923386,
0.013330633752048016,
-0.0038050892762839794,
-0.05881020426750183,
0.08417316526174545,
-0.017873510718345642,
0.014846937730908394,
-0.0404234379529953,
0.028036167845129967,
-0.026505520567297935,
0.010715239681303501,
0.04800551012158394,
-0.003501025028526783,
-0.054741550236940384,
-0.012610074132680893,
-0.03596670180559158,
0.023616842925548553,
-0.033495962619781494,
-0.036198023706674576,
0.005939659662544727,
0.007703867275267839,
0.005208147224038839,
-0.005667741410434246,
0.00837183278053999,
0.016207817941904068,
-0.040071386843919754,
-0.015806712210178375,
0.03080982342362404,
0.0033218045718967915,
-0.0013598717050626874,
0.06772376596927643,
0.032893069088459015,
0.010458252392709255,
0.06059591472148895,
0.027286475524306297,
0.053681109100580215,
0.026230549439787865,
-0.06761542707681656,
0.0036075750831514597,
-0.00008941398846218362,
-0.0007710119825787842,
-0.045148931443691254,
0.023994160816073418,
-0.030877916142344475,
-0.03889282047748566,
0.046922143548727036,
0.014245675876736641,
0.04134353622794151,
-0.011306426487863064,
-0.00941227376461029,
0.03550807759165764,
-0.03763745352625847,
-0.07603051513433456,
-0.000799905916210264,
-0.0027474327944219112,
0.0593608021736145,
0.05948592722415924,
0.007853526622056961,
-0.026060156524181366,
-0.01184934563934803,
-0.004100531805306673,
0.015999464318156242,
0.023091450333595276,
-0.04371034353971481,
0.03307927027344704,
0.053267765790224075,
-0.03891598805785179,
0.015275906771421432,
0.014187764376401901,
0.07915106415748596,
-0.0034354515373706818,
-0.01159102562814951,
-0.032293085008859634,
0.027255022898316383,
0.0004043739172630012,
0.028401879593729973,
0.06103108823299408,
0.04665636643767357,
-0.01362781971693039,
-0.04023837298154831,
0.02868681214749813,
-0.003896045032888651,
-0.056170012801885605,
-0.055062975734472275,
-0.024247221648693085,
-0.02880512923002243,
-0.031062902882695198,
0.0062198154628276825,
0.01791420951485634,
-0.07416553795337677,
0.0232040174305439,
0.010386520996689796,
0.008296837098896503,
-0.03738931939005852,
0.017935678362846375,
0.08330793678760529,
-0.012467010878026485,
0.006457014009356499,
-0.006240519229322672,
-0.036816924810409546,
-0.010345577262341976,
-0.007472755387425423,
0.01868431456387043,
-0.011745719239115715,
-0.02141658030450344,
-0.003991636913269758,
0.06879071146249771,
0.005771560128778219,
0.016826480627059937,
-0.03047383576631546,
0.01712089590728283,
-0.019707491621375084,
0.0678919106721878,
-0.0449945293366909,
0.03882325440645218,
-0.05586808919906616,
0.007764738984405994,
-0.055576276034116745,
-0.01650889776647091,
-0.053705621510744095,
-0.014744087122380733,
0.014823716133832932,
-0.009593441151082516,
0.044852450489997864,
0.03524722531437874,
-0.01037816982716322,
-0.05614310875535011,
-0.036717336624860764,
-0.009671933948993683,
0.004978974815458059,
0.02165910415351391,
0.025179516524076462,
0.007726517040282488,
-0.0049163950607180595,
-0.037734318524599075,
0.05913528800010681,
-0.0545131154358387,
0.02586423046886921,
0.030963661149144173,
0.006476567592471838,
0.047908615320920944,
0.064448282122612,
0.005552867893129587,
-0.019276496022939682,
-0.04221717268228531,
-0.0019189954036846757,
0.09061076492071152,
0.07607636600732803,
-0.04629110172390938,
-0.04392360895872116,
0.05946726351976395,
0.015038110315799713,
0.059405773878097534,
-0.022005243226885796,
0.005477454978972673,
0.07978901267051697,
0.021682681515812874,
0.04348694533109665,
-0.02356230467557907,
-0.0006835318054072559,
-0.046229179948568344,
-0.05762670189142227,
-0.007842493243515491,
-0.003617582144215703,
-0.05725645273923874,
-0.045730311423540115,
-0.018003392964601517,
-0.00277827144600451,
0.0354740247130394,
-0.0021139951422810555,
-0.014571631327271461,
-0.02594556100666523,
-0.003174069570377469,
0.0014190120855346322,
0.011368336156010628,
0.0132779311388731,
0.02922992594540119,
0.06780596077442169,
0.06473910808563232,
0.023247793316841125,
0.014364250004291534,
0.003184591419994831,
0.07268527150154114,
0.02613152749836445,
-0.024288874119520187,
0.03461991623044014,
-0.049599360674619675,
0.01682271808385849,
0.005636611022055149,
-0.015580985695123672,
-0.023656019940972328,
0.07590892910957336,
0.06252671778202057,
0.03353395685553551,
0.013210773468017578,
0.011946354992687702,
0.05444789677858353,
-0.022695371881127357,
-0.03826049342751503,
-0.011221720837056637,
-0.06819380074739456,
-0.018030863255262375,
-0.042046885937452316,
-0.025165941566228867,
-0.002795134438201785,
-0.04250155761837959,
0.013018771074712276,
-0.0027433005161583424,
-0.012495250441133976,
-0.004037532489746809,
0.02796538546681404,
0.02255069464445114,
-0.0006060252781026065,
0.03835851699113846,
0.03379277512431145,
-0.006390759255737066,
-0.03319131210446358,
0.016135068610310555,
0.007018428761512041,
-0.014905381016433239,
-0.00796154048293829,
0.025683142244815826,
0.009054742753505707,
-0.053791482001543045,
0.02129327692091465,
0.056411344558000565,
0.0005180115695111454,
-0.02483842894434929,
-0.02730085700750351,
0.05222714692354202,
0.00352111947722733,
-0.07267037034034729,
0.027266884222626686,
-0.03513804450631142,
0.030668169260025024,
-0.019424138590693474,
-0.0433172881603241,
-0.012534580193459988,
0.023206880316138268,
-0.016407787799835205,
-0.05245877429842949,
-0.054769013077020645,
-0.00959780439734459,
0.019164156168699265,
-0.00866790022701025,
0.04849880561232567,
-0.023437626659870148,
0.0055252425372600555,
0.024416133761405945,
-0.05540154501795769,
-0.006329412572085857,
-0.034961599856615067,
-0.04592953994870186,
-0.013471809215843678,
-0.0022239398676902056,
-0.01583166792988777,
0.003979830536991358,
0.015805240720510483,
0.0017037808429449797,
0.005239028483629227,
0.003544067731127143,
0.05346528813242912,
-0.08441483974456787,
-0.009700347669422626,
0.034985579550266266,
0.07761555910110474,
0.002695417497307062,
0.06878742575645447,
0.048758700489997864,
-0.00507516972720623,
-0.029979657381772995,
0.04376962035894394,
0.07301457971334457,
0.0017597178230062127,
-0.02037002705037594,
0.013734104111790657,
0.030687956139445305,
-0.006801290437579155,
0.021243752911686897,
-0.03505596145987511,
0.03178874030709267,
0.03597217798233032,
-0.01968289725482464,
0.014196415431797504,
0.010988048277795315,
0.009151606820523739,
-0.01724931225180626,
-0.006948423571884632,
0.02689719758927822,
0.0175660140812397,
0.1139165461063385,
0.045417167246341705,
-0.030382419005036354,
-0.03629355877637863,
0.014897868037223816,
-0.09044199436903,
0.014165512286126614,
0.018958838656544685,
-0.03448747470974922,
0.007243959698826075,
-0.04317818954586983,
-0.025302575901150703,
-0.0438394621014595,
-0.0035288743674755096,
-0.06955914199352264,
-0.03695472702383995,
-0.0039038832765072584,
-0.059234172105789185,
-0.026226984336972237,
0.04668906703591347,
-0.0077595096081495285,
0.048232875764369965,
0.008269001729786396,
-0.02753494307398796,
-0.015127808786928654,
-0.06217552348971367,
-0.03466988354921341,
0.02576393075287342,
-0.04692723602056503,
-0.01726936176419258,
0.048745617270469666,
0.01524338312447071,
-0.03898203372955322,
0.0069538806565105915,
0.012317375279963017,
0.02902195230126381,
-0.03818289563059807,
0.020642707124352455,
0.05838897451758385,
-0.012058289721608162,
0.0676255151629448,
0.003799854079261422,
0.02458829991519451,
-0.061478618532419205,
0.07709979265928268,
0.0069811646826565266,
0.027705030515789986,
-0.003386878641322255,
-0.0018130855169147253,
0.07803865522146225,
0.011095701716840267,
-0.04978910833597183,
-0.07276085764169693,
-0.03690663352608681,
0.025716127827763557,
0.017354169860482216,
0.03940582647919655,
-0.0390482097864151,
-0.08189275115728378,
-0.0066931964829564095,
-0.06342015415430069,
0.03566749766469002,
0.05014336481690407,
0.05948500707745552,
0.016850870102643967,
0.014156037010252476,
0.007672764826565981,
-0.05264194682240486,
-0.0012720192316919565,
0.011456678621470928,
-0.05345951393246651,
-0.016530610620975494,
-0.00558070745319128,
0.0032457171473652124,
0.002304942812770605,
-0.0063342503271996975,
0.016668984666466713,
0.04721134901046753,
0.07475420832633972,
-0.021633142605423927,
0.016202686354517937,
0.027896851301193237,
-0.027260977774858475,
-0.058553826063871384,
-0.033324919641017914,
-0.0056341830641031265,
-0.008261525072157383,
0.01594705879688263,
-0.026879018172621727,
-0.04872402176260948,
0.054236169904470444,
-0.0040323915891349316,
-0.012737625278532505,
0.02891148440539837,
-0.02588646113872528,
-0.043827254325151443,
0.025322487577795982,
0.052154459059238434,
0.09149158000946045,
-0.004616504535079002,
0.027426086366176605,
-0.011981734074652195,
-0.027509309351444244,
0.07607830315828323,
-0.009549873881042004,
-0.013941185548901558,
-0.029151925817131996,
-0.009809581562876701,
-0.021873587742447853,
0.02640649862587452,
0.009409128688275814,
-0.04863622039556503,
0.025203706696629524,
0.000004197973339614691,
0.032852716743946075,
0.03445408120751381,
-0.10391438752412796,
-0.004988336935639381,
-0.04161912202835083,
-0.008885160088539124,
0.012963468208909035,
0.09920675307512283,
0.07560835778713226,
-0.07483439892530441,
0.010072807781398296,
0.0026847030967473984,
0.07173801958560944,
0.0682528093457222,
0.03350745886564255,
-0.041480086743831635,
0.0370139554142952,
-0.08008188009262085,
0.0015064905164763331,
0.015795087441802025,
0.0005276838201098144,
-0.015241499058902264,
0.07534527778625488,
-0.05279691144824028,
-0.027297331020236015,
0.0055866423062980175,
0.026301829144358635,
0.014694933779537678,
-0.006245538126677275,
0.023847967386245728,
-0.06312807649374008,
-0.039294447749853134,
0.007099153473973274,
-0.03000064752995968,
-0.00869060680270195,
-0.0020096770022064447,
-0.01982182264328003,
-0.002658276120200753,
0.004989330191165209,
-0.04101701080799103,
0.027610881254076958,
0.006037316285073757,
0.0179616529494524,
-0.05824878066778183,
0.04306016117334366,
-0.041694775223731995,
0.022824939340353012,
0.03501388058066368,
0.02623419277369976,
-0.014779054559767246,
0.021439652889966965,
-0.002121805911883712,
-0.0345894917845726,
0.007495298516005278,
0.02189275249838829,
0.007728532887995243,
0.018753739073872566,
-0.015950361266732216,
-0.00020705611677840352,
0.03826602175831795,
-0.00927747879177332,
-0.03469199687242508,
0.01777089573442936,
-0.02604333497583866,
-0.002538247499614954,
0.033464960753917694,
0.004624383058398962,
-0.04637828841805458,
-0.020740296691656113,
0.01985122077167034,
0.025066636502742767,
0.042354948818683624,
0.02744385413825512,
0.03902284428477287,
-0.019447792321443558,
-0.06747253984212875,
0.010487204417586327,
0.007568238768726587,
-0.08621390908956528,
0.008008220233023167,
0.018512610346078873,
0.0801306962966919,
0.0248529352247715,
-0.058668263256549835,
0.033692196011543274,
-0.03182060271501541,
-0.0704333707690239,
-0.007438973989337683,
-0.005150945857167244,
0.0015018077101558447,
0.024049988016486168,
-0.018709417432546616,
-0.02880118228495121,
0.01544432993978262,
-0.06437641382217407,
-0.05855833739042282,
0.07467914372682571,
0.014596141874790192,
0.03393549844622612,
0.03290321305394173,
0.047717947512865067,
0.030194243416190147,
0.04814101383090019,
-0.07645756006240845,
0.018100211396813393,
-0.04055760055780411,
-0.005485257599502802,
0.04154446721076965,
-0.011306898668408394,
-0.01082755345851183,
0.05725792422890663,
0.04157136380672455,
-0.009268046356737614,
-0.02562747150659561,
-0.05786270648241043,
0.04835498705506325,
-0.03183388710021973,
0.02615910954773426,
-0.009994695894420147,
-0.025932546705007553,
0.0002676981093827635,
-0.02501339092850685,
0.04876474663615227,
0.0028620215598493814,
0.007303211838006973,
0.0064224982634186745,
-0.023279931396245956,
-0.007873008958995342,
0.03205384314060211,
0.015261364169418812,
0.009012777358293533,
0.00846271775662899,
0.0324905663728714,
-0.07642355561256409,
-0.05014532431960106,
0.04392817243933678,
0.038177426904439926,
0.008954598568379879,
0.0006682502571493387,
0.0044467998668551445,
-0.03735887631773949,
0.009596038609743118,
0.02286664769053459,
0.0054574888199567795,
-0.009962869808077812,
-0.025354774668812752,
-0.05962302163243294,
-0.026892805472016335,
0.00615988252684474,
-0.02039646916091442,
0.006657770369201899,
-0.011763026006519794,
0.00327374879270792,
0.03229154273867607,
-0.037060149013996124,
-0.032693181186914444,
0.08102524280548096,
0.025659602135419846,
-0.022667154669761658,
0.0034679851960390806,
-0.04529291018843651,
-0.03154970332980156,
-0.0012495892588049173,
-0.00892188772559166,
0.005976551212370396,
-0.048753637820482254,
-0.03600577265024185,
-0.024303605780005455,
0.043868452310562134,
-0.031825073063373566,
0.035825543105602264,
0.0052867759950459,
0.025740619748830795,
0.03346746042370796,
-0.009833301417529583,
0.006430778652429581,
-0.041406236588954926,
0.011861593462526798,
-0.03548406809568405,
0.00505932979285717,
-0.046993438154459,
-0.04060712456703186,
-0.0009116475703194737,
-0.045695092529058456,
0.07912394404411316,
-0.0031971426215022802,
-0.030567316338419914,
-0.025921691209077835,
-0.028879869729280472,
-0.05843520164489746,
-0.03732794150710106,
-0.044287312775850296,
-0.03381069004535675,
0.04024490714073181,
0.01847486011683941,
-0.05954127013683319,
-0.010692537762224674,
-0.0006005333852954209,
-0.023363793268799782,
-0.002384248888120055,
-0.04310300946235657,
-0.029826128855347633,
0.028263447806239128,
0.000724645156878978,
0.01216983888298273,
-0.015554774552583694,
-0.037920884788036346,
-0.004755125846713781,
0.044689446687698364,
-0.014872629195451736,
0.022053338587284088,
0.037770915776491165,
0.00725675979629159,
-0.005472702439874411,
0.00826779194176197,
0.015088279731571674,
0.007836811244487762,
0.028041236102581024,
0.08059035986661911,
0.02857282944023609,
-0.010615051724016666,
0.09131836146116257,
0.01088840700685978,
-0.027224158868193626,
0.014111794531345367,
-0.020005319267511368,
-0.0252463947981596,
-0.010792995803058147,
-0.028816156089305878,
-0.014754999428987503,
0.028382135555148125,
-0.04385232552886009,
-0.022235354408621788,
-0.0346083827316761,
-0.015642862766981125,
-0.08229687064886093,
-0.043955735862255096,
0.013470843434333801,
-0.04043281078338623,
-0.03272286802530289,
0.011380257084965706,
-0.038169071078300476,
-0.021084921434521675,
-0.004265558440238237,
0.004754791036248207,
0.0020980294793844223,
0.01178048923611641,
-0.029683975502848625,
0.01340223103761673,
-0.02196686714887619,
0.03221609443426132,
-0.0615302212536335,
0.004326674621552229,
-0.0012014632811769843,
-0.0370585173368454,
-0.06372622400522232,
-0.0037648805882781744,
-0.03685848414897919,
0.0380978137254715,
0.012718125246465206,
0.014155319891870022,
-0.022701142355799675,
-0.004226527642458677,
0.016578705981373787,
-0.03797871246933937,
-0.01775064878165722,
0.015993857756257057,
0.062319058924913406,
0.013909228146076202,
0.08088363707065582,
-0.029219843447208405,
0.014677395112812519,
-0.026855936273932457,
-0.005992146208882332,
0.004988894332200289,
0.02460797131061554,
-0.03213243931531906,
-0.022963760420680046,
0.007279847748577595,
0.023565039038658142,
0.04700144752860069,
0.026186546310782433,
0.04722112789750099,
0.019319698214530945,
-0.007194292265921831,
-0.051171474158763885,
0.010852862149477005,
-0.001979297958314419,
0.030925670638680458,
-0.05356050282716751,
-0.07991816848516464,
-0.005289973225444555,
-0.02204994484782219,
-0.051326483488082886,
0.01883089356124401,
-0.017245708033442497,
0.047221455723047256,
0.0416073240339756,
0.0058427974581718445,
-0.02063797414302826,
-0.061922769993543625,
-0.027550378814339638,
-0.07053278386592865,
0.0018253508023917675,
-0.022293882444500923,
0.05725777521729469,
-0.052328191697597504,
-0.012674191035330296,
0.03331951051950455,
-0.03428035229444504,
0.020639747381210327,
0.019220486283302307,
-0.0515032596886158,
-0.03322002664208412,
-0.04675755649805069,
0.024380387738347054,
0.06604927033185959,
-0.052316825836896896,
-0.05666618421673775,
-0.03766478970646858,
-0.04308309778571129,
-0.0032908450812101364,
0.06546465307474136,
0.0014240951277315617,
-0.04357330873608589,
0.021654650568962097,
0.040159691125154495,
0.007236826233565807,
0.03996677324175835,
0.024542415514588356,
-0.008574570529162884,
0.028364311903715134,
-0.005771036259829998,
0.009723682887852192,
-0.03554411232471466,
0.031322162598371506
] |
[
8.621964454650879,
-1.7233364582061768
] |
Mesoscale and Nanoscale Physics
|
Condensed-Matter Physics
|
cond-mat-mes-hall
|
na
|
na
|
2007-04-01T07:36:16
|
No abstract given; compares pairs of languages from World Atlas of Language
Structures.
|
Pairwise comparisons of typological profiles (of languages)
|
physics.soc-ph
|
0704.0071
| 2,007
|
[
-0.012425155378878117,
-0.004385731648653746,
-0.00013318954734131694,
-0.05956652760505676,
0.008496412076056004,
-0.017498645931482315,
-0.01831933856010437,
0.004997583571821451,
-0.06675483286380768,
0.006505402270704508,
-0.05632622167468071,
0.01964123733341694,
0.03216185048222542,
0.001946711097843945,
0.009101726114749908,
-0.03518032282590866,
0.04449911043047905,
-0.009626926854252815,
0.014605607837438583,
-0.019432898610830307,
-0.02961050160229206,
0.01666106842458248,
0.0162900909781456,
0.014559507369995117,
0.0698975920677185,
0.005761472973972559,
0.014915229752659798,
-0.02863127924501896,
-0.09406352788209915,
0.012572466395795345,
0.03891057148575783,
-0.022639214992523193,
0.04859601706266403,
0.01248121540993452,
-0.05227354168891907,
0.012872894294559956,
0.07580959051847458,
-0.00012190671259304509,
-0.010747664608061314,
0.03578139469027519,
0.05088848993182182,
0.07751914113759995,
-0.0146712651476264,
-0.020203519612550735,
0.043980278074741364,
-0.039429035037755966,
0.01930076628923416,
0.019581960514187813,
0.015944506973028183,
-0.039580002427101135,
-0.005688290111720562,
0.02911565452814102,
0.01266719214618206,
-0.022800995036959648,
0.04489629715681076,
-0.006564750336110592,
0.023164885118603706,
-0.023336021229624748,
0.039258938282728195,
-0.05054159089922905,
0.00949032697826624,
0.0443856380879879,
-0.035283833742141724,
0.019897565245628357,
0.027627980336546898,
-0.04463835060596466,
-0.047555048018693924,
0.009917045943439007,
-0.0023659393191337585,
-0.06861093640327454,
0.01617644727230072,
0.017063332721590996,
0.008075769059360027,
0.0383969247341156,
-0.049970049411058426,
0.010772978886961937,
0.01762859709560871,
0.009296154603362083,
0.018512321636080742,
0.05700649321079254,
0.004218189977109432,
0.03267638012766838,
0.05700363591313362,
0.049705564975738525,
0.06413348764181137,
-0.023835746571421623,
0.012180258519947529,
0.022337235510349274,
-0.051647234708070755,
0.08176342397928238,
0.0017362900543957949,
-0.03838595002889633,
0.05722259730100632,
0.07337647676467896,
-0.0835651233792305,
0.002419120166450739,
-0.013963398523628712,
0.017879175022244453,
0.012153895571827888,
-0.05701697990298271,
-0.016364742070436478,
0.06006534397602081,
0.010903898626565933,
-0.02809188887476921,
0.05700620636343956,
-0.01983981393277645,
0.03643517568707466,
0.028679698705673218,
-0.06223281845450401,
-0.03197367116808891,
-0.04352755472064018,
0.026758575811982155,
-0.023883875459432602,
0.024141086265444756,
-0.07617441564798355,
-0.05817441642284393,
0.02710922434926033,
-0.08937864750623703,
-0.017398053780198097,
0.04363134130835533,
0.007175639271736145,
-0.08005017787218094,
-0.031294140964746475,
0.05861569568514824,
0.03598446026444435,
0.02511470951139927,
-0.03592540696263313,
-0.0005118170520290732,
-0.007963638752698898,
-0.045733824372291565,
0.0390794612467289,
0.01596398837864399,
0.03911879286170006,
0.0008327491814270616,
-0.016751162707805634,
0.053544044494628906,
-0.019801592454314232,
-0.049930330365896225,
0.0025655380450189114,
-0.0202373918145895,
-0.007401065900921822,
0.03845325857400894,
-0.03881825879216194,
-0.05551396310329437,
0.05671946331858635,
-0.0580543652176857,
0.021646849811077118,
-0.04527551680803299,
0.01152573898434639,
-0.0037168117705732584,
0.04718220233917236,
0.04311908036470413,
0.039240527898073196,
0.06043671816587448,
-0.07846206426620483,
-0.0323251411318779,
0.014314468018710613,
0.048657625913619995,
-0.013432263396680355,
-0.019252976402640343,
-0.0052894665859639645,
-0.018081065267324448,
-0.003451201133430004,
0.02171708643436432,
-0.021258212625980377,
0.0035399217158555984,
0.017440499737858772,
0.015808146446943283,
0.021403787657618523,
0.0280245840549469,
-0.031212473288178444,
0.003044312121346593,
-0.016205137595534325,
-0.02099800854921341,
0.02815910242497921,
0.010035636834800243,
-0.0049524689093232155,
-0.03172209486365318,
-0.0016888012178242207,
0.020324641838669777,
0.03466564789414406,
-0.0027670252602547407,
0.019142277538776398,
0.05827530473470688,
-0.009993228130042553,
-0.03119632415473461,
-0.002827224088832736,
-0.04362598434090614,
-0.0372130423784256,
0.012712182477116585,
0.011387098580598831,
-0.0003269264998380095,
-0.029388107359409332,
-0.07031737267971039,
0.025956138968467712,
-0.044092535972595215,
0.02390395663678646,
0.00964878685772419,
0.01830133982002735,
-0.0657033622264862,
-0.024445444345474243,
0.0037293960340321064,
-0.07133740186691284,
0.01978534832596779,
-0.0928424671292305,
0.02698737196624279,
-0.009075484238564968,
-0.011616731062531471,
0.03609084710478783,
0.0022383504547178745,
0.04198791831731796,
0.02440674975514412,
-0.014751906506717205,
-0.016602318733930588,
-0.022579215466976166,
-0.01272423192858696,
0.005118559114634991,
0.0023405130486935377,
-0.04025307670235634,
-0.026777049526572227,
0.03317796066403389,
-0.0410354845225811,
-0.008544781245291233,
0.017724156379699707,
0.06979667395353317,
-0.022315099835395813,
-0.03422766178846359,
0.002619013888761401,
-0.024001367390155792,
-0.027956029400229454,
-0.01984904147684574,
-0.10025976598262787,
0.05712398141622543,
-0.0546884760260582,
-0.014188396744430065,
0.012432542629539967,
0.04392325505614281,
0.050390277057886124,
0.022151125594973564,
0.019073788076639175,
0.023228630423545837,
-0.02633705362677574,
-0.008632025681436062,
0.059752751141786575,
-0.002481915056705475,
-0.02655726857483387,
-0.01715245470404625,
0.044136520475149155,
-0.011106422170996666,
0.047817010432481766,
-0.01442386768758297,
0.0012981140753254294,
0.018111910670995712,
0.048813510686159134,
0.029618822038173676,
-0.005588712636381388,
0.01784415729343891,
0.002036184072494507,
0.013384628109633923,
0.02077455259859562,
0.019755374640226364,
-0.06609725952148438,
0.0009633409790694714,
-0.07225161045789719,
-0.012972570955753326,
0.02950412966310978,
0.04249303787946701,
-0.028937235474586487,
0.015111093409359455,
-0.04245489835739136,
-0.04514375701546669,
0.0023554873187094927,
0.00886321347206831,
0.050662606954574585,
-0.049224961549043655,
0.02873518317937851,
-0.03195996955037117,
-0.013295953162014484,
-0.011649565771222115,
0.01988903619349003,
-0.013382786884903908,
0.025154629722237587,
0.02274417318403721,
0.03923453763127327,
0.04175926372408867,
0.05474008619785309,
0.05186937376856804,
0.009594958275556564,
-0.005028607789427042,
-0.005352153442800045,
-0.028453011065721512,
0.03185883164405823,
0.04330884665250778,
0.06027531996369362,
0.016953062266111374,
0.04224841669201851,
0.01465053390711546,
-0.016931913793087006,
0.0463058166205883,
-0.021416353061795235,
0.0338234044611454,
0.01601077988743782,
0.02209923416376114,
0.029158292338252068,
0.08185093104839325,
-0.04047633334994316,
0.021213466301560402,
-0.04968726634979248,
0.017755376175045967,
0.021789975464344025,
-0.005719214212149382,
0.020787714049220085,
-0.04769989475607872,
-0.030278893187642097,
-0.037703074514865875,
0.0420280322432518,
0.06700143963098526,
0.023347968235611916,
0.022171813994646072,
-0.0011699822498485446,
-0.003170742653310299,
-0.04184455797076225,
0.03386182337999344,
-0.044040098786354065,
0.006602604407817125,
0.04891844093799591,
0.02079431153833866,
0.031095540151000023,
-0.056429289281368256,
0.02838457189500332,
0.0027719212230294943,
0.06303491443395615,
-0.015256110578775406,
-0.03984639793634415,
-0.022882331162691116,
0.03427201136946678,
-0.04410889744758606,
-0.029525212943553925,
-0.01572311669588089,
-0.025446977466344833,
-0.0077976044267416,
-0.011473886668682098,
0.0015976043650880456,
-0.008162817917764187,
0.0021139804739505053,
0.03026503697037697,
-0.038834087550640106,
-0.0020972283091396093,
0.07524492591619492,
0.005545780062675476,
-0.029075320810079575,
0.05884021520614624,
0.010041464120149612,
-0.0015807339223101735,
-0.011632177978754044,
0.029041342437267303,
0.0704333707690239,
-0.04711293801665306,
0.049905456602573395,
-0.01592787727713585,
0.02910631150007248,
-0.03529835119843483,
0.008661273866891861,
-0.04514233395457268,
-0.01534765213727951,
0.02245361916720867,
0.04202868789434433,
0.04869193211197853,
0.05381207540631294,
-0.0446433499455452,
-0.03249483183026314,
-0.033014748245477676,
0.0010135621996596456,
0.013561426661908627,
0.07242927700281143,
-0.0037071839906275272,
-0.010915229097008705,
-0.0023963223211467266,
-0.034250080585479736,
0.0024191690608859062,
0.11553481966257095,
-0.0034008994698524475,
0.04940784350037575,
0.03787548094987869,
0.012977919541299343,
-0.05034299194812775,
-0.07609400153160095,
0.06861446052789688,
-0.027464596554636955,
0.01667950302362442,
-0.015295281074941158,
-0.023385215550661087,
-0.05130567401647568,
0.034056030213832855,
-0.020339058712124825,
0.019044620916247368,
0.013791235163807869,
-0.01673802174627781,
-0.037418946623802185,
0.05088048055768013,
-0.019615087658166885,
-0.05053635686635971,
-0.018103545531630516,
0.016613243147730827,
-0.039266541600227356,
-0.028179502114653587,
0.0002322469517821446,
-0.05545732006430626,
-0.003773388219997287,
-0.013680841773748398,
-0.005731097422540188,
-0.010625203140079975,
0.002448858693242073,
-0.03823535516858101,
-0.030268322676420212,
-0.006400416139513254,
0.03616347908973694,
-0.05482478067278862,
-0.001420220942236483,
-0.0013377898139879107,
-0.003519143210723996,
0.04416245222091675,
0.011441522277891636,
-0.0171335618942976,
0.017656881362199783,
-0.0038318040315061808,
-0.016416603699326515,
0.0429190956056118,
0.009092803113162518,
-0.0020424530375748873,
0.035230737179517746,
0.017636284232139587,
0.03732481226325035,
0.03179381415247917,
-0.04455515369772911,
-0.0042625307105481625,
0.05321614071726799,
0.02579663321375847,
0.008782604709267616,
-0.030769510194659233,
-0.03385863080620766,
-0.02207711525261402,
-0.024765662848949432,
0.008336744271218777,
0.055190712213516235,
0.08161129057407379,
0.026575913652777672,
-0.01962646283209324,
-0.040386028587818146,
-0.0094746770337224,
0.04100548103451729,
0.01830398663878441,
0.003810544265434146,
-0.01379459723830223,
0.07982524484395981,
-0.00017641860176809132,
0.024112960323691368,
0.004510041326284409,
0.03972185030579567,
0.0599396638572216,
0.005036408081650734,
-0.028584329411387444,
-0.030974335968494415,
-0.02927449345588684,
0.036936234682798386,
-0.0037920591421425343,
-0.04884818196296692,
0.0329531729221344,
-0.07107171416282654,
0.0138710867613554,
-0.001953370403498411,
-0.02013533003628254,
0.0293227918446064,
-0.02949688397347927,
-0.007326677907258272,
0.030938275158405304,
0.022113138809800148,
-0.013807190582156181,
-0.025485869497060776,
-0.004053626209497452,
0.004633978009223938,
0.001696758670732379,
-0.03327621519565582,
-0.04273523762822151,
-0.005643199197947979,
0.05125964432954788,
-0.028045527637004852,
-0.003644145792350173,
-0.03137512132525444,
0.030548186972737312,
0.009671736508607864,
-0.006933543365448713,
0.00010673048382159323,
-0.021433526650071144,
-0.059338249266147614,
-0.04197285696864128,
-0.007968315854668617,
0.02760181576013565,
0.05289235711097717,
0.011729256249964237,
-0.008217724971473217,
0.036425281316041946,
-0.013729468919336796,
0.02267792448401451,
0.016118083149194717,
0.006310664117336273,
0.0675526037812233,
-0.016557326540350914,
0.002041605766862631,
0.05635270103812218,
0.08106105774641037,
0.007862378843128681,
0.0054448749870061874,
0.06755504757165909,
0.03493344411253929,
-0.04938509315252304,
0.04091622307896614,
-0.0038254589308053255,
-0.03955380991101265,
-0.020132824778556824,
-0.03746277093887329,
0.013240820728242397,
-0.034542251378297806,
0.0725632980465889,
-0.054243139922618866,
0.016945134848356247,
0.0034045022912323475,
-0.06318657100200653,
-0.05595209077000618,
0.00017033243784680963,
-0.011671777814626694,
0.024997776374220848,
-0.009558803401887417,
-0.023246973752975464,
0.04723586514592171,
-0.02448478899896145,
-0.024199804291129112,
0.015785766765475273,
-0.025717005133628845,
0.023443354293704033,
-0.014414536766707897,
0.007595956325531006,
-0.0075822509825229645,
0.004462233744561672,
0.011234505102038383,
-0.016417741775512695,
-0.08995015174150467,
-0.012361211702227592,
-0.026704244315624237,
-0.03860379382967949,
-0.053946368396282196,
-0.014028823934495449,
0.0335761196911335,
-0.04288606345653534,
0.022063514217734337,
-0.060026977211236954,
0.02613753080368042,
-0.03175130859017372,
-0.03780415654182434,
-0.04179536551237106,
-0.0006162960780784488,
-0.0021518568973988295,
0.02620742842555046,
-0.02543218806385994,
0.023818563669919968,
-0.06010626256465912,
-0.06738326698541641,
0.024994896724820137,
0.0030101845040917397,
-0.0006149474647827446,
0.01801169291138649,
-0.01401499193161726,
-0.017035072669386864,
0.05341069772839546,
0.02227594144642353,
-0.043737635016441345,
0.024502446874976158,
0.009851351380348206,
-0.012754068709909916,
-0.04671443626284599,
0.001000670832581818,
-0.05215989425778389,
-0.011389768682420254,
-0.020821448415517807,
-0.06346362829208374,
0.032382864505052567,
0.0022582265082746744,
-0.004603004083037376,
-0.006731362082064152,
0.02656475082039833,
-0.008687683381140232,
-0.03223401680588722,
-0.0039376490749418736,
-0.034381408244371414,
-0.029205843806266785,
-0.006759171839803457,
0.006710683926939964,
0.10240816324949265,
-0.047806836664676666,
-0.04568320885300636,
-0.0020997123792767525,
0.03261476010084152,
0.041993603110313416,
-0.04517383128404617,
0.05696349963545799,
0.050269708037376404,
-0.014149371534585953,
0.0211239755153656,
-0.050131529569625854,
-0.010366248898208141,
-0.012523433193564415,
0.05554668977856636,
-0.026610488072037697,
0.002642690436914563,
0.012704149819910526,
-0.051841724663972855,
0.03768623247742653,
-0.055283986032009125,
-0.021751118823885918,
-0.06843866407871246,
0.0012711723102256656,
-0.1008724644780159,
0.043855324387550354,
-0.06349516659975052,
0.022800078615546227,
0.0018136764410883188,
-0.010558712296187878,
-0.014724976383149624,
0.0029976116493344307,
0.034281231462955475,
-0.019075853750109673,
0.032406408339738846,
-0.03345866873860359,
-0.043695662170648575,
-0.05556868389248848,
-0.019252512603998184,
-0.06754118949174881,
-0.0023310233373194933,
0.04155859351158142,
0.02477453090250492,
0.03929435834288597,
-0.01483995746821165,
-0.001429630909115076,
-0.010483043268322945,
0.061666857451200485,
-0.025336479768157005,
-0.025200529024004936,
0.007352551445364952,
-0.004877271596342325,
-0.024058979004621506,
0.08647195994853973,
0.09169384837150574,
0.0029681299347430468,
0.011207837611436844,
0.004669107496738434,
-0.006115444004535675,
0.04748329520225525,
-0.021927304565906525,
-0.01843230053782463,
0.058144956827163696,
-0.011892735958099365,
-0.026068557053804398,
-0.05224210023880005,
0.0011795326136052608,
0.007763377856463194,
0.017006251960992813,
0.0047356546856462955,
-0.050867218524217606,
0.030588002875447273,
0.014137445949018002,
-0.033007245510816574,
0.012670778669416904,
-0.017687374725937843,
-0.06087292730808258,
-0.017165618017315865,
0.022022737190127373,
0.007035703398287296,
-0.05377410724759102,
-0.00023280225286725909,
-0.05049562081694603,
0.03335748240351677,
0.0038119021337479353,
0.00010936609032796696,
-0.0008156968979164958,
0.003927262499928474,
-0.03656561300158501,
-0.01276793610304594,
-0.06468835473060608,
-0.01236112229526043,
-0.07467777281999588,
-0.002303515328094363,
-0.01222142018377781,
0.01604715920984745,
-0.060465190559625626,
0.00025985451065935194,
0.011027846485376358,
-0.022774454206228256,
-0.0406881608068943,
0.0037637893110513687,
0.03797653689980507,
0.06688416004180908,
0.03188663348555565,
-0.020167335867881775,
0.048692867159843445,
-0.0581231489777565,
-0.02797798626124859,
0.05022897198796272,
0.027406293898820877,
0.02035796456038952,
-0.05873691290616989,
-0.016314087435603142,
0.025309234857559204,
0.07325369119644165,
0.025361401960253716,
0.016359418630599976,
-0.03543880954384804,
0.020392347127199173,
-0.045666277408599854,
0.04120125249028206,
-0.05353020876646042,
0.016605552285909653,
-0.02948547713458538,
0.023029077798128128,
0.03317556902766228,
-0.055683813989162445,
0.01113354042172432,
0.006076904945075512,
-0.015234904363751411,
0.02857816405594349,
0.010848846286535263,
-0.023464364930987358,
-0.018855009227991104,
-0.05025069788098335,
0.057076793164014816,
-0.055876608937978745,
0.055141374468803406,
-0.01637249067425728,
0.10194966942071915,
-0.09804486483335495,
-0.008397557772696018,
-0.045661408454179764,
0.023275595158338547,
-0.0070396652445197105,
0.10080662369728088,
-0.013870080932974815,
-0.015009579248726368,
0.003501636441797018,
0.05629922077059746,
0.053016915917396545,
0.014188752509653568,
-0.005046074744313955,
-0.048117272555828094,
0.0048102717846632,
0.0014660116285085678,
-0.0390051044523716,
0.030428128316998482,
0.003345034783706069,
0.023109812289476395,
0.10083502531051636,
0.0064916834235191345,
-0.004047921858727932,
-0.037911027669906616,
0.01873607747256756,
0.008287622593343258,
0.014616655185818672,
0.05196249112486839,
-0.03572599217295647,
-0.02672027051448822
] |
[
2.270690441131592,
11.84695053100586
] |
Physics and Society
|
General Physics
|
physics-soc-ph
|
na
|
na
|
2007-04-01T07:58:53
|
In present paper we propose seemingly new method for finding solutions of
some types of nonlinear PDEs in closed form. The method is based on
decomposition of nonlinear operators on sequence of operators of lower orders.
It is shown that decomposition process can be done by iterative procedure(s),
each step of which is reduced to solution of some auxiliary PDEs system(s) for
one dependent variable. Moreover, we find on this way the explicit expression
of the first-order PDE(s) for first integral of decomposable initial PDE.
Remarkably that this first-order PDE is linear if initial PDE is linear in its
highest derivatives.
The developed method is implemented in Maple procedure, which can really
solve many of different order PDEs with different number of independent
variables. Examples of PDEs with calculated their general solutions demonstrate
a potential of the method for automatic solving of nonlinear PDEs.
|
The decomposition method and Maple procedure for finding first integrals
of nonlinear PDEs of any order with any number of independent variables
|
math-ph math.MP
|
0704.0072
| 2,007
|
[
0.04853589087724686,
-0.016044622287154198,
0.014250391162931919,
-0.00790315493941307,
0.01789500005543232,
-0.03305785730481148,
-0.02261159010231495,
0.04408709704875946,
-0.06007824093103409,
0.009665336459875107,
-0.0905960276722908,
0.03614648059010506,
-0.029194599017500877,
0.027652859687805176,
-0.018128851428627968,
-0.027927374467253685,
0.023031702265143394,
-0.0013528227573260665,
-0.060653652995824814,
-0.015926791355013847,
-0.006904625799506903,
0.016873333603143692,
-0.034705616533756256,
0.007530590984970331,
0.07744994759559631,
0.03674869239330292,
0.022186346352100372,
-0.005732071585953236,
-0.04354040324687958,
0.03230984881520271,
0.03369082883000374,
-0.06106872484087944,
0.026019912213087082,
-0.028552327305078506,
-0.050992488861083984,
0.04497701674699783,
0.06404011696577072,
-0.03968159109354019,
0.032196126878261566,
0.023790651932358742,
-0.012748777866363525,
-0.03603338450193405,
0.043577246367931366,
-0.019828442484140396,
-0.02475464530289173,
-0.01416579820215702,
0.016186878085136414,
-0.014576142653822899,
0.012205139733850956,
0.018155474215745926,
0.0422917939722538,
0.004896915052086115,
0.006276234518736601,
-0.08876034617424011,
-0.029848357662558556,
0.03570974990725517,
0.00449033360928297,
-0.017411286011338234,
0.05413525924086571,
-0.012940258719027042,
0.02228718250989914,
0.017219435423612595,
0.010124348104000092,
-0.020715931430459023,
0.023933516815304756,
-0.08113095909357071,
0.0065130372531712055,
-0.003842870006337762,
0.02574831247329712,
0.005653616972267628,
0.01659650169312954,
-0.027009230107069016,
0.018016748130321503,
-0.021267540752887726,
-0.0077164010144770145,
0.0033730005379766226,
0.021750595420598984,
-0.033573172986507416,
-0.005547761917114258,
0.04373007267713547,
0.009421663358807564,
-0.00829029269516468,
0.07328789681196213,
0.006315490696579218,
0.06453026831150055,
-0.02704152837395668,
0.0390690341591835,
-0.0033437313977628946,
-0.05114782229065895,
0.03954119607806206,
-0.014212282374501228,
0.009029087610542774,
0.023635240271687508,
0.08125688135623932,
-0.05768855661153793,
0.05398575961589813,
-0.03496520593762398,
0.018145330250263214,
0.016469551250338554,
-0.08571719378232956,
0.021749161183834076,
-0.021930668503046036,
0.019216088578104973,
-0.03704378381371498,
0.09155348688364029,
0.007758451625704765,
0.0353722982108593,
0.009788237512111664,
-0.03167347609996796,
-0.020389504730701447,
-0.028525637462735176,
0.002117156982421875,
-0.028423311188817024,
-0.011566503904759884,
-0.011592436581850052,
-0.025160815566778183,
0.023288019001483917,
-0.09641079604625702,
0.003045220859348774,
0.06688503175973892,
-0.01372828334569931,
0.007672946434468031,
0.03574634715914726,
0.04694416746497154,
0.024555178359150887,
0.011395526118576527,
-0.028427833691239357,
0.02665645070374012,
0.025360306724905968,
-0.04477706179022789,
0.006681129336357117,
-0.006393612362444401,
-0.0336611270904541,
0.016950760036706924,
0.04176463559269905,
0.023794881999492645,
-0.04614882916212082,
-0.04875272512435913,
0.005473552271723747,
-0.024171501398086548,
0.03799067810177803,
-0.01971476338803768,
0.0014452784089371562,
0.02270563878118992,
0.032875873148441315,
-0.031230933964252472,
0.01876094378530979,
-0.06454771757125854,
-0.05295397713780403,
0.0019031224073842168,
0.01865253411233425,
0.007533000782132149,
-0.011966148391366005,
0.0018350876634940505,
-0.02641472965478897,
-0.0207597017288208,
-0.008887924253940582,
-0.0043223402462899685,
0.02362411469221115,
-0.038910266011953354,
0.00013370228407438844,
0.00398446898907423,
-0.033412568271160126,
0.0228081364184618,
-0.04418344050645828,
0.012709115631878376,
-0.022023560479283333,
-0.008446008898317814,
0.04590897634625435,
-0.013276547193527222,
-0.03595526143908501,
-0.015051448717713356,
-0.037511181086301804,
-0.019263077527284622,
0.05631980672478676,
0.04384069889783859,
-0.017409173771739006,
-0.06030909717082977,
0.020997272804379463,
-0.0014799829805269837,
0.03757072612643242,
0.01676512323319912,
0.02959630824625492,
0.04928766191005707,
0.030177097767591476,
0.0035722178872674704,
-0.0003858923737425357,
-0.001134373596869409,
0.03017696924507618,
-0.05237918719649315,
0.03744733706116676,
0.0570562481880188,
-0.022397879511117935,
-0.049016449600458145,
0.018596557900309563,
0.012037658132612705,
0.03340993821620941,
-0.012866279110312462,
-0.007028284016996622,
-0.03607572242617607,
0.02430460788309574,
0.0021083038300275803,
-0.0228293314576149,
0.014776988886296749,
-0.0697324275970459,
0.0872965157032013,
0.02964264154434204,
0.04147679731249809,
0.0363144651055336,
0.004836921580135822,
0.04739895462989807,
-0.008216931484639645,
0.015115344896912575,
0.011589818634092808,
-0.05503467097878456,
-0.02247443050146103,
0.03263283520936966,
-0.020643943920731544,
-0.03405346721410751,
0.038406435400247574,
0.018571527674794197,
-0.036040034145116806,
-0.03330434858798981,
0.019100774079561234,
0.011566431261599064,
0.036111339926719666,
-0.018639450892806053,
0.007985454052686691,
-0.012978006154298782,
-0.056559812277555466,
-0.027195779606699944,
-0.07140424102544785,
0.004918952006846666,
-0.006810422986745834,
0.023017698898911476,
0.0014775421004742384,
-0.025802310556173325,
0.005490338895469904,
0.043633077293634415,
0.07329229265451431,
-0.0036931687500327826,
0.00028378734714351594,
0.042276106774806976,
0.018765168264508247,
-0.059807196259498596,
-0.016784803941845894,
0.012418769299983978,
0.01488723885267973,
-0.06178617477416992,
0.0036782221868634224,
-0.005296298302710056,
0.004330743104219437,
-0.0018518775468692183,
0.03499741479754448,
0.03204062581062317,
-0.002038040431216359,
-0.06929244101047516,
0.07402903586626053,
0.014429761096835136,
-0.08114444464445114,
0.023713193833827972,
-0.010492192581295967,
0.0019665996078401804,
0.012502496130764484,
-0.06216299161314964,
0.019402913749217987,
-0.01776605285704136,
-0.059189580380916595,
0.028119811788201332,
-0.042417384684085846,
-0.013182797469198704,
0.04154837876558304,
0.02397402562201023,
0.05348413810133934,
-0.0197205301374197,
-0.02464732713997364,
0.008908595889806747,
0.004953361116349697,
-0.02908765710890293,
-0.006677788682281971,
-0.03760965168476105,
-0.024901337921619415,
-0.06720291823148727,
-0.0030650487169623375,
0.03802773728966713,
-0.015695977956056595,
0.08318797498941422,
-0.01503942720592022,
0.005968599580228329,
-0.016384530812501907,
-0.04036897048354149,
0.0021903410088270903,
0.0062018586322665215,
0.009091107174754143,
-0.015273959375917912,
0.0644022524356842,
0.09387920796871185,
-0.05477859824895859,
0.015254940837621689,
-0.01226022932678461,
-0.04748332500457764,
0.007906554266810417,
0.041856858879327774,
-0.005237125791609287,
0.01702287420630455,
0.02536746673285961,
-0.0018434454686939716,
0.011252646334469318,
0.0026574034709483385,
0.04186803102493286,
0.008264286443591118,
0.019495388492941856,
-0.02611132524907589,
-0.020405646413564682,
-0.06853291392326355,
0.05990589037537575,
0.05948524922132492,
-0.06261017173528671,
0.10075636953115463,
0.061137665063142776,
-0.02112308144569397,
-0.08972446620464325,
0.051129039376974106,
-0.06464184820652008,
0.029620526358485222,
0.019965142011642456,
-0.02088908851146698,
0.033912450075149536,
-0.06025298312306404,
-0.0015727711142972112,
-0.013324592262506485,
0.07603543996810913,
-0.022196585312485695,
0.04273247718811035,
-0.0016881100600585341,
-0.04821295291185379,
-0.040868423879146576,
-0.04473656788468361,
-0.0028081766795367002,
-0.03219550848007202,
0.04421650618314743,
-0.030769070610404015,
-0.05728602409362793,
-0.031613439321517944,
-0.026071827858686447,
-0.02986498735845089,
-0.006844998337328434,
0.03863196447491646,
0.03774813935160637,
0.0044082398526370525,
-0.051999419927597046,
-0.025349168106913567,
0.02041289396584034,
-0.036646101623773575,
-0.01383230835199356,
0.031840622425079346,
0.0669049546122551,
-0.006055252626538277,
0.04049933701753616,
0.036787595599889755,
0.027760520577430725,
-0.010072573088109493,
0.022188955917954445,
0.048277951776981354,
0.028879158198833466,
0.04021424427628517,
0.029450492933392525,
0.017055267468094826,
-0.04635901004076004,
-0.05363377928733826,
-0.0486912839114666,
-0.007981210947036743,
0.053866878151893616,
-0.01318448781967163,
0.013342654332518578,
-0.018023943528532982,
-0.0381304994225502,
0.0051345499232411385,
0.02813085913658142,
0.016391413286328316,
0.05119985714554787,
-0.004810796584933996,
0.05055292323231697,
0.05305403843522072,
0.01133506279438734,
0.07733414322137833,
-0.0271884948015213,
-0.038158584386110306,
0.020962106063961983,
-0.02785450965166092,
0.06224494427442551,
-0.035706132650375366,
-0.03012688457965851,
0.046369221061468124,
-0.011067071929574013,
0.01643229089677334,
0.006462086923420429,
0.008503690361976624,
-0.035840488970279694,
-0.05251029133796692,
-0.055899109691381454,
-0.11396247893571854,
-0.013611490838229656,
0.012841214425861835,
0.0266372449696064,
0.041468117386102676,
-0.016095547005534172,
-0.06239091232419014,
0.04387453570961952,
-0.0019181169336661696,
0.003273835638538003,
-0.006034318823367357,
-0.023386463522911072,
-0.055524665862321854,
0.030741611495614052,
0.0045782229863107204,
0.07003510743379593,
-0.02067236788570881,
0.010909132659435272,
-0.015422860160470009,
0.011459462344646454,
0.05029529333114624,
-0.08096285164356232,
0.03620770946145058,
-0.055038027465343475,
-0.0008557504625059664,
0.0031572484876960516,
0.013792270794510841,
0.026753848418593407,
-0.05644708871841431,
-0.022431254386901855,
-0.004422597587108612,
-0.0025235512293875217,
0.03024437464773655,
-0.04713776335120201,
-0.010248559527099133,
0.06905587762594223,
0.021698812022805214,
-0.0018208648543804884,
0.022452427074313164,
0.011349938809871674,
-0.020783912390470505,
0.002815495477989316,
-0.0010531486477702856,
0.06962203234434128,
0.04791882261633873,
0.10698029398918152,
-0.022358914837241173,
-0.04264909029006958,
-0.04694128781557083,
0.053991857916116714,
0.028351522982120514,
-0.02010118030011654,
0.011848563328385353,
0.06548319011926651,
-0.016035890206694603,
0.0021649508271366358,
-0.003779515391215682,
0.008974897675216198,
0.07627319544553757,
0.04555298388004303,
0.05985231697559357,
-0.008058479055762291,
0.013871455565094948,
-0.001272619585506618,
0.011496253311634064,
-0.02359943836927414,
0.023339925333857536,
0.005908636376261711,
0.05700325220823288,
0.010507762432098389,
0.02149100974202156,
0.0597318597137928,
-0.03948390483856201,
-0.047000035643577576,
-0.04256465658545494,
0.005404215306043625,
-0.017209665849804878,
0.011409659869968891,
0.0541609525680542,
-0.010877367109060287,
-0.04013077914714813,
-0.04143863543868065,
0.01200298685580492,
0.0009773008059710264,
0.0193173810839653,
-0.026751426979899406,
-0.029422538354992867,
-0.009639458730816841,
-0.046206988394260406,
-0.006390790920704603,
0.07211026549339294,
0.014148828573524952,
0.026874201372265816,
-0.0029629780910909176,
-0.04547269269824028,
0.027709132060408592,
-0.040671754628419876,
0.05020055174827576,
-0.004156014882028103,
-0.0654274970293045,
-0.006537942215800285,
-0.047447964549064636,
0.00675647659227252,
0.02527426928281784,
0.03400401398539543,
-0.0022599068470299244,
-0.059210244566202164,
-0.015050912275910378,
0.027231404557824135,
0.036655593663454056,
0.0002627806970849633,
0.042700618505477905,
0.04817524179816246,
0.0038068469148129225,
-0.06615380197763443,
0.03434707596898079,
0.026563063263893127,
-0.04581600800156593,
0.0009894908871501684,
0.05140794813632965,
-0.0061594415456056595,
0.004544026218354702,
0.02721461094915867,
-0.04422120377421379,
0.01592358574271202,
-0.054185062646865845,
-0.02505681850016117,
-0.0032470058649778366,
-0.02953929640352726,
-0.027366403490304947,
0.015603926032781601,
-0.0027416350785642862,
-0.008115529082715511,
-0.003453073790296912,
-0.03916384279727936,
-0.058787137269973755,
0.008934160694479942,
0.023409854620695114,
0.0628456175327301,
-0.04859147593379021,
0.026258107274770737,
0.028761839494109154,
0.0019562591332942247,
-0.0013640961842611432,
-0.009492039680480957,
-0.047566007822752,
0.040987059473991394,
-0.013877175748348236,
-0.024835703894495964,
0.01472037099301815,
-0.0903313085436821,
0.02656647562980652,
-0.06849158555269241,
0.00005363237141864374,
-0.012858763337135315,
0.01085542980581522,
-0.04315761476755142,
-0.027270738035440445,
0.005791100207716227,
-0.001389696029946208,
-0.053567297756671906,
0.0495791956782341,
0.028121354058384895,
-0.03860858082771301,
-0.10467702895402908,
0.024050531908869743,
0.008725849911570549,
0.009441458620131016,
-0.01180264726281166,
-0.012964439578354359,
-0.03889326751232147,
0.017530323937535286,
0.04968440532684326,
0.023930778726935387,
-0.010806431993842125,
0.021457891911268234,
0.0044202739372849464,
-0.004353520926088095,
0.009956504218280315,
-0.044174253940582275,
0.007082717958837748,
0.02652701549232006,
-0.014730761758983135,
-0.07962968200445175,
0.03254064545035362,
-0.02403116039931774,
-0.05816442146897316,
0.04443761706352234,
0.005113381892442703,
0.042722996324300766,
-0.009188784286379814,
-0.05017341300845146,
-0.02559821680188179,
-0.0060703144408762455,
0.01441483199596405,
0.07342173159122467,
0.01440190989524126,
0.02583245187997818,
-0.012876829132437706,
-0.00800561998039484,
0.004493473097681999,
0.039616312831640244,
-0.05548268184065819,
-0.007658934686332941,
0.0693058893084526,
0.05331287905573845,
0.04435563459992409,
0.020351100713014603,
-0.016629816964268684,
0.008186710998415947,
0.04094429314136505,
-0.06701451539993286,
-0.04833458364009857,
0.011804546229541302,
-0.04851498454809189,
0.06511923670768738,
-0.017248179763555527,
0.0268806554377079,
-0.03592534735798836,
-0.0051680500619113445,
-0.01998700201511383,
-0.013841592706739902,
-0.045079417526721954,
-0.01759522594511509,
0.025075536221265793,
-0.00808433536440134,
-0.10099531710147858,
0.023367565125226974,
0.04432153329253197,
0.02056805044412613,
-0.01817876473069191,
-0.01332783605903387,
-0.032801564782857895,
-0.014123561792075634,
0.012018129229545593,
-0.038038305938243866,
0.005680025089532137,
-0.007190303411334753,
0.05155329033732414,
0.004409207962453365,
-0.03181225061416626,
0.024261923506855965,
-0.028018612414598465,
0.022694464772939682,
0.04949770122766495,
0.03781738504767418,
0.02184361219406128,
0.0010925879469141364,
0.00850827805697918,
0.08144088834524155,
0.09365880489349365,
-0.01558187697082758,
0.013941685669124126,
-0.021685699000954628,
-0.009010444395244122,
0.02217463217675686,
0.0018400026019662619,
-0.0013374057598412037,
0.030241988599300385,
-0.01675087958574295,
-0.0022656451910734177,
-0.0013717502588406205,
-0.04946339130401611,
0.035335130989551544,
-0.018590787425637245,
0.02676459588110447,
0.023262029513716698,
-0.048365235328674316,
0.03267507627606392,
-0.045211754739284515,
-0.06751358509063721,
-0.01679021678864956,
-0.021068261936306953,
0.007360119838267565,
0.04966161027550697,
0.019698182120919228,
-0.026647813618183136,
-0.00480164447799325,
-0.03663171827793121,
-0.039436761289834976,
0.0013153795152902603,
-0.02533780410885811,
0.0050687482580542564,
-0.006886036600917578,
-0.010969260707497597,
-0.005884031765162945,
0.018651973456144333,
0.00036621803883463144,
-0.02862841822206974,
0.013551599346101284,
0.020228762179613113,
0.03421489894390106,
-0.10110335797071457,
0.04607001692056656,
-0.03579186648130417,
-0.05746807903051376,
0.05102759227156639,
0.019444575533270836,
0.02790660969913006,
-0.019892388954758644,
-0.00715100159868598,
-0.03697473928332329,
0.039565134793519974,
-0.06462071090936661,
-0.05335570126771927,
-0.04008058086037636,
-0.006606370210647583,
-0.024965917691588402,
0.042059678584337234,
-0.012519781477749348,
0.015837671235203743,
0.04547029733657837,
0.042406003922224045,
0.008675003424286842,
0.015420105308294296,
-0.03219478204846382,
-0.03295958787202835,
-0.045261647552251816,
-0.00040179217467084527,
0.03646133095026016,
0.019865186884999275,
-0.025361565873026848,
0.018252931535243988,
0.0038192032370716333,
-0.01986418105661869,
0.010878000408411026,
0.054155558347702026,
0.002943662228062749,
-0.021951254457235336,
0.0027217252645641565,
-0.05259901285171509,
-0.019518926739692688,
0.07460064440965652,
-0.010167577303946018,
-0.0490914024412632,
-0.04306551814079285,
-0.05600263550877571,
-0.06553515791893005,
0.013144107535481453,
0.015715928748250008,
-0.07417652755975723,
-0.021950995549559593,
0.024769380688667297,
0.05341161787509918,
-0.01617080718278885,
-0.04585370421409607,
0.04248061031103134,
0.021038448438048363,
0.020947687327861786,
0.020668793469667435,
-0.03704387694597244,
0.0465288907289505,
-0.000624244858045131,
0.023535991087555885,
0.033191610127687454,
-0.05332944169640541,
0.0007240436971187592,
0.03832017630338669,
-0.016339439898729324,
-0.015271374955773354,
0.0009569744579494,
0.01579643413424492,
0.0402815043926239,
0.03512163087725639,
0.0011545546585693955,
-0.01856372132897377,
-0.0070075239054858685
] |
[
3.874945640563965,
2.5980923175811768
] |
Mathematical Physics
|
General Physics
|
math-ph
|
na
|
na
|
2007-04-01T08:40:19
|
We treat Koll\'ar's injectivity theorem from the analytic (or differential
geometric) viewpoint. More precisely, we give a curvature condition which
implies Koll\'ar type cohomology injectivity theorems. Our main theorem is
formulated for a compact K\"ahler manifold, but the proof uses the space of
harmonic forms on a Zariski open set with a suitable complete K\"ahler metric.
We need neither covering tricks, desingularizations, nor Leray's spectral
sequence.
|
A transcendental approach to Koll\'ar's injectivity theorem
|
math.AG
|
0704.0073
| 2,007
|
[
-0.014631628058850765,
0.026834936812520027,
0.010860594920814037,
-0.041148558259010315,
-0.013052381575107574,
0.05399859696626663,
0.022615008056163788,
-0.018195947632193565,
-0.05170778930187225,
0.03728112950921059,
-0.02049201726913452,
-0.02257867343723774,
0.07952422648668289,
0.03040548413991928,
0.025470484048128128,
-0.012924750335514545,
-0.014429022558033466,
0.019548624753952026,
0.006461933255195618,
-0.03075374849140644,
-0.04173092171549797,
-0.006987948901951313,
-0.008407738991081715,
-0.04332837089896202,
0.11559166014194489,
-0.014127242378890514,
0.060766417533159256,
-0.03641991317272186,
-0.007875792682170868,
-0.0035752018447965384,
0.043798722326755524,
-0.032452717423439026,
-0.0010253444779664278,
-0.016944095492362976,
-0.07123034447431564,
-0.01788914017379284,
0.09905275702476501,
0.012899558991193771,
-0.03859776258468628,
0.0014875857159495354,
0.06423182785511017,
-0.021116483956575394,
0.061240583658218384,
-0.014677473343908787,
0.018964938819408417,
0.02194342389702797,
0.01844325102865696,
0.027462992817163467,
0.006423608865588903,
-0.04336027428507805,
-0.010258212685585022,
0.0529802069067955,
-0.015321006998419762,
-0.0801483690738678,
-0.03428514674305916,
-0.010729961097240448,
0.02401072345674038,
-0.048317015171051025,
0.0766167864203453,
0.0016353564569726586,
-0.015058624558150768,
0.0021813218481838703,
-0.035763856023550034,
0.04537621885538101,
0.00290255737490952,
-0.06265620142221451,
-0.009194493293762207,
-0.043514907360076904,
0.01815166510641575,
-0.02151339128613472,
0.02109648659825325,
-0.03778680041432381,
0.09998204559087753,
0.011361359618604183,
-0.03012446127831936,
0.028927182778716087,
-0.0010758632561191916,
-0.030656252056360245,
0.01781105063855648,
-0.00411956524476409,
0.009558472782373428,
-0.031857334077358246,
0.09283606708049774,
-0.05133417248725891,
0.03143095597624779,
-0.012599303387105465,
0.05346478521823883,
0.028092028573155403,
-0.035125982016325,
0.033344294875860214,
0.019998762756586075,
-0.024338524788618088,
0.018614064902067184,
0.08239030838012695,
-0.027500975877046585,
-0.0022027946542948484,
-0.00257415440864861,
0.01572810299694538,
-0.02640119008719921,
-0.057789165526628494,
-0.009118574671447277,
0.012413485907018185,
0.023937145248055458,
0.01905524544417858,
0.1254863739013672,
-0.01940343715250492,
-0.01211103331297636,
0.02696942910552025,
-0.002783889416605234,
-0.04133608564734459,
-0.04001832753419876,
0.007675261236727238,
0.027928650379180908,
0.005037923343479633,
0.009339499287307262,
-0.018009504303336143,
0.05498870462179184,
-0.0550302229821682,
0.001950529869645834,
0.07234145700931549,
-0.010759417898952961,
-0.020374631509184837,
0.0004986714920960367,
0.013158655725419521,
0.011875991709530354,
0.06603662669658661,
-0.052531614899635315,
-0.05421958491206169,
0.03730980306863785,
-0.011149394325911999,
0.021994831040501595,
0.04869291931390762,
-0.025096867233514786,
0.021192636340856552,
0.07722346484661102,
0.015232903882861137,
-0.0010817375732585788,
-0.03694678470492363,
0.05789172649383545,
0.0048056296072900295,
0.0030045213643461466,
-0.0014808137202635407,
0.01045901793986559,
0.017023395746946335,
-0.007291995454579592,
-0.05151726305484772,
0.03655378520488739,
-0.04586353898048401,
-0.010305732488632202,
0.015194549225270748,
0.0019790700171142817,
0.029729215428233147,
-0.0211492907255888,
0.005249985959380865,
-0.008130953647196293,
-0.027053799480199814,
-0.04718411713838577,
0.022661395370960236,
0.07471027225255966,
-0.023290012031793594,
-0.01177951693534851,
0.07617350667715073,
-0.0181499645113945,
0.03309112787246704,
-0.0063383751548826694,
0.008494849316775799,
-0.002940460341051221,
0.036935582756996155,
-0.027260398492217064,
0.01414186879992485,
0.008557910099625587,
0.03350827470421791,
-0.011722470633685589,
-0.0327780544757843,
0.016728555783629417,
-0.03468174859881401,
-0.059287626296281815,
-0.04490287974476814,
0.022037358954548836,
-0.03274489939212799,
-0.010037277825176716,
-0.011526650749146938,
0.04326261579990387,
0.011289505288004875,
0.059706736356019974,
0.021215291693806648,
-0.0006024758331477642,
-0.006244514603167772,
-0.04626399278640747,
-0.02490331418812275,
0.043526750057935715,
0.05355888232588768,
0.001540292869322002,
0.03169479966163635,
0.008763907477259636,
-0.017258673906326294,
0.0872870534658432,
-0.006719578988850117,
0.01225782185792923,
-0.02760705165565014,
0.0128860492259264,
0.026106499135494232,
0.02129964716732502,
0.012408412992954254,
-0.01699557900428772,
0.06564614176750183,
-0.04455652832984924,
0.0018911416409537196,
0.03083847649395466,
-0.020927490666508675,
0.07412388920783997,
-0.03048800304532051,
0.009875254705548286,
-0.017489759251475334,
0.01843424327671528,
0.0011935721850022674,
-0.0036938206758350134,
-0.04221510887145996,
-0.038090769201517105,
0.0064031886868178844,
0.04132286086678505,
-0.017964275553822517,
-0.010245166718959808,
0.0006079000304453075,
-0.015780070796608925,
0.02875305525958538,
-0.0405622199177742,
-0.05255590379238129,
-0.031320344656705856,
-0.00774352578446269,
-0.033410392701625824,
-0.09462378919124603,
0.06211483106017113,
0.01717900112271309,
0.03041839599609375,
-0.012630974873900414,
0.001921079820021987,
0.014959128573536873,
0.04786521941423416,
0.07036026567220688,
0.002768303034827113,
0.00037937171873636544,
0.029173510149121284,
-0.03678261116147041,
-0.05993412435054779,
-0.04422365128993988,
-0.029166074469685555,
0.015064933337271214,
-0.04163091629743576,
0.030925096943974495,
0.03337763994932175,
0.016713298857212067,
0.044189658015966415,
-0.006203390192240477,
0.03712737560272217,
0.005306003149598837,
-0.043251682072877884,
0.02247905358672142,
-0.006203017197549343,
-0.06632991880178452,
0.03317906707525253,
-0.05554269254207611,
-0.04240664094686508,
-0.04973561316728592,
-0.10871211439371109,
0.03580733761191368,
-0.001816729549318552,
-0.024750303477048874,
0.017357688397169113,
-0.03932818025350571,
0.03425131365656853,
0.013111134991049767,
0.07429302483797073,
0.06865809112787247,
-0.023415878415107727,
0.02809416875243187,
-0.013896942138671875,
-0.004982314072549343,
-0.0286429300904274,
-0.0027396741788834333,
-0.06136609613895416,
-0.04289541393518448,
-0.03509742394089699,
0.01080508902668953,
0.012758491560816765,
0.013661607168614864,
-0.007175765000283718,
0.01073976419866085,
-0.018945632502436638,
0.03335721418261528,
-0.02356567792594433,
-0.04648362845182419,
-0.016044730320572853,
0.05284504592418671,
-0.025632591918110847,
0.05328832194209099,
0.005129506811499596,
-0.00924146082252264,
0.010045111179351807,
0.03382215276360512,
0.006043494213372469,
0.0013809187803417444,
-0.003458022139966488,
-0.03364542871713638,
0.030377089977264404,
0.0339738093316555,
0.0044233775697648525,
-0.014190038666129112,
0.002023343462496996,
-0.026560761034488678,
-0.041456110775470734,
-0.02790818363428116,
-0.02148505672812462,
0.026540787890553474,
-0.021810391917824745,
0.06341341882944107,
-0.038055311888456345,
0.0030904922168701887,
0.031117169186472893,
-0.02289927378296852,
0.029532240703701973,
-0.006482957396656275,
-0.023096991702914238,
-0.04957915097475052,
0.007959689013659954,
-0.02812287211418152,
-0.0755385234951973,
0.00460605276748538,
0.012362859211862087,
-0.0504259429872036,
-0.058806370943784714,
0.08769345283508301,
-0.00999544933438301,
0.009920923039317131,
-0.04520589858293533,
0.01981888711452484,
-0.04478105902671814,
0.058035675436258316,
-0.004463396035134792,
0.025542061775922775,
0.021736927330493927,
-0.045724689960479736,
-0.07141873240470886,
-0.005761404056102037,
-0.026700928807258606,
0.03882329910993576,
-0.04759104549884796,
0.030321987345814705,
0.026332085952162743,
0.006275487598031759,
-0.06283010542392731,
-0.028923768550157547,
0.04059586301445961,
-0.013660687021911144,
-0.005513035226613283,
0.027208659797906876,
0.06139766052365303,
0.022603940218687057,
0.05016937106847763,
-0.02697664499282837,
0.057350534945726395,
-0.04015221819281578,
0.013311119750142097,
0.027417615056037903,
0.0657576322555542,
0.051845818758010864,
0.02812659926712513,
-0.05085234344005585,
-0.02974891848862171,
0.03950268402695656,
-0.054859865456819534,
-0.05395060032606125,
0.0018682627705857158,
0.021026350557804108,
-0.001482757623307407,
-0.04438047483563423,
-0.04884561523795128,
0.05464416742324829,
-0.0017566423630341887,
-0.03433844447135925,
0.031345151364803314,
0.04681761562824249,
0.05408463999629021,
0.013973725028336048,
0.02611846663057804,
0.03655554726719856,
-0.05564394220709801,
-0.006920801009982824,
-0.0033617536537349224,
0.014292590320110321,
0.002554631559178233,
-0.018581505864858627,
-0.0037774050142616034,
0.04535272717475891,
-0.028914086520671844,
-0.01703852415084839,
0.045478153973817825,
0.03296849504113197,
0.011476722545921803,
-0.02205807715654373,
-0.010955525562167168,
-0.06271970272064209,
0.004263262264430523,
-0.025744164362549782,
-0.02641456015408039,
-0.00608782609924674,
0.06172111630439758,
-0.03398552164435387,
0.06729999929666519,
-0.04972919076681137,
0.04255904629826546,
-0.06358497589826584,
-0.00019494544540066272,
-0.09143988788127899,
0.09826822578907013,
-0.013669988140463829,
0.02178080752491951,
-0.0591985322535038,
0.015379312448203564,
0.007839742116630077,
-0.04677643999457359,
0.0410841703414917,
-0.021369267255067825,
-0.004621713422238827,
0.054966993629932404,
0.06744103878736496,
0.014179760590195656,
0.019876087084412575,
-0.01396331749856472,
-0.023723728954792023,
-0.01987585425376892,
0.026474373415112495,
-0.0045942687429487705,
-0.003351835301145911,
-0.057588472962379456,
-0.008810997940599918,
-0.017342131584882736,
-0.00821327231824398,
-0.019216248765587807,
-0.027999557554721832,
0.054370176047086716,
-0.01710020937025547,
-0.013796724379062653,
-0.044126518070697784,
0.024485984817147255,
0.05075853690505028,
0.04556189477443695,
-0.05354820191860199,
-0.034264225512742996,
-0.05172768235206604,
0.0658336728811264,
-0.003861845936626196,
-0.03437424078583717,
0.029566975310444832,
0.0020003931131213903,
-0.014244905672967434,
-0.045066192746162415,
-0.03131565824151039,
-0.011605778709053993,
0.038595739752054214,
0.07211802154779434,
0.013021419756114483,
-0.009987030178308487,
0.026843518018722534,
0.03238840773701668,
0.014246314764022827,
-0.0731876865029335,
0.012449784204363823,
0.011776481755077839,
0.009520166553556919,
-0.010784615762531757,
0.046580832451581955,
0.030574996024370193,
-0.035408325493335724,
0.009162229485809803,
0.0057356408797204494,
0.027321595698595047,
-0.02769423834979534,
-0.04069414362311363,
0.01463230699300766,
0.00008793512097327039,
-0.01000126451253891,
0.0022316239774227142,
0.010042211972177029,
-0.05145234614610672,
0.022823363542556763,
0.02752501331269741,
-0.02213261090219021,
-0.015220150351524353,
0.0003308619780000299,
-0.01742052659392357,
0.050740260630846024,
0.01590270921587944,
0.016192587092518806,
-0.038499098271131516,
0.002491255756467581,
0.006116381846368313,
-0.045215100049972534,
0.004510058090090752,
-0.004622234497219324,
-0.01814616471529007,
0.01028328575193882,
-0.0015193591825664043,
0.024294255301356316,
-0.00750044547021389,
0.01882120594382286,
0.031182579696178436,
-0.022026488557457924,
-0.016265859827399254,
-0.021999122574925423,
0.013360126875340939,
0.04275035485625267,
-0.0012338616652414203,
0.07766145467758179,
0.004995523951947689,
-0.025144951418042183,
-0.05395147576928139,
0.009250283241271973,
-0.03562121465802193,
0.020087486132979393,
0.04248847812414169,
0.011169971898198128,
-0.013637367635965347,
-0.020977675914764404,
-0.013926535844802856,
0.06067762151360512,
-0.02502881921827793,
-0.0908735916018486,
0.03419763967394829,
-0.04764212667942047,
0.02595161832869053,
0.0035849851556122303,
0.03278560936450958,
-0.043219130486249924,
0.03743781894445419,
-0.02296765334904194,
0.025527458637952805,
0.04308869689702988,
-0.026173634454607964,
0.013766779564321041,
-0.035396382212638855,
0.012095524929463863,
-0.02172744646668434,
0.0443241260945797,
0.03964579105377197,
0.00035646362812258303,
-0.05701526626944542,
0.04786597192287445,
0.014347804710268974,
-0.030867578461766243,
-0.011298810131847858,
-0.06713535636663437,
0.0595196969807148,
-0.07729678601026535,
0.0022651671897619963,
-0.060471855103969574,
0.04210967198014259,
-0.04072066396474838,
-0.04653641954064369,
-0.024425853043794632,
0.03409098833799362,
-0.04488233104348183,
0.021928509697318077,
-0.005219429265707731,
-0.008135831914842129,
-0.08560138940811157,
0.014921893365681171,
0.011178195476531982,
0.04969619959592819,
-0.043680690228939056,
-0.01281533483415842,
-0.032424405217170715,
0.010579070076346397,
0.034759700298309326,
-0.012467056512832642,
-0.023197630420327187,
0.009877755306661129,
-0.03681771829724312,
-0.05607852712273598,
-0.007065892219543457,
0.040523380041122437,
-0.05184469744563103,
0.03942244127392769,
-0.05279620736837387,
-0.0557214580476284,
0.02401323802769184,
-0.024418560788035393,
-0.026922564953565598,
0.045052047818899155,
0.02135917916893959,
0.014566706493496895,
0.00177043117582798,
-0.024455677717924118,
0.0003444150206632912,
-0.004536210093647242,
-0.01755809783935547,
0.022445350885391235,
0.045507535338401794,
0.003542386693879962,
-0.04499375447630882,
0.014333180151879787,
-0.01995336078107357,
0.09650906920433044,
-0.01751110330224037,
0.011702091433107853,
0.0712529718875885,
-0.0008495851652696729,
0.027738312259316444,
-0.0231215450912714,
0.011456308886408806,
0.007874589413404465,
-0.03403514251112938,
-0.025357019156217575,
-0.050543610006570816,
0.05386907234787941,
0.014639564789831638,
0.039653316140174866,
-0.03823067247867584,
0.03340236842632294,
-0.04812568053603172,
0.02942817285656929,
-0.05083898454904556,
0.013102628290653229,
0.02520584501326084,
0.057409707456827164,
-0.002174575114622712,
-0.03001907281577587,
-0.04279083386063576,
0.013827456161379814,
0.105324886739254,
-0.012834588065743446,
-0.026237022131681442,
-0.06098876893520355,
-0.037689656019210815,
-0.017407149076461792,
-0.03225819393992424,
-0.01857929863035679,
0.025783775374293327,
0.027398256585001945,
0.046313442289829254,
0.026071732863783836,
0.0020655563566833735,
0.0059236520901322365,
0.019600503146648407,
0.04671413451433182,
0.020923351868987083,
-0.009573392570018768,
-0.00448097288608551,
-0.041270580142736435,
0.00017579247651156038,
0.06799224764108658,
0.05723555013537407,
-0.03972078114748001,
-0.025270575657486916,
-0.0004049474955536425,
0.0038807415403425694,
0.022788161411881447,
-0.004505034536123276,
-0.03127893805503845,
-0.003351886523887515,
0.00781427975744009,
0.030487632378935814,
0.040910691022872925,
-0.018730949610471725,
0.014422290958464146,
0.005001482553780079,
-0.020898571237921715,
-0.10243327915668488,
-0.0563206784427166,
0.049043674021959305,
0.014013305306434631,
-0.023352105170488358,
-0.008337566629052162,
-0.013081260956823826,
-0.045348215848207474,
-0.006133807823061943,
-0.0018205137457698584,
0.06614498049020767,
-0.01317950151860714,
-0.0267886221408844,
-0.034812312573194504,
0.005596690345555544,
0.06900870054960251,
0.00022400372836273164,
-0.006747215986251831,
-0.014949493110179901,
-0.010615489445626736,
-0.043217435479164124,
-0.07709930837154388,
-0.03848445788025856,
0.021259117871522903,
0.005266532301902771,
0.019559023901820183,
-0.049958374351263046,
0.027335209771990776,
-0.02918938547372818,
-0.03088594600558281,
-0.0010774757247418165,
-0.013724899850785732,
0.049894314259290695,
-0.01745567098259926,
0.008007668890058994,
-0.024880794808268547,
0.024611415341496468,
-0.05328138917684555,
-0.026255613192915916,
0.027358904480934143,
0.013921469449996948,
-0.02716478332877159,
0.07034897804260254,
0.01356923021376133,
0.030858399346470833,
-0.008080900646746159,
0.015153750777244568,
0.05452591925859451,
-0.0027997049037367105,
-0.005579610355198383,
-0.0669054388999939,
-0.015925373882055283,
-0.07068060338497162,
0.015120080672204494,
-0.0356631875038147,
-0.0009688100544735789,
0.000038912556192371994,
-0.031280238181352615,
-0.04390805587172508,
0.018484245985746384,
-0.026902975514531136,
-0.020612230524420738,
-0.005388591438531876,
0.000340720871463418,
0.03482687845826149,
-0.011901501566171646,
0.035436540842056274,
-0.04921852797269821,
0.001088866963982582,
-0.04908641427755356,
0.014950900338590145,
-0.033723603934049606,
-0.021474197506904602,
-0.011308036744594574,
-0.022304385900497437,
0.013983719982206821,
0.01707371138036251,
-0.029938992112874985,
0.01715429127216339,
-0.05155584588646889,
0.004890616051852703,
0.03573888912796974,
0.034799691289663315,
-0.04162799194455147,
0.060546547174453735,
0.026696132495999336,
-0.01025070995092392,
0.010948453098535538,
-0.02704164944589138,
0.010731855407357216,
0.028279384598135948,
0.06043362617492676,
-0.024859951809048653,
0.03739326819777489,
0.03223555535078049,
-0.00015100491873454303,
0.09009705483913422,
-0.011226924136281013,
0.020381448790431023,
-0.033158306032419205,
-0.03625864535570145
] |
[
0.4533168375492096,
1.057193398475647
] |
Algebraic Geometry
|
Mathematics
|
math-AG
|
na
|
na
|
2007-04-01T09:34:47
|
This paper is an exposition of the so-called injective Morita contexts (in
which the connecting bimodule morphisms are injective) and Morita
$\alpha$contexts (in which the connecting bimodules enjoy some local
projectivity in the sense of Zimmermann-Huisgen). Motivated by situations in
which only one trace ideal is in action, or the compatibility between the
bimodule morphisms is not needed, we introduce the notions of Morita
semi-contexts and Morita data, and investigate them. Injective Morita data will
be used (with the help of static and adstatic modules) to establish
equivalences between some intersecting subcategories related to subcategories
of modules that are localized or colocalized by trace ideals of a Morita datum.
We end up with applications of Morita $\alpha$-contexts to $\ast$-modules and
injective right wide Morita contexts.
|
Injective Morita contexts (revisited)
|
math.RA
|
0704.0074
| 2,007
|
[
0.002959377598017454,
0.04066703841090202,
0.0022859121672809124,
-0.07410083711147308,
-0.0032209036871790886,
-0.023198209702968597,
0.03777969256043434,
-0.007002044469118118,
-0.03372696787118912,
0.025323549285531044,
-0.07064901292324066,
0.04111366719007492,
0.04094349592924118,
-0.016950244084000587,
-0.04583004117012024,
0.005434797145426273,
0.005470947828143835,
0.04308655485510826,
0.014400889165699482,
-0.0062188273295760155,
0.014846902340650558,
0.005011195316910744,
-0.02158988267183304,
-0.021360719576478004,
0.10015689581632614,
0.014706749469041824,
0.06670280545949936,
0.012265303172171116,
-0.022016799077391624,
0.006119236350059509,
0.07689383625984192,
-0.0757010281085968,
-0.0037804010789841413,
-0.030107861384749413,
-0.06751036643981934,
-0.024500805884599686,
0.04430206120014191,
-0.010932227596640587,
-0.023057596758008003,
0.09322952479124069,
0.06653311848640442,
-0.006509931292384863,
-0.022304745391011238,
-0.03742699325084686,
-0.00788030307739973,
0.003022497519850731,
-0.006589547265321016,
-0.018373453989624977,
0.03960453346371651,
-0.054571572691202164,
-0.028029538691043854,
0.05423766374588013,
0.01885911636054516,
-0.03331457078456879,
-0.011938118375837803,
0.01258463878184557,
-0.005643052514642477,
-0.05377088114619255,
0.016055285930633545,
-0.04835405945777893,
-0.006310713477432728,
0.010199956595897675,
-0.006088291760534048,
0.04122590646147728,
-0.024812476709485054,
-0.07219589501619339,
-0.030671363696455956,
0.004036139231175184,
-0.05124702677130699,
-0.016519393771886826,
-0.00027729253633879125,
0.020318739116191864,
0.04376927763223648,
0.035079553723335266,
-0.05178266018629074,
0.00956560205668211,
0.009616484865546227,
-0.02308805286884308,
0.036551497876644135,
0.015211421996355057,
0.016960203647613525,
-0.08023939281702042,
0.07690010219812393,
0.027536604553461075,
0.09185877442359924,
0.008991447277367115,
0.03902154043316841,
0.028673039749264717,
-0.055008601397275925,
0.036492135375738144,
0.043828919529914856,
0.007627238053828478,
0.052141930907964706,
0.04846092313528061,
-0.04296839237213135,
0.035538289695978165,
-0.03237678483128548,
0.025043299421668053,
-0.027985094115138054,
-0.03547742962837219,
0.009063029661774635,
0.02266489714384079,
0.03958192467689514,
0.05839752405881882,
0.04446849226951599,
0.02360190451145172,
0.02267320267856121,
0.0019556067418307066,
-0.008103101514279842,
0.018360992893576622,
-0.034052688628435135,
0.0009085803758352995,
-0.0046184128150343895,
-0.019534457474946976,
-0.009327545762062073,
-0.007052662316709757,
0.07207219302654266,
-0.10212752223014832,
-0.01760568656027317,
0.04801177233457565,
0.028493475168943405,
-0.025213606655597687,
0.008132199756801128,
0.0023751063272356987,
0.022634003311395645,
-0.004377426113933325,
-0.08066239207983017,
0.0006305261631496251,
0.013094790279865265,
-0.01910494454205036,
0.024699952453374863,
0.009348949417471886,
-0.012983391992747784,
0.0037719756364822388,
0.006640967912971973,
-0.01007347647100687,
-0.028346585109829903,
-0.09039290249347687,
0.03862810134887695,
-0.0200120247900486,
0.0063979486003518105,
-0.018265480175614357,
-0.04249884933233261,
-0.003348390571773052,
-0.005598351825028658,
-0.09793788939714432,
0.05796579644083977,
-0.013266215100884438,
0.013831932097673416,
-0.006490856874734163,
-0.0015273571480065584,
0.03770725429058075,
-0.010717893950641155,
0.06114957854151726,
-0.05253905802965164,
-0.05121047794818878,
-0.06462248414754868,
0.010456490330398083,
0.027660252526402473,
0.006284781731665134,
0.0005155153339728713,
0.04658825695514679,
-0.022831691429018974,
0.0031651745084673166,
-0.026978736743330956,
0.01757431961596012,
0.030466606840491295,
0.020371148362755775,
0.02777642197906971,
-0.033186815679073334,
0.033729810267686844,
0.015949923545122147,
-0.04474687948822975,
-0.05024611949920654,
0.04153480380773544,
0.011878074146807194,
-0.030249064788222313,
-0.04219675809144974,
0.057094134390354156,
-0.018380984663963318,
-0.026955360546708107,
-0.03429491072893143,
-0.030108565464615822,
0.026210997253656387,
-0.003077441593632102,
-0.006314719095826149,
0.0017979955300688744,
-0.01821383461356163,
-0.03556478023529053,
0.007859528064727783,
0.0060300203040242195,
0.02290743961930275,
-0.02944827824831009,
-0.016847431659698486,
-0.024399977177381516,
-0.05365610495209694,
0.06254681199789047,
-0.005725300870835781,
0.02684726193547249,
-0.04253334924578667,
0.017533734440803528,
-0.03325771540403366,
-0.021221207454800606,
0.05137207731604576,
-0.028267215937376022,
0.05660347640514374,
0.010408046655356884,
0.02066369168460369,
0.01817416027188301,
-0.0323343351483345,
0.06248078495264053,
-0.018444042652845383,
-0.0224698968231678,
0.010723238810896873,
-0.0713375061750412,
0.007326518185436726,
0.023198088631033897,
-0.045209065079689026,
-0.013132547028362751,
0.02011735551059246,
-0.008401922881603241,
-0.04151974245905876,
-0.00494946725666523,
-0.008167605847120285,
0.06251496076583862,
-0.006518213078379631,
-0.005553088616579771,
0.023149270564317703,
-0.06603243947029114,
-0.023838596418499947,
-0.09017314016819,
-0.06628791242837906,
0.040991321206092834,
-0.030906325206160545,
0.028753891587257385,
0.04128357395529747,
-0.020465796813368797,
0.0878373235464096,
0.05169167369604111,
0.037144891917705536,
0.009154572151601315,
-0.009792746976017952,
0.031713470816612244,
-0.017146220430731773,
-0.04865530505776405,
-0.020315926522016525,
-0.019022637978196144,
-0.004922680091112852,
-0.026471588760614395,
0.07829102873802185,
0.0018879936542361975,
0.045805566012859344,
0.05622468516230583,
0.015908557921648026,
0.015872465446591377,
-0.018774177879095078,
-0.0011308122193440795,
-0.011501849628984928,
0.022214004769921303,
-0.0279679074883461,
0.050257738679647446,
-0.07509758323431015,
-0.028339585289359093,
-0.04424593970179558,
0.011079147458076477,
-0.022623103111982346,
0.022108543664216995,
-0.050523873418569565,
-0.029475770890712738,
-0.009129507467150688,
-0.05205845832824707,
0.03223395347595215,
0.0755101814866066,
0.003129916498437524,
-0.002918756101280451,
0.025488773360848427,
-0.032366521656513214,
-0.022136684507131577,
-0.030590005218982697,
-0.012247374281287193,
-0.015905773267149925,
-0.039014797657728195,
-0.0021056411787867546,
-0.018015000969171524,
-0.017920510843396187,
0.0227030161768198,
-0.007646407000720501,
-0.003307524835690856,
0.02255767025053501,
0.011108745820820332,
0.006237815134227276,
-0.018648646771907806,
0.014948463998734951,
0.08563123643398285,
0.00802714005112648,
0.04721071571111679,
0.04261653497815132,
0.023029746487736702,
0.02393377386033535,
-0.00712268752977252,
-0.01399761438369751,
0.0592675618827343,
0.010639938525855541,
-0.056424424052238464,
0.0779065191745758,
-0.02622872218489647,
-0.009671091102063656,
-0.0248896311968565,
-0.002567398827522993,
0.015314280055463314,
-0.03158937022089958,
-0.011869206093251705,
-0.008547293953597546,
-0.001117562293075025,
-0.0425252728164196,
0.05732030048966408,
0.04936505854129791,
0.0010335779516026378,
0.06947827339172363,
-0.05173822119832039,
0.014375878497958183,
0.012577114626765251,
0.0585586354136467,
-0.039780259132385254,
-0.025874968618154526,
0.036821670830249786,
-0.017333554103970528,
0.05393540859222412,
0.0006375022348947823,
-0.024996595457196236,
-0.01126318983733654,
0.05743396282196045,
-0.02520623616874218,
-0.01856035739183426,
-0.0504537969827652,
-0.00575705710798502,
-0.057696275413036346,
0.019301576539874077,
-0.008622102439403534,
0.042726825922727585,
0.049739450216293335,
0.007657923270016909,
0.025087324902415276,
-0.030294382944703102,
0.003218340687453747,
0.04841193929314613,
-0.04167107120156288,
-0.000998336123302579,
0.029162820428609848,
0.056118905544281006,
-0.04193183034658432,
-0.033498071134090424,
0.002766043646261096,
-0.008188191801309586,
-0.06299979239702225,
0.020181605592370033,
0.05214245244860649,
-0.03569867089390755,
0.0872766301035881,
0.013363181613385677,
0.06713937222957611,
-0.004452274646610022,
0.006452847737818956,
0.008445052430033684,
0.024735089391469955,
0.022609708830714226,
0.015955746173858643,
-0.02339909039437771,
-0.008837083354592323,
-0.003058489877730608,
0.023068392649292946,
-0.03427605703473091,
0.043059028685092926,
0.01453697681427002,
0.00329186231829226,
-0.0072355023585259914,
-0.05730614438652992,
0.0449787862598896,
0.047072380781173706,
0.031508125364780426,
0.0477769710123539,
0.005307157523930073,
0.08521553128957748,
0.005548195913434029,
0.017720546573400497,
0.024098388850688934,
0.014295627363026142,
0.05789067596197128,
-0.012313772924244404,
-0.06257994472980499,
-0.03356216475367546,
-0.022047080099582672,
0.016549544408917427,
0.010053027421236038,
0.032811108976602554,
-0.035306911915540695,
-0.019222522154450417,
-0.007615306414663792,
0.041939206421375275,
-0.010685442015528679,
-0.05199176073074341,
-0.08172956854104996,
0.002966778352856636,
-0.03316851332783699,
-0.04881015419960022,
0.042453281581401825,
-0.030461937189102173,
-0.0341302789747715,
0.1051136702299118,
-0.061597052961587906,
0.0403951071202755,
0.011683845892548561,
0.00002727426544879563,
-0.025303974747657776,
0.061120372265577316,
-0.017378313466906548,
0.037080440670251846,
0.014667343348264694,
0.0016159926308318973,
0.012822404503822327,
-0.015705937519669533,
0.03492406755685806,
-0.026239709928631783,
0.0044410270638763905,
0.00909255351871252,
0.012658451683819294,
-0.009305131621658802,
-0.02510225586593151,
0.026688983663916588,
0.02210497483611107,
0.016816923394799232,
0.04385010898113251,
0.034595850855112076,
0.02504286728799343,
-0.06127215921878815,
-0.05298464000225067,
-0.0217252466827631,
-0.0060088601894676685,
-0.00149592908564955,
-0.015392851084470749,
0.032122716307640076,
-0.03756236284971237,
-0.01668579690158367,
-0.04247118905186653,
0.0018766808789223433,
0.03611074015498161,
0.04377089813351631,
-0.00922392774373293,
-0.008459488861262798,
0.022206159308552742,
0.005980703979730606,
0.03565603867173195,
0.004617658909410238,
-0.03960629552602768,
0.04680981859564781,
-0.0013092235894873738,
-0.020949745550751686,
-0.0470644012093544,
-0.001460289815440774,
0.0677611231803894,
0.0028989946004003286,
0.013333418406546116,
-0.02542484737932682,
0.05081801861524582,
0.050717487931251526,
-0.053513482213020325,
-0.039187438786029816,
0.01843833737075329,
-0.03599194809794426,
0.03775652125477791,
0.031158694997429848,
0.03430001810193062,
-0.015301438048481941,
-0.043653298169374466,
0.015185060910880566,
0.021791348233819008,
0.011228677816689014,
-0.03838493674993515,
-0.012890650890767574,
0.06869643181562424,
0.010449065826833248,
-0.030224468559026718,
0.000796220323536545,
-0.04375769570469856,
-0.01814250834286213,
0.03936149552464485,
0.025210175663232803,
-0.007141218986362219,
0.01430510263890028,
-0.022515907883644104,
0.02403414249420166,
-0.00048127336776815355,
0.02123964950442314,
0.033172961324453354,
-0.07359953969717026,
-0.01955142803490162,
0.00996134802699089,
0.04034792631864548,
0.024873191490769386,
-0.021700695157051086,
-0.0016697235405445099,
0.020186981186270714,
0.016570087522268295,
0.05476123467087746,
0.03775554895401001,
0.013727473095059395,
0.04727103188633919,
-0.019854705780744553,
-0.02531573548913002,
0.006990456487983465,
0.04030011221766472,
0.04139808565378189,
-0.04995812848210335,
0.06681769341230392,
0.032685745507478714,
-0.024767138063907623,
0.02096419408917427,
0.02332296222448349,
-0.09271987527608871,
-0.0437781848013401,
-0.030019942671060562,
-0.019474633038043976,
0.011577721685171127,
-0.047619160264730453,
-0.03950246050953865,
0.03574308753013611,
-0.025481639429926872,
-0.11939159780740738,
0.04777314513921738,
0.0033513635862618685,
-0.017388921231031418,
0.013915607705712318,
0.03648407384753227,
0.006609942764043808,
0.04392247274518013,
0.004861441906541586,
-0.04744328558444977,
0.02498064562678337,
0.012707501649856567,
0.04257030785083771,
-0.02346133626997471,
0.012022646144032478,
-0.00512565765529871,
-0.024180352687835693,
-0.02637386880815029,
0.008274721913039684,
-0.020048346370458603,
0.00020909223530907184,
-0.04420904070138931,
-0.05013211816549301,
0.046542130410671234,
0.006416506599634886,
-0.0002669373352546245,
-0.11937222629785538,
0.0031273956410586834,
-0.019918393343687057,
0.019025102257728577,
-0.004467343911528587,
-0.043436456471681595,
0.00540243461728096,
-0.015155558474361897,
-0.005013493821024895,
0.010770220309495926,
0.041348349303007126,
-0.03074774146080017,
-0.08064444363117218,
-0.015194266103208065,
0.006419457029551268,
0.03841157630085945,
-0.03221447765827179,
0.05532550811767578,
-0.07292727380990982,
0.014301912859082222,
0.01878960244357586,
-0.024184247478842735,
-0.0031757482793182135,
-0.0013614031486213207,
0.05097091197967529,
0.0014539806870743632,
0.0031262526754289865,
-0.006859065964818001,
-0.040919192135334015,
-0.0007333321264013648,
-0.008671543560922146,
-0.04049854725599289,
0.0010063230292871594,
-0.04520968347787857,
-0.056813113391399384,
0.03624124825000763,
-0.009228215552866459,
0.014728927053511143,
-0.020882774144411087,
0.020807113498449326,
-0.03291533514857292,
-0.02670491859316826,
-0.030111486092209816,
0.02807740494608879,
0.027991199865937233,
-0.05467933043837547,
-0.08846130222082138,
0.032750651240348816,
0.032904114574193954,
0.08850277960300446,
-0.033447153866291046,
0.02067479118704796,
0.09396287053823471,
-0.012895099818706512,
0.018039211630821228,
0.02396879345178604,
-0.019319290295243263,
0.013993624597787857,
0.008380455896258354,
-0.059190478175878525,
0.017284518107771873,
-0.011418397538363934,
-0.06163187325000763,
-0.02133074961602688,
-0.042458754032850266,
-0.0022445900831371546,
-0.018169404938817024,
0.012925424613058567,
-0.0463181771337986,
0.010465673170983791,
0.011058163829147816,
-0.03669191896915436,
-0.0062153395265340805,
-0.016496196389198303,
-0.014883531257510185,
-0.004500045906752348,
0.05673970654606819,
-0.013645286671817303,
-0.04230335354804993,
-0.03696563467383385,
-0.056700676679611206,
-0.009376614354550838,
0.025670422241091728,
-0.012300505302846432,
0.011906400322914124,
-0.03284415602684021,
0.04722065478563309,
-0.0066846623085439205,
-0.003028880339115858,
-0.016855495050549507,
0.031467121094465256,
0.08079574257135391,
-0.06088268384337425,
0.0010869018733501434,
-0.00042314024176448584,
0.04063839837908745,
0.0425967201590538,
0.12432655692100525,
0.0905861034989357,
-0.03871313855051994,
0.039031509310007095,
-0.04904453456401825,
0.02261417917907238,
0.002548979129642248,
0.006847744341939688,
-0.03301936760544777,
0.03718637675046921,
-0.012051472440361977,
0.006933894474059343,
-0.023836586624383926,
0.009452379308640957,
0.03380768746137619,
-0.028916308656334877,
0.0013065508101135492,
-0.018191762268543243,
-0.02540007047355175,
0.002244123723357916,
-0.018967581912875175,
-0.04191048815846443,
-0.03878447040915489,
-0.01895337924361229,
-0.07514604181051254,
-0.015207052230834961,
-0.010227327235043049,
0.03565811365842819,
-0.019940542057156563,
-0.03754705190658569,
0.00038878218038007617,
0.009528633207082748,
0.002265487564727664,
-0.005382177885621786,
0.026939570903778076,
-0.03638993203639984,
-0.028345802798867226,
-0.022986290976405144,
-0.05983317643404007,
-0.04686924070119858,
0.02123934216797352,
0.006648149341344833,
0.02753111533820629,
-0.028170006349682808,
0.01283398550003767,
-0.01680793985724449,
-0.009110404178500175,
0.010778838768601418,
0.007173491176217794,
0.03856134042143822,
0.025049174204468727,
-0.0018711865413933992,
-0.01235003862529993,
0.028873605653643608,
-0.028830237686634064,
-0.01913011632859707,
0.00495031988248229,
0.07173746824264526,
0.00832903292030096,
-0.010404841974377632,
-0.03973925858736038,
0.046287037432193756,
0.018808919936418533,
-0.028048524633049965,
-0.00579451210796833,
0.03694700449705124,
-0.019129779189825058,
-0.05892892926931381,
-0.006101443897932768,
-0.014438332989811897,
0.039695728570222855,
-0.002747143153101206,
-0.035623930394649506,
0.020893022418022156,
-0.07817966490983963,
-0.024376459419727325,
0.030933354049921036,
-0.04210037738084793,
0.06706066429615021,
0.016357041895389557,
-0.005502955988049507,
-0.05127875134348869,
-0.03082352690398693,
0.04323619604110718,
-0.04134536162018776,
0.02736416831612587,
-0.010985278524458408,
-0.020147155970335007,
-0.03347551450133324,
-0.033533975481987,
-0.0263485386967659,
-0.07035248726606369,
-0.0054463110864162445,
0.027122966945171356,
-0.058422356843948364,
0.03578241914510727,
-0.01761617884039879,
0.008864064700901508,
0.00810220930725336,
0.012033789418637753,
-0.020670803263783455,
0.01907181181013584,
0.009480206295847893,
0.026445936411619186,
0.015915237367153168,
0.06892455369234085,
-0.006682941690087318,
0.031277403235435486,
0.09148609638214111,
-0.005634371656924486,
0.05136054381728172,
-0.0026799605693668127,
0.018324047327041626,
0.011006692424416542,
-0.0029881203081458807,
0.03459469601511955,
-0.024077599868178368,
-0.020534850656986237
] |
[
1.0580182075500488,
1.5932472944259644
] |
Rings and Algebras
|
Mathematics
|
math-RA
|
na
|
na
|
2007-04-01T09:45:55
|
There has been important experimental progress in the sector of heavy baryons
in the past several years. We study the strong decays of the S-wave, P-wave,
D-wave and radially excited charmed baryons using the $^3P_0$ model. After
comparing the calculated decay pattern and total width with the available data,
we discuss the possible internal structure and quantum numbers of those charmed
baryons observed recently.
|
Strong decays of charmed baryons
|
hep-ph hep-ex nucl-ex
|
0704.0075
| 2,007
|
[
0.002878842642530799,
0.024388205260038376,
0.0010624270653352141,
-0.033372920006513596,
0.04053696617484093,
0.03661784902215004,
-0.0010297080734744668,
0.0270233154296875,
0.007872844114899635,
-0.05436423793435097,
-0.06764116138219833,
0.03490901365876198,
-0.02371646836400032,
-0.014185475185513496,
0.05859548971056938,
-0.03386233001947403,
0.051264725625514984,
-0.040319643914699554,
0.0033121362794190645,
-0.002784186974167824,
-0.018952129408717155,
-0.03474528342485428,
-0.0310987439006567,
-0.03674815595149994,
0.05731809884309769,
0.010897080413997173,
0.03723210468888283,
0.020040489733219147,
-0.033426541835069656,
0.029562046751379967,
0.04581302031874657,
-0.08152863383293152,
0.0018919934518635273,
-0.045784927904605865,
-0.04018865153193474,
0.005293306894600391,
0.07953030616044998,
0.05008719116449356,
-0.020118096843361855,
0.029334839433431625,
0.06613349914550781,
-0.016797304153442383,
0.04604000225663185,
-0.059352241456508636,
-0.013670478947460651,
-0.01206623762845993,
0.027284426614642143,
0.015635201707482338,
0.021381504833698273,
-0.010590999387204647,
-0.029647141695022583,
0.004506716039031744,
0.05652932822704315,
-0.0626249685883522,
0.03104632906615734,
0.031876448541879654,
-0.006931412033736706,
-0.07102662324905396,
0.058195654302835464,
0.0015307380817830563,
0.050585370510816574,
0.06424986571073532,
-0.008906982839107513,
-0.007575612980872393,
0.027505243197083473,
-0.016801776364445686,
-0.06294688582420349,
0.017168669030070305,
-0.039462972432374954,
-0.0614871084690094,
0.055110007524490356,
-0.018305182456970215,
-0.010554492473602295,
-0.016101129353046417,
-0.032670047134160995,
-0.005618900526314974,
-0.018985478207468987,
-0.05217106267809868,
-0.033411603420972824,
0.016758030280470848,
0.02352183498442173,
-0.0281319972127676,
-0.02012212574481964,
0.03521692380309105,
0.050920285284519196,
-0.0002471124171279371,
0.01895047165453434,
0.003779187798500061,
-0.023509889841079712,
0.026811739429831505,
0.032937418669462204,
-0.018310360610485077,
0.005563009530305862,
0.045917265117168427,
-0.07473916560411453,
0.011675546877086163,
0.0013470491394400597,
0.05959416925907135,
-0.027854200452566147,
-0.021601645275950432,
0.009073528461158276,
-0.009513256140053272,
0.02589958906173706,
0.030724087730050087,
0.07063205540180206,
0.07560964673757553,
0.010736053809523582,
-0.04055292531847954,
0.024664880707859993,
0.04042403772473335,
-0.08998596668243408,
-0.004976782016456127,
0.029865216463804245,
-0.00833367183804512,
-0.03315936401486397,
-0.002504839561879635,
0.033519111573696136,
-0.07542777806520462,
-0.02230888418853283,
0.0926094651222229,
0.060955312103033066,
0.004749111831188202,
-0.03343086317181587,
0.035000793635845184,
0.010138149373233318,
0.0008262360352091491,
-0.06384316831827164,
-0.012693124823272228,
0.03377366438508034,
-0.016372956335544586,
-0.0011578429257497191,
0.004180409014225006,
-0.05294867232441902,
-0.020258817821741104,
0.041509319096803665,
0.03776279836893082,
-0.014075628481805325,
-0.042413756251335144,
0.038289811462163925,
-0.00618004659190774,
0.022747093811631203,
0.03171374648809433,
0.022442754358053207,
0.006330564618110657,
0.012303931638598442,
-0.03178422898054123,
0.050470270216464996,
-0.0028211153112351894,
-0.02078443020582199,
0.025276778265833855,
0.07726594060659409,
0.028725463896989822,
0.020876923575997353,
0.02129514329135418,
-0.09685487300157547,
-0.05207747593522072,
-0.0331232063472271,
0.00440676836296916,
-0.02483213134109974,
0.03406811133027077,
0.007542639039456844,
0.02344427816569805,
-0.0788930132985115,
0.02643691934645176,
-0.024474481120705605,
-0.0028278299141675234,
0.019933070987462997,
-0.011128528043627739,
0.010586973279714584,
0.02449066936969757,
-0.06264554709196091,
-0.01899169199168682,
-0.0007353012333624065,
-0.03351164236664772,
0.004896603990346193,
0.010484454222023487,
-0.0331512987613678,
-0.020613593980669975,
0.0216121394187212,
0.004196146968752146,
0.016506684944033623,
-0.013611853122711182,
-0.0015417360700666904,
0.03342502936720848,
-0.011366527527570724,
0.036754440516233444,
0.027833400294184685,
-0.01607358083128929,
0.009027023799717426,
-0.02585601434111595,
0.013455242849886417,
0.01804797723889351,
0.028055883944034576,
-0.03442346677184105,
-0.0011029522866010666,
-0.046338167041540146,
0.0606367364525795,
-0.04786089435219765,
0.01982441544532776,
-0.021581633016467094,
-0.033046845346689224,
-0.042804017663002014,
-0.02708612009882927,
-0.008694128133356571,
0.01610877551138401,
0.03232603147625923,
0.031164491549134254,
0.011212310753762722,
0.007350378669798374,
0.029177937656641006,
0.05861890688538551,
0.04190071299672127,
-0.0071667213924229145,
0.035110216587781906,
0.0030601280741393566,
-0.012715802527964115,
-0.009700650349259377,
-0.003991311881691217,
0.004346203990280628,
0.026535535231232643,
-0.009944853372871876,
0.0018569226376712322,
-0.00887865386903286,
-0.01418186817318201,
0.03453313186764717,
0.04213756322860718,
-0.04126898944377899,
0.027286890894174576,
0.0013143435353413224,
-0.04751725122332573,
-0.006543867755681276,
-0.018801802769303322,
0.03924573212862015,
-0.0415753610432148,
-0.010745946317911148,
0.0035525888670235872,
-0.028860636055469513,
0.007038209121674299,
0.028836224228143692,
0.0023212372325360775,
0.021305646747350693,
-0.031019067391753197,
0.0013892920687794685,
-0.04766390845179558,
-0.044681042432785034,
-0.01102613378316164,
-0.006527947727590799,
0.0017578431870788336,
-0.027638208121061325,
0.03624775633215904,
0.0476086251437664,
0.0261062141507864,
0.035483237355947495,
0.07256478071212769,
-0.004328042734414339,
-0.009500717744231224,
-0.02579866163432598,
0.049626581370830536,
-0.029194070026278496,
-0.07354394346475601,
0.013911847025156021,
-0.05123746022582054,
-0.01360658835619688,
-0.04245661199092865,
-0.03755601868033409,
-0.023873286321759224,
0.0269008781760931,
-0.039250317960977554,
-0.030817855149507523,
-0.027176043018698692,
-0.01739785447716713,
0.06917338073253632,
0.04646313562989235,
0.05205658823251724,
0.010905472561717033,
0.010534158907830715,
0.01327494252473116,
-0.000651176436804235,
-0.04745376110076904,
-0.04066678509116173,
-0.038617853075265884,
0.0032942479010671377,
-0.03992849215865135,
0.015970520675182343,
-0.02310110814869404,
-0.008735034614801407,
0.03591352701187134,
-0.009392069652676582,
0.009156515821814537,
0.05380851402878761,
-0.01832524873316288,
0.018024668097496033,
0.03305784985423088,
0.05248267203569412,
0.012787333689630032,
0.07068440318107605,
0.062346287071704865,
-0.03765912353992462,
0.016458768397569656,
-0.017764156684279442,
0.04721740633249283,
0.03299722075462341,
-0.05081445723772049,
-0.033954303711652756,
0.022438639774918556,
0.00665545929223299,
-0.011873291805386543,
0.03091580793261528,
0.02793097123503685,
0.01105917152017355,
0.012361224740743637,
0.029516683891415596,
0.005907012149691582,
0.015223279595375061,
-0.06251749396324158,
0.03750321641564369,
-0.020501758903265,
0.03801105543971062,
0.06027468666434288,
0.017207259312272072,
0.03881193324923515,
-0.039266880601644516,
0.01948447898030281,
-0.10598132759332657,
0.021429533138871193,
0.030333803966641426,
-0.0015358420787379146,
-0.006539316847920418,
-0.05801886320114136,
-0.039889801293611526,
-0.04928208142518997,
0.006608936935663223,
-0.006277649197727442,
-0.012681259773671627,
-0.012001398019492626,
0.04092850536108017,
0.012688438408076763,
0.05741764232516289,
0.01964525692164898,
-0.006502973381429911,
0.05249779298901558,
-0.033251821994781494,
-0.07140340656042099,
-0.04578794538974762,
0.019825147464871407,
0.0055791768245399,
-0.050160087645053864,
-0.005757038947194815,
0.05441541224718094,
-0.008335357531905174,
-0.04718064144253731,
0.04434138908982277,
-0.017914971336722374,
-0.04609958082437515,
-0.02219526655972004,
0.010835261084139347,
-0.024110302329063416,
0.016187265515327454,
0.06922176480293274,
-0.00991139654070139,
0.022533642128109932,
0.008114920929074287,
0.06421124935150146,
-0.021577885374426842,
-0.03803284093737602,
0.023153670132160187,
0.014132832176983356,
0.03366747498512268,
0.05224413424730301,
-0.05625559389591217,
-0.02846502885222435,
-0.05569077283143997,
0.03674541413784027,
0.03493601456284523,
0.0654878243803978,
-0.010674217715859413,
-0.06723477691411972,
-0.0004611061012838036,
-0.04519397020339966,
0.01700710877776146,
0.06101390719413757,
-0.006836877204477787,
0.039726778864860535,
0.023887060582637787,
-0.0033984456676989794,
0.00738094886764884,
-0.015466071665287018,
-0.007335858419537544,
-0.07551302015781403,
-0.02977239340543747,
0.005515845492482185,
-0.02445623278617859,
-0.0048478166572749615,
0.04414316639304161,
0.007479823660105467,
-0.08749553561210632,
0.07484699785709381,
-0.024262171238660812,
0.0024462202563881874,
0.022412734106183052,
-0.10230682790279388,
-0.023174678906798363,
-0.00887338723987341,
-0.017312461510300636,
-0.0376027449965477,
0.03888243809342384,
-0.047980885952711105,
-0.07813642919063568,
0.00912539754062891,
-0.02303026244044304,
0.0010262319119647145,
0.009776170365512371,
0.002475285204127431,
-0.12263727188110352,
-0.006277286447584629,
0.008818631991744041,
0.011202586814761162,
-0.03501167893409729,
0.022701166570186615,
-0.03163487836718559,
0.03378814831376076,
0.07996512949466705,
-0.009913618676364422,
0.0511225163936615,
-0.007143521681427956,
0.0005436386563815176,
0.004582575522363186,
-0.0026983756106346846,
0.004820854403078556,
-0.05309576913714409,
0.0696805939078331,
-0.01101046521216631,
-0.010917347855865955,
0.04428404942154884,
-0.0297587588429451,
0.0457250252366066,
0.025903912261128426,
-0.009530830197036266,
-0.003399541601538658,
0.05020027980208397,
0.0894002765417099,
-0.026188217103481293,
-0.010188647545874119,
-0.0016543890815228224,
0.043058909475803375,
0.05762962996959686,
0.007945803925395012,
-0.023480389267206192,
0.031783491373062134,
-0.03443613275885582,
0.01681765541434288,
0.030313048511743546,
-0.023109370842576027,
0.03275571018457413,
0.10073670744895935,
-0.02345242165029049,
0.004794965498149395,
0.01685299165546894,
0.01952231116592884,
0.06191306933760643,
-0.03040263056755066,
-0.02896692045032978,
-0.006690177600830793,
-0.002571504097431898,
0.011902321130037308,
-0.04342472925782204,
-0.039012908935546875,
-0.026991616934537888,
0.008786986581981182,
0.02812853455543518,
0.008703788742423058,
-0.01847132295370102,
0.02621549740433693,
0.011109619401395321,
-0.08411138504743576,
-0.04931120574474335,
-0.008174841292202473,
-0.02523740567266941,
0.027835063636302948,
0.06176665425300598,
0.03767893463373184,
0.008281947113573551,
-0.0629962608218193,
-0.007656169589608908,
-0.021171770989894867,
0.04033374413847923,
-0.022979386150836945,
-0.014108712784945965,
-0.059670452028512955,
0.007140139117836952,
0.0013620340032503009,
0.0724250003695488,
0.02201383002102375,
0.021433988586068153,
-0.032135188579559326,
0.004530613776296377,
-0.010557390749454498,
0.001041183597408235,
0.03257022798061371,
0.005959608592092991,
-0.026992058381438255,
-0.01917494647204876,
0.008252153173089027,
-0.007243753410875797,
0.008302495814859867,
-0.013707675039768219,
-0.07793724536895752,
-0.10684212297201157,
-0.008784106932580471,
-0.03516373038291931,
-0.02848026528954506,
0.02227160893380642,
0.0772646963596344,
0.05060116946697235,
0.0013691990170627832,
-0.016555525362491608,
-0.007626528386026621,
0.06890933215618134,
-0.005270684137940407,
0.03162161633372307,
-0.028740905225276947,
0.019125251099467278,
0.018171288073062897,
-0.03990919515490532,
-0.004414593800902367,
0.024610374122858047,
-0.01728121004998684,
-0.05802660062909126,
0.04697590321302414,
-0.06064407154917717,
0.002294751815497875,
0.02179855667054653,
-0.00019615056226029992,
0.02359938621520996,
0.013952644541859627,
-0.05220934376120567,
-0.006729535758495331,
0.018407193943858147,
-0.03068295307457447,
-0.005405979696661234,
0.037545930594205856,
0.02745181694626808,
-0.0026069493032991886,
0.0075478027574718,
-0.03418584167957306,
-0.05426580458879471,
-0.03587866574525833,
-0.01851518079638481,
-0.014343086630105972,
0.0025016674771904945,
0.04056553170084953,
-0.03943557292222977,
0.005708592943847179,
-0.07015182077884674,
0.03844636678695679,
-0.008210385218262672,
-0.0022902742493897676,
-0.04907609894871712,
-0.03876389190554619,
-0.03170577436685562,
-0.02256721258163452,
0.03242636099457741,
0.049432627856731415,
0.03296178951859474,
0.014873247593641281,
-0.06350968778133392,
-0.0657140463590622,
-0.00045049749314785004,
0.0005870235618203878,
-0.02431454509496689,
0.0009928587824106216,
0.008571838960051537,
-0.05068804696202278,
0.028080180287361145,
-0.02805246226489544,
-0.05799498036503792,
0.057677917182445526,
-0.010337748564779758,
-0.014930137433111668,
-0.041640814393758774,
0.01469122339040041,
-0.007983244024217129,
0.04762405529618263,
0.037797410041093826,
-0.04212155193090439,
0.05689137056469917,
-0.005555259995162487,
0.002150860382243991,
0.0667065978050232,
-0.02506263740360737,
-0.0074188667349517345,
-0.010389342904090881,
-0.01686793379485607,
-0.011830986477434635,
0.005960366223007441,
0.035190314054489136,
0.02009180560708046,
-0.0333038754761219,
-0.029287803918123245,
-0.040365204215049744,
0.0056699649430811405,
0.04019664227962494,
0.05126431956887245,
-0.023341747000813484,
0.0689479261636734,
-0.00445131678134203,
0.008186660706996918,
0.006869749631732702,
-0.012997706420719624,
0.068047434091568,
0.013640420511364937,
0.01190390344709158,
0.00041631798376329243,
-0.0702744722366333,
0.013022352010011673,
-0.07235672324895859,
0.10352152585983276,
-0.01072062086313963,
0.039695270359516144,
-0.03544614836573601,
-0.0036084637977182865,
-0.03714153915643692,
0.012651876546442509,
0.0032197441905736923,
0.009945365600287914,
0.062981516122818,
-0.02358943037688732,
-0.07837033271789551,
-0.04109974950551987,
0.033911753445863724,
0.010582437738776207,
-0.00607211422175169,
0.02217555232346058,
-0.028970565646886826,
-0.012411238625645638,
0.010166341438889503,
0.016470853239297867,
0.015890922397375107,
0.04312531650066376,
0.004443948157131672,
0.03200092911720276,
-0.050205815583467484,
0.020042002201080322,
-0.03020426072180271,
-0.025662245228886604,
0.030785880982875824,
0.02605120837688446,
0.034478701651096344,
0.03264191001653671,
-0.014029416255652905,
0.07502768933773041,
0.04482771083712578,
-0.00046418674173764884,
0.012691334821283817,
0.029259605333209038,
-0.049408502876758575,
0.04585348442196846,
0.024251146242022514,
-0.06597375869750977,
-0.023249635472893715,
0.012354237958788872,
-0.05285346880555153,
0.008416812866926193,
0.022165045142173767,
0.06458780914545059,
0.00628650700673461,
-0.041230618953704834,
-0.03417053446173668,
-0.043790072202682495,
0.04752485081553459,
0.011967733502388,
-0.028540056198835373,
-0.05828693509101868,
-0.05445147678256035,
-0.03378208726644516,
0.028845880180597305,
-0.008739853277802467,
-0.03131471201777458,
0.008049758151173592,
-0.05438588187098503,
-0.010761718265712261,
0.03291172906756401,
-0.05921339988708496,
0.0336683988571167,
0.01948850229382515,
0.02568245120346546,
-0.028539558872580528,
-0.03521181270480156,
-0.030963975936174393,
0.011178592219948769,
0.002924923785030842,
0.008648078888654709,
-0.024210812523961067,
-0.052662238478660583,
-0.008944529108703136,
-0.00129285070579499,
-0.0820087417960167,
-0.0034607835114002228,
-0.012310713529586792,
0.061157308518886566,
-0.009722593240439892,
0.03765946626663208,
-0.02730763517320156,
0.03546765074133873,
0.020114554092288017,
-0.002717752940952778,
-0.03199993818998337,
-0.00917443074285984,
0.04224260896444321,
0.03880315274000168,
-0.0047139739617705345,
-0.00039649734389968216,
0.0646209791302681,
0.04374866187572479,
0.06261364370584488,
0.011811250820755959,
-0.009873349219560623,
-0.06507150083780289,
0.0415680892765522,
-0.0051285503432154655,
-0.020729195326566696,
-0.012216242030262947,
-0.02623523399233818,
0.05175168439745903,
-0.013533077202737331,
-0.06036127731204033,
0.0053102546371519566,
-0.0012134648859500885,
0.09166211634874344,
0.02609415352344513,
-0.02502841129899025,
-0.009754832834005356,
-0.06543591618537903,
0.022995442152023315,
-0.026714591309428215,
0.006106224842369556,
-0.009076510556042194,
-0.008202524855732918,
-0.03353146091103554,
-0.006893946323543787,
0.024250458925962448,
-0.04705632105469704,
0.011506162583827972,
-0.021652091294527054,
0.03495976701378822,
-0.021186169236898422,
-0.04349147900938988,
0.024893589317798615,
0.09186244010925293,
-0.011779558844864368,
0.00790819339454174,
0.005099026020616293,
-0.025020236149430275,
0.02893197536468506,
-0.03151613101363182,
-0.0030435090884566307,
0.022635795176029205,
-0.004660781938582659,
0.017146769911050797,
-0.03461456671357155,
0.039733998477458954,
0.032756928354501724,
0.02817693166434765,
0.01363848615437746,
0.021483415737748146,
-0.015835296362638474,
-0.070805624127388,
0.02293814904987812
] |
[
14.677845001220703,
-2.832991361618042
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
hep-ex
|
nucl-ex
|
2007-04-01T17:33:15
|
Precision tests of the Kobayashi-Maskawa model of CP violation are discussed,
pointing out possible signatures for other sources of CP violation and for new
flavor-changing operators. The current status of the most accurate tests is
summarized.
|
CP violation in beauty decays
|
hep-ph hep-ex
|
0704.0076
| 2,007
|
[
0.01153060793876648,
0.0010933623416349292,
0.006797606125473976,
-0.022021064534783363,
0.03199766203761101,
0.02184988744556904,
0.055888641625642776,
0.033856287598609924,
-0.024675091728568077,
0.012653011828660965,
-0.07176407426595688,
0.04349304735660553,
0.05577344819903374,
0.009859681129455566,
0.022272156551480293,
-0.024111779406666756,
0.06278388202190399,
-0.044414930045604706,
-0.003366262884810567,
0.02291102334856987,
0.0004789939848706126,
0.007431295234709978,
-0.053889837116003036,
-0.037003643810749054,
0.09058138728141785,
0.038092635571956635,
0.012544376775622368,
0.05046558752655983,
-0.02856488525867462,
0.05409133806824684,
0.05377917364239693,
-0.06676751375198364,
0.011737028136849403,
-0.04827575758099556,
0.01736486330628395,
-0.056607719510793686,
0.12274955213069916,
0.012878614477813244,
0.024801034480333328,
0.06517612189054489,
0.0858345702290535,
0.01965303160250187,
-0.011921114288270473,
-0.012993134558200836,
0.011197969317436218,
0.004309177398681641,
0.038011543452739716,
0.011894101276993752,
0.03950217738747597,
-0.008329416625201702,
-0.0031207266729325056,
0.003253257367759943,
0.03789495304226875,
-0.042954739183187485,
-0.006306384690105915,
0.020532554015517235,
0.013696175999939442,
-0.020921606570482254,
0.00893386173993349,
-0.006229599006474018,
0.017319638282060623,
0.05046127364039421,
-0.008881394751369953,
0.04580647498369217,
0.04568229243159294,
-0.09728683531284332,
-0.014138538390398026,
-0.006768888793885708,
-0.035929735749959946,
-0.037953171879053116,
0.03853294253349304,
0.026661342009902,
0.017244625836610794,
0.06197706237435341,
-0.025083089247345924,
-0.04110890254378319,
-0.027540337294340134,
-0.035494737327098846,
-0.0034104420337826014,
-0.013315542601048946,
0.008630559779703617,
-0.04037829115986824,
0.0053951311856508255,
0.07642319053411484,
0.07557277381420135,
-0.03501759469509125,
-0.01248981337994337,
0.06203620508313179,
-0.03418659046292305,
0.03437969088554382,
0.05683000758290291,
-0.019389363005757332,
0.03165803104639053,
0.01099115889519453,
-0.028854073956608772,
0.011402013711631298,
0.025479856878519058,
0.021085046231746674,
-0.045535486191511154,
0.005840159486979246,
0.004854097496718168,
0.0667353942990303,
-0.0008818220812827349,
0.04446166008710861,
0.04103383794426918,
0.014755039475858212,
0.043635692447423935,
0.02158427983522415,
-0.033384762704372406,
-0.03776587173342705,
-0.041119687259197235,
0.026935873553156853,
-0.02321096509695053,
0.0033009937033057213,
-0.09376395493745804,
-0.04306735098361969,
-0.006575263570994139,
-0.08055450767278671,
-0.028606247156858444,
0.02675546705722809,
0.005510225426405668,
-0.005148043856024742,
-0.017935600131750107,
0.030804313719272614,
0.011316563002765179,
0.014149613678455353,
-0.08093148469924927,
-0.016145450994372368,
0.00036131078377366066,
-0.004479569382965565,
-0.0064275795593857765,
0.04409400746226311,
-0.04807726666331291,
0.007147051393985748,
-0.0016359605360776186,
0.010655825026333332,
0.01634415239095688,
-0.02999214455485344,
0.0479019358754158,
-0.06814564019441605,
-0.028138909488916397,
0.006129610352218151,
0.030811302363872528,
0.023698044940829277,
0.0313354916870594,
-0.07827336341142654,
0.029114192351698875,
0.017869947478175163,
-0.0035346192307770252,
0.03970921412110329,
0.07179100066423416,
0.003981463611125946,
0.022239884361624718,
-0.005520819686353207,
-0.050492092967033386,
-0.020113471895456314,
-0.03916352614760399,
0.018273714929819107,
-0.018884476274251938,
0.011382455006241798,
0.009052167646586895,
0.013717486523091793,
0.0016162380343303084,
0.015425213612616062,
-0.06098586320877075,
0.011051942594349384,
0.005559000186622143,
0.049976103007793427,
-0.0017922702245414257,
-0.008296803571283817,
-0.016172541305422783,
-0.0192862581461668,
-0.0034738320391625166,
-0.01199395302683115,
0.01060415431857109,
0.04040861129760742,
-0.004150195978581905,
-0.03820705786347389,
0.01949000172317028,
-0.019031070172786713,
0.003386419266462326,
-0.02312743477523327,
-0.006256310269236565,
0.03307317942380905,
-0.01502255443483591,
0.01737823896110058,
-0.008640392683446407,
-0.08170705288648605,
-0.0027950771618634462,
-0.04075276851654053,
-0.02745984122157097,
0.025142380967736244,
-0.005257801618427038,
-0.0014316505985334516,
0.014726720750331879,
-0.04377932846546173,
-0.01277436874806881,
-0.07545455545186996,
0.009487123228609562,
-0.04738500714302063,
-0.08578426390886307,
-0.018183238804340363,
-0.07555558532476425,
0.00424927519634366,
-0.006914348341524601,
0.07568737864494324,
0.003459889441728592,
-0.019875947386026382,
-0.00007232802454382181,
-0.000013343279533728492,
0.052640628069639206,
0.03510228544473648,
0.015572278760373592,
-0.0021706006955355406,
-0.010866031050682068,
0.033431023359298706,
0.022394729778170586,
-0.0160226933658123,
-0.005861441604793072,
0.014848385006189346,
0.03559496998786926,
-0.013028096407651901,
0.009507554583251476,
0.013800200074911118,
0.015982266515493393,
0.0765642374753952,
-0.04749355837702751,
-0.03014754317700863,
-0.02620886266231537,
-0.056705575436353683,
-0.01038648746907711,
-0.009582879953086376,
0.019444875419139862,
0.01893172785639763,
0.017072709277272224,
0.04181056097149849,
-0.017903991043567657,
0.015719754621386528,
0.036415841430425644,
0.001970522804185748,
0.007515830919146538,
-0.003135346109047532,
-0.021365847438573837,
0.00961763970553875,
-0.055450789630413055,
0.02585221827030182,
-0.020115472376346588,
0.009842483326792717,
-0.02494540810585022,
0.008935642428696156,
-0.0006543646450154483,
0.030856695026159286,
0.039446547627449036,
0.05920044332742691,
0.04542464390397072,
-0.004678497090935707,
-0.015478032641112804,
0.06959524750709534,
-0.03888319060206413,
-0.007818386889994144,
0.01949676312506199,
-0.059990253299474716,
-0.05208958312869072,
-0.06226231902837753,
-0.02286546118557453,
-0.006661025807261467,
-0.012356185354292393,
-0.027553442865610123,
-0.033480603247880936,
-0.04159135743975639,
0.0021822613198310137,
0.05234382674098015,
0.04261943697929382,
0.04775619134306908,
0.03389865532517433,
-0.00266597350127995,
-0.010750195011496544,
-0.00466447276994586,
-0.02247166819870472,
-0.014778969809412956,
-0.06371758133172989,
-0.008055118843913078,
-0.03734397515654564,
-0.0497034527361393,
0.023010220378637314,
0.030547024682164192,
-0.031118350103497505,
-0.03936748579144478,
0.02004176564514637,
0.034214265644550323,
-0.023234613239765167,
-0.018092529848217964,
0.03426689654588699,
0.0468004010617733,
-0.004079021979123354,
0.08056865632534027,
0.08594698458909988,
0.019154805690050125,
0.04721532016992569,
0.026996353641152382,
0.055877700448036194,
0.02482471987605095,
-0.010555597022175789,
0.01802513375878334,
0.04536997526884079,
0.019442597404122353,
0.026346813887357712,
0.020008500665426254,
0.12040775269269943,
0.019240019842982292,
-0.02712295763194561,
0.04715215414762497,
-0.02241857349872589,
-0.033847223967313766,
-0.01678466610610485,
-0.01814032346010208,
-0.01785004884004593,
0.04358751326799393,
0.021423572674393654,
-0.03124457411468029,
0.05885519087314606,
0.008023575879633427,
0.02369074337184429,
-0.05013871565461159,
-0.0036057548131793737,
0.013778281398117542,
0.0018736411584541202,
0.02372056618332863,
-0.004624673165380955,
0.005880777258425951,
0.033343665301799774,
0.047036975622177124,
-0.03480239585042,
0.01901794970035553,
0.02107708901166916,
0.025907855480909348,
0.011140785180032253,
0.052374958992004395,
-0.03817759081721306,
-0.0019823333714157343,
0.02821362018585205,
-0.021182233467698097,
0.01525174081325531,
-0.05069735273718834,
-0.0015618700999766588,
0.02036242000758648,
-0.046623051166534424,
0.02759263664484024,
0.053296107798814774,
0.050500839948654175,
0.015455305576324463,
-0.010110045783221722,
-0.02125868760049343,
-0.03331565111875534,
-0.026792475953698158,
0.03968709334731102,
0.020264439284801483,
-0.010837672278285027,
0.04647727683186531,
0.013257822953164577,
0.07654672861099243,
0.011872885748744011,
0.08014241605997086,
-0.03642451390624046,
0.012809474021196365,
0.023867512121796608,
0.010907681658864021,
0.05458445847034454,
0.01865343563258648,
-0.07791928946971893,
-0.024396061897277832,
-0.06037445738911629,
0.041156869381666183,
0.003899370087310672,
0.05673053488135338,
0.022126639261841774,
-0.01547916978597641,
0.0430920235812664,
0.009262457489967346,
0.023418139666318893,
0.0031367617193609476,
-0.012862157076597214,
0.02171008475124836,
-0.0013557664351537824,
0.008381777442991734,
0.01449152547866106,
-0.07266644388437271,
-0.0065658302046358585,
-0.019196895882487297,
-0.04661281034350395,
0.0058164033107459545,
-0.03684784844517708,
-0.04497790336608887,
0.030024372041225433,
0.017852764576673508,
-0.07237622141838074,
0.011722424067556858,
-0.0352645106613636,
0.008872770704329014,
-0.005569305270910263,
-0.05471080169081688,
-0.03398405387997627,
0.002992938505485654,
-0.011493568308651447,
-0.02577088214457035,
0.009912960231304169,
-0.06540707498788834,
0.0037061593029648066,
0.05496526509523392,
0.05178738385438919,
-0.018300874158740044,
0.016223659738898277,
-0.03157541900873184,
-0.0669877678155899,
0.04009803757071495,
-0.017548343166708946,
0.004339477978646755,
0.0046107470989227295,
0.0720565989613533,
-0.04759224131703377,
0.007800299674272537,
0.026812978088855743,
-0.04385893791913986,
0.01712178997695446,
-0.025085588917136192,
-0.021774711087346077,
-0.02721451222896576,
0.03411077335476875,
0.02378641627728939,
-0.057297151535749435,
0.043374042958021164,
0.011591515503823757,
-0.01834171451628208,
0.03569977357983589,
-0.036623962223529816,
0.023719986900687218,
0.006340138614177704,
-0.00004544715557130985,
0.00010944987297989428,
0.05128283426165581,
0.07744187116622925,
-0.023457258939743042,
-0.0006201731157489121,
-0.02581312321126461,
0.04293547943234444,
0.03824367746710777,
0.04840866103768349,
-0.02927449159324169,
-0.010582108981907368,
0.01164017990231514,
0.0055704484693706036,
0.008240091614425182,
-0.0007293737726286054,
0.019387178122997284,
0.04832669720053673,
-0.03946027532219887,
0.05440238490700722,
0.005857035052031279,
0.012031369842588902,
0.05456863343715668,
0.017321165651082993,
0.008552259765565395,
0.034682370722293854,
-0.004945514723658562,
0.021254081279039383,
-0.017757151275873184,
-0.03573622182011604,
-0.03205406665802002,
-0.00841959286481142,
0.009650605730712414,
-0.04878866672515869,
-0.010384333319962025,
0.0334046371281147,
0.008175376802682877,
-0.02258329838514328,
-0.009098158217966557,
-0.016490023583173752,
-0.012820583768188953,
-0.017484288662672043,
0.06746679544448853,
-0.002491583814844489,
0.012190922163426876,
-0.05977505072951317,
-0.03115457110106945,
-0.032690443098545074,
0.0546647384762764,
-0.030165662989020348,
-0.017678312957286835,
0.026765456423163414,
-0.026554932817816734,
0.03965054079890251,
0.08975528180599213,
0.021927790716290474,
0.007405138574540615,
0.01087228674441576,
0.0006340743857435882,
-0.03488340973854065,
0.03289804235100746,
0.05205727368593216,
-0.0347488634288311,
-0.020998595282435417,
0.018040738999843597,
0.05994414538145065,
0.01491610612720251,
0.00428144121542573,
-0.0039367955178022385,
-0.014452086761593819,
-0.1100175604224205,
-0.0132483234629035,
-0.022769881412386894,
0.04868631437420845,
0.05884264409542084,
0.007828496396541595,
0.035320982336997986,
0.012892181985080242,
0.012530194595456123,
-0.03242958337068558,
0.006794874556362629,
-0.032714735716581345,
-0.03619205579161644,
0.009885826148092747,
-0.003179469844326377,
-0.03001910261809826,
0.003171814838424325,
-0.03239094093441963,
0.046796537935733795,
-0.027107829228043556,
-0.06581417471170425,
0.02894873544573784,
-0.09920305013656616,
0.015729308128356934,
0.026438504457473755,
-0.011809444054961205,
-0.0004104727122467011,
0.02122814580798149,
-0.04396810755133629,
0.015374771319329739,
-0.017377955839037895,
0.0007546275737695396,
0.041412584483623505,
-0.029199792072176933,
0.06243548542261124,
0.00268554943613708,
0.03178420290350914,
-0.006812060251832008,
-0.03601057082414627,
-0.08573107421398163,
0.03285475820302963,
-0.0567772351205349,
-0.04973018541932106,
-0.004988263826817274,
-0.028189731761813164,
0.014810344204306602,
-0.06697285175323486,
0.06697047501802444,
-0.0316929891705513,
0.014030439779162407,
-0.013447185978293419,
-0.10861161351203918,
-0.05590616911649704,
0.0019552200101315975,
0.002935366239398718,
0.05706882104277611,
-0.037856124341487885,
0.046557992696762085,
-0.09382909536361694,
-0.07386355102062225,
-0.007588614709675312,
-0.0011096170637756586,
-0.006542761344462633,
0.006370599381625652,
-0.025187646970152855,
-0.06567282974720001,
-0.005810459144413471,
-0.024691075086593628,
-0.027198588475584984,
0.015580317936837673,
-0.0124159324914217,
-0.010136500932276249,
-0.06120622158050537,
0.02581687830388546,
-0.09072719514369965,
0.007448467426002026,
-0.03959985077381134,
-0.029443340376019478,
0.02935096062719822,
-0.0443023145198822,
-0.0006643921951763332,
0.05278142914175987,
-0.0003148354880977422,
-0.035479314625263214,
-0.0708257406949997,
-0.006838595494627953,
0.016565589234232903,
-0.014053412713110447,
-0.036011986434459686,
-0.05463217571377754,
-0.021155808120965958,
-0.01619822159409523,
-0.04044420272111893,
-0.019741268828511238,
0.03663264587521553,
0.06325702369213104,
-0.03674262389540672,
0.019054017961025238,
0.028260571882128716,
0.00042201520409435034,
0.06303614377975464,
0.02549193985760212,
-0.011963983066380024,
-0.011542280204594135,
0.014382172375917435,
-0.03576436638832092,
-0.06199414283037186,
0.005287939216941595,
-0.06688486039638519,
0.08720710128545761,
-0.00929055456072092,
-0.029479404911398888,
-0.014138889499008656,
0.0005177921848371625,
-0.040847573429346085,
0.03239655867218971,
-0.06762243807315826,
-0.0003017034032382071,
0.061930008232593536,
0.030728613957762718,
-0.06835449486970901,
-0.005332160275429487,
0.05396401137113571,
-0.032635632902383804,
-0.0013935969909653068,
-0.010864568874239922,
-0.01914183236658573,
-0.03852061182260513,
0.01362743228673935,
-0.025256432592868805,
0.016356632113456726,
-0.01906651444733143,
0.006240774877369404,
0.05662227049469948,
-0.012068306095898151,
0.021737197414040565,
-0.03091392293572426,
0.02446623332798481,
0.018120693042874336,
0.019118135794997215,
0.059130895882844925,
-0.013838200829923153,
-0.019994234666228294,
0.055332887917757034,
0.053177360445261,
0.02094823308289051,
0.014383262023329735,
0.02381204254925251,
0.030584875494241714,
0.06328442692756653,
-0.015916695818305016,
-0.020402343943715096,
-0.06562795490026474,
-0.014127453789114952,
-0.04747699201107025,
0.0086887301877141,
-0.01961696706712246,
0.060083288699388504,
-0.040623679757118225,
-0.0007128461147658527,
-0.07250367850065231,
-0.01444826927036047,
0.03251621499657631,
0.008793765679001808,
-0.0012305512791499496,
-0.008835545741021633,
-0.05439860373735428,
-0.024570325389504433,
-0.00839486625045538,
-0.04941163957118988,
0.04916922003030777,
0.015242889523506165,
-0.0052927169017493725,
0.01392802968621254,
0.00394201185554266,
0.02790927141904831,
0.019914621487259865,
-0.01785087212920189,
-0.01945159025490284,
-0.029618525877594948,
-0.0030771170277148485,
-0.0528048612177372,
-0.018658814951777458,
0.004077600315213203,
0.04448096081614494,
0.010830972343683243,
-0.07651858776807785,
0.010241028852760792,
-0.027262570336461067,
-0.025162985548377037,
0.028062624856829643,
0.012798724696040154,
0.038878850638866425,
-0.01889260858297348,
0.017308184877038002,
0.002498835325241089,
-0.005407250020653009,
0.038940347731113434,
-0.00786474347114563,
-0.005020012613385916,
0.013171300292015076,
0.01493790466338396,
0.0456419363617897,
-0.042030662298202515,
0.011925313621759415,
0.051129553467035294,
0.03596300259232521,
0.00650272611528635,
-0.045544859021902084,
-0.021728690713644028,
-0.0689215138554573,
0.029620446264743805,
-0.015437635593116283,
0.0206613689661026,
-0.033404771238565445,
-0.04649950936436653,
0.022958489134907722,
0.0015339202946051955,
-0.0662044808268547,
0.01108075212687254,
0.009144317358732224,
0.03173351287841797,
-0.005880281329154968,
-0.011335761286318302,
-0.01609296165406704,
-0.07656344771385193,
0.002248383592814207,
-0.054179515689611435,
0.04875912889838219,
-0.00571323512122035,
0.02871348150074482,
-0.04686835780739784,
-0.03652031719684601,
-0.014230096712708473,
-0.08881929516792297,
-0.006013220176100731,
-0.013175134547054768,
-0.019499344751238823,
-0.035850852727890015,
-0.05097690224647522,
0.05029786750674248,
0.07313631474971771,
0.02788827382028103,
0.01873091235756874,
-0.005506305024027824,
-0.047807350754737854,
0.025990145280957222,
-0.03091503120958805,
-0.0059502930380403996,
0.01629883050918579,
0.008177760057151318,
0.06600695103406906,
-0.023320455104112625,
0.0015410427004098892,
0.0007517717895098031,
0.018573880195617676,
0.008405770175158978,
-0.016183504834771156,
-0.01978383958339691,
-0.005396027117967606,
0.016165537759661674
] |
[
15.812235832214355,
-3.10827374458313
] |
High Energy Physics - Phenomenology
|
General Physics
|
hep-ph
|
hep-ex
|
na
|
2007-04-01T09:49:01
|
The Dark Energy problem is forcing us to re-examine our models and our
understanding of relativity and space-time. Here a novel idea of Fundamental
Forces is introduced. This allows us to perceive the General Theory of
Relativity and Einstein's Equation from a new pesrpective. In addition to
providing us with an improved understanding of space and time, it will be shown
how it leads to a resolution of the Dark Energy problem.
|
Universal Forces and the Dark Energy Problem
|
physics.gen-ph
|
0704.0077
| 2,007
|
[
-0.00599408894777298,
0.07476086914539337,
-0.006487310864031315,
-0.035936158150434494,
0.0216160099953413,
0.0346277616918087,
-0.03698705509305,
0.04525388032197952,
-0.07035139203071594,
0.007366732228547335,
0.03327912837266922,
0.03395064175128937,
0.0231685359030962,
-0.021180368959903717,
0.017755769193172455,
-0.014819593168795109,
0.02546299621462822,
-0.025189600884914398,
-0.0033233435824513435,
0.0072602806612849236,
0.014953997917473316,
-0.019119128584861755,
0.033041421324014664,
-0.05955839157104492,
0.05195987597107887,
-0.0021991513203829527,
0.02312568575143814,
-0.00929799024015665,
-0.05726226046681404,
-0.009215539321303368,
0.08307535946369171,
-0.03195234760642052,
0.05817440152168274,
-0.028555436059832573,
-0.016771091148257256,
-0.031541526317596436,
0.018435798585414886,
0.02581065520644188,
0.013938351534307003,
0.030113419517874718,
0.01267945021390915,
0.02240634523332119,
-0.014848719350993633,
-0.017948530614376068,
0.046209000051021576,
-0.005570093169808388,
0.01033499650657177,
-0.05974194034934044,
0.021025951951742172,
-0.03741789236664772,
-0.0025099334307014942,
0.02113296091556549,
0.02806949056684971,
-0.03437098115682602,
-0.03430020809173584,
-0.00457711610943079,
0.022911230102181435,
-0.02897452935576439,
0.05547550693154335,
0.005094728898257017,
0.011147242039442062,
0.05797430872917175,
0.006383662577718496,
-0.017689283937215805,
-0.016873927786946297,
-0.04664307460188866,
-0.012004714459180832,
-0.004584828391671181,
0.01570161245763302,
-0.06809656322002411,
0.0153677212074399,
-0.018669527024030685,
0.016699617728590965,
0.036207251250743866,
0.005234227515757084,
-0.002539339242503047,
0.07411447912454605,
0.01585005596280098,
-0.027647066861391068,
-0.015535551123321056,
-0.0058441804721951485,
-0.02260739915072918,
0.07236195355653763,
0.039334625005722046,
0.09397248923778534,
-0.035839635878801346,
0.019643371924757957,
0.026936262845993042,
0.00934112910181284,
0.051071278750896454,
0.024810638278722763,
0.010115857236087322,
0.0781354010105133,
0.06766858696937561,
-0.05588856711983681,
0.0139862559735775,
0.013750098645687103,
0.04160498455166817,
-0.023406460881233215,
-0.013552447780966759,
-0.04937472194433212,
0.03394594416022301,
-0.022390227764844894,
0.02264735847711563,
0.05479324981570244,
0.03631250187754631,
-0.0321957990527153,
0.021272016689181328,
0.012366772629320621,
0.0004166454018559307,
-0.12703488767147064,
-0.00545814074575901,
0.021971222013235092,
-0.027157986536622047,
0.0027802407275885344,
-0.0671442523598671,
0.0633515790104866,
-0.062033142894506454,
-0.02664179541170597,
0.03501029685139656,
-0.02547893486917019,
0.015828872099518776,
0.04206382483243942,
0.03301467001438141,
-0.00034301672712899745,
-0.038846515119075775,
-0.02669195830821991,
-0.02345256507396698,
-0.004612302873283625,
-0.05336965247988701,
0.010011217556893826,
-0.0042982082813978195,
-0.05691676586866379,
-0.00443415530025959,
0.022723320871591568,
0.08217070251703262,
-0.018668539822101593,
-0.004234898369759321,
0.02653924562036991,
0.03313060477375984,
0.010053244419395924,
-0.022805802524089813,
-0.015295364893972874,
-0.011649658903479576,
-0.0012045621406286955,
-0.02857060916721821,
-0.024430684745311737,
-0.02296094223856926,
-0.021476270630955696,
-0.008853670209646225,
0.006947359070181847,
0.049685508012771606,
-0.008008276112377644,
-0.013861596584320068,
-0.008043576031923294,
-0.02530333399772644,
-0.055785536766052246,
0.015496763400733471,
0.010075410827994347,
-0.04491434618830681,
0.032885726541280746,
0.02077118679881096,
-0.0407993458211422,
0.02011423371732235,
-0.031907957047224045,
0.032447699457407,
0.030045993626117706,
-0.002784490119665861,
0.0510047972202301,
0.03612133860588074,
-0.049817174673080444,
-0.004833770450204611,
-0.0024907109327614307,
-0.014845872297883034,
0.018591079860925674,
0.0032234806567430496,
0.06416783481836319,
-0.09650087356567383,
0.0037836534902453423,
0.0038136858493089676,
0.04438384622335434,
-0.04433330148458481,
0.028914926573634148,
-0.021836981177330017,
0.035046737641096115,
0.042797598987817764,
-0.016557713970541954,
0.011080089956521988,
-0.006154727656394243,
-0.012412354350090027,
0.002175165805965662,
0.017751624807715416,
0.006148175802081823,
-0.012833540327847004,
0.01497871894389391,
-0.02260681241750717,
0.04304531216621399,
-0.028706425800919533,
-0.0184030719101429,
-0.015494679100811481,
-0.039621032774448395,
0.013403004966676235,
-0.009163721464574337,
-0.00174611690454185,
0.02789466083049774,
0.06601259857416153,
-0.005440671928226948,
0.044074397534132004,
0.0667617917060852,
-0.013524465262889862,
0.1022007092833519,
-0.014075164683163166,
0.03173351660370827,
-0.01294037513434887,
-0.0770738273859024,
-0.031170230358839035,
0.016439536586403847,
-0.008356349542737007,
-0.042049992829561234,
0.07002829760313034,
-0.015487413853406906,
0.0182335264980793,
-0.027992846444249153,
0.07948359847068787,
0.04085654765367508,
-0.014966582879424095,
-0.051322754472494125,
-0.07438965886831284,
-0.045166462659835815,
-0.05936170369386673,
-0.007595552131533623,
-0.007521247491240501,
0.07409024983644485,
0.04062756523489952,
0.0426507331430912,
0.011042463593184948,
-0.025329187512397766,
0.019383981823921204,
0.044820137321949005,
0.03374401107430458,
-0.015210826881229877,
-0.03805001825094223,
0.05228274688124657,
-0.04209987819194794,
-0.03431965783238411,
-0.012348298914730549,
0.0033146070782095194,
-0.022730236873030663,
0.041483692824840546,
0.0013190978206694126,
0.002908030990511179,
-0.04156012088060379,
-0.04121268168091774,
0.03228198364377022,
0.040415309369564056,
-0.03555110841989517,
-0.05208693817257881,
0.07262684404850006,
-0.08444377779960632,
-0.0564129576086998,
0.03588241711258888,
0.002369766356423497,
0.0023364322260022163,
0.015255448408424854,
-0.045572154223918915,
0.012118739075958729,
-0.025275250896811485,
0.013499611988663673,
-0.015934038907289505,
-0.04133795574307442,
0.011301728896796703,
0.024581290781497955,
0.032974280416965485,
-0.02302469126880169,
-0.021506916731595993,
0.028749654069542885,
0.01519344188272953,
-0.03679912909865379,
-0.004803919233381748,
0.014702890999615192,
-0.07805558294057846,
0.03713337704539299,
-0.09946957230567932,
0.02387176640331745,
-0.009785669855773449,
0.019342567771673203,
0.0018307106802240014,
-0.05550484359264374,
0.008922850713133812,
0.010497628711163998,
-0.008297733031213284,
0.04997929558157921,
0.013927889056503773,
0.011933288536965847,
-0.010920190252363682,
0.059193458408117294,
0.08301156014204025,
-0.02485029399394989,
-0.03229638934135437,
-0.012349640019237995,
-0.008386904373764992,
-0.03528410568833351,
0.016350340098142624,
0.009017926640808582,
-0.03286952152848244,
-0.03018117882311344,
0.0038886924739927053,
-0.011841940693557262,
0.013071850873529911,
0.022361014038324356,
-0.02643514983355999,
0.06930628418922424,
-0.01975731924176216,
-0.0012489681830629706,
-0.061361998319625854,
0.019560659304261208,
0.04015565663576126,
0.0008116723038256168,
0.0715961679816246,
-0.018106814473867416,
0.031200530007481575,
-0.034745533019304276,
-0.009339326992630959,
-0.053279731422662735,
0.021050872281193733,
0.06068756803870201,
-0.00013297544501256198,
0.005456898361444473,
-0.05666466802358627,
0.015615066513419151,
0.03214423730969429,
0.04562210664153099,
-0.0414225198328495,
0.014783099293708801,
-0.015927134081721306,
0.009596511721611023,
-0.01179848238825798,
0.023412158712744713,
0.024406608194112778,
0.006684694439172745,
-0.005567418411374092,
-0.052076660096645355,
-0.06981208175420761,
0.009015427902340889,
-0.028234761208295822,
0.018409185111522675,
-0.01656007021665573,
-0.05674571171402931,
0.06470844894647598,
-0.016022900119423866,
-0.054466135799884796,
-0.012952125631272793,
0.014225726015865803,
-0.010721390135586262,
0.001285472884774208,
0.016356628388166428,
0.09576200693845749,
0.011874849908053875,
0.025679340586066246,
0.01661527343094349,
0.0025169518776237965,
-0.014626383781433105,
0.024049056693911552,
0.006146666128188372,
0.011991139501333237,
0.005668817553669214,
0.016422152519226074,
0.02666507475078106,
-0.031029848381876945,
-0.07825923711061478,
-0.004634330049157143,
-0.02153647504746914,
0.011761371977627277,
0.032334912568330765,
0.04680779576301575,
-0.0428912527859211,
-0.03457712009549141,
0.023544801399111748,
-0.002223895164206624,
-0.02703952230513096,
0.07956969738006592,
0.04920637980103493,
0.003849530592560768,
0.04088043421506882,
0.004889512434601784,
0.03121485933661461,
-0.05985143035650253,
-0.04886806383728981,
-0.013091049157083035,
0.03439883142709732,
0.0012460213620215654,
0.007286846172064543,
-0.03207148611545563,
0.036781176924705505,
0.007654382381588221,
-0.02736903913319111,
0.044707007706165314,
-0.016036342829465866,
-0.011691608466207981,
-0.02150777354836464,
-0.0034005381166934967,
-0.057709746062755585,
0.006435425952076912,
-0.010219469666481018,
-0.042501699179410934,
0.06581605225801468,
0.03107624500989914,
-0.08125396817922592,
0.050591789186000824,
0.01465427316725254,
0.020551186054944992,
0.012612700462341309,
-0.011939515359699726,
-0.06856852024793625,
0.07046441733837128,
-0.011818959377706051,
0.017054352909326553,
-0.016209987923502922,
0.031133808195590973,
0.007943223230540752,
0.048245422542095184,
0.10735362768173218,
-0.0042624869383871555,
-0.03193632885813713,
-0.04115539416670799,
0.02170674502849579,
0.0033038777764886618,
-0.004856435116380453,
-0.002829988021403551,
-0.04618948698043823,
0.03597712889313698,
0.006244631949812174,
-0.012091014534235,
0.02798376977443695,
-0.06972333788871765,
-0.007329314947128296,
0.019107887521386147,
-0.012447160668671131,
-0.009048380888998508,
0.0659545361995697,
0.05575386434793472,
-0.01318063773214817,
0.02672553062438965,
-0.009358706884086132,
0.004925074987113476,
0.09435462951660156,
0.046907443553209305,
-0.016703370958566666,
-0.04849083349108696,
-0.00232951738871634,
0.053724829107522964,
0.009222275577485561,
0.019765054807066917,
-0.011266498826444149,
0.07743033766746521,
-0.0025189730804413557,
-0.02072448469698429,
-0.018456151708960533,
0.002883011009544134,
0.07102517038583755,
0.027042271569371223,
0.04354157671332359,
-0.030333878472447395,
0.05766337737441063,
0.032180242240428925,
-0.03825277090072632,
-0.014408162795007229,
-0.003929064609110355,
-0.04671046510338783,
0.012975260615348816,
-0.008624589070677757,
-0.00320845702663064,
0.011174779385328293,
0.023417403921484947,
-0.04179859533905983,
-0.0213844645768404,
-0.005187263712286949,
-0.020649874582886696,
0.00496328342705965,
0.02250465378165245,
0.01781533844769001,
0.015406347811222076,
0.032913174480199814,
-0.0034546442329883575,
-0.032658711075782776,
0.053521305322647095,
-0.0234521497040987,
0.03262951970100403,
-0.02098945528268814,
-0.03526156023144722,
-0.02190065197646618,
0.038682203739881516,
0.021943146362900734,
-0.024945316836237907,
-0.04143998399376869,
0.003832001006230712,
0.013364030048251152,
0.003386411815881729,
0.006850454956293106,
-0.03813019394874573,
-0.005063606426119804,
0.025321729481220245,
0.04901924356818199,
0.009308810345828533,
0.0030264921952039003,
0.027692977339029312,
-0.0012997854501008987,
-0.04994102567434311,
-0.027965931221842766,
0.04884280264377594,
-0.014372157864272594,
0.00792499165982008,
0.05966600030660629,
0.06164136528968811,
0.01570596732199192,
-0.0390063114464283,
0.06746827811002731,
0.017488421872258186,
-0.06805454194545746,
-0.026944752782583237,
-0.028784099966287613,
0.007255464792251587,
0.0511472225189209,
0.004172225017100573,
-0.025785939767956734,
0.03844800963997841,
-0.023213019594550133,
0.0025399657897651196,
0.0312353502959013,
-0.001992393983528018,
0.005151150282472372,
0.019590698182582855,
0.010443780571222305,
-0.07280270755290985,
0.01895352452993393,
-0.03876292705535889,
0.012733280658721924,
0.010518022812902927,
0.018610352650284767,
0.006392630748450756,
-0.024908917024731636,
0.03030175343155861,
0.05342243239283562,
0.033598706126213074,
0.007985617965459824,
-0.04313826560974121,
-0.07759290188550949,
0.007609772030264139,
0.002231395337730646,
-0.06536981463432312,
0.010280563496053219,
-0.03245219960808754,
-0.007557708770036697,
-0.03675734996795654,
0.009122167713940144,
-0.03440888598561287,
0.025341268628835678,
-0.0813923105597496,
-0.06539075076580048,
0.009958011098206043,
0.007825188338756561,
-0.022327126935124397,
0.02056010067462921,
-0.002509410260245204,
0.026257365942001343,
-0.11105091124773026,
-0.002267268253490329,
-0.02121143974363804,
0.037127185612916946,
-0.04649380221962929,
0.019979774951934814,
-0.004183413460850716,
-0.00724772596731782,
-0.0008752475259825587,
0.004244804847985506,
-0.07578040659427643,
0.02929271012544632,
-0.03543991595506668,
-0.07980417460203171,
-0.011222909204661846,
-0.03890657424926758,
-0.012177425436675549,
0.045719753950834274,
-0.03823886811733246,
-0.05478468909859657,
0.010772359557449818,
-0.07625310868024826,
-0.018849115818738937,
0.03413701429963112,
-0.03490401431918144,
0.057606592774391174,
-0.043473128229379654,
0.02992737852036953,
-0.027450399473309517,
-0.09409327059984207,
0.005283784586936235,
0.05489455163478851,
-0.024861853569746017,
-0.035305749624967575,
0.016257300972938538,
-0.042305123060941696,
0.03800972178578377,
0.0668768361210823,
0.0006339292740449309,
0.06743599474430084,
0.007929678075015545,
-0.047947388142347336,
0.016232501715421677,
0.04532703384757042,
-0.018588930368423462,
0.032068878412246704,
0.03964875638484955,
-0.06898713111877441,
-0.031085051596164703,
-0.006236321292817593,
-0.022562380880117416,
0.05875799432396889,
0.006980711128562689,
0.055277321487665176,
-0.020509056746959686,
-0.005317171569913626,
-0.011782788671553135,
0.0868479534983635,
-0.04572794958949089,
0.012408733367919922,
-0.022830165922641754,
-0.07892518490552902,
-0.05389169976115227,
0.010337268933653831,
0.07093384861946106,
-0.029543235898017883,
-0.03835613280534744,
-0.038520608097314835,
0.02999074012041092,
-0.03036542981863022,
0.016453957185149193,
0.016998842358589172,
0.04521598294377327,
-0.006088120862841606,
0.025681540369987488,
0.0013470618287101388,
-0.03923998028039932,
0.0038449743296951056,
-0.001317727961577475,
-0.011315587908029556,
-0.02011840045452118,
0.04006059095263481,
-0.00047763032489456236,
-0.0035657852422446012,
0.03250179812312126,
0.07508031278848648,
0.0031533208675682545,
0.02108391746878624,
0.019426608458161354,
-0.024326644837856293,
0.035893514752388,
0.0015481931623071432,
-0.045277759432792664,
0.014461067505180836,
-0.005044641904532909,
0.009720148518681526,
-0.014012211002409458,
-0.008216485381126404,
-0.004727468825876713,
-0.024702591821551323,
0.0020916408393532038,
0.022159051150083542,
-0.07364373654127121,
-0.02580218017101288,
0.033590640872716904,
0.005564406514167786,
-0.06541706621646881,
-0.04370678588747978,
-0.02957778237760067,
-0.07817231863737106,
-0.01202462799847126,
-0.027979057282209396,
0.036762986332178116,
0.025321142747998238,
0.001015263726003468,
0.007825416512787342,
0.05825651064515114,
-0.006232042331248522,
-0.007643265184015036,
-0.03151484578847885,
-0.03066745214164257,
0.033603791147470474,
-0.026783322915434837,
-0.061704088002443314,
-0.02949530817568302,
-0.003718900727108121,
0.025997167453169823,
0.0011964741861447692,
-0.07679001986980438,
0.0260927677154541,
-0.044304873794317245,
-0.029877817258238792,
0.06029321253299713,
0.06095801293849945,
0.03183381259441376,
-0.047605790197849274,
-0.023417290300130844,
-0.006864823400974274,
0.028738848865032196,
-0.06030412018299103,
-0.01069067232310772,
-0.016443511471152306,
-0.001573670539073646,
0.007889287546277046,
0.014311629347503185,
-0.0003509985108394176,
0.017182009294629097,
0.040440332144498825,
0.020385680720210075,
-0.0018224524101242423,
0.0025815004482865334,
0.0013389226514846087,
-0.029636960476636887,
-0.0029146329034119844,
-0.028436429798603058,
0.026679128408432007,
-0.05110018327832222,
-0.05263484641909599,
-0.0005500066909007728,
-0.0067024752497673035,
-0.03962980583310127,
-0.004665987100452185,
-0.04044607654213905,
0.05262444540858269,
-0.019108306616544724,
-0.002321339910849929,
0.00024945306358858943,
-0.047477565705776215,
0.012449140660464764,
-0.0183743666857481,
0.0408061258494854,
-0.020011261105537415,
0.01623675413429737,
-0.04639733210206032,
0.00823400728404522,
0.040920689702034,
-0.06975247710943222,
-0.024932658299803734,
0.040024153888225555,
-0.0021094854455441236,
-0.058876991271972656,
-0.057230863720178604,
0.037159934639930725,
0.08356760442256927,
0.033507898449897766,
-0.017037564888596535,
0.008317763917148113,
-0.006723146885633469,
-0.03263409808278084,
0.04590211436152458,
-0.051222022622823715,
0.011546393856406212,
0.006236955523490906,
-0.004168281797319651,
-0.02278468757867813,
0.029587335884571075,
0.016890574246644974,
-0.006159891840070486,
0.035710182040929794,
0.00024023086007218808,
-0.004375741351395845,
-0.02285141497850418,
0.04594272002577782
] |
[
13.619156837463379,
2.8638336658477783
] |
General Physics
|
General Physics
|
physics-gen-ph
|
na
|
na
|
2007-04-01T10:08:25
|
We present a critical review about the study of linear perturbations of
matched spacetimes including gauge problems. We analyse the freedom introduced
in the perturbed matching by the presence of background symmetries and revisit
the particular case of spherically symmetry in n-dimensions. This analysis
includes settings with boundary layers such as brane world models and shell
cosmologies.
|
Linear perturbations of matched spacetimes: the gauge problem and
background symmetries
|
gr-qc
|
0704.0078
| 2,007
|
[
0.017924683168530464,
0.052830770611763,
-0.007220606319606304,
-0.0608520433306694,
-0.013540806248784065,
0.0674012154340744,
0.05752355605363846,
0.01869090273976326,
-0.0216154046356678,
0.018830928951501846,
-0.027723833918571472,
0.026111457496881485,
-0.005769833456724882,
0.04823431745171547,
0.02909832075238228,
-0.006107585038989782,
0.07737857103347778,
0.059669092297554016,
-0.0047019110061228275,
-0.0713462084531784,
-0.010566430166363716,
-0.021760305389761925,
0.007672317326068878,
-0.0585634782910347,
0.05617300420999527,
-0.006418259348720312,
0.0628151223063469,
-0.027697548270225525,
-0.024394849315285683,
0.02092164196074009,
0.10036426782608032,
0.006735815200954676,
0.026238538324832916,
-0.06473042815923691,
-0.042033083736896515,
-0.030741963535547256,
0.03928124159574509,
0.0033280272036790848,
0.01516694761812687,
0.0368826724588871,
0.031293563544750214,
-0.04376085847616196,
-0.024086283519864082,
-0.0048783025704324245,
0.022701524198055267,
0.02143961749970913,
0.03242744877934456,
-0.012216740287840366,
0.03356969356536865,
-0.0037456124555319548,
-0.024092592298984528,
0.04201982542872429,
0.05322593078017235,
-0.08682847023010254,
-0.002128330757841468,
0.011476915329694748,
0.03879345580935478,
-0.020472891628742218,
0.06651770323514938,
0.05209939554333687,
0.016843996942043304,
0.04207167401909828,
-0.04015278071165085,
0.009731159545481205,
0.005895458161830902,
-0.05033079534769058,
-0.04298344627022743,
-0.01231321133673191,
-0.003558509983122349,
-0.018685970455408096,
0.046238090842962265,
-0.018695101141929626,
0.014211595989763737,
0.038029465824365616,
-0.032408200204372406,
0.01512349396944046,
0.02570274844765663,
0.012701055034995079,
-0.011838557198643684,
-0.00015478147543035448,
-0.010220619849860668,
-0.03800440579652786,
0.03203423693776131,
0.032844509929418564,
0.09097659587860107,
-0.0511743426322937,
0.008242032490670681,
0.05834362283349037,
-0.069093257188797,
0.03262589871883392,
0.02688245102763176,
-0.028580617159605026,
0.019938265904784203,
0.031071001663804054,
-0.03813297674059868,
0.05203578993678093,
-0.005173389799892902,
-0.007096973247826099,
-0.03340265154838562,
-0.0313541442155838,
-0.010567660443484783,
0.07618560642004013,
-0.024126645177602768,
0.021529147401452065,
0.07546751201152802,
0.02985132858157158,
0.05332855507731438,
0.01618870720267296,
0.0015713056782260537,
-0.04057048633694649,
-0.064320869743824,
-0.01703774556517601,
0.0038220405112951994,
-0.026583483442664146,
-0.06514981389045715,
-0.05056402087211609,
0.07805439829826355,
-0.09895679354667664,
-0.02110103704035282,
0.05448503792285919,
0.012077424675226212,
-0.002251742174848914,
-0.00665456335991621,
0.015185833908617496,
0.041371215134859085,
0.003701948095113039,
-0.07690376043319702,
-0.01428330596536398,
0.056556180119514465,
-0.001731988973915577,
0.031161276623606682,
0.0034269921015948057,
-0.05751800909638405,
0.02417415753006935,
0.013234739191830158,
0.001748262089677155,
-0.032228536903858185,
-0.015866205096244812,
0.0211041197180748,
0.0007128003053367138,
-0.020437952131032944,
-0.03559098765254021,
0.0314377062022686,
-0.008115464821457863,
0.05120889097452164,
-0.0732586681842804,
0.02669646590948105,
-0.05035191401839256,
-0.042513735592365265,
-0.021822253242135048,
0.03999105468392372,
0.06700918823480606,
0.05772223696112633,
0.017673220485448837,
-0.045590490102767944,
-0.025873921811580658,
-0.02748861350119114,
-0.00912393257021904,
0.04989505186676979,
-0.03303840011358261,
0.005682716146111488,
0.02886199951171875,
-0.03209569677710533,
0.06346719712018967,
-0.03144088014960289,
0.0201913733035326,
0.00515780271962285,
0.013969666324555874,
0.01724124141037464,
0.04598439112305641,
-0.06498946994543076,
-0.028101185336709023,
-0.010546669363975525,
-0.021756401285529137,
-0.01081178616732359,
0.03680223226547241,
0.0019214710919186473,
-0.05120617151260376,
0.01906767673790455,
-0.025259505957365036,
0.07267696410417557,
-0.0498434454202652,
0.022850191220641136,
0.01573694869875908,
-0.013493960723280907,
0.005275622010231018,
-0.028538694605231285,
-0.040215473622083664,
-0.04675057530403137,
0.008184412494301796,
0.02486274391412735,
0.02358456701040268,
-0.01675935462117195,
-0.02764911949634552,
-0.007909934036433697,
-0.004819750320166349,
0.0776137039065361,
-0.04313725233078003,
-0.026483384892344475,
-0.06319430470466614,
-0.04068852961063385,
0.023391585797071457,
-0.03347847983241081,
0.00019803023315034807,
-0.016617579385638237,
0.06569536030292511,
0.002273227320984006,
0.04521191120147705,
-0.0044226208701729774,
-0.012354987673461437,
0.035663723945617676,
0.0061920518055558205,
0.00458415225148201,
-0.0009052098030224442,
-0.06190413236618042,
0.009693168103694916,
0.003557878080755472,
-0.01076648198068142,
-0.03691563755273819,
0.0734998881816864,
0.03680714592337608,
-0.010734477080404758,
0.04257573187351227,
0.039090171456336975,
0.06751297414302826,
0.012656218372285366,
-0.00988221075385809,
0.021526210010051727,
-0.004259019624441862,
-0.012270967476069927,
-0.007983135990798473,
-0.02416970767080784,
0.041963160037994385,
0.005158683750778437,
0.014676162973046303,
0.0057030473835766315,
0.01913551054894924,
0.03660043329000473,
0.006868538446724415,
0.015512571670114994,
-0.005287561099976301,
0.06658731400966644,
-0.011903041042387486,
0.022235695272684097,
-0.03906314820051193,
0.0036102321464568377,
-0.02596082165837288,
-0.024027349427342415,
-0.046298570930957794,
0.011017431505024433,
0.018839258700609207,
-0.00973751861602068,
-0.0021463402081280947,
0.030842693522572517,
0.025494657456874847,
-0.04264978691935539,
-0.04531092569231987,
0.08124381303787231,
-0.051069531589746475,
-0.03596702590584755,
0.05256945267319679,
-0.015047209337353706,
-0.01544325239956379,
-0.03682073950767517,
-0.0531318336725235,
0.009698501788079739,
0.018444320186972618,
-0.0036219896283000708,
-0.0011719001922756433,
-0.02602062188088894,
-0.0008937689126469195,
0.08662202954292297,
0.04608510062098503,
0.0784728154540062,
-0.019638221710920334,
-0.007214379962533712,
0.04668307304382324,
-0.04131267964839935,
0.006823426112532616,
-0.058388784527778625,
-0.05128392204642296,
-0.004296793136745691,
-0.055603303015232086,
-0.039172567427158356,
0.017790935933589935,
-0.03411060571670532,
0.0191875658929348,
-0.03789648413658142,
0.012883450835943222,
0.07072972506284714,
-0.03703371062874794,
0.0009947434300556779,
0.011196721345186234,
0.044787999242544174,
0.018336713314056396,
0.08012279868125916,
0.05307319760322571,
-0.05717603117227554,
-0.027612177655100822,
0.033607255667448044,
0.007610797882080078,
-0.00844663381576538,
-0.013231414370238781,
0.0252549909055233,
0.03813532367348671,
-0.050863396376371384,
-0.03925694525241852,
-0.030851569026708603,
0.042425695806741714,
0.03774719312787056,
-0.007083852309733629,
0.021346241235733032,
-0.024894554167985916,
0.04491950199007988,
-0.061349719762802124,
0.08018307387828827,
0.03915291652083397,
-0.021660679951310158,
0.06136160343885422,
0.021482178941369057,
0.014995133504271507,
-0.0024339966475963593,
0.030036170035600662,
-0.03279883414506912,
0.011566950008273125,
0.026213591918349266,
0.013338479213416576,
0.018775437027215958,
-0.06622647494077682,
-0.006547595374286175,
0.03183620050549507,
0.008795017376542091,
0.017469603568315506,
-0.0011682072654366493,
0.009575319476425648,
0.021519571542739868,
-0.03799174353480339,
0.013098499737679958,
-0.0317641943693161,
0.015004098415374756,
0.012985674664378166,
-0.027365749701857567,
-0.028212765231728554,
-0.04214394465088844,
-0.005448454525321722,
0.04483247920870781,
-0.03676531836390495,
-0.02134593017399311,
0.024047983810305595,
0.01442604698240757,
-0.03621044382452965,
-0.014304191805422306,
0.00203540176153183,
-0.011087680235505104,
-0.030837494879961014,
0.06406930834054947,
0.0893656387925148,
-0.0024173324927687645,
0.07209121435880661,
-0.01127314567565918,
0.012455716729164124,
-0.026611296460032463,
-0.02572438307106495,
-0.02017763815820217,
0.030843835324048996,
0.033405810594558716,
0.022333677858114243,
-0.038756370544433594,
0.02111406810581684,
-0.07585064321756363,
-0.019889434799551964,
-0.022354653105139732,
0.017954207956790924,
0.03801929950714111,
0.0787079930305481,
-0.025667963549494743,
-0.08572573214769363,
-0.011389055289328098,
-0.011577366851270199,
-0.031616393476724625,
0.06081084907054901,
-0.004560324363410473,
0.004271319136023521,
-0.007976124994456768,
0.015694444999098778,
0.02530106157064438,
-0.0039242529310286045,
0.022975677624344826,
-0.0420059897005558,
-0.023446574807167053,
0.014249904081225395,
-0.06997068226337433,
-0.024746840819716454,
-0.022317131981253624,
-0.0024782507680356503,
-0.027771104127168655,
0.006030353717505932,
0.016109440475702286,
0.062222715467214584,
-0.013288459740579128,
0.012642482295632362,
-0.03918103873729706,
0.008330500684678555,
-0.02798018418252468,
-0.00723082572221756,
-0.01271935272961855,
-0.04399853199720383,
-0.020008690655231476,
0.04005574434995651,
0.014693209901452065,
-0.0037731723859906197,
0.03696458786725998,
-0.029473820701241493,
-0.12198638916015625,
0.04752891883254051,
-0.01578996330499649,
0.024768780916929245,
-0.032409437000751495,
0.05194416269659996,
-0.07474653422832489,
-0.003710046410560608,
0.07538168132305145,
-0.020365484058856964,
-0.017518898472189903,
0.010522611439228058,
0.011899609118700027,
0.0020286175422370434,
-0.03417981043457985,
0.0005569375352934003,
-0.05214288458228111,
0.02736639603972435,
-0.006495944224298,
-0.006599240005016327,
0.0750221312046051,
-0.043538764119148254,
-0.022908667102456093,
-0.03805430606007576,
0.007354441564530134,
-0.03791026398539543,
-0.0018399308901280165,
0.049060989171266556,
-0.04756224527955055,
0.03429362177848816,
-0.02212338335812092,
-0.01106812059879303,
0.06385809928178787,
0.018074847757816315,
-0.04881969839334488,
-0.017979800701141357,
-0.00587928993627429,
0.03917722776532173,
-0.013612596318125725,
0.02682029828429222,
0.002880059415474534,
0.04037776216864586,
-0.027520865201950073,
0.0337548702955246,
0.03128040209412575,
0.03484593331813812,
0.05020201951265335,
0.038033563643693924,
0.02014230564236641,
0.017120767384767532,
-0.005659108050167561,
-0.0050127943977713585,
-0.03176455944776535,
0.012441537342965603,
0.03448629006743431,
-0.01768582873046398,
0.049891795963048935,
0.04239616543054581,
-0.005096449051052332,
0.020682523027062416,
0.0029111120384186506,
-0.08719118684530258,
0.0290440171957016,
-0.0012525737984105945,
-0.03569580242037773,
-0.045326218008995056,
0.02132132090628147,
-0.005645130295306444,
0.007898194715380669,
0.020551109686493874,
0.025490019470453262,
-0.037860117852687836,
0.0127842016518116,
-0.007311963941901922,
0.010717857629060745,
-0.012027754448354244,
0.013227068819105625,
0.02368803881108761,
0.004950268194079399,
0.007596793118864298,
-0.013613940216600895,
-0.02781260572373867,
0.004760697949677706,
-0.007258699741214514,
0.02212388999760151,
0.005139264278113842,
-0.03147169202566147,
0.023822326213121414,
0.011950593441724777,
0.07210827618837357,
-0.011146764270961285,
-0.0211173165589571,
0.02826019562780857,
-0.007526991423219442,
-0.06427118182182312,
-0.009753608144819736,
0.03453592583537102,
-0.017190128564834595,
0.05598157271742821,
0.03383046016097069,
0.029569832608103752,
0.008332707919180393,
-0.053919222205877304,
0.019991688430309296,
-0.016783365979790688,
-0.03604511171579361,
-0.019326327368617058,
-0.025318995118141174,
0.009930073283612728,
0.0076511879451572895,
-0.028961999341845512,
-0.034200556576251984,
0.05214422196149826,
-0.026367615908384323,
-0.035006083548069,
0.012436731718480587,
-0.015875382348895073,
0.0006277430802583694,
0.017708109691739082,
-0.01218655239790678,
-0.046201858669519424,
0.053049538284540176,
-0.06862036138772964,
-0.012764086946845055,
0.0484064556658268,
0.03101443685591221,
-0.00855004508048296,
-0.008065742440521717,
-0.028818033635616302,
0.018801609054207802,
-0.008527543395757675,
0.0038434865418821573,
-0.021957939490675926,
-0.07420285046100616,
0.05039777234196663,
-0.017715586349368095,
-0.06929795444011688,
-0.020463328808546066,
-0.0028529150877147913,
0.02045658603310585,
-0.06048160418868065,
-0.01605154387652874,
-0.04516207054257393,
0.0009032430825755,
-0.05316019430756569,
-0.10186240077018738,
-0.03618795424699783,
-0.012619280256330967,
-0.013220700435340405,
0.0563277043402195,
-0.012706557288765907,
-0.040603771805763245,
-0.10495287925004959,
-0.06426636874675751,
-0.0244040098041296,
0.03294944390654564,
0.03547193855047226,
-0.024527767673134804,
-0.020665450021624565,
-0.029075030237436295,
0.033453602343797684,
0.012019374407827854,
-0.029641645029187202,
0.020048292353749275,
-0.008710631169378757,
-0.0346079021692276,
0.01766519621014595,
-0.04899457469582558,
-0.03026198409497738,
0.013444178737699986,
-0.05031346529722214,
-0.06168419495224953,
0.012096925638616085,
0.0027869592886418104,
0.0034628799185156822,
0.07845619320869446,
-0.03645217418670654,
0.013833418488502502,
-0.05574389919638634,
0.008855393156409264,
0.0495772548019886,
-0.0319046713411808,
0.010562378913164139,
0.007451257668435574,
-0.012835430912673473,
-0.06846576184034348,
-0.01861042156815529,
0.01756150834262371,
0.013935902155935764,
0.09167934209108353,
-0.004776085261255503,
0.06659156829118729,
0.056110043078660965,
-0.04249553382396698,
-0.014872613362967968,
-0.014463873580098152,
0.048106785863637924,
0.04351223260164261,
-0.0033943932503461838,
-0.06096908822655678,
-0.03754071146249771,
-0.008525579236447811,
-0.039158307015895844,
0.047998666763305664,
-0.03303079679608345,
0.038954559713602066,
-0.018541725352406502,
0.02717171423137188,
-0.026601986959576607,
-0.045544981956481934,
-0.07266735285520554,
0.023738078773021698,
0.0342177152633667,
-0.014303067699074745,
-0.07875961810350418,
0.0030952428933233023,
0.019079919904470444,
-0.005853879731148481,
-0.045508574694395065,
-0.05561131238937378,
-0.05460774153470993,
0.009464500471949577,
-0.002621470484882593,
-0.019260572269558907,
0.049452368170022964,
-0.051824405789375305,
0.03341132402420044,
0.010393552482128143,
-0.012773735448718071,
0.018035754561424255,
0.013789338059723377,
0.006983491592109203,
0.014752272516489029,
0.05386408045887947,
0.011640479788184166,
-0.0035348215606063604,
0.0036822666879743338,
0.040347542613744736,
0.10041378438472748,
-0.03889509662985802,
0.06997781991958618,
-0.03630506619811058,
-0.003902020398527384,
0.009481251239776611,
0.02128540724515915,
-0.04080666974186897,
-0.04340914264321327,
-0.03581194952130318,
0.01893949694931507,
-0.04351460188627243,
0.0025252338964492083,
0.022999828681349754,
0.014338579960167408,
-0.0024036795366555452,
-0.0025188978761434555,
0.020650211721658707,
0.036594998091459274,
-0.05323471128940582,
-0.03355211764574051,
-0.01323308702558279,
0.040263768285512924,
-0.02601008675992489,
0.012783720158040524,
-0.011283478699624538,
0.017398087307810783,
0.0223674513399601,
-0.035763926804065704,
0.04094856232404709,
-0.02004438079893589,
-0.0026036901399493217,
0.034171342849731445,
-0.011483046226203442,
-0.008010238409042358,
0.013895691372454166,
-0.013480296358466148,
-0.05262140557169914,
-0.018183328211307526,
0.021405698731541634,
0.024910788983106613,
-0.008619286119937897,
-0.06037204712629318,
0.001555595314130187,
-0.0016374763799831271,
-0.016006361693143845,
0.03530123829841614,
-0.018820224329829216,
-0.006382765714079142,
0.004187020473182201,
0.011127174831926823,
-0.03142409026622772,
-0.011187938041985035,
-0.0043664718978106976,
-0.028729602694511414,
-0.004462609998881817,
0.004713547881692648,
-0.000026068821171065792,
0.06431154906749725,
-0.05466284230351448,
0.028379064053297043,
0.07455002516508102,
-0.012937542982399464,
0.09556484967470169,
-0.04086118936538696,
-0.010297853499650955,
-0.011804117821156979,
0.04605579003691673,
-0.05073416233062744,
0.01712229661643505,
-0.008772735483944416,
-0.01981835812330246,
0.033200908452272415,
-0.007541722618043423,
-0.04421525448560715,
0.022294359281659126,
-0.024266911670565605,
0.06404341757297516,
-0.002599352039396763,
-0.0038090136367827654,
-0.034595560282468796,
-0.05761807784438133,
0.03504088521003723,
-0.022211385890841484,
0.021228309720754623,
-0.015689991414546967,
-0.023220587521791458,
-0.033644914627075195,
-0.02990712597966194,
0.004120390396565199,
-0.06768286973237991,
0.03523033857345581,
-0.0005268369568511844,
-0.026043318212032318,
0.008153306320309639,
-0.04147624969482422,
0.042768608778715134,
0.005725936032831669,
-0.0028346735052764416,
0.009678023867309093,
-0.0035951388999819756,
0.01070354413241148,
-0.004620089661329985,
0.020602477714419365,
0.022872451692819595,
-0.0005842174869030714,
0.0032447664998471737,
0.05882013961672783,
-0.020827174186706543,
0.0654766857624054,
0.0043776570819318295,
0.024579958990216255,
0.06336405128240585,
-0.02232974022626877,
0.017857979983091354,
-0.030797887593507767,
0.04775604233145714
] |
[
13.278088569641113,
2.211451292037964
] |
General Relativity and Quantum Cosmology
|
General Physics
|
gr-qc
|
na
|
na
|
2007-04-02T15:04:48
|
We define nonselfadjoint operator algebras with generators $L_{e_1},...,
L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of
the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=
(u_{i,j,k,l})$ is an $nm \times nm$ unitary matrix. These algebras, which
generalise the analytic Toeplitz algebras of rank 2 graphs with a single
vertex, are classified up to isometric isomorphism in terms of the matrix $u$.
|
Operator algebras associated with unitary commutation relations
|
math.OA
|
0704.0079
| 2,007
|
[
-0.08250748366117477,
0.025311680510640144,
-0.00878508947789669,
0.0005454472848214209,
-0.028032489120960236,
-0.02155349962413311,
-0.005451063625514507,
0.0485202893614769,
0.030390404164791107,
0.015639232471585274,
-0.09870708733797073,
-0.007634405512362719,
0.018501760438084602,
0.008055463433265686,
-0.05390428006649017,
0.002653649542480707,
0.02586451545357704,
0.03258911147713661,
-0.011807601898908615,
-0.03587500378489494,
-0.08989179134368896,
0.042262133210897446,
-0.02779005840420723,
-0.011446703225374222,
0.09554137289524078,
-0.023257767781615257,
0.06813021004199982,
0.008429146371781826,
-0.02875952608883381,
0.014851149171590805,
0.07504269480705261,
-0.007992519065737724,
0.02804655209183693,
-0.03638531640172005,
-0.022354476153850555,
-0.04000403359532356,
0.06806378066539764,
-0.02490433305501938,
0.034947123378515244,
0.013479232788085938,
0.020723946392536163,
-0.023907767608761787,
-0.010219593532383442,
-0.023796869441866875,
0.012266662903130054,
-0.04543537274003029,
0.02037176303565502,
0.01927720010280609,
0.021479124203324318,
0.00022384892508853227,
0.009984949603676796,
0.020497754216194153,
0.0332765132188797,
-0.05177977681159973,
-0.019574085250496864,
0.03841278702020645,
-0.01481707114726305,
-0.017548803240060806,
0.060828372836112976,
0.05215348303318024,
-0.004772481974214315,
0.002874267054721713,
-0.036526113748550415,
0.008493236266076565,
0.014652085490524769,
-0.05528287589550018,
-0.01925073005259037,
0.05064548924565315,
-0.03339669480919838,
0.0276902224868536,
0.01000976748764515,
0.007333843503147364,
0.031250402331352234,
0.027230825275182724,
-0.019694793969392776,
-0.03519969806075096,
0.016961021348834038,
0.02681000903248787,
0.02714349515736103,
0.012666825205087662,
0.02832614816725254,
0.0025404910556972027,
0.0487903356552124,
0.06933340430259705,
-0.005549290683120489,
0.011293680407106876,
0.007383211050182581,
0.028837008401751518,
-0.05126553028821945,
0.020356856286525726,
0.013851252384483814,
0.0398247167468071,
0.01866534911096096,
0.08518502116203308,
-0.05309657007455826,
-0.012478849850594997,
0.020267974585294724,
0.0036707003600895405,
-0.009347183629870415,
-0.05046673119068146,
0.009171469137072563,
0.07343745231628418,
0.02518865093588829,
-0.017708534374833107,
0.08312009274959564,
0.039081115275621414,
0.033396992832422256,
0.0028399601578712463,
-0.05354879051446915,
0.03219522908329964,
-0.049147829413414,
0.0001846557279350236,
-0.0047539109364151955,
-0.022019563242793083,
-0.030248047783970833,
0.006467374041676521,
0.02917085774242878,
-0.1107504665851593,
0.004403890576213598,
0.030516132712364197,
0.04830041527748108,
-0.031307488679885864,
0.026540853083133698,
0.0508292019367218,
0.008492628112435341,
0.05155905336141586,
0.01189802959561348,
0.028177794069051743,
0.046463631093502045,
-0.05208183079957962,
0.03816622868180275,
-0.01951712556183338,
-0.02581208012998104,
0.05105304718017578,
0.03439037501811981,
0.062005817890167236,
-0.05604146420955658,
-0.030881082639098167,
0.004652266390621662,
-0.0035178412217646837,
-0.02643330954015255,
0.03477276861667633,
-0.04899890720844269,
-0.0033881741110235453,
0.05924214795231819,
-0.06693890690803528,
0.02000858634710312,
-0.07025618106126785,
-0.01727624051272869,
0.005883486941456795,
0.010110903531312943,
0.06567320972681046,
-0.002500635338947177,
-0.031226860359311104,
-0.0403173603117466,
-0.03739656135439873,
-0.007523732725530863,
-0.0204161386936903,
0.03421863913536072,
-0.01882946491241455,
0.027696942910552025,
-0.0012454267125576735,
0.005401451140642166,
0.05703520029783249,
-0.0364217609167099,
-0.008743801154196262,
0.05290786176919937,
0.04817821457982063,
0.07536255568265915,
0.030647002160549164,
-0.012930075637996197,
0.01181186456233263,
-0.012869683094322681,
-0.023234659805893898,
0.037414465099573135,
-0.0027186917141079903,
0.010473922826349735,
-0.031842224299907684,
0.015345146879553795,
0.03096751496195793,
0.0001309509389102459,
0.01641889289021492,
0.027339141815900803,
0.004750827793031931,
0.0012949061347171664,
0.015897322446107864,
-0.03255537897348404,
-0.013624971732497215,
-0.017063193023204803,
0.01593729481101036,
-0.009988795965909958,
0.05882711708545685,
-0.021816620603203773,
-0.04669349268078804,
-0.05065079405903816,
-0.007505748886615038,
0.013652353547513485,
0.002716966439038515,
-0.04496947303414345,
-0.016271820291876793,
0.03828170523047447,
-0.05608952417969704,
-0.0849866047501564,
0.01045401580631733,
-0.04721396416425705,
0.07163697481155396,
0.001568034291267395,
0.06485781073570251,
0.017476165667176247,
-0.017799830064177513,
0.005791815463453531,
-0.015991738066077232,
0.01590975746512413,
-0.006570946425199509,
-0.025806179270148277,
-0.04660063236951828,
0.009789190255105495,
-0.08397945761680603,
-0.06067829951643944,
0.04636413976550102,
0.06091584637761116,
0.005594792775809765,
-0.029557939618825912,
-0.0030195782892405987,
0.007108780089765787,
0.019860727712512016,
0.02045173943042755,
-0.030528580769896507,
-0.0146665433421731,
-0.028965244069695473,
0.023760385811328888,
-0.05859225615859032,
0.05631169304251671,
-0.010367274284362793,
-0.00695536844432354,
-0.03545793890953064,
-0.0025442861951887608,
0.05232267081737518,
0.050824832171201706,
0.0450739786028862,
0.05298607423901558,
-0.028870880603790283,
0.02032949961721897,
-0.00394193222746253,
-0.03076814115047455,
-0.01638065092265606,
0.0653449147939682,
-0.02748558484017849,
-0.016078438609838486,
0.04827405884861946,
-0.06570342183113098,
-0.026588626205921173,
0.0023197766859084368,
0.029646312817931175,
0.002854771213606,
-0.03665580227971077,
-0.033479444682598114,
0.0093085877597332,
0.009928975254297256,
-0.04498521611094475,
0.02444293722510338,
-0.010244354605674744,
0.012053243815898895,
-0.01893596537411213,
-0.04601486399769783,
-0.010025265626609325,
0.03587871044874191,
-0.026507550850510597,
0.005990762263536453,
0.011926730163395405,
-0.0469135083258152,
-0.0015098623698577285,
0.03830933943390846,
0.028705736622214317,
-0.022672051563858986,
-0.0135564636439085,
-0.009800607338547707,
-0.035012491047382355,
-0.06677927821874619,
0.0008082053391262889,
-0.031914860010147095,
0.0161108560860157,
-0.031387604773044586,
0.024518217891454697,
0.00504238111898303,
-0.0000012179356190245016,
0.04499797523021698,
-0.008476250804960728,
0.010079757310450077,
0.02252194657921791,
-0.009908531792461872,
0.03623513504862785,
0.0071442462503910065,
0.02669094130396843,
0.013091514818370342,
0.038121044635772705,
0.019170546904206276,
0.01578626222908497,
-0.017037492245435715,
0.0709676444530487,
-0.01978728547692299,
0.006041927263140678,
0.018394997343420982,
0.004701013211160898,
0.018943684175610542,
0.025355204939842224,
-0.017742764204740524,
-0.06443028897047043,
0.03362559527158737,
0.061208244413137436,
-0.07950770109891891,
0.03502366691827774,
0.010845753364264965,
-0.03994784876704216,
0.00773766590282321,
0.020000087097287178,
0.026733415201306343,
0.011013505980372429,
0.019351307302713394,
-0.02895490452647209,
0.004376502707600594,
-0.051830440759658813,
0.014968029223382473,
-0.022277124226093292,
0.00039327246486209333,
0.005053416825830936,
0.01783718913793564,
0.08985414355993271,
0.0010259579867124557,
-0.016350582242012024,
0.009455733001232147,
0.032443270087242126,
0.022730184718966484,
0.010360264219343662,
-0.035985711961984634,
-0.054367538541555405,
0.034957047551870346,
0.004253495018929243,
-0.01558163482695818,
-0.08576876670122147,
-0.01460141222923994,
-0.058175887912511826,
-0.017537884414196014,
-0.04011949151754379,
-0.04619289189577103,
-0.004813660401850939,
-0.060688965022563934,
0.020632781088352203,
-0.004248262848705053,
-0.006030622869729996,
-0.05672699585556984,
0.03184286877512932,
0.02209261804819107,
-0.00046860595466569066,
0.004233637824654579,
0.021902218461036682,
0.05944860354065895,
-0.005568706430494785,
0.02498479187488556,
0.007153621409088373,
-0.008718959987163544,
-0.043300092220306396,
0.05219168961048126,
0.007809251081198454,
0.004064685199409723,
0.02839420922100544,
0.009299163706600666,
0.010122714564204216,
0.045416735112667084,
-0.0000010926725053650443,
-0.008095075376331806,
-0.023752447217702866,
0.033199552446603775,
0.004718183074146509,
-0.03816165775060654,
-0.01191448699682951,
-0.009871270507574081,
0.012659684754908085,
-0.028092479333281517,
0.0010233581997454166,
0.03863775357604027,
-0.02027605101466179,
0.05347060784697533,
0.028106026351451874,
0.036447733640670776,
0.043666768819093704,
0.004490090999752283,
0.013354284688830376,
-0.0392414927482605,
0.02347159944474697,
-0.007566255051642656,
-0.0504252091050148,
-0.009447845630347729,
0.0195767804980278,
-0.017927642911672592,
-0.025707470253109932,
0.03417413681745529,
-0.008919771760702133,
-0.016903415322303772,
-0.02661203034222126,
0.0018802682170644403,
-0.09059591591358185,
0.007560367230325937,
-0.004289674572646618,
-0.03898845240473747,
0.06949984282255173,
-0.010799098759889603,
-0.051060523837804794,
0.05161205306649208,
0.017900483682751656,
0.03381168469786644,
0.043735068291425705,
0.04086197912693024,
-0.06135428696870804,
-0.0014450870221480727,
0.00318474555388093,
0.03899712488055229,
0.011492320336401463,
-0.016898896545171738,
0.0023764357902109623,
-0.06720719486474991,
0.04750770702958107,
0.013503951951861382,
0.0005835160845890641,
0.028917547315359116,
-0.03544551879167557,
-0.010867987759411335,
0.035565219819545746,
0.0035462407395243645,
-0.006884620524942875,
-0.018695931881666183,
0.014226389117538929,
0.018526727333664894,
0.03440311923623085,
-0.07814963907003403,
-0.016862086951732635,
0.04870662838220596,
0.04521889239549637,
-0.005681256297975779,
0.0032758128363639116,
0.0579017773270607,
-0.0165870301425457,
0.01736234314739704,
0.008296141400933266,
0.026391927152872086,
0.042442675679922104,
0.07818862795829773,
-0.0027967686764895916,
-0.055423978716135025,
-0.01797066628932953,
0.050881147384643555,
0.06064936891198158,
0.02623896859586239,
-0.0172314140945673,
0.04294760897755623,
-0.021896766498684883,
-0.007314576301723719,
0.0015926442574709654,
0.042247969657182693,
0.017458871006965637,
0.047411222010850906,
-0.02348673902451992,
-0.039311423897743225,
-0.00038664473686367273,
-0.03450318053364754,
-0.02052251622080803,
-0.07529062032699585,
0.06148059293627739,
0.009456015191972256,
0.029979372397065163,
0.0007679731934331357,
0.02174724079668522,
0.03037625551223755,
0.016820820048451424,
0.035039737820625305,
0.0011717438464984298,
0.016109688207507133,
-0.03600970655679703,
-0.06722854822874069,
0.03708847984671593,
0.015716958791017532,
-0.017593733966350555,
-0.027632789686322212,
0.0030074322130531073,
0.02865138277411461,
0.0885230079293251,
-0.026241932064294815,
0.012125913053750992,
0.03267635777592659,
-0.01782604493200779,
0.00020499597303569317,
0.029776616021990776,
-0.03568858280777931,
0.026308871805667877,
-0.07325024157762527,
-0.024089137092232704,
-0.013348816893994808,
0.024353131651878357,
0.030773382633924484,
0.0037951467093080282,
-0.02758403867483139,
0.056938715279102325,
0.017093591392040253,
0.02594617009162903,
0.02855648659169674,
-0.036547742784023285,
0.013251123949885368,
-0.03194473311305046,
0.005418797954916954,
0.0018082240130752325,
0.06895028799772263,
0.04675241932272911,
0.054622091352939606,
0.06389196217060089,
0.02242954447865486,
-0.024218298494815826,
0.010994864627718925,
-0.04796820506453514,
-0.09009096026420593,
-0.01151079311966896,
0.019060231745243073,
0.021827872842550278,
0.029664354398846626,
-0.014627066440880299,
-0.0837947428226471,
0.029886426404118538,
0.006338092964142561,
-0.0632532611489296,
0.0008930350886657834,
0.01490106899291277,
0.009785361588001251,
0.012930619530379772,
0.002895069308578968,
-0.07587645202875137,
0.026914825662970543,
-0.03501617908477783,
0.00038365356158465147,
0.008523734286427498,
-0.0581846758723259,
0.0236522164195776,
-0.0059676640667021275,
-0.010806647129356861,
0.0007152158650569618,
0.019290344789624214,
0.04145878925919533,
-0.051868610084056854,
-0.05828073248267174,
0.0072067296132445335,
-0.005651766899973154,
0.010215303860604763,
0.014192107133567333,
-0.05001171678304672,
-0.011778969317674637,
-0.11357028037309647,
0.04015957564115524,
-0.06433168798685074,
-0.038249269127845764,
-0.03746718168258667,
-0.02568543516099453,
0.032611072063446045,
0.03810202702879906,
0.07220036536455154,
-0.02492431364953518,
0.01764632761478424,
0.05998849496245384,
-0.08458282798528671,
-0.03315701708197594,
0.034576255828142166,
0.01959526352584362,
0.05145128443837166,
0.020468363538384438,
-0.0031358564738184214,
-0.001673573162406683,
-0.011461443267762661,
-0.02950645238161087,
-0.03347157686948776,
0.028226129710674286,
-0.033475179225206375,
-0.013504143804311752,
-0.03820265084505081,
-0.022159870713949203,
-0.06857101619243622,
-0.013825167901813984,
0.004830990452319384,
-0.06873302161693573,
-0.0045452844351530075,
-0.0017171562649309635,
-0.050294969230890274,
0.06230541318655014,
0.020385511219501495,
-0.005172670818865299,
0.005218357313424349,
-0.009632077068090439,
0.020529909059405327,
0.0009437129483558238,
0.03660013526678085,
0.019700659438967705,
0.03608187288045883,
0.033072445541620255,
-0.08332301676273346,
-0.026882315054535866,
0.019558798521757126,
0.05240602046251297,
0.017400290817022324,
-0.0038300154265016317,
0.11000065505504608,
-0.05539853870868683,
0.04258333146572113,
0.020092662423849106,
-0.004924897104501724,
-0.052726149559020996,
-0.008574309758841991,
-0.019922157749533653,
-0.036322444677352905,
-0.06796447932720184,
-0.04441355913877487,
0.015845434740185738,
-0.01467140018939972,
-0.007182000204920769,
-0.060442280024290085,
-0.02044246904551983,
-0.0553903691470623,
0.01194066647440195,
0.002021075924858451,
-0.0018446339527145028,
0.0321490541100502,
0.012345603667199612,
-0.06374970823526382,
0.02428104542195797,
0.0820799469947815,
-0.005302086938172579,
-0.04704176262021065,
-0.032611243426799774,
-0.05440952628850937,
-0.03837110847234726,
-0.015122553333640099,
-0.02052425965666771,
0.031203554943203926,
0.02735256962478161,
0.02777271345257759,
0.001974361017346382,
-0.007023622281849384,
-0.036472026258707047,
0.004626425914466381,
0.015849336981773376,
0.03942442685365677,
-0.004559711087495089,
0.004284647759050131,
-0.02288404479622841,
0.03506072610616684,
0.09438397735357285,
0.06859499216079712,
-0.06587257981300354,
0.033130720257759094,
-0.03972180187702179,
-0.004959455691277981,
0.06686487793922424,
-0.016323426738381386,
0.010643859393894672,
-0.015145475044846535,
-0.011978445574641228,
0.005254773423075676,
-0.02070319466292858,
-0.026623807847499847,
-0.005366922356188297,
-0.0357816182076931,
0.009261595085263252,
-0.05514533072710037,
-0.02985302172601223,
-0.000003907288828486344,
-0.02747654728591442,
-0.07523543387651443,
0.00004159080344834365,
-0.036884747445583344,
-0.09875119477510452,
0.02400088682770729,
0.03049958124756813,
0.02976008877158165,
-0.009222207590937614,
-0.037567634135484695,
-0.00831927452236414,
0.04109454154968262,
0.011569411493837833,
-0.019402923062443733,
-0.0015351417241618037,
0.0012213123263791203,
0.012410368770360947,
-0.046413008123636246,
0.022684279829263687,
-0.04534006863832474,
0.013624000363051891,
0.029911959543824196,
0.02824268490076065,
-0.0665043517947197,
-0.029446173459291458,
-0.01931408792734146,
-0.0559871681034565,
0.04341506212949753,
-0.03010425716638565,
-0.0014715759316459298,
-0.016716323792934418,
0.012887245044112206,
-0.07835561037063599,
0.04744923487305641,
-0.06488801538944244,
-0.05522281676530838,
-0.002952591748908162,
0.04180605337023735,
0.024364423006772995,
0.002598494989797473,
-0.031193438917398453,
-0.022456757724285126,
0.016165319830179214,
0.015558967366814613,
0.05593734234571457,
-0.049896009266376495,
-0.028829248622059822,
-0.02463761530816555,
0.0054361228831112385,
-0.01330818235874176,
0.062113117426633835,
-0.026068156585097313,
-0.06302124261856079,
0.0027335656341165304,
-0.03736874461174011,
-0.06455930322408676,
0.007033591624349356,
-0.0016232773195952177,
0.04517202451825142,
0.027021460235118866,
-0.028128037229180336,
-0.010787773877382278,
-0.060911595821380615,
0.055269356817007065,
-0.055925820022821426,
-0.02915177494287491,
-0.039138536900281906,
-0.014833438210189342,
0.002358874771744013,
0.016544930636882782,
0.0003190009156242013,
-0.04796262085437775,
-0.005927660036832094,
0.02857576683163643,
0.05027884989976883,
-0.005688289180397987,
-0.04733331874012947,
-0.0366084910929203,
0.02448641136288643,
0.02857072837650776,
-0.04783317446708679,
0.021992290392518044,
-0.01676434651017189,
0.015809306874871254,
0.035637736320495605,
0.011354533024132252,
-0.010866234079003334,
0.05314270034432411,
0.042610108852386475,
-0.009349457919597626,
0.053117476403713226,
0.05126361548900604,
0.001512350863777101,
0.03430912271142006,
-0.022601133212447166,
0.009895076043903828,
-0.04480902850627899,
0.004160346928983927
] |
[
1.891591191291809,
2.753103017807007
] |
Operator Algebras
|
Mathematics
|
math-OA
|
na
|
na
|
2007-04-01T10:20:37
|
We show that the globular cluster mass function (GCMF) in the Milky Way
depends on cluster half-mass density (rho_h) in the sense that the turnover
mass M_TO increases with rho_h while the width of the GCMF decreases. We argue
that this is the expected signature of the slow erosion of a mass function that
initially rose towards low masses, predominantly through cluster evaporation
driven by internal two-body relaxation. We find excellent agreement between the
observed GCMF -- including its dependence on internal density rho_h, central
concentration c, and Galactocentric distance r_gc -- and a simple model in
which the relaxation-driven mass-loss rates of clusters are approximated by
-dM/dt = mu_ev ~ rho_h^{1/2}. In particular, we recover the well-known
insensitivity of M_TO to r_gc. This feature does not derive from a literal
``universality'' of the GCMF turnover mass, but rather from a significant
variation of M_TO with rho_h -- the expected outcome of relaxation-driven
cluster disruption -- plus significant scatter in rho_h as a function of r_gc.
Our conclusions are the same if the evaporation rates are assumed to depend
instead on the mean volume or surface densities of clusters inside their tidal
radii, as mu_ev ~ rho_t^{1/2} or mu_ev ~ Sigma_t^{3/4} -- alternative
prescriptions that are physically motivated but involve cluster properties
(rho_t and Sigma_t) that are not as well defined or as readily observable as
rho_h. In all cases, the normalization of mu_ev required to fit the GCMF
implies cluster lifetimes that are within the range of standard values
(although falling towards the low end of this range). Our analysis does not
depend on any assumptions or information about velocity anisotropy in the
globular cluster system.
|
Shaping the Globular Cluster Mass Function by Stellar-Dynamical
Evaporation
|
astro-ph
|
0704.0080
| 2,007
|
[
-0.0033972631208598614,
0.031142394989728928,
-0.003079390386119485,
-0.03660532832145691,
0.045910321176052094,
0.03138615936040878,
0.07066492736339569,
0.006858050357550383,
-0.04300711303949356,
-0.015268664807081223,
-0.0686831995844841,
0.030661650002002716,
0.06313059478998184,
-0.0028940236661583185,
0.06116402894258499,
-0.020703135058283806,
-0.008063186891376972,
-0.06810138374567032,
0.006914379075169563,
0.08372219651937485,
-0.05582473427057266,
-0.046362172812223434,
-0.02914506569504738,
-0.03459181264042854,
0.08156993240118027,
0.05305185914039612,
0.04713701456785202,
0.022344525903463364,
-0.053701236844062805,
0.0550537183880806,
0.09558017551898956,
-0.036604829132556915,
-0.015206538140773773,
-0.06354231387376785,
-0.02150249481201172,
-0.012857381254434586,
0.019329864531755447,
-0.028348786756396294,
0.017882859334349632,
0.03016686998307705,
0.03232433646917343,
-0.06587718427181244,
0.06674602627754211,
0.002819177694618702,
0.009935129433870316,
0.04134667292237282,
0.01096053421497345,
-0.006319208536297083,
0.006460258271545172,
-0.04516484588384628,
-0.012415981851518154,
0.015413627959787846,
0.013498952612280846,
-0.053981468081474304,
-0.04593869671225548,
0.01203092560172081,
0.02495213784277439,
-0.029871143400669098,
0.03963972255587578,
-0.04342395439743996,
0.046979617327451706,
0.003695983439683914,
-0.040935974568128586,
0.005183826200664043,
-0.0029003466479480267,
-0.04688754305243492,
-0.03753593564033508,
0.0178346186876297,
0.0026583257131278515,
-0.0646909773349762,
0.019791023805737495,
0.036602750420570374,
-0.007525708060711622,
0.014095941558480263,
-0.03522995859384537,
0.018512364476919174,
0.012360487133264542,
-0.002627990208566189,
-0.01834747940301895,
0.002997803268954158,
-0.048590343445539474,
-0.023282678797841072,
0.016866089776158333,
0.03746798262000084,
0.054138634353876114,
0.039756547659635544,
-0.02290271408855915,
0.009570490568876266,
-0.0574997253715992,
0.039268311113119125,
0.010931645520031452,
-0.02993079647421837,
0.05028538778424263,
0.03508853539824486,
-0.04425755888223648,
0.026799529790878296,
0.016734035685658455,
0.03450885787606239,
-0.019429080188274384,
0.012444973923265934,
0.027967175468802452,
0.03850794956088066,
0.020293524488806725,
0.01197762880474329,
0.06892325729131699,
0.015300407074391842,
0.03352314606308937,
0.01858513243496418,
0.02959049493074417,
-0.0021925957407802343,
-0.05164481699466705,
-0.05095893517136574,
0.008800956420600414,
0.0077971904538571835,
-0.028595639392733574,
-0.05337869003415108,
0.06102791056036949,
-0.07160583138465881,
0.0073133124969899654,
0.027655471116304398,
0.03081982024013996,
-0.006475639529526234,
-0.015476972796022892,
0.009814244695007801,
-0.0416468121111393,
0.001679692417383194,
-0.030543550848960876,
-0.00844591110944748,
0.010110924951732159,
-0.018353620544075966,
-0.019573045894503593,
0.00016096972103696316,
-0.055417753756046295,
0.014571229927241802,
0.020418822765350342,
0.005494317039847374,
-0.03471728041768074,
-0.018000787124037743,
-0.053609512746334076,
-0.03670597821474075,
0.015389230102300644,
0.010974623262882233,
0.06190807744860649,
0.006529441103339195,
-0.019241314381361008,
-0.04147402569651604,
-0.017532767727971077,
-0.009370517916977406,
-0.021121546626091003,
-0.016672324389219284,
-0.00042782907257787883,
0.051234785467386246,
0.005637087859213352,
0.034477852284908295,
-0.0029443614184856415,
-0.04648616164922714,
-0.011177043430507183,
-0.005585279315710068,
0.0003511943214107305,
0.03316456452012062,
0.002349065151065588,
0.00706440256908536,
-0.002901327097788453,
0.06123209372162819,
-0.07049001753330231,
0.012720208615064621,
0.0765601322054863,
0.011616156436502934,
0.014258678071200848,
0.0003581379714887589,
-0.046907924115657806,
-0.016355399042367935,
-0.026793884113430977,
0.0005167658673599362,
-0.004036582075059414,
-0.005109999794512987,
0.061301086097955704,
-0.05002006143331528,
-0.023907095193862915,
0.02494208700954914,
0.0718894675374031,
-0.06746078282594681,
0.018889017403125763,
0.0004817009612452239,
0.0671444907784462,
-0.0032197730615735054,
0.033093977719545364,
-0.02042461559176445,
-0.015575160272419453,
0.011288261972367764,
-0.004725347738713026,
0.0042509716004133224,
-0.027893269434571266,
-0.009639624506235123,
0.02401905506849289,
-0.01717512682080269,
0.06775609403848648,
-0.04272414743900299,
-0.02492610178887844,
0.030780011788010597,
-0.05974858999252319,
-0.04394003376364708,
-0.019300758838653564,
0.006517210975289345,
0.023170288652181625,
0.03993901610374451,
0.014439146965742111,
0.01642603799700737,
0.03719620779156685,
-0.011388626880943775,
0.07644713670015335,
0.006033273879438639,
-0.049473196268081665,
0.005392349790781736,
0.015529663302004337,
0.005499514285475016,
-0.01214007567614317,
-0.02905549481511116,
-0.000058782228734344244,
0.0292244590818882,
-0.03632515296339989,
-0.000785372918471694,
-0.011478765867650509,
-0.006427520886063576,
0.05547847971320152,
0.005296436604112387,
-0.01772559992969036,
-0.011212725192308426,
0.0036575132980942726,
-0.030105043202638626,
0.018192527815699577,
0.00046531695988960564,
0.04016735777258873,
0.028343552723526955,
0.008064025081694126,
-0.01374838873744011,
-0.025917302817106247,
0.0405082143843174,
0.012925826013088226,
-0.0026063984259963036,
0.040143080055713654,
0.011609635315835476,
0.006238257512450218,
-0.04856285825371742,
-0.05741864815354347,
-0.060508523136377335,
0.012745114043354988,
-0.023291656747460365,
-0.019760675728321075,
0.0027825103607028723,
0.020237626507878304,
0.0016239332035183907,
0.055226221680641174,
-0.013574071228504181,
0.051562730222940445,
-0.03037242777645588,
-0.07748492062091827,
0.038165852427482605,
-0.03893380984663963,
-0.06055436283349991,
0.05795140564441681,
-0.044064901769161224,
0.03811195492744446,
-0.07132664322853088,
-0.03852497413754463,
-0.017762158066034317,
-0.003845134750008583,
-0.022164711728692055,
-0.009964190423488617,
-0.015146126039326191,
0.007882914505898952,
0.03457304462790489,
0.07510095089673996,
0.046114321798086166,
-0.019693685695528984,
0.07531611621379852,
-0.00734434649348259,
-0.026281127706170082,
0.008664539083838463,
0.0014387742849066854,
-0.05097998306155205,
-0.0018020522547885776,
-0.05045824497938156,
-0.015962427482008934,
-0.02239658497273922,
0.015547399409115314,
0.03902730718255043,
0.016692835837602615,
-0.009414637461304665,
0.03216942399740219,
-0.007311849854886532,
-0.024534735828638077,
0.011446968652307987,
0.06539223343133926,
0.049065522849559784,
0.09156326949596405,
0.08166191726922989,
0.007728319149464369,
-0.012371244840323925,
-0.024777382612228394,
0.0020806132815778255,
-0.022847846150398254,
-0.03461655601859093,
0.002071552677080035,
-0.01701987348496914,
0.036008890718221664,
-0.015845192596316338,
-0.008539874106645584,
0.008626053109765053,
-0.0175620224326849,
0.02248571626842022,
0.04252380132675171,
-0.021203991025686264,
0.014451413415372372,
-0.03148190677165985,
0.0211800504475832,
0.0023700420279055834,
-0.012709523551166058,
0.06357518583536148,
0.0022468373645097017,
0.010223045013844967,
-0.040733978152275085,
0.011226512491703033,
-0.08039476722478867,
-0.013884308747947216,
0.02262626774609089,
0.004539667163044214,
-0.048830706626176834,
-0.01582941971719265,
0.006404480431228876,
-0.031848229467868805,
0.04206220433115959,
-0.04787754267454147,
0.004037434700876474,
-0.03362556919455528,
0.048667505383491516,
-0.03068995289504528,
0.035502586513757706,
0.016004573553800583,
0.0432266965508461,
-0.021693898364901543,
-0.03819619119167328,
-0.04010920599102974,
-0.007520803716033697,
-0.01828569918870926,
0.029405996203422546,
-0.03411899134516716,
-0.02250499464571476,
0.08888133615255356,
-0.04154107719659805,
-0.02895169146358967,
-0.006113231647759676,
0.04273927956819534,
0.0036924132145941257,
-0.02923552878201008,
0.04021180421113968,
0.05183333158493042,
-0.08708395063877106,
0.057282932102680206,
-0.003595241578295827,
-0.016149403527379036,
-0.06543539464473724,
0.03758830204606056,
0.009462255984544754,
0.038722116500139236,
0.009000769816339016,
0.007741025183349848,
0.058442629873752594,
-0.024640968069434166,
-0.04961143061518669,
-0.05837634205818176,
-0.012868136167526245,
0.03648703172802925,
0.09059787541627884,
0.06151650846004486,
-0.004188354592770338,
0.007502275053411722,
0.06381925195455551,
-0.01956530287861824,
0.023171067237854004,
0.08704257011413574,
0.016391059383749962,
0.03230205923318863,
-0.02166631817817688,
-0.016437064856290817,
-0.03888282552361488,
-0.03505256772041321,
-0.010174197144806385,
-0.016263866797089577,
-0.0017373742302879691,
-0.0024381205439567566,
-0.032021664083004,
-0.020620528608560562,
-0.03407704085111618,
0.01485428772866726,
-0.010452162474393845,
0.05800944194197655,
-0.011381604708731174,
0.044705361127853394,
0.014876323752105236,
-0.05287674069404602,
-0.06821264326572418,
-0.007053595967590809,
-0.053360939025878906,
-0.015964092686772346,
0.01338283997029066,
-0.05626688525080681,
-0.06510064005851746,
0.013549666851758957,
-0.03730134665966034,
0.0329669751226902,
0.009430396370589733,
0.006129872985184193,
-0.047026753425598145,
0.06138590723276138,
-0.009585574269294739,
0.020482948049902916,
0.009737079963088036,
0.02482224814593792,
0.015200112015008926,
-0.027784263715147972,
0.06359688192605972,
-0.02306344546377659,
-0.039450544863939285,
-0.023013899102807045,
0.028372354805469513,
0.008564348332583904,
0.008599145337939262,
0.01523978915065527,
-0.06979402899742126,
0.07050931453704834,
0.0014155447715893388,
0.010103159584105015,
0.024788225069642067,
-0.06018363684415817,
0.023251639679074287,
0.03887137770652771,
-0.04679577797651291,
-0.04632794111967087,
0.002892512595281005,
0.03618510812520981,
-0.08139914274215698,
-0.00906908418983221,
-0.007661882322281599,
0.05053521320223808,
0.07854010164737701,
0.05699574202299118,
-0.02648882381618023,
-0.048646479845047,
-0.012508423067629337,
0.023164764046669006,
-0.024427780881524086,
0.010670392774045467,
0.029952147975564003,
0.07107120752334595,
-0.0034671637695282698,
0.014043765142560005,
0.03544843941926956,
0.06023496016860008,
0.06269579380750656,
-0.03624211996793747,
0.06598639488220215,
0.019853325560688972,
0.024720778688788414,
0.03991282358765602,
-0.03259267657995224,
0.016093038022518158,
-0.03454623743891716,
0.0336669459939003,
0.08056601136922836,
-0.03655119985342026,
0.02357281930744648,
0.05328034982085228,
-0.01332071702927351,
-0.023024117574095726,
-0.011490237899124622,
0.015699602663517,
-0.05692260339856148,
0.03587218374013901,
-0.0037393660750240088,
-0.003331346670165658,
0.01712859608232975,
0.026308288797736168,
0.012686021625995636,
-0.010690287686884403,
0.06878786534070969,
0.014258182607591152,
0.0012444130843505263,
-0.004773695953190327,
0.05579278990626335,
0.0078578544780612,
0.01006638165563345,
0.011343183927237988,
-0.0022656917572021484,
0.016794664785265923,
-0.028372883796691895,
-0.003983982838690281,
-0.04218973219394684,
0.011888528242707253,
-0.03497239574790001,
-0.04625494405627251,
0.01496694516390562,
0.023897195234894753,
0.009026406332850456,
0.012470659799873829,
0.0624224916100502,
-0.0538359098136425,
-0.08691532909870148,
-0.005250753369182348,
0.013586090877652168,
0.00887660775333643,
0.061506155878305435,
0.0750434398651123,
0.07717809826135635,
0.03529929369688034,
-0.05106522515416145,
0.015910103917121887,
0.06772785633802414,
0.01340462826192379,
-0.0026071302127093077,
-0.02182599902153015,
0.006047524511814117,
-0.013986109755933285,
0.03706692159175873,
-0.029656890779733658,
0.04719645902514458,
-0.005446568597108126,
-0.0873841792345047,
0.034716084599494934,
-0.0299126785248518,
0.008230644278228283,
-0.024189982563257217,
0.021979376673698425,
-0.03432958573102951,
0.008821049705147743,
-0.028116848319768906,
-0.023242473602294922,
0.05817319452762604,
0.021741775795817375,
-0.013319007121026516,
-0.0036827553994953632,
0.02029118686914444,
0.005895390175282955,
0.01334803830832243,
0.010338673368096352,
-0.010312107391655445,
-0.04051246866583824,
-0.004506370052695274,
0.007713711354881525,
-0.05724567547440529,
-0.005832586903125048,
-0.02904321998357773,
0.042473096400499344,
-0.02843414433300495,
0.011737282387912273,
0.009824582375586033,
0.010036167688667774,
-0.034451235085725784,
-0.05818435922265053,
-0.004524456337094307,
-0.06985839456319809,
0.01008367445319891,
0.06788790971040726,
0.027500126510858536,
0.06347891688346863,
-0.13242053985595703,
-0.024150216951966286,
-0.012475112453103065,
0.05682217329740524,
-0.03195533528923988,
-0.0071294475346803665,
-0.0610504113137722,
-0.005485439673066139,
0.032006580382585526,
0.03337531536817551,
-0.000755088112782687,
-0.0027478693518787622,
-0.009594525210559368,
-0.015018202364444733,
-0.0314975306391716,
-0.014067349024116993,
-0.054087646305561066,
0.04708927869796753,
-0.007530101574957371,
-0.009909795597195625,
-0.004747066646814346,
-0.0067300815135240555,
-0.02248949557542801,
0.07810299843549728,
-0.0035506291314959526,
-0.034814026206731796,
-0.01374296098947525,
-0.014523651450872421,
-0.061987973749637604,
-0.06440193206071854,
-0.002818400040268898,
-0.05634189397096634,
-0.018861917778849602,
-0.02192523330450058,
-0.056980982422828674,
0.01714235357940197,
0.03991750627756119,
0.07981915026903152,
-0.05527123808860779,
0.052627671509981155,
0.011726434342563152,
-0.018655823543667793,
0.039318546652793884,
0.008743132464587688,
0.000003983477654401213,
-0.03981084004044533,
-0.008807546459138393,
0.013779080472886562,
-0.07257861644029617,
0.009692275896668434,
-0.012524998746812344,
0.06900541484355927,
0.04277563467621803,
-0.03159669414162636,
-0.015542939305305481,
-0.018733158707618713,
-0.04218599945306778,
0.011353952810168266,
-0.08880718052387238,
-0.03324408456683159,
0.009431138634681702,
-0.0007718402775935829,
-0.06803183257579803,
-0.0018313736654818058,
0.03039524145424366,
-0.001289153704419732,
-0.006657725665718317,
-0.02463090978562832,
-0.027757510542869568,
-0.029821190983057022,
0.0009633788140490651,
-0.03742929920554161,
0.05022569000720978,
0.023185105994343758,
0.007174250669777393,
0.0756300687789917,
-0.07464950531721115,
-0.009843775071203709,
0.029826201498508453,
-0.02989133633673191,
0.01633772999048233,
0.027297092601656914,
0.05302241072058678,
0.008138972334563732,
0.00004309697760618292,
0.030991416424512863,
0.041651830077171326,
0.02466447837650776,
0.021491391584277153,
0.028301145881414413,
0.033632028847932816,
0.018115274608135223,
0.018751399591565132,
-0.016101829707622528,
-0.0032087136059999466,
-0.08435827493667603,
-0.006389100570231676,
0.07377993315458298,
0.0043157003819942474,
0.04352826252579689,
-0.029867157340049744,
0.036343954503536224,
-0.04630815610289574,
-0.000332693598465994,
-0.04929429665207863,
-0.006366745103150606,
-0.01423015259206295,
-0.06521867960691452,
-0.05060461163520813,
-0.04250039532780647,
-0.019765205681324005,
0.009055664762854576,
-0.026406439021229744,
-0.010178531520068645,
-0.0165812149643898,
0.021199550479650497,
0.006882247049361467,
0.025889573618769646,
0.012966780923306942,
-0.026959925889968872,
0.021774059161543846,
-0.07244377583265305,
-0.03990980237722397,
0.009231768548488617,
-0.012894771061837673,
-0.04195147380232811,
0.00530650420114398,
0.018925070762634277,
-0.04363835230469704,
-0.05774834379553795,
0.031019631773233414,
-0.0163290873169899,
0.026373248547315598,
0.02330312691628933,
-0.01746908761560917,
-0.0033040689304471016,
0.020312611013650894,
-0.0054817297495901585,
0.012862312607467175,
0.021343965083360672,
0.007400176487863064,
-0.031525883823633194,
0.052034229040145874,
-0.016619671136140823,
-0.0247074943035841,
0.007874282076954842,
-0.03529299423098564,
0.033311810344457626,
0.010570933111011982,
0.04879609867930412,
-0.03619317337870598,
-0.030659561976790428,
-0.032288700342178345,
0.015650194138288498,
-0.002512283157557249,
-0.0191974900662899,
-0.012476347386837006,
-0.012885130941867828,
0.011081337928771973,
0.012745607644319534,
-0.04429306834936142,
-0.00943711306899786,
-0.029849691316485405,
0.031068362295627594,
0.012770194560289383,
-0.05396072566509247,
-0.011525635607540607,
-0.021787099540233612,
-0.025046035647392273,
-0.014220740646123886,
0.009876611642539501,
0.04651040583848953,
0.012904923409223557,
-0.07848111540079117,
-0.015294210985302925,
-0.019180694594979286,
-0.08106754720211029,
0.017643127590417862,
0.00921543873846531,
-0.009251892566680908,
-0.03548477217555046,
-0.03682355210185051,
0.04659896343946457,
0.03975396603345871,
0.01652689091861248,
0.007980075664818287,
0.024884164333343506,
-0.06070941686630249,
0.012924578040838242,
0.011158572509884834,
-0.02410769648849964,
0.029332585632801056,
0.04202137142419815,
-0.0044063604436814785,
-0.006353521719574928,
0.00862946454435587,
-0.06520751863718033,
-0.005432114005088806,
0.04756247624754906,
0.043306224048137665,
0.024318404495716095,
0.004528313409537077,
0.0389903299510479
] |
[
15.106500625610352,
6.881671905517578
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
na
|
na
|
2007-04-02T13:06:59
|
We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In
the case of Poincare algebra it is shown that almost all classical r-matrices
of S. Zakrzewski classification correspond to twisted deformations of Abelian
and Jordanian types. A part of twists corresponding to the r-matrices of
Zakrzewski classification are given in explicit form.
|
Quantum Deformations of Relativistic Symmetries
|
math.QA hep-th math-ph math.MP math.RT
|
0704.0081
| 2,007
|
[
-0.03304392844438553,
0.00310581480152905,
-0.011802511289715767,
-0.007609215099364519,
-0.007558856159448624,
0.0070042600855231285,
0.04833979532122612,
0.030133288353681564,
-0.019976604729890823,
0.03546290472149849,
-0.08997203409671783,
0.018257496878504753,
-0.024904288351535797,
-0.018082180991768837,
0.025365624576807022,
-0.015545938163995743,
0.022463448345661163,
0.02650887705385685,
-0.00021706255211029202,
-0.021134067326784134,
-0.03889717906713486,
-0.07084231078624725,
-0.04115266725420952,
-0.016304394230246544,
0.08419061452150345,
-0.025126418098807335,
0.050334278494119644,
-0.03782057389616966,
-0.04091620072722435,
0.014910838566720486,
0.05975460261106491,
0.0020725007634609938,
-0.010113248601555824,
-0.08332385867834091,
-0.014879979193210602,
-0.08340338617563248,
0.11402228474617004,
0.0021467660553753376,
0.010649433359503746,
0.012408743612468243,
-0.017797358334064484,
-0.06504164636135101,
-0.011641379445791245,
-0.006269810721278191,
0.04495532065629959,
0.0038829976692795753,
0.03540365397930145,
0.021233467385172844,
0.015363657847046852,
-0.001281472505070269,
0.007755377795547247,
0.0024034820962697268,
0.007992809638381004,
-0.0685681626200676,
-0.01127946749329567,
0.019475745037198067,
0.018034158274531364,
-0.011491338722407818,
0.04614771157503128,
0.03201834484934807,
-0.0057132733054459095,
0.02675396203994751,
-0.03624524921178818,
0.03526461496949196,
0.020752064883708954,
-0.005452692974358797,
-0.014274714514613152,
0.02460353448987007,
-0.028190501034259796,
-0.0115983160212636,
0.04505309462547302,
-0.02278064377605915,
0.06292451918125153,
0.03700213506817818,
-0.017921434715390205,
-0.0021028006449341774,
0.02162851020693779,
0.006825796328485012,
0.00275749946013093,
-0.0065283156000077724,
0.0096846679225564,
-0.04093446955084801,
0.045708850026130676,
0.02905818447470665,
0.04163258150219917,
0.04104733467102051,
0.022379359230399132,
0.0500321164727211,
-0.03702476993203163,
-0.004373377654701471,
0.039687562733888626,
-0.04125300422310829,
0.029946036636829376,
0.1043628603219986,
-0.0689622238278389,
0.019555922597646713,
-0.019123146310448647,
0.0588839128613472,
-0.03285503014922142,
-0.048839304596185684,
-0.014726131223142147,
0.039034318178892136,
0.026584159582853317,
0.006576751358807087,
0.06614086776971817,
-0.010460144840180874,
0.0068949139676988125,
-0.006444625556468964,
-0.02033047378063202,
-0.014046719297766685,
-0.09638053923845291,
0.004839245695620775,
0.020405229181051254,
0.02536219358444214,
-0.046589091420173645,
-0.031209100037813187,
0.018538009375333786,
-0.07541011273860931,
-0.025306984782218933,
0.08859184384346008,
0.03257499635219574,
-0.018634537234902382,
0.02956859953701496,
0.06847652047872543,
0.015109939500689507,
0.011977729387581348,
-0.0606258362531662,
0.0021586031652987003,
0.07112861424684525,
-0.05611087381839752,
0.02247999608516693,
0.04585262015461922,
0.009789843112230301,
-0.0009986868826672435,
0.005220723804086447,
0.06194333732128143,
0.0112305274233222,
-0.05813228711485863,
0.039138298481702805,
-0.026169491931796074,
0.026117965579032898,
0.03093666583299637,
0.006131115835160017,
-0.017542989924550056,
0.03940233960747719,
-0.13357900083065033,
0.004677197430282831,
-0.04218912124633789,
-0.03931741416454315,
0.04917055368423462,
0.026061786338686943,
0.04026683419942856,
-0.0005955121014267206,
0.03004320338368416,
0.005164851900190115,
-0.016529249027371407,
0.0031085971277207136,
-0.010142780840396881,
0.009532910771667957,
0.03877444192767143,
0.03592865541577339,
-0.027843473479151726,
-0.0385722778737545,
0.06095755472779274,
-0.021294912323355675,
0.05161039158701897,
0.018120640888810158,
0.028356827795505524,
0.015150570310652256,
0.036332421004772186,
-0.0504424124956131,
-0.04465257003903389,
-0.04043169319629669,
-0.047696761786937714,
0.01435088086873293,
0.035661544650793076,
-0.019274286925792694,
-0.03536268323659897,
0.02912392094731331,
0.001916120178066194,
0.00956505723297596,
-0.04160864278674126,
0.011549661867320538,
0.022470496594905853,
0.010607123374938965,
0.03467559814453125,
-0.013555468991398811,
-0.017483124509453773,
-0.041555557399988174,
-0.04684825241565704,
0.021810201928019524,
0.05619272217154503,
0.000004377536242827773,
-0.08478221297264099,
-0.01879963092505932,
-0.039851028472185135,
0.03486572951078415,
0.006398332770913839,
-0.00744676124304533,
0.00268316688016057,
0.01642543636262417,
0.006892053410410881,
-0.02401883900165558,
-0.011067776940762997,
-0.0027363612316548824,
0.05859190970659256,
-0.008073096163570881,
0.02249056100845337,
0.01080329529941082,
0.0009196368628181517,
0.11312620341777802,
-0.002143154153600335,
0.04134379327297211,
-0.0019826292991638184,
-0.02075732871890068,
0.027985310181975365,
0.04101739451289177,
-0.03929387778043747,
-0.054854754358530045,
0.0823853462934494,
0.011285524815320969,
-0.022168414667248726,
0.02771744877099991,
0.022719325497746468,
0.013196843676269054,
-0.00009571382543072104,
-0.052874546498060226,
-0.026778336614370346,
0.018213612958788872,
-0.05474952608346939,
-0.051186006516218185,
-0.002651764079928398,
0.008803490549325943,
0.02286781556904316,
-0.0038141850382089615,
0.02079181745648384,
-0.02267065830528736,
0.006609382573515177,
0.10339906811714172,
-0.00320974993519485,
0.030486075207591057,
0.02726677618920803,
-0.0065187206491827965,
-0.011584686115384102,
-0.03477631136775017,
0.021106740459799767,
-0.017249710857868195,
-0.022100521251559258,
0.0022716594394296408,
0.02037111297249794,
-0.0051540713757276535,
-0.043402720242738724,
-0.021009530872106552,
0.02822139859199524,
0.05086582899093628,
-0.015492923557758331,
-0.07114925235509872,
0.045117590576410294,
0.014805317856371403,
-0.058986514806747437,
0.025104476138949394,
0.021134309470653534,
-0.01230236329138279,
-0.043411366641521454,
-0.062362704426050186,
0.028018934652209282,
0.017341813072562218,
-0.02065526880323887,
-0.013864544220268726,
-0.02033386565744877,
-0.06106959283351898,
0.07552789151668549,
0.025403069332242012,
0.054780203849077225,
-0.0020629833452403545,
-0.047885529696941376,
-0.026399264112114906,
-0.035981182008981705,
-0.08476381748914719,
-0.007437779102474451,
-0.05255997180938721,
-0.005590459797531366,
-0.01968621462583542,
-0.02223816141486168,
0.01688937097787857,
0.003963950090110302,
-0.005563418380916119,
-0.024116765707731247,
-0.04492047056555748,
0.03247380629181862,
-0.00945000909268856,
0.03423474356532097,
-0.0004947714041918516,
-0.003442266723141074,
0.00033452283241786063,
0.04491899907588959,
0.0466931015253067,
0.015156460925936699,
-0.004446046426892281,
0.07805505394935608,
-0.0006139991455711424,
-0.03061390481889248,
-0.006294745020568371,
0.0020930496975779533,
0.06663171947002411,
0.010157513432204723,
-0.0016459462931379676,
0.013371157459914684,
0.06761475652456284,
-0.02236306667327881,
-0.05582461506128311,
0.0002161994925700128,
-0.011337775737047195,
0.015963219106197357,
-0.05757300928235054,
0.0025451621040701866,
0.010401600040495396,
-0.0011062795529142022,
0.08328881859779358,
-0.01639922522008419,
0.01433493010699749,
-0.05392850190401077,
0.04725108668208122,
-0.03382832556962967,
0.04668640345335007,
0.05125568062067032,
-0.021756241098046303,
0.011355379596352577,
0.00728459982201457,
-0.04158259928226471,
-0.02795080654323101,
-0.0040993234142661095,
-0.00001234468163602287,
-0.026258530095219612,
-0.008831789717078209,
0.02969937212765217,
-0.07882053405046463,
0.013759788125753403,
-0.05967547371983528,
-0.06794638931751251,
0.007340760435909033,
-0.1037273034453392,
-0.000040383816667599604,
-0.022633394226431847,
-0.01563606970012188,
-0.005839409772306681,
-0.026250377297401428,
-0.021732620894908905,
0.05228240415453911,
0.03431424871087074,
-0.07095079123973846,
-0.007132135797291994,
0.01610380969941616,
0.013086037710309029,
0.016645750030875206,
0.04732998088002205,
0.019945334643125534,
0.030965354293584824,
0.060532346367836,
-0.01164648775011301,
0.010929961688816547,
-0.030181581154465675,
0.01470078807324171,
0.001868348685093224,
-0.03137839585542679,
0.03998344764113426,
-0.005947310011833906,
-0.02420279197394848,
-0.0057280235923826694,
-0.00696576340124011,
-0.03848475217819214,
-0.034226153045892715,
0.04312920197844505,
0.006772935856133699,
0.03317319601774216,
-0.010076960548758507,
-0.04316217824816704,
0.021158937364816666,
0.0025180152151733637,
-0.013758694753050804,
0.03074823133647442,
-0.0011635374976322055,
0.06765369325876236,
0.03692774847149849,
0.013870428316295147,
0.04458674415946007,
-0.060076139867305756,
-0.012948079034686089,
-0.011380800046026707,
0.011746472679078579,
0.001733636250719428,
-0.02971019223332405,
-0.0050864750519394875,
0.018853802233934402,
-0.04237419366836548,
-0.013969692401587963,
0.06761747598648071,
-0.02557341568171978,
-0.036063939332962036,
-0.00441345851868391,
-0.06052478030323982,
-0.050547052174806595,
0.011252745985984802,
-0.010249336250126362,
-0.01712692156434059,
0.0323670394718647,
0.006260042544454336,
-0.044821400195360184,
0.0695301741361618,
0.0059795803390443325,
-0.021466538310050964,
0.03430707007646561,
0.028348283842206,
-0.08352084457874298,
0.04732972010970116,
0.035861704498529434,
0.023338682949543,
-0.025004012510180473,
0.011710762977600098,
-0.033347830176353455,
0.0016494530718773603,
0.0719219222664833,
0.054103389382362366,
0.009858972392976284,
0.033301353454589844,
-0.018430933356285095,
0.026780078187584877,
0.017380177974700928,
0.0015160087496042252,
-0.03729618340730667,
0.0014942424604669213,
-0.014522528275847435,
0.017254896461963654,
0.0008387838024646044,
-0.031000753864645958,
-0.03440183028578758,
-0.017499534413218498,
0.03065970540046692,
0.012607412412762642,
0.028836075216531754,
0.07703685015439987,
-0.0027595311403274536,
0.012037284672260284,
-0.008675936609506607,
0.02807493507862091,
0.0545894019305706,
0.014442254789173603,
0.003349807346239686,
-0.03919430449604988,
0.011125188320875168,
0.03730783984065056,
-0.010022181086242199,
0.00976994726806879,
-0.0022130899596959352,
0.11124847084283829,
-0.03900205343961716,
-0.004587563686072826,
-0.006064616143703461,
0.06610936671495438,
0.09761083871126175,
0.01014840230345726,
0.0033490511123090982,
0.003169977804645896,
0.0358123704791069,
-0.014393943361938,
0.0015458294656127691,
-0.07866235077381134,
0.044091470539569855,
-0.02258744090795517,
0.06898309290409088,
0.006466989871114492,
-0.026840075850486755,
-0.0055526429787278175,
0.01598907634615898,
-0.015743808820843697,
0.066431425511837,
-0.02056989260017872,
-0.018992742523550987,
-0.030177155509591103,
0.040231332182884216,
0.02069130353629589,
-0.005256439559161663,
-0.04312537610530853,
-0.04127504304051399,
-0.019863374531269073,
0.03555434197187424,
0.0037565184757113457,
-0.006157924421131611,
-0.0005178208812139928,
-0.03434424847364426,
0.009263630956411362,
0.010902320966124535,
-0.004741419572383165,
-0.019657257944345474,
-0.04404281824827194,
0.026195136830210686,
-0.0078756557777524,
-0.010589093901216984,
0.010007287375628948,
0.0061280736699700356,
0.009842958301305771,
0.043100904673337936,
0.02041236124932766,
-0.012734154239296913,
0.02609305828809738,
-0.0031157885678112507,
0.0038615036755800247,
-0.024094412103295326,
-0.023732617497444153,
0.020134346559643745,
0.0011354301823303103,
0.031890466809272766,
0.0694032683968544,
0.021143203601241112,
0.04289877042174339,
0.0018195010488852859,
0.003706185845658183,
0.014047312550246716,
-0.047585804015398026,
-0.022114546969532967,
-0.04765738174319267,
-0.03902167081832886,
0.016336139291524887,
-0.033179815858602524,
-0.027483884245157242,
0.0294522475451231,
-0.00764715950936079,
-0.05769282206892967,
0.018720975145697594,
-0.04069610312581062,
0.01384704653173685,
-0.025308910757303238,
0.06024640053510666,
-0.03894001618027687,
0.03175359591841698,
-0.03912633657455444,
0.02344570681452751,
-0.0013220316031947732,
-0.005703529808670282,
0.07268945872783661,
0.02551158331334591,
-0.015536406077444553,
0.011495158076286316,
0.013672182336449623,
-0.01747799664735794,
-0.045327067375183105,
-0.074712373316288,
0.02503374218940735,
-0.03661045432090759,
-0.01866014674305916,
-0.016270514577627182,
-0.03157342970371246,
-0.004453833680599928,
-0.06216208636760712,
-0.001362916431389749,
-0.049940191209316254,
-0.018532687798142433,
-0.049401555210351944,
-0.05883584916591644,
0.037792522460222244,
0.039723869413137436,
0.012087206356227398,
0.009982726536691189,
-0.002728646621108055,
0.01729934848845005,
-0.11300133913755417,
-0.020587652921676636,
-0.007048414088785648,
0.048987314105033875,
0.04909685626626015,
0.003851451212540269,
0.015208633616566658,
-0.05804842710494995,
0.02621219865977764,
-0.0012518641306087375,
-0.05776236578822136,
0.03906205669045448,
-0.029999617487192154,
-0.044405803084373474,
0.016470443457365036,
0.02666141279041767,
-0.03655560687184334,
-0.017859499901533127,
-0.01759118214249611,
-0.0487559475004673,
0.0505361370742321,
-0.012926997616887093,
0.0025265421718358994,
0.036870092153549194,
0.014006083831191063,
-0.01300145499408245,
0.02624187245965004,
-0.04481475055217743,
0.017384620383381844,
-0.052245352417230606,
0.0021493243984878063,
0.04144146665930748,
0.025094211101531982,
-0.018723350018262863,
-0.011528350412845612,
0.004322082735598087,
-0.036567918956279755,
0.05969659984111786,
0.010740578174591064,
0.027525773271918297,
0.020091738551855087,
-0.05073991045355797,
0.04241851344704628,
0.005436831619590521,
0.045177873224020004,
-0.0025615098420530558,
0.012165158987045288,
-0.027288690209388733,
-0.014369630254805088,
-0.008542061783373356,
-0.030525457113981247,
0.020329570397734642,
-0.04608997702598572,
0.03327931836247444,
-0.07587013393640518,
0.015976428985595703,
0.0068666692823171616,
-0.055935122072696686,
-0.04995463043451309,
0.02420620620250702,
0.05373462662100792,
-0.01097461860626936,
-0.038143452256917953,
-0.013015344738960266,
0.06643884629011154,
-0.018689006567001343,
-0.028996434062719345,
-0.03607473894953728,
0.012288604862987995,
-0.00961841456592083,
0.0038679519202560186,
-0.06486964970827103,
0.027674341574311256,
0.017393263056874275,
0.10540425777435303,
0.030697284266352654,
-0.055794697254896164,
-0.027921995148062706,
-0.02216576226055622,
0.02801678702235222,
-0.020823867991566658,
-0.01549713034182787,
-0.02509669028222561,
-0.045290250331163406,
-0.001080840826034546,
0.09144750982522964,
0.08959826827049255,
0.002877618884667754,
0.02461223118007183,
-0.025047698989510536,
-0.007250992115586996,
0.06034296005964279,
-0.043223582208156586,
-0.02693904936313629,
-0.02901989035308361,
-0.02394717186689377,
-0.02402188628911972,
-0.0003776053199544549,
-0.024262016639113426,
0.02686595357954502,
0.0003811763017438352,
0.005180694162845612,
-0.024431491270661354,
-0.038962215185165405,
0.06831391900777817,
-0.07169285416603088,
-0.03350859880447388,
-0.0041067954152822495,
-0.028177184984087944,
-0.04345749318599701,
-0.006452377885580063,
-0.0034089749678969383,
0.020729804411530495,
-0.029387952759861946,
-0.043219152837991714,
-0.013178637251257896,
0.0510493628680706,
-0.03481535613536835,
0.05176679044961929,
-0.047342997044324875,
-0.001126459101215005,
0.050969984382390976,
0.0038950699381530285,
-0.016385991126298904,
-0.03755759820342064,
0.0376715324819088,
0.015487206168472767,
0.01651410013437271,
-0.018939578905701637,
-0.012418387457728386,
0.015076338313519955,
-0.017095457762479782,
-0.008761034347116947,
-0.03612231835722923,
-0.0014483395498245955,
-0.043024372309446335,
0.06091378256678581,
-0.00309579586610198,
0.037274014204740524,
-0.0037406650371849537,
-0.014502540230751038,
-0.039311569184064865,
0.012950175441801548,
0.016079451888799667,
0.030505254864692688,
-0.021717948839068413,
-0.02710101008415222,
0.05246347561478615,
0.0012581347255036235,
0.09076736122369766,
-0.00754566490650177,
0.016432344913482666,
-0.014312967658042908,
0.03663189336657524,
-0.05773894488811493,
0.022535424679517746,
-0.0058406200259923935,
-0.05590946227312088,
0.006819946691393852,
-0.035224661231040955,
-0.06727803498506546,
0.018743129447102547,
-0.012047290802001953,
0.020414253696799278,
-0.020919539034366608,
-0.009611069224774837,
-0.002404644852504134,
-0.07205792516469955,
0.04670072719454765,
-0.027453914284706116,
0.02786359190940857,
-0.02278241328895092,
-0.00005907473314437084,
0.02623308077454567,
0.028591720387339592,
0.014360157772898674,
-0.03218043968081474,
0.02385241910815239,
0.01874370500445366,
-0.00540059432387352,
-0.05913081020116806,
-0.018097704276442528,
0.016435690224170685,
0.03377315402030945,
-0.002575257094576955,
-0.05125565826892853,
0.01290887501090765,
-0.007346367929130793,
0.04433886334300041,
-0.024159107357263565,
0.011831805109977722,
-0.036663565784692764,
-0.026374174281954765,
0.06430503726005554,
0.0030486900359392166,
0.0835292711853981,
0.002899987855926156,
0.024665595963597298,
0.030165622010827065,
-0.03086860291659832,
0.0002405491832178086,
-0.05352431908249855,
0.01581183634698391
] |
[
2.531972646713257,
0.7303021550178528
] |
Quantum Algebra
|
Mathematics
|
math-QA
|
hep-th
|
math-ph
|
2007-04-01T12:26:50
|
We investigate dynamical properties of bright solitons with a finite
background in the F=1 spinor Bose-Einstein condensate (BEC), based on an
integrable spinor model which is equivalent to the matrix nonlinear
Schr\"{o}dinger equation with a self-focusing nonlineality. We apply the
inverse scattering method formulated for nonvanishing boundary conditions. The
resulting soliton solutions can be regarded as a generalization of those under
vanishing boundary conditions. One-soliton solutions are derived in an explicit
manner. According to the behaviors at the infinity, they are classified into
two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies
the ferromagnetic state with nonzero total spin and the PS-type implies the
polar state, where the total spin amounts to zero. We also discuss two-soliton
collisions. In particular, the spin-mixing phenomenon is confirmed in a
collision involving the DW-type. The results are consistent with those of the
previous studies for bright solitons under vanishing boundary conditions and
dark solitons. As a result, we establish the robustness and the usefulness of
the multiple matter-wave solitons in the spinor BECs.
|
Matter-Wave Bright Solitons with a Finite Background in Spinor
Bose-Einstein Condensates
|
cond-mat.other cond-mat.stat-mech
|
0704.0082
| 2,007
|
[
-0.04232683777809143,
0.04398981109261513,
0.0019875802099704742,
-0.0015343086561188102,
0.06621753424406052,
0.007160584907978773,
0.03872472047805786,
0.017388291656970978,
-0.014268067665398121,
-0.044824596494436264,
-0.07047002017498016,
0.019641395658254623,
0.00466389674693346,
0.013260729610919952,
-0.016350291669368744,
-0.0140101108700037,
0.03305371105670929,
-0.011918283067643642,
0.003091038903221488,
-0.02200169488787651,
-0.01445548702031374,
0.0016967064002528787,
-0.023084113374352455,
-0.04818558320403099,
0.07213889062404633,
-0.004961135797202587,
0.014933059923350811,
-0.004785399418324232,
-0.025959886610507965,
0.04267559573054314,
0.06143084913492203,
-0.047007400542497635,
0.004871591459959745,
-0.005170518532395363,
-0.03872404620051384,
-0.008166813291609287,
0.06943733245134354,
-0.02623782865703106,
-0.03252781182527542,
0.05861399695277214,
0.08234065771102905,
-0.020182132720947266,
0.020297912880778313,
-0.05928582325577736,
0.01500124391168356,
0.0202636756002903,
0.006229485385119915,
0.0013882709899917245,
0.013494253158569336,
0.016719909384846687,
0.010768796317279339,
0.03661327436566353,
0.03701651841402054,
0.010129701346158981,
0.02304709330201149,
0.060483213514089584,
-0.004581392277032137,
0.0026090173050761223,
0.037566591054201126,
-0.0024185318034142256,
0.00021808645396959037,
0.010442303493618965,
0.004022693727165461,
0.02252538688480854,
0.009161367081105709,
-0.06672024726867676,
-0.04923802614212036,
-0.01303932350128889,
-0.02714976668357849,
-0.015362192876636982,
0.020053675398230553,
-0.022262023761868477,
0.04165928438305855,
0.08692657202482224,
-0.022561389952898026,
-0.005853617563843727,
0.011670950800180435,
-0.027610672637820244,
-0.03483978286385536,
-0.013204643502831459,
-0.023478640243411064,
-0.0633029118180275,
0.0308634415268898,
0.005776375997811556,
0.031134871765971184,
0.05080495402216911,
0.03323280066251755,
0.0428975410759449,
-0.03950611501932144,
0.03260476887226105,
0.03075265698134899,
-0.0026343525387346745,
0.009055839851498604,
0.016344333067536354,
0.021506257355213165,
0.045255307108163834,
-0.016172025352716446,
-0.017785897478461266,
-0.0026938063092529774,
-0.024949287995696068,
-0.03515435382723808,
0.048849668353796005,
0.01367359422147274,
-0.0030308321584016085,
0.07945086807012558,
0.029196249321103096,
0.04587830603122711,
0.009108477272093296,
0.0036561121232807636,
-0.010663120076060295,
-0.06632203608751297,
-0.03804360702633858,
0.021760964766144753,
-0.0103609012439847,
-0.03271019458770752,
-0.03991984948515892,
0.0012575312284752727,
-0.018520593643188477,
0.01726326160132885,
0.06892523169517517,
0.00909939780831337,
0.030259957537055016,
0.029985353350639343,
0.04792626202106476,
0.006028506904840469,
0.03440329059958458,
-0.006052450742572546,
-0.06351730227470398,
0.01056384015828371,
-0.021920323371887207,
-0.0022057557944208384,
0.0022791544906795025,
-0.011498266831040382,
0.002435478614643216,
0.03787326067686081,
0.033470988273620605,
-0.028929010033607483,
-0.03966798633337021,
0.02362804487347603,
0.013569830916821957,
0.027727443724870682,
-0.005589902866631746,
-0.007984817959368229,
0.009125499054789543,
-0.01983647793531418,
-0.0819353386759758,
0.03358296677470207,
-0.08619029074907303,
-0.019865773618221283,
-0.04071363806724548,
0.012824475765228271,
0.034212835133075714,
0.014865218661725521,
0.041593845933675766,
-0.03106164187192917,
-0.0307486392557621,
0.011373770423233509,
-0.004464875441044569,
0.007730306591838598,
-0.030180396512150764,
0.04347676783800125,
0.038062747567892075,
-0.0497220940887928,
0.037693873047828674,
-0.029336431995034218,
0.03553498163819313,
0.027813365682959557,
0.05166982114315033,
0.05235282704234123,
0.04261220246553421,
-0.03889789804816246,
-0.022296467795968056,
0.004789615515619516,
0.0019295228412374854,
0.06956880539655685,
0.013521491549909115,
-0.003655538195744157,
-0.05747225880622864,
0.01650761067867279,
0.04638049378991127,
0.042018428444862366,
-0.02550993114709854,
0.008132314309477806,
0.028475167229771614,
0.04723600670695305,
0.02225496433675289,
-0.008197048678994179,
0.001052024308592081,
-0.005854669027030468,
-0.006123654544353485,
0.012482093647122383,
-0.019351188093423843,
-0.012558787129819393,
-0.03781195729970932,
-0.01262040063738823,
-0.05333666130900383,
0.07351695001125336,
-0.029828140512108803,
0.004477029666304588,
-0.06388891488313675,
-0.013808321207761765,
0.015345164574682713,
-0.007874262519180775,
0.0008189684594981372,
-0.030621757730841637,
0.06677243113517761,
-0.01113544125109911,
0.022915245965123177,
0.05329102277755737,
-0.028336718678474426,
0.06991351395845413,
-0.028775915503501892,
-0.03661685064435005,
0.020195847377181053,
-0.05458692088723183,
0.009660917334258556,
0.009787650778889656,
-0.02896648272871971,
-0.06871837377548218,
0.10071948915719986,
0.02550678327679634,
0.020327258855104446,
0.0005852696485817432,
0.008284061215817928,
0.06751332432031631,
0.006659346632659435,
0.0008158713462762535,
-0.01179377268999815,
-0.05865149199962616,
0.00428315345197916,
-0.038271643221378326,
-0.003714454360306263,
0.06186430901288986,
0.009859133511781693,
0.007803231943398714,
0.011249298229813576,
0.017152251675724983,
0.05286538973450661,
-0.004845470655709505,
0.0018131742253899574,
0.012954938225448132,
-0.00978524424135685,
-0.027290405705571175,
-0.01692231558263302,
-0.04145112633705139,
-0.015249975025653839,
-0.05090389400720596,
-0.005859569646418095,
-0.01782606914639473,
0.017537828534841537,
0.062116820365190506,
-0.06340556591749191,
0.028391126543283463,
0.028481964021921158,
-0.019047953188419342,
-0.04711247608065605,
0.0020440241787582636,
0.08505730330944061,
-0.047920458018779755,
-0.07616792619228363,
0.03077399916946888,
-0.05524078756570816,
0.007341180928051472,
-0.018776370212435722,
-0.0006816398818045855,
0.05157644301652908,
0.00917988270521164,
0.0039941249415278435,
-0.045114412903785706,
0.009972549974918365,
0.02019069343805313,
0.01565651409327984,
0.03693317994475365,
0.010051882825791836,
-0.02599763497710228,
0.02337106689810753,
0.017282065004110336,
-0.03144727647304535,
-0.00673181377351284,
-0.015338274650275707,
-0.06185026839375496,
-0.024574164301156998,
-0.04852396249771118,
-0.0986383855342865,
-0.041937243193387985,
-0.008967316709458828,
0.03893034905195236,
0.02995923161506653,
-0.006942651234567165,
0.015538650564849377,
-0.05030731111764908,
-0.02062266133725643,
0.07055500149726868,
0.03783698379993439,
0.007463257294148207,
0.07186019420623779,
0.05915508419275284,
0.007110121194273233,
-0.006650806404650211,
0.052487753331661224,
-0.0024385624565184116,
-0.0020255479030311108,
-0.023341814056038857,
0.001414371421560645,
0.010751456953585148,
0.011172282509505749,
0.012225858867168427,
-0.00881384126842022,
0.006641693413257599,
0.026435719802975655,
-0.0010243462165817618,
0.058471277356147766,
-0.002891160547733307,
0.021336741745471954,
-0.0014478160301223397,
0.07943291962146759,
0.027250561863183975,
0.009874100796878338,
0.09687822312116623,
-0.024813273921608925,
-0.024026598781347275,
-0.0003206661785952747,
0.02281845733523369,
-0.028058094903826714,
-0.01920303888618946,
0.02834361605346203,
-0.021975329145789146,
0.014923554845154285,
-0.036958228796720505,
0.025877829641103745,
0.009663918986916542,
0.039396826177835464,
0.004485059529542923,
-0.0357818566262722,
-0.03459278494119644,
0.0178577471524477,
-0.03551264852285385,
0.04326478764414787,
-0.03651165962219238,
0.028275618329644203,
-0.007978751324117184,
-0.07740006595849991,
-0.05000118166208267,
-0.027272656559944153,
-0.018076784908771515,
0.0022798108402639627,
-0.030524693429470062,
-0.013802454806864262,
0.04682184383273125,
0.03879339620471001,
-0.046331364661455154,
-0.017639504745602608,
-0.005502562038600445,
0.0241971705108881,
-0.04349866509437561,
0.03606337681412697,
0.0721830502152443,
0.024831172078847885,
0.055658675730228424,
0.019677480682730675,
0.03425335884094238,
-0.02799960970878601,
0.05716618895530701,
-0.000798311026301235,
0.05990356579422951,
0.016167379915714264,
-0.02387002669274807,
-0.007029584143310785,
-0.002073433017358184,
-0.06970889866352081,
-0.027056876569986343,
-0.039000362157821655,
0.037223078310489655,
0.053873881697654724,
-0.011497052386403084,
-0.015724072232842445,
-0.09488418698310852,
-0.018405906856060028,
-0.028585702180862427,
-0.010924984700977802,
0.060871560126543045,
-0.013579895719885826,
0.026156926527619362,
-0.018244264647364616,
0.017559850588440895,
0.045636218041181564,
0.004070129711180925,
-0.007494336925446987,
-0.03202645108103752,
-0.011814833618700504,
-0.007627387996762991,
-0.013969912193715572,
-0.02286524511873722,
0.03669529780745506,
0.03633569926023483,
0.005493935663253069,
-0.02521226927638054,
-0.03116334043443203,
-0.01660657860338688,
0.002673207549378276,
-0.07762599736452103,
-0.07115624099969864,
-0.01284305565059185,
-0.0453529916703701,
-0.00827078614383936,
-0.025716079398989677,
-0.06324714422225952,
-0.04857078939676285,
0.004946236032992601,
-0.0022367278579622507,
-0.006903474219143391,
0.03178395703434944,
-0.06037038937211037,
-0.060178570449352264,
0.04628891870379448,
-0.0510215237736702,
0.08224410563707352,
-0.019276317209005356,
0.027940018102526665,
-0.022665761411190033,
0.022281644865870476,
0.02527669630944729,
-0.05404272302985191,
-0.00046466049388982356,
-0.032968465238809586,
-0.0751858800649643,
-0.0178651362657547,
-0.017461545765399933,
-0.022020651027560234,
-0.03817620500922203,
0.0037299501709640026,
0.007868831977248192,
0.01120817381888628,
0.04127943888306618,
-0.07736442238092422,
0.03941868990659714,
-0.024586429819464684,
-0.03479761257767677,
0.011939052492380142,
0.015217456966638565,
0.029711619019508362,
-0.019193129613995552,
-0.02242152765393257,
-0.022118670865893364,
0.0420435294508934,
0.07721647620201111,
0.03390340507030487,
-0.06600261479616165,
0.005769682582467794,
0.012088765390217304,
0.02887764573097229,
0.02760692499577999,
-0.025044582784175873,
0.012292669154703617,
0.06332859396934509,
-0.023875661194324493,
-0.005108750890940428,
0.03653250262141228,
0.0020082779228687286,
0.05764903500676155,
0.04864386469125748,
0.03989758715033531,
-0.005784910172224045,
0.016030456870794296,
-0.06183888763189316,
-0.03216128423810005,
0.02643243409693241,
-0.037759825587272644,
0.03508540615439415,
0.0324409194290638,
-0.015801234170794487,
0.01559559628367424,
0.052972130477428436,
0.027187520638108253,
-0.03757795691490173,
0.05152178555727005,
0.02071186900138855,
-0.016154471784830093,
-0.08046793192625046,
0.059800051152706146,
0.0538017675280571,
-0.04191891476511955,
-0.029260054230690002,
-0.06380205601453781,
-0.04112135246396065,
0.023475652560591698,
0.0018168220994994044,
0.06918977946043015,
-0.04246055334806442,
0.0071222116239368916,
-0.011291582137346268,
0.046004507690668106,
-0.054181043058633804,
-0.010769126936793327,
-0.020673206076025963,
-0.07304911315441132,
0.0022541165817528963,
-0.0011487803421914577,
-0.022077202796936035,
0.009053711779415607,
-0.030641673132777214,
-0.05255639925599098,
0.04318136349320412,
0.015807989984750748,
-0.03440269082784653,
0.06657253950834274,
-0.003848931984975934,
-0.0578758679330349,
0.002939242171123624,
0.007316560950130224,
-0.023997332900762558,
0.017958471551537514,
0.034272998571395874,
0.11294356733560562,
-0.006657992023974657,
-0.0787864476442337,
0.018202440813183784,
0.005976701620966196,
-0.09541478753089905,
0.026646297425031662,
-0.03915409371256828,
-0.012901253066956997,
-0.006971284281462431,
0.03835894912481308,
-0.05998898297548294,
0.033539775758981705,
0.004216569010168314,
-0.03822097182273865,
0.05993490666151047,
-0.002388446591794491,
0.010723047889769077,
0.011875670403242111,
0.05333346128463745,
-0.004288773518055677,
0.05949662625789642,
-0.02890697680413723,
0.0077681588008999825,
0.053245801478624344,
-0.02251444384455681,
-0.003837442258372903,
0.026922039687633514,
-0.014125719666481018,
0.010171891190111637,
0.011427497491240501,
0.017708670347929,
-0.04236956313252449,
-0.06937553733587265,
0.017702432349324226,
-0.04566756263375282,
-0.06272523105144501,
-0.012131224386394024,
-0.04905664920806885,
-0.007932620123028755,
-0.0010570655576884747,
0.02662075310945511,
-0.03808772936463356,
-0.037572555243968964,
-0.02027461864054203,
-0.006867724936455488,
0.005332218017429113,
-0.007987570948898792,
-0.00961831770837307,
-0.006472997833043337,
-0.023761210963129997,
-0.06128483638167381,
-0.07263360172510147,
-0.03943171724677086,
0.006336990278214216,
0.021634962409734726,
-0.013238583691418171,
-0.009114679880440235,
-0.03153146058320999,
-0.0378706194460392,
-0.008152107708156109,
0.01171264797449112,
-0.0621650256216526,
0.06965578347444534,
-0.005905397702008486,
-0.03031734563410282,
-0.01340431533753872,
-0.033399175852537155,
-0.002242168178781867,
0.011276707984507084,
0.01679137535393238,
0.018971720710396767,
0.002669211011379957,
-0.010418704710900784,
-0.026171257719397545,
0.04842325299978256,
-0.0025156023912131786,
0.025073138996958733,
-0.017750918865203857,
0.0036121667362749577,
-0.04565223306417465,
0.023575933650135994,
0.004077007994055748,
-0.0008127551409415901,
0.0039034767542034388,
-0.03647767752408981,
-0.049139510840177536,
0.0317629911005497,
-0.013890823349356651,
0.05580805242061615,
0.05124611780047417,
-0.011166879907250404,
0.07971435785293579,
-0.012395326048135757,
0.02230333723127842,
-0.011309133842587471,
0.07975983619689941,
0.008928918279707432,
0.0001364927738904953,
-0.05268754065036774,
-0.04915716126561165,
-0.022659530863165855,
-0.04533494636416435,
0.027007466182112694,
0.0026816537138074636,
0.051554251462221146,
-0.049056556075811386,
0.031653743237257004,
-0.020791351795196533,
0.060253508388996124,
-0.04573299363255501,
0.010206855833530426,
0.009147100150585175,
0.010952387005090714,
-0.053217776119709015,
-0.008578628301620483,
0.06431403011083603,
0.04532638192176819,
-0.007767830044031143,
-0.0577654093503952,
-0.059101469814777374,
-0.0273608211427927,
0.04087480902671814,
-0.022045286372303963,
0.005348467733711004,
-0.026386456564068794,
0.018164148554205894,
0.01743546687066555,
0.00748460041359067,
-0.0002380643563810736,
-0.006860921625047922,
0.013151653110980988,
0.09788001328706741,
0.006518421694636345,
0.013766296207904816,
-0.0076369307935237885,
0.026983529329299927,
0.0820850282907486,
0.019090328365564346,
-0.0244916882365942,
0.029046297073364258,
-0.05004142224788666,
-0.04256074130535126,
0.0720062330365181,
-0.021193241700530052,
-0.04867272824048996,
-0.01105087623000145,
-0.01625840738415718,
-0.034969691187143326,
-0.07032217085361481,
-0.020020682364702225,
0.01841294951736927,
0.02693633735179901,
0.0334433913230896,
-0.05336757376790047,
0.004221972543746233,
0.042214684188365936,
0.0021917144767940044,
-0.045364171266555786,
-0.05555729568004608,
-0.0362529531121254,
-0.05151878297328949,
-0.015614424832165241,
0.029144519940018654,
0.015770185738801956,
0.039396949112415314,
-0.07176967710256577,
0.002543287118896842,
-0.017171116545796394,
-0.005940111353993416,
0.018925726413726807,
0.025268331170082092,
0.06823490560054779,
0.007143729366362095,
-0.010391882620751858,
-0.042844172567129135,
-0.009949794039130211,
0.056521881371736526,
0.029712507501244545,
-0.002483497140929103,
-0.04826491326093674,
0.03527452424168587,
-0.03546565771102905,
-0.03907047212123871,
0.04010973125696182,
0.007109479978680611,
-0.015106702223420143,
-0.018659982830286026,
0.02195107191801071,
-0.04363415017724037,
0.036616887897253036,
-0.028774742037057877,
-0.056099940091371536,
-0.016971809789538383,
-0.009077748283743858,
0.02532646618783474,
-0.00806745421141386,
0.00043900765012949705,
0.03596138581633568,
0.0581803061068058,
0.00010278561239829287,
0.05784446746110916,
0.01895061321556568,
-0.031569112092256546,
-0.03518395125865936,
0.015886317938566208,
0.043076034635305405,
0.008081847801804543,
0.004205240868031979,
-0.08657371252775192,
0.06503590941429138,
0.007367220241576433,
-0.04521580785512924,
-0.0007255939417518675,
0.033746395260095596,
0.051182471215724945,
-0.01118697039783001,
-0.013077838346362114,
-0.0098123075440526,
-0.05568603053689003,
-0.017507631331682205,
-0.0007182069821283221,
0.026502510532736778,
-0.004901156760752201,
0.014887342229485512,
0.0014919297536835074,
-0.01420257706195116,
0.040680572390556335,
-0.07570695132017136,
0.0556689016520977,
-0.04258910194039345,
0.010106400586664677,
-0.002509976737201214,
-0.04121379926800728,
0.011471294797956944,
0.05948808789253235,
-0.0059767914935946465,
0.006759628187865019,
-0.0012722929241135716,
0.007714787032455206,
0.024557944387197495,
0.008442332036793232,
-0.0019086621468886733,
0.0038249569479376078,
-0.019880566745996475,
0.029312506318092346,
-0.021275460720062256,
0.058288056403398514,
-0.07827501744031906,
0.003636210458353162,
0.05857265368103981,
-0.0024542943574488163,
0.0116437878459692,
-0.04454902186989784,
0.015135210007429123
] |
[
8.099637985229492,
-0.4941007196903229
] |
Other Condensed Matter
|
Condensed-Matter Physics
|
cond-mat-other
|
cond-mat-stat-mech
|
na
|
2007-04-01T12:38:03
|
The path integral over Euclidean geometries for the recently suggested
density matrix of the Universe is shown to describe a microcanonical ensemble
in quantum cosmology. This ensemble corresponds to a uniform (weight one)
distribution in phase space of true physical variables, but in terms of the
observable spacetime geometry it is peaked about complex saddle-points of the
{\em Lorentzian} path integral. They are represented by the recently obtained
cosmological instantons limited to a bounded range of the cosmological
constant. Inflationary cosmologies generated by these instantons at late stages
of expansion undergo acceleration whose low-energy scale can be attained within
the concept of dynamically evolving extra dimensions. Thus, together with the
bounded range of the early cosmological constant, this cosmological ensemble
suggests the mechanism of constraining the landscape of string vacua and,
simultaneously, a possible solution to the dark energy problem in the form of
the quasi-equilibrium decay of the microcanonical state of the Universe.
|
Why there is something rather than nothing (out of everything)?
|
hep-th
|
0704.0083
| 2,007
|
[
-0.0005958575056865811,
0.04005230590701103,
0.0032661680597811937,
-0.04393986240029335,
-0.00563772302120924,
0.05822614207863808,
-0.000994513975456357,
-0.006531454157084227,
-0.09037373214960098,
-0.009472020901739597,
-0.03630588948726654,
0.020039359107613564,
0.05243333801627159,
0.04305937886238098,
0.0003420021675992757,
-0.0038107470609247684,
-0.010849430225789547,
-0.0025539675261825323,
0.021448200568556786,
-0.021075738593935966,
-0.005732541438192129,
-0.05946136638522148,
0.020511524751782417,
-0.02850620448589325,
0.08725246787071228,
-0.011672882363200188,
0.05221705883741379,
-0.016147000715136528,
-0.03665236756205559,
0.014313936233520508,
0.0652446374297142,
-0.047868333756923676,
0.028532398864626884,
-0.007333437446504831,
-0.03724679723381996,
-0.03263218700885773,
0.06537427008152008,
0.0055449772626161575,
0.03389009088277817,
0.007579949218779802,
0.008336931467056274,
-0.020456338301301003,
-0.038254301995038986,
-0.007032852619886398,
0.01509077101945877,
0.019586659967899323,
0.025753185153007507,
0.0029054859187453985,
0.027462409809231758,
-0.06145985424518585,
-0.023564063012599945,
0.02736344374716282,
-0.0038699700962752104,
-0.04367591440677643,
0.012502855621278286,
0.02312556467950344,
0.03582686930894852,
-0.07779140770435333,
0.048577554523944855,
0.01705363765358925,
0.017351996153593063,
-0.0004570667224470526,
0.03659866005182266,
0.07157909870147705,
0.0575096420943737,
-0.03441488742828369,
-0.061845507472753525,
0.00015143903146963567,
-0.027323784306645393,
-0.06309030205011368,
0.04762088134884834,
-0.03637084364891052,
0.008857938461005688,
0.0035470861475914717,
-0.011404698714613914,
0.010190977714955807,
0.03917932137846947,
0.024806059896945953,
0.01644320599734783,
0.0010872484417632222,
-0.03813879191875458,
-0.016765689477324486,
-0.010675771161913872,
0.006845788098871708,
0.08304413408041,
-0.018293453380465508,
0.029763132333755493,
0.022063249722123146,
-0.051917411386966705,
0.026462236419320107,
0.04827175661921501,
-0.0036688228137791157,
0.050647445023059845,
0.010968278162181377,
-0.04970575124025345,
0.020135266706347466,
-0.015990108251571655,
0.062164951115846634,
-0.02653304673731327,
-0.05020160600543022,
0.017952810972929,
0.039498068392276764,
0.01770681142807007,
-0.015852371230721474,
0.07261045277118683,
0.028533857315778732,
-0.046446677297353745,
0.006712901405990124,
0.03223268315196037,
-0.03144948184490204,
-0.08654574304819107,
-0.0058157010935246944,
-0.018432075157761574,
-0.045759011059999466,
-0.03449001908302307,
-0.05229749158024788,
0.05605810880661011,
-0.07875551283359528,
-0.010477027855813503,
0.058129336684942245,
-0.01812138222157955,
-0.023205844685435295,
0.0028484442736953497,
0.050759732723236084,
-0.00707334466278553,
0.018819009885191917,
-0.025315074250102043,
-0.050531450659036636,
-0.007701594848185778,
-0.03774034604430199,
0.00370216672308743,
0.02547319047152996,
-0.06016572564840317,
-0.023947473615407944,
0.029364507645368576,
-0.026203472167253494,
-0.010794179514050484,
-0.07474777102470398,
0.031203337013721466,
0.0034523019567131996,
0.024102719500660896,
-0.03684099018573761,
-0.018189024180173874,
-0.008026912808418274,
0.010145926848053932,
-0.06281374394893646,
0.01463410072028637,
-0.036060404032468796,
-0.03987796604633331,
-0.021226217970252037,
0.02232738584280014,
0.050486691296100616,
0.02631511725485325,
0.015966447070240974,
-0.040413957089185715,
-0.006080243270844221,
-0.00134573457762599,
0.03351982682943344,
0.01148577407002449,
-0.023796234279870987,
0.005833146162331104,
0.03627021238207817,
-0.012740585021674633,
0.018976153805851936,
-0.05468505620956421,
-0.007945730350911617,
0.03853554651141167,
0.006582083646208048,
0.0013376809656620026,
0.03583196923136711,
-0.007812947034835815,
-0.048992011696100235,
-0.042290348559617996,
-0.024039650335907936,
0.012724545784294605,
-0.0009258741629309952,
0.04138285294175148,
-0.05730171129107475,
0.018761496990919113,
-0.003181077539920807,
0.06487296521663666,
-0.017463319003582,
0.017752548679709435,
0.029682373628020287,
0.01852012239396572,
0.0204496830701828,
0.021983370184898376,
-0.019938932731747627,
0.0034260733518749475,
-0.05710119009017944,
0.07207570225000381,
-0.0004705587634816766,
-0.0073874713853001595,
-0.049474287778139114,
0.015817217528820038,
-0.02883564867079258,
0.0648178830742836,
-0.04909196496009827,
-0.004036726430058479,
-0.05559525266289711,
-0.0023958974052220583,
0.019055409356951714,
-0.05216119810938835,
0.01070205494761467,
-0.008040162734687328,
0.04808272421360016,
0.02651982009410858,
0.032981988042593,
0.027342088520526886,
-0.02293315902352333,
0.10938451439142227,
-0.019681882113218307,
0.014051994308829308,
0.028645921498537064,
-0.045486945658922195,
-0.03373095020651817,
0.05288667976856232,
-0.04747713357210159,
-0.017319001257419586,
0.05371217429637909,
-0.003883178811520338,
0.004273806232959032,
0.007499528117477894,
-0.009376097470521927,
0.07984677702188492,
0.019712626934051514,
-0.05413999781012535,
-0.05136210843920708,
-0.045797038823366165,
0.01667613349854946,
-0.04325564578175545,
-0.04919314756989479,
0.006594499107450247,
0.02296401560306549,
0.02709444798529148,
-0.023341676220297813,
0.03200678527355194,
0.013537941500544548,
0.01923375017940998,
0.07834318280220032,
0.05559694394469261,
-0.02665901929140091,
-0.002493728883564472,
-0.0582851842045784,
-0.01946798525750637,
-0.04967973753809929,
0.011002273298799992,
-0.01167211402207613,
-0.048145025968551636,
0.025491898879408836,
0.03843400627374649,
-0.04839453846216202,
0.02349771559238434,
0.03127015754580498,
0.036870043724775314,
-0.02338128723204136,
-0.02781301736831665,
0.016441302374005318,
-0.04777856171131134,
-0.044249262660741806,
0.04494494944810867,
-0.03510424867272377,
0.0063966913148760796,
-0.028491362929344177,
-0.042403046041727066,
0.006316946353763342,
-0.0033347418066114187,
-0.022015675902366638,
-0.06162678077816963,
-0.021081380546092987,
-0.013760006986558437,
0.03896036744117737,
0.0021540855523198843,
0.022473400458693504,
0.01641828939318657,
0.06817716360092163,
0.00925307348370552,
-0.02950335666537285,
0.021272720769047737,
-0.02865859679877758,
-0.05878090858459473,
0.014745684340596199,
-0.05855035036802292,
-0.006061548367142677,
-0.04494434595108032,
0.0009348215535283089,
0.02109125629067421,
-0.02224533073604107,
0.018903471529483795,
0.018483396619558334,
-0.0028085019439458847,
0.007357792463153601,
0.0011023497208952904,
0.07919567078351974,
0.03431619331240654,
0.028635725378990173,
0.013277299702167511,
-0.019426163285970688,
-0.023370664566755295,
-0.004488250240683556,
-0.007819050922989845,
-0.016167890280485153,
0.03967713564634323,
-0.054124608635902405,
-0.007493607699871063,
0.029482482001185417,
0.02345156855881214,
-0.009774090722203255,
0.028823476284742355,
-0.011210169643163681,
0.005211214069277048,
0.04603990167379379,
-0.03454086184501648,
-0.002690675901249051,
-0.019753867760300636,
0.05929608643054962,
0.06415083259344101,
0.017577609047293663,
0.1005917638540268,
-0.032941319048404694,
0.025636110454797745,
-0.021459126845002174,
-0.03057737462222576,
-0.02198627218604088,
0.01775488071143627,
0.02822353132069111,
-0.006904983893036842,
-0.03630096837878227,
-0.002875687088817358,
0.019015757367014885,
0.019124656915664673,
0.013689083978533745,
-0.019272739067673683,
0.018466394394636154,
-0.05234365910291672,
-0.022506937384605408,
-0.0473487451672554,
0.03478839248418808,
0.008571187034249306,
0.015849562361836433,
-0.05579372122883797,
-0.027018513530492783,
-0.03472220525145531,
-0.01352862361818552,
-0.0046564568765461445,
0.03596249222755432,
-0.031812120229005814,
-0.002225461881607771,
0.05702194571495056,
-0.005839350633323193,
-0.034717682749032974,
-0.024877620860934258,
0.022438116371631622,
-0.029887422919273376,
-0.08246908336877823,
0.06661929935216904,
0.06333024799823761,
-0.0328189879655838,
0.09060662239789963,
0.023360582068562508,
0.021649295464158058,
-0.06087637320160866,
0.026129242032766342,
-0.025800621137022972,
0.019104117527604103,
0.031054837629199028,
0.013298362493515015,
0.0005238523590378463,
-0.012019707821309566,
0.023131005465984344,
-0.014415938407182693,
-0.03898833692073822,
-0.005030449014157057,
0.025269126519560814,
0.07897049188613892,
0.01194714941084385,
-0.03585396707057953,
-0.013302682898938656,
-0.018279340118169785,
-0.022014187648892403,
0.08927447348833084,
0.02957049012184143,
0.059141818434000015,
0.009183989837765694,
0.020547984167933464,
0.0687975063920021,
-0.08771045506000519,
-0.03243269398808479,
-0.011051502078771591,
-0.028520505875349045,
-0.0024471059441566467,
-0.019087253138422966,
-0.04975870996713638,
0.02079813741147518,
-0.015260813757777214,
-0.004358192905783653,
0.03502310812473297,
-0.015416627749800682,
-0.014158659614622593,
0.01746957190334797,
-0.034454889595508575,
-0.07721471041440964,
0.0052890293300151825,
-0.005750895012170076,
-0.0020285164937376976,
-0.000051644212362589315,
0.006725133862346411,
-0.051573727279901505,
0.05866272747516632,
-0.00053931720321998,
0.03411471098661423,
0.02542266994714737,
0.0105924466624856,
-0.06939022988080978,
0.015513340942561626,
-0.0258755162358284,
0.056209370493888855,
-0.044504281133413315,
0.022422881796956062,
-0.01881711184978485,
-0.015240500681102276,
0.07757054269313812,
-0.003972558304667473,
0.011159325949847698,
-0.03573649004101753,
0.03345509245991707,
-0.003021546406671405,
0.01982339844107628,
-0.03909074887633324,
-0.011689610779285431,
0.024340646341443062,
0.00842076912522316,
0.03345388546586037,
0.04174498841166496,
-0.053527384996414185,
-0.011724463663995266,
-0.013238836079835892,
-0.04566788673400879,
-0.008574827574193478,
0.029399050399661064,
0.0594780407845974,
-0.06739142537117004,
0.0007283447193913162,
0.004402495920658112,
0.04115006700158119,
0.07827214896678925,
0.040107809007167816,
-0.04936300963163376,
-0.07985963672399521,
-0.006377143785357475,
0.05079129710793495,
0.026521367952227592,
0.016393931582570076,
0.013836794532835484,
0.10116325318813324,
-0.0511167012155056,
-0.0014811301371082664,
-0.0014193181414157152,
0.06256496161222458,
0.0361163355410099,
-0.010497494600713253,
0.07719728350639343,
-0.035374850034713745,
0.03915756195783615,
0.010938145220279694,
-0.007157160900533199,
-0.0573730394244194,
0.04171811416745186,
-0.00978031475096941,
0.08362238854169846,
0.013097402639687061,
0.017738962545990944,
0.006290159188210964,
-0.016353607177734375,
-0.0384322851896286,
0.0022925951052457094,
0.016131501644849777,
-0.029104573652148247,
0.01778077892959118,
0.04558354988694191,
0.006841124501079321,
-0.017085108906030655,
-0.014479213394224644,
0.015544732101261616,
0.015405992045998573,
0.07427061349153519,
-0.023913780227303505,
0.017285769805312157,
-0.03485187143087387,
0.018007511273026466,
-0.01337907649576664,
0.015272355638444424,
0.01070514228194952,
0.007353386376053095,
0.005555847194045782,
-0.03476051613688469,
0.03454207256436348,
-0.009415154345333576,
0.037780169397592545,
-0.06753723323345184,
-0.03679695725440979,
0.034408148378133774,
0.004895533435046673,
-0.015678245574235916,
-0.013725155964493752,
0.033955205231904984,
-0.0052470858208835125,
-0.034766700118780136,
0.003136418294161558,
0.029833875596523285,
0.00865446962416172,
0.04769333824515343,
0.02950579859316349,
0.07776682823896408,
0.0461990162730217,
-0.08730217069387436,
0.027407018467783928,
0.052527375519275665,
-0.05249972641468048,
-0.014829845167696476,
-0.042948637157678604,
0.021210534498095512,
0.027132639661431313,
-0.0015055257827043533,
-0.008794953115284443,
0.05398412048816681,
0.01476020086556673,
-0.06651268154382706,
0.04765855520963669,
0.0017499218229204416,
0.020260948687791824,
-0.002153725828975439,
-0.016344422474503517,
-0.03789292648434639,
0.002259376458823681,
-0.030908457934856415,
-0.015039259567856789,
0.0741088017821312,
0.0402318499982357,
0.015102512203156948,
-0.03254108503460884,
-0.03914487361907959,
-0.013962985947728157,
0.012126819230616093,
0.02542572095990181,
-0.04404318332672119,
-0.11714935302734375,
0.05642371252179146,
0.03409062698483467,
-0.06758631020784378,
-0.018296275287866592,
-0.018340829759836197,
-0.000698067422490567,
-0.04633432254195213,
-0.03449840843677521,
0.031267568469047546,
-0.009648243896663189,
-0.006302185356616974,
-0.04879728704690933,
-0.009839767590165138,
0.00588289275765419,
0.00803664606064558,
0.039478786289691925,
-0.016674648970365524,
-0.013187834993004799,
-0.08326619863510132,
-0.020804287865757942,
-0.031535692512989044,
0.04864409193396568,
-0.007313970010727644,
0.018045194447040558,
-0.00975353829562664,
0.038466501981019974,
0.08343914896249771,
-0.00527843926101923,
-0.04697256162762642,
0.034258995205163956,
-0.01563609205186367,
-0.07702403515577316,
-0.0316629558801651,
-0.047076813876628876,
-0.012074277736246586,
0.010335777886211872,
-0.032381441444158554,
-0.04058752581477165,
0.011015566065907478,
-0.02683553472161293,
-0.0476083867251873,
0.03173210099339485,
0.0183770302683115,
-0.01247763354331255,
0.017991818487644196,
-0.016743941232562065,
-0.013111974112689495,
-0.09556134045124054,
0.02439945749938488,
0.018526557832956314,
-0.023280035704374313,
-0.06983838975429535,
-0.025135304778814316,
-0.017386745661497116,
0.029204117134213448,
0.08597054332494736,
-0.0323820561170578,
0.06547326594591141,
0.025314630940556526,
-0.035096026957035065,
0.049596063792705536,
-0.009064937010407448,
0.019970733672380447,
0.03932151198387146,
0.04303564503788948,
-0.020099764689803123,
-0.01535317674279213,
0.01817947067320347,
-0.007630191743373871,
0.08151262998580933,
-0.010724198073148727,
-0.019608359783887863,
-0.03003835119307041,
-0.010685564018785954,
-0.04485621675848961,
0.0023145838640630245,
-0.06373200565576553,
0.01422715000808239,
-0.008226597681641579,
-0.026768961921334267,
-0.006011189427226782,
0.026659877970814705,
0.06879737228155136,
-0.0353923998773098,
0.0016193900955840945,
-0.009014966897666454,
0.030776768922805786,
-0.05708117038011551,
0.04348304122686386,
-0.032826486974954605,
0.0076465788297355175,
0.014008166268467903,
0.026701228693127632,
0.03925742208957672,
-0.06238824129104614,
-0.004355316516011953,
0.018191780894994736,
-0.004739152267575264,
0.050073668360710144,
-0.0011474936036393046,
-0.029531368985772133,
0.0034785340540111065,
-0.007954052649438381,
0.08230915665626526,
0.05077950656414032,
0.02308596856892109,
-0.004368301946669817,
-0.03666039556264877,
0.0014235983835533261,
-0.0027705607935786247,
-0.019159868359565735,
-0.037900835275650024,
-0.05880587548017502,
-0.01885254867374897,
0.023098761215806007,
-0.010324000380933285,
-0.014256644062697887,
0.05295143276453018,
-0.02532673068344593,
0.025606032460927963,
-0.046467047184705734,
-0.03612544760107994,
0.007091268431395292,
-0.013953008688986301,
-0.015777790918946266,
-0.06542002409696579,
-0.018740659579634666,
-0.043587878346443176,
-0.02513568289577961,
-0.03219100087881088,
0.019608167931437492,
0.018856437876820564,
-0.0011848624562844634,
0.02825177274644375,
0.023741407319903374,
0.05143089219927788,
-0.012194664217531681,
0.012227092869579792,
-0.037453942000865936,
0.02756652981042862,
-0.05987592041492462,
-0.05898796766996384,
-0.025787770748138428,
0.015338342636823654,
-0.01640862599015236,
-0.0057179881259799,
-0.0750228613615036,
0.023128222674131393,
0.01722140610218048,
-0.03291882202029228,
0.016152167692780495,
0.006273800507187843,
0.027049299329519272,
0.007834324613213539,
-0.0010844223434105515,
-0.009685618802905083,
0.022113531827926636,
-0.015438517555594444,
-0.006014534272253513,
0.0836397260427475,
0.04635130241513252,
-0.019940316677093506,
0.0035880482755601406,
0.0003831599315162748,
0.003924837335944176,
0.03342469781637192,
0.018999550491571426,
0.02810727059841156,
0.02657460793852806,
0.009089200757443905,
-0.02275467850267887,
-0.015113555826246738,
-0.03608034923672676,
-0.011365131475031376,
-0.033175814896821976,
-0.03887651115655899,
0.031245365738868713,
0.00580985751003027,
-0.05417202413082123,
0.0234646238386631,
-0.05198836699128151,
0.02346714958548546,
-0.023102838546037674,
-0.007647995837032795,
-0.013356449082493782,
-0.022472046315670013,
0.015375417657196522,
-0.05543394014239311,
0.046448711305856705,
-0.017613830044865608,
0.03142404183745384,
-0.029509631916880608,
-0.00018672992882784456,
-0.014060671441257,
-0.05203225836157799,
0.016887549310922623,
0.02231776900589466,
-0.008611139841377735,
-0.03527810797095299,
-0.0494406595826149,
0.03299163654446602,
0.07894565910100937,
-0.03984244167804718,
-0.028749436140060425,
-0.05467637628316879,
-0.011970918625593185,
0.019959252327680588,
0.0075967092998325825,
0.014366500079631805,
0.03584006428718567,
0.005131750833243132,
0.0403008759021759,
-0.005992600228637457,
0.05719829350709915,
-0.007063668221235275,
0.03867536038160324,
0.049331873655319214,
-0.012895705178380013,
0.03297048807144165,
-0.009749393910169601,
0.01458405889570713
] |
[
13.310816764831543,
2.075201988220215
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-04-01T12:54:14
|
We employ granular hydrodynamics to investigate a paradigmatic problem of
clustering of particles in a freely cooling dilute granular gas. We consider
large-scale hydrodynamic motions where the viscosity and heat conduction can be
neglected, and one arrives at the equations of ideal gas dynamics with an
additional term describing bulk energy losses due to inelastic collisions. We
employ Lagrangian coordinates and derive a broad family of exact non-stationary
analytical solutions that depend only on one spatial coordinate. These
solutions exhibit a new type of singularity, where the gas density blows up in
a finite time when starting from smooth initial conditions. The density blowups
signal formation of close-packed clusters of particles. As the density blow-up
time $t_c$ is approached, the maximum density exhibits a power law $\sim
(t_c-t)^{-2}$. The velocity gradient blows up as $\sim - (t_c-t)^{-1}$ while
the velocity itself remains continuous and develops a cusp (rather than a shock
discontinuity) at the singularity. The gas temperature vanishes at the
singularity, and the singularity follows the isobaric scenario: the gas
pressure remains finite and approximately uniform in space and constant in time
close to the singularity. An additional exact solution shows that the density
blowup, of the same type, may coexist with an "ordinary" shock, at which the
hydrodynamic fields are discontinuous but finite. We confirm stability of the
exact solutions with respect to small one-dimensional perturbations by solving
the ideal hydrodynamic equations numerically. Furthermore, numerical solutions
show that the local features of the density blowup hold universally,
independently of details of the initial and boundary conditions.
|
Formation of density singularities in ideal hydrodynamics of freely
cooling inelastic gases: a family of exact solutions
|
cond-mat.soft nlin.PS physics.flu-dyn
|
0704.0084
| 2,007
|
[
0.01950114779174328,
0.0010151714086532593,
-0.00020695787679869682,
-0.032746102660894394,
0.047145307064056396,
-0.0027155790012329817,
0.00947275198996067,
0.03193818777799606,
-0.055019695311784744,
0.0472218357026577,
-0.06320387125015259,
0.0407881885766983,
0.04236979782581329,
0.009875836782157421,
-0.0020933421328663826,
-0.02266402542591095,
0.003693633945658803,
-0.02056061662733555,
-0.007629944011569023,
0.04264551028609276,
-0.006335852202028036,
-0.024623863399028778,
0.024577835574746132,
-0.043888237327337265,
0.09642580896615982,
-0.015587655827403069,
0.03589583560824394,
0.00003483551699901,
-0.01946314424276352,
0.010712326504290104,
0.04304824024438858,
-0.005158023908734322,
-0.031951334327459335,
-0.04648490622639656,
-0.04604636877775192,
-0.030823227018117905,
0.05181112885475159,
-0.03565756976604462,
0.012457486242055893,
0.0035982790868729353,
0.06456354260444641,
-0.042538709938526154,
0.02826923504471779,
-0.018959835171699524,
0.027852682396769524,
0.046227384358644485,
0.016206353902816772,
-0.015064720064401627,
0.03413597121834755,
0.0346464067697525,
0.0022269526962190866,
0.010521077550947666,
-0.03570006415247917,
-0.07566969841718674,
-0.02514042519032955,
0.0567905530333519,
0.016127029433846474,
-0.00974706094712019,
0.05700302869081497,
-0.012732542119920254,
0.0208574328571558,
0.003704517614096403,
-0.0444367490708828,
-0.029812391847372055,
0.012857812456786633,
-0.09520957618951797,
-0.05562218278646469,
0.014532997272908688,
0.005430921446532011,
-0.04469854012131691,
0.05418691039085388,
-0.019101016223430634,
0.031052524223923683,
-0.01409155037254095,
-0.02842562459409237,
0.006338511593639851,
-0.049631375819444656,
-0.012479930184781551,
-0.02132456563413143,
-0.030049538239836693,
0.026988042518496513,
0.00967866089195013,
0.037535883486270905,
-0.014009961858391762,
0.03565235435962677,
0.014401569962501526,
0.02397654578089714,
0.006897499319165945,
-0.04748399555683136,
0.025762399658560753,
-0.00213281880132854,
0.006795303896069527,
0.05614989623427391,
0.05873899534344673,
-0.024654945358633995,
-0.017545901238918304,
-0.005241899285465479,
0.06955316662788391,
-0.023130804300308228,
-0.0021897698752582073,
0.012502865865826607,
0.02517688274383545,
0.0010968713322654366,
-0.02174517884850502,
0.05209117382764816,
0.004068831913173199,
-0.0006475950940512121,
0.019269676879048347,
0.020849978551268578,
-0.04588216543197632,
-0.047747425734996796,
-0.021300479769706726,
0.0093529112637043,
0.0006851793732494116,
-0.04066963493824005,
-0.022407010197639465,
0.06320148706436157,
-0.05755665525794029,
-0.018592223525047302,
0.0954786092042923,
-0.019198022782802582,
0.015375271439552307,
-0.02285686694085598,
0.05195149406790733,
0.04667087271809578,
0.020153002813458443,
-0.012958803214132786,
-0.01315431110560894,
-0.047375548630952835,
-0.00966615229845047,
0.023676393553614616,
0.01854611001908779,
-0.06252528727054596,
-0.009014114737510681,
0.05732337012887001,
0.021353010088205338,
-0.04345357418060303,
-0.00554989418014884,
0.05721518397331238,
-0.023373302072286606,
0.018306177109479904,
0.005113229155540466,
0.010262204334139824,
0.0033934242092072964,
0.032010942697525024,
-0.07471474260091782,
-0.01794711872935295,
-0.041271574795246124,
-0.040072474628686905,
-0.01935357041656971,
0.01747817173600197,
0.060728687793016434,
0.03003002516925335,
0.009848101995885372,
-0.035610295832157135,
-0.011073336005210876,
-0.025344301015138626,
0.01883416622877121,
0.0720752701163292,
0.007204348221421242,
0.006625453010201454,
0.011887751519680023,
-0.019257985055446625,
0.05131160095334053,
-0.060278814285993576,
0.057085227221250534,
0.03347909823060036,
0.009536310099065304,
0.049658603966236115,
0.035713598132133484,
-0.060618530958890915,
-0.0492219515144825,
-0.0494573637843132,
0.011995919048786163,
0.01734112575650215,
-0.03315635398030281,
0.0031862622126936913,
-0.037307754158973694,
-0.0030690974090248346,
-0.07615841925144196,
0.06287068128585815,
-0.030216440558433533,
0.045395199209451675,
-0.004089781083166599,
0.029222000390291214,
0.04242038354277611,
-0.007937414571642876,
0.004565468989312649,
-0.029753100126981735,
-0.02609441988170147,
0.030524153262376785,
0.01992284134030342,
-0.07331257313489914,
-0.028315812349319458,
-0.001401103800162673,
0.0017138761468231678,
0.09545239061117172,
-0.06463444232940674,
-0.035207752138376236,
-0.03430559113621712,
-0.0318613201379776,
0.03053617849946022,
-0.0370660275220871,
0.04960999637842178,
-0.0053811329416930676,
0.021157091483473778,
0.009878858923912048,
0.04096943140029907,
0.020308535546064377,
0.008342042565345764,
0.04685857519507408,
0.0013243239372968674,
-0.017593957483768463,
0.02565889060497284,
0.012220149859786034,
-0.021828187629580498,
-0.020748047158122063,
-0.009153672493994236,
-0.018610430881381035,
0.04992390424013138,
-0.01701374351978302,
0.0011165261967107654,
-0.03269622474908829,
0.026071418076753616,
0.08958215266466141,
-0.041207678616046906,
0.030978048220276833,
-0.06513367593288422,
-0.03000577539205551,
-0.019758589565753937,
-0.052624061703681946,
-0.010657412000000477,
0.056448932737112045,
-0.022031381726264954,
-0.02720353938639164,
-0.0012652564328163862,
-0.04899146407842636,
0.008627546951174736,
0.041589293628931046,
0.038100242614746094,
0.0066229249350726604,
-0.009888227097690105,
0.005540634039789438,
-0.015737492591142654,
-0.06921497732400894,
-0.004295548889786005,
-0.013939639553427696,
0.0076671564020216465,
-0.004002646543085575,
0.02038482576608658,
0.024975301697850227,
0.007276157848536968,
0.0365414135158062,
0.05938052758574486,
0.07076364010572433,
-0.0322222001850605,
-0.07164286822080612,
0.0639534667134285,
-0.011554259806871414,
-0.059028543531894684,
0.04133275896310806,
-0.0020186379551887512,
-0.012251567095518112,
-0.0813693255186081,
-0.0739467665553093,
0.07050477713346481,
0.033042632043361664,
-0.06508927792310715,
-0.02962067909538746,
-0.02110416442155838,
0.029080888256430626,
0.054561227560043335,
0.05179878696799278,
0.06263761222362518,
-0.023953430354595184,
0.07528083026409149,
0.030923986807465553,
0.006200106348842382,
-0.006010070443153381,
0.00308318343013525,
-0.08178827166557312,
-0.018155567348003387,
-0.04381929710507393,
0.004227253142744303,
0.0005882488330826163,
-0.028308361768722534,
0.03184455260634422,
0.02746819145977497,
0.03995998576283455,
-0.0031410218216478825,
-0.003126012859866023,
-0.013316933996975422,
0.02666466124355793,
0.07738407701253891,
0.017940610647201538,
0.07120580971240997,
0.0352424792945385,
0.006184312514960766,
-0.00024757618666626513,
0.0009875788819044828,
0.013222821056842804,
-0.011002080515027046,
-0.0033165225759148598,
0.025106679648160934,
-0.010153753682971,
0.02886376529932022,
-0.018395382910966873,
-0.053368180990219116,
-0.0026176818646490574,
-0.03278486058115959,
0.05330241098999977,
0.053376805037260056,
-0.025955678895115852,
-0.0040447604842484,
-0.02734280936419964,
0.03134794533252716,
0.052482739090919495,
-0.021330732852220535,
0.09653344005346298,
-0.01920056715607643,
-0.027521731331944466,
-0.021893035620450974,
0.02206716127693653,
-0.08933410793542862,
0.0035942986141890287,
0.046793997287750244,
-0.016481008380651474,
-0.009812385775148869,
-0.032850753515958786,
0.012172846123576164,
-0.08563095331192017,
0.020870665088295937,
-0.021047603338956833,
-0.02530425228178501,
-0.019083037972450256,
-0.018032176420092583,
-0.04891229048371315,
0.06711222976446152,
0.012293378822505474,
0.01156796794384718,
0.0034569918643683195,
-0.044185735285282135,
-0.030974984169006348,
-0.06027492880821228,
-0.028569327667355537,
0.019184568896889687,
-0.01776149496436119,
0.007635830901563168,
0.06264738738536835,
0.01692625880241394,
-0.006569413468241692,
-0.016681745648384094,
0.026981936767697334,
-0.025650234892964363,
-0.015882540494203568,
0.03267596662044525,
0.06595686823129654,
-0.07545918971300125,
0.07715274393558502,
0.00786274392157793,
0.015374048613011837,
-0.030741486698389053,
0.0395866334438324,
0.05553663894534111,
0.032864026725292206,
-0.016062455251812935,
-0.011996576562523842,
-0.013039844110608101,
0.004154846537858248,
-0.0746566653251648,
-0.05562887340784073,
-0.02750370465219021,
0.028266172856092453,
0.06381159275770187,
0.05638282373547554,
0.003215175587683916,
-0.06214684620499611,
0.03603850305080414,
0.013052981346845627,
-0.028483763337135315,
0.05313991755247116,
-0.01965540274977684,
0.03393584489822388,
0.009619553573429585,
0.01254914328455925,
0.05821749567985535,
-0.025114858523011208,
0.008839836344122887,
-0.0030353975016623735,
-0.021596863865852356,
0.0428188182413578,
-0.04351390153169632,
-0.008212239481508732,
0.0030901660211384296,
-0.0015239899512380362,
-0.046791087836027145,
0.0181590523570776,
-0.02804187498986721,
-0.038578614592552185,
-0.0052797566168010235,
-0.029252689331769943,
-0.06190295144915581,
-0.01630706898868084,
-0.05462479218840599,
0.015076721087098122,
-0.03850790858268738,
-0.01762443222105503,
-0.08057089895009995,
0.0349280945956707,
-0.034494977444410324,
0.044992100447416306,
0.0031310326885432005,
0.018790708854794502,
-0.046529125422239304,
0.08728359639644623,
-0.03828883543610573,
0.035705603659152985,
-0.005939228925853968,
0.014354906976222992,
-0.025926748290657997,
0.006474309600889683,
0.033569369465112686,
-0.03216152265667915,
-0.015896961092948914,
-0.03147571533918381,
-0.021836739033460617,
0.04552799463272095,
0.02554704062640667,
0.0006298300577327609,
-0.07354645431041718,
0.01713559590280056,
-0.015415726229548454,
-0.008078236132860184,
0.026668312028050423,
-0.044835858047008514,
-0.02426627278327942,
-0.007347723934799433,
-0.03956843540072441,
0.0030080480501055717,
0.06593300402164459,
0.050382763147354126,
-0.01717918924987316,
0.020220130681991577,
0.0068997666239738464,
0.0994839072227478,
0.08015549182891846,
0.04980648308992386,
-0.029473649337887764,
-0.03556861728429794,
0.018957771360874176,
0.024322081357240677,
-0.016250895336270332,
-0.008661198429763317,
0.03443114832043648,
0.05995960161089897,
-0.015276261605322361,
-0.03353916108608246,
-0.0317951962351799,
0.020741727203130722,
0.03130413591861725,
-0.0035168586764484644,
0.024263393133878708,
-0.0052950698882341385,
0.06114248186349869,
-0.019236592575907707,
-0.05215427652001381,
0.027577105909585953,
-0.0025619524531066418,
-0.00042176665738224983,
0.0002746691752690822,
-0.0007761988672427833,
0.016769083216786385,
0.032280173152685165,
-0.012050009332597256,
-0.023274078965187073,
-0.020573904737830162,
0.04045875743031502,
-0.0665532723069191,
0.02168683335185051,
0.03088250756263733,
0.035770900547504425,
-0.022931793704628944,
-0.005112586542963982,
-0.009162421338260174,
-0.01843038573861122,
0.04904932156205177,
-0.009458783082664013,
0.02529970556497574,
0.03051404282450676,
-0.006363287568092346,
0.021926576271653175,
0.03005783073604107,
-0.022387197241187096,
0.01850942336022854,
-0.04033511132001877,
-0.050498876720666885,
-0.006625075824558735,
-0.014838307164609432,
-0.002299719024449587,
-0.02332300692796707,
-0.01980474218726158,
-0.01537563931196928,
-0.011943221092224121,
0.02530636638402939,
0.03106853924691677,
0.0623849593102932,
-0.011338641867041588,
-0.03383181244134903,
-0.005743535701185465,
0.005781679414212704,
-0.002853184938430786,
0.06524283438920975,
0.08999694138765335,
0.07289081811904907,
-0.009267856366932392,
-0.043795231729745865,
0.03093428909778595,
-0.010004804469645023,
-0.0823640450835228,
-0.027054622769355774,
0.04492110013961792,
-0.0015019358834251761,
-0.009719436056911945,
0.05733560025691986,
-0.0433453768491745,
0.03339704871177673,
-0.05887286365032196,
-0.03805817663669586,
0.06059391796588898,
0.002547432202845812,
0.023181740194559097,
0.013017776422202587,
0.010677207261323929,
-0.050444360822439194,
-0.03132505342364311,
-0.024013888090848923,
-0.004831831436604261,
0.03343040123581886,
0.007765140384435654,
0.008799896575510502,
-0.006354195531457663,
0.010104415938258171,
0.0004957737401127815,
-0.020598476752638817,
0.03681479021906853,
-0.008844773285090923,
-0.09162916243076324,
0.03424185886979103,
0.0000716206050128676,
-0.04150428995490074,
0.017556339502334595,
-0.05256309360265732,
0.04329761862754822,
-0.07228279858827591,
0.02024286426603794,
-0.0561346560716629,
0.018367215991020203,
-0.07058750838041306,
-0.09414436668157578,
0.0032669727224856615,
-0.046947259455919266,
0.030603276565670967,
0.03529293090105057,
-0.004694128409028053,
-0.011041002348065376,
-0.11051684617996216,
-0.05790311098098755,
-0.008862889371812344,
0.052279770374298096,
-0.022856807336211205,
-0.019427837803959846,
-0.033322446048259735,
0.040495265275239944,
-0.011803160421550274,
0.03532007709145546,
-0.04053743928670883,
0.026641279458999634,
0.03906186670064926,
-0.03380650281906128,
0.036383006721735,
-0.04944456368684769,
0.012872135266661644,
0.0670546442270279,
0.016528530046343803,
-0.021985109895467758,
-0.026570826768875122,
-0.06650632619857788,
-0.03165210038423538,
0.032416731119155884,
0.018348991870880127,
0.02835688367486,
-0.05559058114886284,
-0.03331487998366356,
-0.03998073562979698,
-0.06244505196809769,
0.00860978476703167,
-0.011248967610299587,
-0.0017200025031343102,
-0.06342949718236923,
-0.04371630400419235,
0.00004224548683851026,
0.031125731766223907,
0.009945626370608807,
0.0053469217382371426,
0.014529092237353325,
0.02847456932067871,
0.03686026111245155,
0.01843874156475067,
-0.04567264765501022,
0.03026801533997059,
0.0019065835513174534,
-0.010309254750609398,
-0.025209350511431694,
-0.05578180402517319,
-0.008401005528867245,
0.009242585860192776,
0.07901933044195175,
-0.005223823245614767,
0.03235865384340286,
-0.03283344954252243,
0.02098100818693638,
-0.06452879309654236,
0.027203654870390892,
-0.08861111849546432,
0.013850242830812931,
0.0018486856715753675,
-0.044431526213884354,
-0.045198723673820496,
0.02252168208360672,
0.03623966872692108,
0.035938385874032974,
-0.005258772987872362,
-0.06402628123760223,
-0.00950388703495264,
-0.00518293771892786,
0.011883231811225414,
-0.02476767636835575,
0.043666061013936996,
0.034399669617414474,
0.027788782492280006,
0.05861422419548035,
0.008730961941182613,
0.022349169477820396,
0.03424865007400513,
-0.020512230694293976,
0.06992509961128235,
-0.0047736200504004955,
0.0009710329468362033,
0.012815802358090878,
-0.02657880261540413,
0.02917901985347271,
0.0315898098051548,
0.0003428838972467929,
0.0671943724155426,
0.002766148652881384,
0.021225150674581528,
0.054516490548849106,
-0.04258162900805473,
0.0010547918500378728,
-0.004144487902522087,
-0.016848936676979065,
0.0208408422768116,
0.04402679577469826,
-0.007320071570575237,
0.01789713278412819,
-0.006022958550602198,
-0.005781210958957672,
-0.05297687277197838,
-0.011129838414490223,
-0.01425669901072979,
0.008897996507585049,
0.02607796899974346,
-0.04175712168216705,
-0.041536614298820496,
-0.025062091648578644,
0.004542025737464428,
0.026265468448400497,
0.04445868730545044,
0.027718456462025642,
-0.011791542172431946,
-0.003489920636638999,
-0.006249588914215565,
0.000043389856728026643,
-0.007292754482477903,
0.027978021651506424,
0.008880114182829857,
-0.007063994649797678,
-0.03006812557578087,
-0.036867622286081314,
-0.028291083872318268,
0.002413201844319701,
0.025231672450900078,
0.022356778383255005,
-0.03867143765091896,
0.0032541323453187943,
0.01906701922416687,
-0.0011908201267942786,
-0.009116895496845245,
-0.005472762510180473,
0.02683841623365879,
-0.02007705345749855,
0.017765283584594727,
-0.0035382634960114956,
0.03011939860880375,
-0.02982890047132969,
-0.03261703625321388,
0.05578554421663284,
0.009228858165442944,
-0.0007098516798578203,
0.041449740529060364,
0.004089660942554474,
0.002631367649883032,
0.040077388286590576,
0.02167423442006111,
0.05071236565709114,
-0.03452999144792557,
-0.02708069607615471,
-0.056005802005529404,
0.027963809669017792,
-0.005578117445111275,
0.03815240412950516,
0.01036234200000763,
-0.0282549187541008,
0.02135477401316166,
0.023171843960881233,
-0.06516431272029877,
-0.03551895543932915,
-0.0041888500563800335,
0.010442076250910759,
-0.0070885238237679005,
-0.036871761083602905,
0.01695450209081173,
-0.036759212613105774,
0.007106579840183258,
0.012020234949886799,
-0.008619521744549274,
-0.023611603304743767,
0.008390441536903381,
-0.00964471884071827,
-0.010871877893805504,
-0.02877543866634369,
-0.049439687281847,
0.05785553902387619,
-0.00007784354966133833,
-0.041652120649814606,
-0.0708511546254158,
-0.0314432829618454,
0.051154062151908875,
0.05319821089506149,
-0.021576406434178352,
0.0073744929395616055,
-0.014152460731565952,
-0.004213851410895586,
-0.044928427785634995,
-0.004012562334537506,
-0.012628906406462193,
0.0005557021941058338,
0.019290167838335037,
0.04040253534913063,
-0.03951264172792435,
-0.03224622458219528,
-0.04329273849725723,
0.06088460981845856,
0.03926819562911987,
0.002742680022493005,
0.010084778070449829,
0.0011280461912974715,
0.0017883998807519674
] |
[
6.817751884460449,
3.601853847503662
] |
Soft Condensed Matter
|
Condensed-Matter Physics
|
cond-mat-soft
|
nlin-PS
|
physics-flu-dyn
|
2007-04-01T12:55:02
|
We discuss a universality property of any covariant field theory in
space-time expanded around pp-wave backgrounds. According to this property the
space-time lagrangian density evaluated on a restricted set of field
configurations, called universal sector, turns out to be same around all the
pp-waves, even off-shell, with same transverse space and same profiles for the
background scalars. In this paper we restrict our discussion to tensorial
fields only. In the context of bosonic string theory we consider on-shell
pp-waves and argue that universality requires the existence of a universal
sector of world-sheet operators whose correlation functions are insensitive to
the pp-wave nature of the metric and the background gauge flux. Such results
can also be reproduced using the world-sheet conformal field theory. We also
study such pp-waves in non-polynomial closed string field theory (CSFT). In
particular, we argue that for an off-shell pp-wave ansatz with flat transverse
space and dilaton independent of transverse coordinates the field redefinition
relating the low energy effective field theory and CSFT with all the massive
modes integrated out is at most quadratic in fields. Because of this
simplification it is expected that the off-shell pp-waves can be identified on
the two sides. Furthermore, given the massless pp-wave field configurations, an
iterative method for computing the higher massive modes using the CSFT
equations of motion has been discussed. All our bosonic string theory analyses
can be generalised to the common Neveu-Schwarz sector of superstrings.
|
A Universality in PP-Waves
|
hep-th
|
0704.0085
| 2,007
|
[
0.021975290030241013,
0.04813501983880997,
0.00022959716443438083,
-0.02246764302253723,
0.04160952568054199,
0.06876593828201294,
0.020485367625951767,
0.021417731419205666,
-0.036608994007110596,
-0.010031805373728275,
-0.060374438762664795,
0.06244568154215813,
-0.0017820255598053336,
0.01401886809617281,
-0.011867167428135872,
-0.05028023570775986,
0.01138553861528635,
0.00461041321977973,
0.006749249063432217,
-0.0057233162224292755,
-0.0033047785982489586,
-0.02902309037744999,
0.011626124382019043,
-0.0023603099398314953,
0.08713161200284958,
-0.02564363367855549,
0.035330746322870255,
-0.028485635295510292,
-0.009644094854593277,
-0.054982803761959076,
0.08954153209924698,
-0.03497682139277458,
0.015249921940267086,
-0.04046621173620224,
-0.00951075367629528,
-0.015209032222628593,
0.016076408326625824,
-0.010122513398528099,
0.03409884497523308,
0.05785740539431572,
0.00968839693814516,
-0.024330249056220055,
0.022027725353837013,
-0.017788786441087723,
-0.0019468455575406551,
-0.040860675275325775,
0.009188797324895859,
-0.004732990637421608,
0.020282266661524773,
0.008603040128946304,
-0.04169068858027458,
-0.0020567981991916895,
0.04202616587281227,
-0.061705976724624634,
-0.029607586562633514,
0.01806206814944744,
0.004956126678735018,
-0.040240779519081116,
0.06796824932098389,
-0.005498392973095179,
-0.008340406231582165,
0.004039441235363483,
-0.008770134299993515,
0.015558386221528053,
0.04307590797543526,
-0.04775405302643776,
-0.04420512169599533,
-0.01857532560825348,
-0.02127169631421566,
-0.05193829908967018,
0.03355633467435837,
-0.0023976804222911596,
-0.004851058591157198,
0.022085614502429962,
0.020358430221676826,
0.015219666995108128,
-0.015272707678377628,
-0.022353149950504303,
-0.014479653909802437,
-0.015967631712555885,
0.016493085771799088,
-0.03038511797785759,
0.01858912967145443,
0.0652228370308876,
0.08714265376329422,
-0.07859112322330475,
0.06922716647386551,
0.03971370309591293,
-0.055359870195388794,
0.051836833357810974,
0.020423246547579765,
0.011239524930715561,
0.04758219048380852,
0.046450383961200714,
-0.06714348495006561,
0.011950033716857433,
-0.003815246047452092,
0.024889366701245308,
-0.015230595134198666,
-0.04805305600166321,
-0.009607968851923943,
0.06155389919877052,
-0.012371448799967766,
0.015330611728131771,
0.03746356815099716,
0.0869075283408165,
-0.0001375692809233442,
0.008858803659677505,
0.019504569470882416,
0.01894836127758026,
-0.0724688395857811,
0.023461846634745598,
0.025269486010074615,
0.013761322945356369,
-0.07367241382598877,
-0.059927552938461304,
0.0025595149490982294,
-0.06908336281776428,
-0.02334379404783249,
0.07776354998350143,
-0.018595222383737564,
-0.027253853157162666,
0.031573742628097534,
0.029898060485720634,
-0.009891008026897907,
-0.019052589312195778,
-0.07121098041534424,
-0.026949623599648476,
0.016974525526165962,
-0.04439729079604149,
0.04268524423241615,
0.028878437355160713,
-0.05327216908335686,
0.02698795683681965,
0.03413853794336319,
0.021624978631734848,
-0.022667773067951202,
-0.0036369336303323507,
0.018359441310167313,
-0.005012803710997105,
-0.047629937529563904,
-0.026173580437898636,
-0.002923822496086359,
-0.02899933233857155,
0.002322474727407098,
-0.0659036934375763,
0.01320855226367712,
-0.05468199402093887,
-0.02692132070660591,
0.01960841566324234,
0.05152500048279762,
0.06607434898614883,
0.003978662192821503,
0.07107670605182648,
-0.036681607365608215,
-0.04401154816150665,
-0.0015448933700099587,
-0.02155512012541294,
0.018652737140655518,
0.0064722211100161076,
0.030682379379868507,
0.0661488026380539,
-0.010421515442430973,
0.06552858650684357,
-0.046849943697452545,
-0.01695968024432659,
0.07237129658460617,
0.03833658993244171,
0.03415293246507645,
-0.002375901211053133,
-0.028142627328634262,
-0.02178574725985527,
-0.012727681547403336,
-0.06718983501195908,
-0.01123459730297327,
0.013998844660818577,
-0.020820029079914093,
-0.04621358588337898,
0.058181729167699814,
0.013465285301208496,
0.0002971538342535496,
-0.010972719639539719,
-0.030524248257279396,
0.02982456423342228,
0.039656031876802444,
0.04625899717211723,
-0.03982912003993988,
-0.032148025929927826,
-0.037827927619218826,
0.010097813792526722,
0.019531043246388435,
-0.004882490262389183,
-0.039224911481142044,
-0.00976061075925827,
-0.004661059007048607,
-0.03651639074087143,
0.05448494106531143,
-0.007564132567495108,
-0.007064361125230789,
-0.06250899285078049,
-0.03644128143787384,
0.033806245774030685,
0.0076543912291526794,
-0.014734900556504726,
0.01829439215362072,
0.05669135972857475,
0.011796142905950546,
0.03939729556441307,
0.07170476019382477,
-0.01011656317859888,
0.05514185503125191,
-0.02335357666015625,
-0.024958612397313118,
0.013736031018197536,
-0.018875718116760254,
-0.005577936302870512,
-0.01624671369791031,
-0.05254290625452995,
-0.06351377815008163,
0.05600455030798912,
0.02901497110724449,
0.020961571484804153,
0.05779477208852768,
0.03309352323412895,
0.04359648376703262,
0.04755625128746033,
-0.03937949612736702,
0.02382769249379635,
0.009461328387260437,
-0.027327079325914383,
-0.026885801926255226,
-0.05090472102165222,
0.05068502202630043,
0.005808193236589432,
-0.007830585353076458,
-0.011530733667314053,
-0.013574209064245224,
0.057976312935352325,
0.018416255712509155,
0.051845137029886246,
0.026597319170832634,
-0.007402915973216295,
-0.0219899732619524,
0.022740069776773453,
-0.010426086373627186,
-0.013416600413620472,
0.0014203280443325639,
0.00037499231984838843,
-0.01809891313314438,
0.03209609538316727,
-0.013879571110010147,
-0.048118602484464645,
0.015026059933006763,
0.0406007282435894,
0.01988850347697735,
-0.010117558762431145,
0.01260149385780096,
0.0611557699739933,
-0.036963656544685364,
-0.06611466407775879,
0.027843579649925232,
-0.032065484672784805,
0.02075834572315216,
-0.033969633281230927,
-0.03682352602481842,
0.033692121505737305,
-0.014645498245954514,
-0.044751010835170746,
-0.025453757494688034,
-0.02032751962542534,
0.006609878037124872,
0.05660184845328331,
0.04553123936057091,
0.023164015263319016,
-0.04108181968331337,
0.022150440141558647,
0.02041381038725376,
0.01208093948662281,
-0.03787803649902344,
-0.015478909015655518,
-0.05732211843132973,
-0.021151909604668617,
-0.02259080484509468,
-0.037064068019390106,
-0.016676167026162148,
-0.026341918855905533,
0.007608881685882807,
-0.04023546352982521,
0.023964380845427513,
0.029584554955363274,
0.009537226520478725,
0.016731172800064087,
0.029414566233754158,
0.054271697998046875,
0.017487820237874985,
0.08086398988962173,
0.08428307622671127,
-0.045886434614658356,
-0.004489563871175051,
0.008727624081075191,
-0.028785662725567818,
-0.022782955318689346,
0.026591813191771507,
-0.029886947944760323,
0.021256225183606148,
-0.030012017115950584,
-0.004969757981598377,
-0.016867682337760925,
0.016224637627601624,
0.009895909577608109,
-0.045611508190631866,
0.038443513214588165,
-0.001083906157873571,
-0.01377256028354168,
-0.04980658367276192,
0.04980694130063057,
0.05385327339172363,
0.006239990703761578,
0.07064329832792282,
0.02742842026054859,
-0.006849587894976139,
0.009341872297227383,
0.020752202719449997,
-0.046969298273324966,
-0.01742824725806713,
0.04513687640428543,
-0.03883926942944527,
0.03013649210333824,
-0.06226610764861107,
-0.019952209666371346,
-0.04846230894327164,
0.028423311188817024,
0.012421884573996067,
0.004994862712919712,
0.002278560772538185,
0.021784765645861626,
0.006614611484110355,
0.028361402451992035,
0.019177431240677834,
0.047319430857896805,
-0.01237451285123825,
-0.06323685497045517,
-0.032532043755054474,
-0.02436174638569355,
-0.045535892248153687,
0.019909875467419624,
-0.014921756461262703,
-0.02728196233510971,
0.0680498406291008,
0.010586535558104515,
-0.07944109290838242,
-0.02234696038067341,
0.028224052861332893,
-0.0050610387697815895,
-0.009224160574376583,
0.06297988444566727,
0.10143860429525375,
0.006465644109994173,
0.06078213453292847,
0.007278777193278074,
-0.02287602610886097,
-0.04718828201293945,
0.018943507224321365,
-0.018803957849740982,
0.0488075315952301,
0.04362192004919052,
-0.0009582610218785703,
-0.04296617582440376,
-0.0031389629002660513,
-0.033011846244335175,
0.00008847950084600598,
-0.05008581653237343,
0.04852553829550743,
0.016253329813480377,
0.03491239994764328,
-0.031143520027399063,
-0.04493436589837074,
0.0002492970088496804,
-0.02662518061697483,
-0.0187419094145298,
0.08821025490760803,
0.019358191639184952,
0.031156692653894424,
-0.0021662525832653046,
-0.013322541490197182,
0.027513699606060982,
-0.03498652204871178,
-0.013098165392875671,
-0.017087535932660103,
0.018915118649601936,
0.00523074995726347,
-0.04590277373790741,
-0.025691602379083633,
-0.007757870946079493,
-0.00789590086787939,
-0.044891972094774246,
0.001700912369415164,
-0.011501161381602287,
0.03512675687670708,
-0.019307052716612816,
-0.009713901206851006,
-0.07330166548490524,
-0.028327113017439842,
-0.03895840793848038,
-0.05047639459371567,
0.007092929910868406,
-0.021586060523986816,
-0.028585055842995644,
0.041284117847681046,
-0.033469945192337036,
0.04005323350429535,
-0.004333156626671553,
-0.014328415505588055,
-0.04634480178356171,
0.09492089599370956,
0.009134667925536633,
0.04952871799468994,
-0.021490557119250298,
0.003543713828548789,
-0.007279004901647568,
0.07015103101730347,
0.07494323700666428,
-0.0016943513182923198,
-0.05628344789147377,
-0.00931627955287695,
0.02529054693877697,
-0.003311910666525364,
-0.0026335977017879486,
-0.02152751386165619,
-0.03248339518904686,
0.03019212745130062,
0.010985182598233223,
0.023753121495246887,
0.0013701807474717498,
-0.08887755125761032,
0.0028903475031256676,
-0.016713570803403854,
0.0015928464708849788,
0.028288044035434723,
0.04318677634000778,
0.02623085118830204,
-0.05304570868611336,
0.01985161006450653,
-0.026570258662104607,
-0.00005081822746433318,
0.07761337608098984,
0.0371847003698349,
-0.03831048682332039,
-0.01726459339261055,
0.0029894812032580376,
-0.01588055118918419,
-0.00766179570928216,
-0.016370777040719986,
-0.008684941567480564,
0.061279069632291794,
-0.034074053168296814,
0.026270205155014992,
0.011774915270507336,
0.061575599014759064,
0.02010895125567913,
0.004906514659523964,
0.014420276507735252,
-0.0036682302597910166,
0.04413164407014847,
0.006370972841978073,
-0.00889244768768549,
-0.03152906149625778,
0.009724807925522327,
-0.002850467571988702,
0.012650628574192524,
0.04644251987338066,
-0.02865651436150074,
0.0316801592707634,
-0.018997536972165108,
-0.09400007128715515,
0.02913404069840908,
0.047709811478853226,
-0.0413220152258873,
-0.04642697051167488,
-0.005409275181591511,
0.050483644008636475,
0.02157013863325119,
0.024892287328839302,
0.02749125473201275,
-0.028426744043827057,
0.052594639360904694,
0.003931319806724787,
0.03411194682121277,
-0.06098092719912529,
-0.016149673610925674,
-0.013296842575073242,
0.03242826834321022,
0.0365920215845108,
0.03002019226551056,
-0.04003072530031204,
-0.04239508509635925,
0.012201479636132717,
-0.03998195379972458,
0.02369796857237816,
-0.03021944873034954,
-0.023893335834145546,
0.00476970337331295,
0.05436626076698303,
0.009709871374070644,
-0.032973989844322205,
0.01817629113793373,
0.016573743894696236,
-0.030092541128396988,
-0.034089718014001846,
0.04345302656292915,
0.015830108895897865,
0.055048927664756775,
-0.01925540901720524,
0.031819574534893036,
-0.016110336408019066,
-0.05621876195073128,
0.02105644717812538,
-0.031683530658483505,
-0.08324633538722992,
-0.03840193897485733,
-0.013769791461527348,
0.04655463248491287,
0.015574443154036999,
-0.012079525738954544,
-0.04849351942539215,
0.05893212929368019,
-0.06488647311925888,
-0.07267720997333527,
0.04063038155436516,
-0.0182611346244812,
0.016939444467425346,
0.005195322446525097,
0.024041302502155304,
-0.01359950378537178,
0.04059029743075371,
-0.021427514031529427,
-0.003766557900235057,
0.034628815948963165,
-0.009657179936766624,
0.030503569170832634,
0.001391350757330656,
-0.011431648395955563,
0.019795475527644157,
-0.04003727063536644,
0.02956072799861431,
-0.033386413007974625,
-0.05072300508618355,
0.012774213217198849,
-0.014451528899371624,
-0.1039666160941124,
-0.026157166808843613,
-0.027479056268930435,
0.009401978924870491,
-0.0713820606470108,
0.008152985945343971,
-0.017651814967393875,
-0.003031101543456316,
-0.020832279697060585,
-0.06720351427793503,
0.0207227673381567,
0.018228458240628242,
-0.014920031651854515,
0.010008287616074085,
-0.03007403016090393,
-0.004349424038082361,
-0.06024802476167679,
-0.024438735097646713,
-0.022535143420100212,
0.030856452882289886,
-0.013195434585213661,
-0.04437322914600372,
0.0048129078932106495,
-0.010369446128606796,
0.04357634484767914,
0.015183303505182266,
-0.04379056394100189,
0.0562412403523922,
0.004029016010463238,
-0.0470893532037735,
-0.025709599256515503,
-0.040863849222660065,
-0.026447968557476997,
-0.0015813491772860289,
-0.023821357637643814,
-0.04359516128897667,
-0.006151885259896517,
0.00200723041780293,
-0.06724465638399124,
0.10320126265287399,
0.0033009694889187813,
-0.008531277999281883,
-0.041625745594501495,
-0.01959768496453762,
0.019031178206205368,
-0.045758914202451706,
0.0008903156849555671,
-0.029617242515087128,
0.04443155229091644,
-0.03666176274418831,
-0.02409806288778782,
0.036808617413043976,
-0.0025258567184209824,
0.07506850361824036,
-0.015684224665164948,
0.0571751706302166,
0.10468203574419022,
0.016531160101294518,
0.006524769123643637,
-0.0053986371494829655,
0.004020813386887312,
0.0022470883559435606,
-0.01355360820889473,
-0.02124420925974846,
-0.03855151683092117,
-0.007504167500883341,
-0.07209030538797379,
0.05073702335357666,
0.02483495883643627,
0.0247498769313097,
-0.029993023723363876,
0.049504414200782776,
-0.04916485771536827,
-0.00833937432616949,
-0.0457725003361702,
-0.015180693939328194,
-0.007501323241740465,
-0.011889379471540451,
-0.06595409661531448,
0.013244514353573322,
0.038479141891002655,
0.009362507611513138,
0.0301788542419672,
-0.016534579917788506,
0.039182305335998535,
-0.018533235415816307,
0.09032940864562988,
-0.0413183756172657,
0.030932364985346794,
-0.016951536759734154,
0.025174580514431,
0.01621910184621811,
-0.0037190334405750036,
0.06818938255310059,
0.004858385305851698,
-0.006619253195822239,
0.06482648104429245,
0.02768479473888874,
-0.0273798406124115,
-0.015725523233413696,
-0.00828872062265873,
0.09590524435043335,
0.06798060983419418,
-0.042339276522397995,
0.028300154954195023,
-0.017300494015216827,
-0.04154299572110176,
0.04714929684996605,
-0.018411552533507347,
-0.02172417938709259,
0.026211079210042953,
-0.004819149617105722,
-0.007141346111893654,
0.012227232567965984,
0.005174357444047928,
0.008370636031031609,
-0.024774916470050812,
0.00051252351840958,
-0.071759432554245,
-0.015957606956362724,
0.045217934995889664,
-0.0015328559093177319,
0.0028932131826877594,
-0.09789085388183594,
-0.029485337436199188,
-0.030876481905579567,
0.013807599432766438,
-0.0362800732254982,
0.03765062615275383,
-0.0032217013649642467,
-0.023643868044018745,
0.03185933455824852,
0.024510079994797707,
0.003410548670217395,
0.03368518501520157,
-0.028344662860035896,
-0.03445854410529137,
0.04812858626246452,
-0.016823092475533485,
-0.02883201651275158,
-0.003108408534899354,
0.020341111347079277,
0.021165551617741585,
0.03666730970144272,
-0.07857669144868851,
0.0064672366715967655,
-0.006105698645114899,
-0.04909210652112961,
0.020509960129857063,
0.033406611531972885,
0.07699912786483765,
0.02020140178501606,
0.03239098936319351,
-0.05149059742689133,
0.02072218619287014,
0.005009486805647612,
-0.03959169611334801,
-0.04185041785240173,
0.017806435003876686,
-0.025615138933062553,
0.00487433560192585,
-0.015767822042107582,
0.016061557456851006,
0.027560915797948837,
0.021739182993769646,
0.06539072841405869,
-0.026891939342021942,
-0.008080868981778622,
-0.024053355678915977,
-0.01718294993042946,
-0.011372258886694908,
0.016048705205321312,
-0.006224806420505047,
-0.06393162906169891,
0.003089058678597212,
0.021708689630031586,
-0.017191065475344658,
-0.010912255384027958,
-0.01497011911123991,
0.060298334807157516,
-0.007001468911767006,
-0.05126571282744408,
-0.016914881765842438,
-0.0306549109518528,
0.08624494820833206,
-0.04798855632543564,
0.006424418650567532,
-0.059397585690021515,
0.0009940739255398512,
-0.03200097009539604,
-0.03614666685461998,
0.014916191808879375,
-0.083035908639431,
-0.000737422495149076,
-0.0053143370896577835,
-0.07074499875307083,
0.014097479172050953,
-0.025948751717805862,
0.03281724452972412,
0.0023738862946629524,
0.0061952234245836735,
0.005899571347981691,
0.015112477354705334,
-0.013583432883024216,
0.02867610938847065,
0.015250029973685741,
-0.0210039671510458,
0.04616588354110718,
0.03879425674676895,
0.08357307314872742,
-0.014859158545732498,
0.032434798777103424,
0.010471661575138569,
0.028725650161504745,
0.014004768803715706,
-0.0003510896931402385,
0.003539087949320674,
-0.01587652787566185,
0.05261602997779846
] |
[
13.169379234313965,
0.7071853280067444
] |
High Energy Physics - Theory
|
General Physics
|
hep-th
|
na
|
na
|
2007-04-01T13:10:43
|
We give a quantitative analysis of clustering in a stochastic model of
one-dimensional gas. At time zero, the gas consists of $n$ identical particles
that are randomly distributed on the real line and have zero initial speeds.
Particles begin to move under the forces of mutual attraction. When particles
collide, they stick together forming a new particle, called cluster, whose mass
and speed are defined by the laws of conservation. We are interested in the
asymptotic behavior of $K_n(t)$ as $n\to \infty$, where $K_n(t)$ denotes the
number of clusters at time $t$ in the system with $n$ initial particles. Our
main result is a functional limit theorem for $K_n(t)$. Its proof is based on
the discovered localization property of the aggregation process, which states
that the behavior of each particle is essentially defined by the motion of
neighbor particles.
|
Clustering in a stochastic model of one-dimensional gas
|
math.PR
|
0704.0086
| 2,007
|
[
0.0033293128944933414,
0.054471660405397415,
-0.00602791178971529,
-0.021986622363328934,
0.04863662272691727,
0.004362062085419893,
0.007879218086600304,
0.003209614660590887,
-0.048365961760282516,
0.029929451644420624,
-0.05172426626086235,
0.02373955212533474,
0.02623567543923855,
0.04358242079615593,
-0.0016115230973809958,
-0.028155911713838577,
0.04610329121351242,
0.00001400552810082445,
-0.0267025213688612,
0.04430754855275154,
-0.017706209793686867,
-0.00733187748119235,
-0.005608821753412485,
-0.024810397997498512,
0.09783448278903961,
0.006457103416323662,
0.03482046350836754,
-0.0024707671254873276,
-0.027792654931545258,
-0.006698744371533394,
0.049133963882923126,
-0.017805321142077446,
-0.022724196314811707,
-0.0886612981557846,
-0.02263471856713295,
-0.0755302682518959,
0.06588257849216461,
-0.06935685873031616,
0.026773961260914803,
0.01853027567267418,
0.09080684930086136,
0.006930680945515633,
0.03908247873187065,
-0.04966186732053757,
0.027385111898183823,
0.06466394662857056,
0.03814905509352684,
0.01468910463154316,
0.05686836689710617,
0.017139041796326637,
-0.026551200076937675,
0.04402359202504158,
-0.05748824030160904,
-0.036578219383955,
-0.020288847386837006,
0.007761070504784584,
0.031043563038110733,
0.0012287325225770473,
0.04859478771686554,
0.03914467617869377,
0.05894366651773453,
0.04239414259791374,
-0.03772468864917755,
-0.004166702274233103,
0.05321912840008736,
-0.04482990503311157,
-0.02637390047311783,
0.046369049698114395,
0.038877956569194794,
-0.0297501552850008,
0.037125248461961746,
0.015553724952042103,
0.010979829356074333,
0.024708131328225136,
-0.03807695955038071,
0.037555549293756485,
-0.003986079711467028,
0.00008850207814248279,
-0.052231088280677795,
0.039656784385442734,
-0.012787164188921452,
0.004362933337688446,
0.00004482296935748309,
-0.0006689721485599875,
0.07371503114700317,
-0.007766542956233025,
0.016879672184586525,
0.011535816825926304,
-0.04530579224228859,
0.034479331225156784,
0.03267510235309601,
0.011775776743888855,
0.042735859751701355,
0.039141323417425156,
-0.03805916756391525,
-0.002752806292846799,
-0.058579713106155396,
0.034772343933582306,
-0.03772464022040367,
-0.043974727392196655,
-0.012090585194528103,
0.05318615213036537,
0.007146794348955154,
-0.03320695832371712,
0.07654270529747009,
-0.005718687083572149,
-0.024661466479301453,
0.03973107412457466,
-0.0009375616209581494,
-0.0612974651157856,
-0.0410931296646595,
-0.008452643640339375,
-0.02151038683950901,
-0.04833437502384186,
-0.03035755455493927,
-0.023138366639614105,
0.037757616490125656,
-0.0421949066221714,
-0.014493209309875965,
0.03182029724121094,
0.02704302966594696,
-0.0273318812251091,
0.013755527324974537,
-0.010204251855611801,
-0.007198828272521496,
0.006635879632085562,
-0.01916871778666973,
0.00806436687707901,
-0.008250911720097065,
-0.030419254675507545,
-0.029521210119128227,
-0.0006290563032962382,
-0.003473549848422408,
-0.03407110273838043,
-0.014896895736455917,
0.020588915795087814,
-0.04541044309735298,
-0.010843470692634583,
0.038167212158441544,
0.0005836820928379893,
-0.004342027008533478,
-0.027476757764816284,
0.03252914920449257,
0.0035518305376172066,
-0.05444888398051262,
-0.04418995976448059,
-0.0015058311400935054,
-0.057885557413101196,
-0.029419057071208954,
-0.04122615233063698,
-0.021975604817271233,
0.053320784121751785,
-0.03227389603853226,
0.024244939908385277,
0.007258026394993067,
-0.05134836211800575,
-0.00132352439686656,
0.03446093201637268,
0.07207363843917847,
-0.03748241066932678,
0.025907067582011223,
0.019503172487020493,
0.0027950690127909184,
0.034341953694820404,
-0.0820419192314148,
-0.0001792806724552065,
0.028776099905371666,
0.005351448897272348,
0.02172546647489071,
0.031187308952212334,
-0.05566805973649025,
-0.06300916522741318,
-0.05613759532570839,
0.009232494980096817,
-0.02189496159553528,
-0.004270480014383793,
-0.04029840603470802,
-0.07777658849954605,
0.010285632684826851,
-0.009828442707657814,
0.11242280900478363,
-0.07316768914461136,
0.02550004981458187,
0.029530106112360954,
0.03504907712340355,
0.016751520335674286,
-0.014717401005327702,
0.007034203968942165,
-0.05274286866188049,
-0.051036082208156586,
0.023612478747963905,
0.02861279807984829,
-0.0384235754609108,
-0.018326662480831146,
0.025908660143613815,
0.003600550815463066,
0.05570005625486374,
-0.06586109846830368,
-0.0022589205764234066,
-0.07081564515829086,
-0.015721391886472702,
0.005489264149218798,
-0.01280955784022808,
0.038280270993709564,
0.017751779407262802,
0.03593168780207634,
-0.0033026295714080334,
0.0377790741622448,
-0.009451525285840034,
0.02679547108709812,
0.04063766077160835,
0.014869448728859425,
0.01040584221482277,
0.030848847702145576,
0.012208989821374416,
-0.0006976310978643596,
0.027185143902897835,
-0.012755205854773521,
0.03185780718922615,
0.007119595538824797,
-0.01577022299170494,
-0.04257091134786606,
-0.015048268251121044,
0.025618460029363632,
0.07639338076114655,
-0.012422680854797363,
-0.013977032154798508,
-0.0402429960668087,
-0.05124910548329353,
0.03157332167029381,
-0.030990250408649445,
0.002755829831585288,
0.029682213440537453,
-0.003024834906682372,
-0.02153906598687172,
0.03277409449219704,
-0.022441089153289795,
0.025359198451042175,
0.04915916174650192,
0.0018676550826057792,
0.0003768601454794407,
-0.02789582498371601,
-0.0013873260468244553,
-0.04101124405860901,
-0.03959066420793533,
-0.022811144590377808,
-0.009881881065666676,
-0.01811867207288742,
-0.026602644473314285,
0.009023508056998253,
0.014911497943103313,
0.030480630695819855,
0.06071872636675835,
-0.007679385133087635,
0.08360417932271957,
-0.0162405613809824,
-0.033235982060432434,
0.08540716022253036,
-0.0009730316232889891,
-0.06623384356498718,
0.037018582224845886,
-0.029851578176021576,
0.021700195968151093,
-0.0768827274441719,
-0.04707133397459984,
0.002377545228227973,
0.03621719032526016,
-0.025148889049887657,
-0.0047539835795760155,
-0.04678313806653023,
-0.016549119725823402,
0.02317449450492859,
0.07871097326278687,
0.09054093062877655,
-0.013117126189172268,
0.04706728830933571,
0.02153570018708706,
-0.03731165826320648,
0.004082510247826576,
-0.0012221077922731638,
-0.05860500410199165,
0.00700381537899375,
-0.05079217627644539,
-0.04577361419796944,
-0.013374889269471169,
-0.0020120686385780573,
0.062373388558626175,
-0.025772634893655777,
0.02560531720519066,
-0.002616846701130271,
-0.017934931442141533,
0.02125171385705471,
0.09371936321258545,
0.09146061539649963,
0.033941976726055145,
0.12565027177333832,
0.054466914385557175,
0.010870566591620445,
0.005548621993511915,
0.043709948658943176,
-0.06472451239824295,
0.012276995927095413,
0.013351468369364738,
0.013274108991026878,
0.03741573169827461,
0.043742310255765915,
-0.023591285571455956,
-0.006153611931949854,
-0.01368637289851904,
0.0024961999151855707,
0.029184997081756592,
0.0812189057469368,
-0.01602333039045334,
-0.0378270223736763,
-0.05017860606312752,
0.031310513615608215,
0.03817938640713692,
0.03251374140381813,
0.03150947019457817,
-0.004254343453794718,
0.012243016622960567,
-0.05402866005897522,
0.03899453952908516,
-0.07996664941310883,
0.047953493893146515,
0.0054168994538486,
-0.033638954162597656,
-0.01399835105985403,
0.023526780307292938,
-0.000470689992653206,
-0.015694506466388702,
-0.011410698294639587,
-0.013037961907684803,
-0.04692469537258148,
-0.04678087681531906,
-0.038671474903821945,
-0.051807403564453125,
0.01415857020765543,
-0.01858045905828476,
0.03883102536201477,
-0.027147619053721428,
-0.020317314192652702,
-0.031198566779494286,
-0.015814291313290596,
-0.02756698802113533,
0.021598294377326965,
0.018369486555457115,
0.008007417432963848,
0.05811598524451256,
0.034287407994270325,
-0.008989917114377022,
-0.038515008985996246,
0.03443186730146408,
-0.014522436074912548,
-0.029645543545484543,
0.02109682373702526,
0.03496042266488075,
-0.0608983039855957,
0.050925496965646744,
-0.012888842262327671,
0.0018604949582368135,
-0.06250806897878647,
0.006334926933050156,
0.05722135305404663,
0.023078657686710358,
0.004170750267803669,
-0.013620893470942974,
0.012472923845052719,
0.044634509831666946,
-0.027961110696196556,
-0.05034051090478897,
-0.04955844208598137,
0.04543539509177208,
0.06565885245800018,
0.06918603181838989,
-0.007660728879272938,
-0.037359148263931274,
0.010845078155398369,
0.02491990104317665,
-0.018758907914161682,
0.067303366959095,
0.0038656010292470455,
0.019883278757333755,
-0.017304835841059685,
0.002710116095840931,
0.04205100238323212,
-0.04259496554732323,
-0.040615059435367584,
-0.02430468238890171,
-0.013423517346382141,
-0.012476840056478977,
-0.053638264536857605,
-0.019065896049141884,
-0.0029411271680146456,
0.004178429022431374,
-0.025176964700222015,
0.05514872446656227,
-0.013038866221904755,
0.013737206347286701,
0.011049086228013039,
0.0027182416524738073,
-0.055736999958753586,
-0.0446481816470623,
-0.07096197456121445,
0.042626768350601196,
-0.0012076246784999967,
0.005874954629689455,
-0.03779323399066925,
0.05405457690358162,
-0.03570687398314476,
-0.0130089670419693,
0.010309615172445774,
0.009834728203713894,
-0.04307543858885765,
0.06590664386749268,
-0.0003248505818191916,
0.039129626005887985,
-0.005896781571209431,
-0.022638211026787758,
-0.016492711380124092,
-0.014648842625319958,
0.01730809547007084,
-0.03605296462774277,
-0.03783521428704262,
-0.029960237443447113,
-0.011449215933680534,
0.022710973396897316,
0.05494514852762222,
-0.03323816508054733,
-0.08366862684488297,
0.011954361572861671,
-0.006793604232370853,
-0.027071986347436905,
0.04011872410774231,
-0.0716196745634079,
0.02087961509823799,
0.06511396169662476,
0.00031636652420274913,
-0.01606861501932144,
0.08993107080459595,
0.02087080478668213,
-0.015530337579548359,
0.0036768969148397446,
0.03114291839301586,
0.05953766778111458,
0.09846477210521698,
0.04423920810222626,
-0.027144163846969604,
-0.052296269685029984,
-0.003610355779528618,
0.056195974349975586,
0.011566122062504292,
-0.031430888921022415,
-0.038903187960386276,
0.06936252117156982,
-0.02222069725394249,
-0.06111152097582817,
0.02537211775779724,
0.05263042077422142,
0.05426871404051781,
-0.008378374390304089,
0.032754529267549515,
0.0073042092844843864,
0.017079729586839676,
-0.03524528816342354,
-0.04997307062149048,
0.034686096012592316,
0.0017741464544087648,
0.017229346558451653,
0.0463847853243351,
-0.0023346375674009323,
-0.0035312818363308907,
0.006577631458640099,
-0.007079887203872204,
-0.003276735544204712,
-0.008871321566402912,
0.05943365767598152,
0.0055765132419764996,
0.04473404213786125,
-0.005116721149533987,
0.02822265960276127,
-0.009998318739235401,
0.0033593829721212387,
-0.016386955976486206,
-0.025062374770641327,
0.029454069212079048,
0.014392878860235214,
-0.004496543202549219,
0.02556348778307438,
-0.030053436756134033,
-0.012303764931857586,
0.042872749269008636,
0.01039817277342081,
0.0027292242739349604,
0.00271278596483171,
-0.04155607894062996,
0.0038615644443780184,
-0.013545430265367031,
0.0030045208986848593,
-0.00302093755453825,
-0.010901850648224354,
-0.024273687973618507,
-0.01586219295859337,
-0.03440352901816368,
-0.010783190838992596,
0.06583913415670395,
-0.02192579209804535,
-0.04449376091361046,
-0.0019684515427798033,
0.03245105594396591,
0.01384953036904335,
0.07618184387683868,
0.06072058156132698,
0.0496896356344223,
0.0053870840929448605,
-0.030166808515787125,
-0.0004790303355548531,
-0.005836046300828457,
-0.06463417410850525,
-0.00505967577919364,
0.04590326547622681,
-0.00395235838368535,
-0.04541544243693352,
0.02457413077354431,
-0.05064208060503006,
0.006336884573101997,
-0.05899374186992645,
-0.03233505040407181,
0.03582148626446724,
0.01618058979511261,
0.015013772062957287,
-0.02447778545320034,
-0.03786103427410126,
-0.030827922746539116,
0.01977423019707203,
0.02064325660467148,
-0.017406217753887177,
0.040985796600580215,
0.035140737891197205,
0.006822315976023674,
-0.03404084965586662,
-0.013474185951054096,
0.0033745206892490387,
-0.018576672300696373,
0.0246213860809803,
-0.017106669023633003,
-0.07859519124031067,
0.038526248186826706,
0.02696806937456131,
-0.02414589747786522,
0.052981261163949966,
-0.011588032357394695,
0.019701920449733734,
-0.09665590524673462,
0.038718078285455704,
-0.013943462632596493,
0.0004737221170216799,
-0.031444333493709564,
-0.0669049471616745,
-0.00014247083163354546,
-0.035653840750455856,
0.0025744130834937096,
0.04317671060562134,
0.014073901809751987,
0.03526114299893379,
-0.10917963087558746,
-0.07696810364723206,
-0.00042918516555801034,
0.03793416917324066,
-0.018447568640112877,
0.027847956866025925,
-0.03560984134674072,
0.034152716398239136,
0.04735802114009857,
0.02994246408343315,
-0.05572497844696045,
0.009263049811124802,
-0.0028323279693722725,
-0.04661707952618599,
0.03222893178462982,
-0.030485840514302254,
-0.02719227410852909,
0.04053088277578354,
-0.031162234023213387,
-0.01345226913690567,
-0.0015785843133926392,
-0.012844158336520195,
-0.0531107634305954,
0.06925518065690994,
0.005350066814571619,
0.027865100651979446,
-0.03886125236749649,
-0.038119927048683167,
-0.026925094425678253,
-0.06550239026546478,
-0.04503299295902252,
-0.02614971436560154,
-0.045904386788606644,
-0.04528447240591049,
-0.02473200112581253,
-0.04486322030425072,
0.016609404236078262,
0.05781371146440506,
0.007380781229585409,
-0.011175189167261124,
0.050613097846508026,
-0.03639083355665207,
-0.0013440261827781796,
-0.0023087821900844574,
0.04113562032580376,
0.00832823384553194,
0.002963910810649395,
-0.017889423295855522,
-0.026887256652116776,
0.037401873618364334,
-0.010409158654510975,
0.06172090768814087,
-0.015272766351699829,
0.03629400581121445,
-0.0792820006608963,
0.036282677203416824,
-0.039936766028404236,
0.023828810080885887,
-0.07792419195175171,
0.007489705458283424,
-0.02582927793264389,
-0.017402781173586845,
-0.0663876160979271,
0.023193320259451866,
0.056383516639471054,
0.019735222682356834,
-0.003539120778441429,
-0.054859623312950134,
-0.016583465039730072,
-0.018971966579556465,
0.005376341287046671,
-0.05106913670897484,
0.028952553868293762,
0.015043351799249649,
0.030218323692679405,
-0.007546478416770697,
-0.018477803096175194,
-0.02901178039610386,
0.040941547602415085,
0.03484100103378296,
0.015171159990131855,
0.016189366579055786,
0.03192991390824318,
-0.029747072607278824,
-0.03003602661192417,
0.026362286880612373,
0.08232242614030838,
-0.034750133752822876,
0.054489657282829285,
0.007652895525097847,
-0.005301293451339006,
0.004016645718365908,
0.011380151845514774,
-0.029342692345380783,
-0.035461463034152985,
-0.04231254383921623,
-0.034546758979558945,
-0.001569276675581932,
-0.029851559549570084,
0.015352142974734306,
0.0322478823363781,
-0.014910541474819183,
-0.041578955948352814,
-0.0325898602604866,
-0.05352696031332016,
0.030068298801779747,
-0.02379046194255352,
-0.019927185028791428,
-0.050275128334760666,
-0.01609315164387226,
0.025976527482271194,
0.01288997195661068,
0.031200159341096878,
0.014849399216473103,
0.010014117695391178,
0.017490744590759277,
0.0017194664105772972,
0.011454564519226551,
0.012992359697818756,
-0.0037612870801240206,
0.026887083426117897,
-0.005441100802272558,
-0.025948476046323776,
-0.06358411908149719,
-0.07028460502624512,
0.015623306855559349,
0.009825976565480232,
-0.005277787335216999,
-0.06023001670837402,
-0.0007688390323892236,
0.00735887186601758,
-0.040480539202690125,
-0.026517467573285103,
-0.02249625325202942,
0.0690290778875351,
0.00430305115878582,
0.019563591107726097,
0.007534863892942667,
0.02288523130118847,
0.005421813111752272,
-0.03536413237452507,
0.005322182085365057,
-0.03149974346160889,
0.014553449116647243,
0.005150815472006798,
0.012166020460426807,
0.04836387187242508,
0.033468350768089294,
0.01627378910779953,
0.038759298622608185,
-0.04100806266069412,
-0.037335678935050964,
-0.04581926763057709,
0.03190650790929794,
0.013122768141329288,
0.022203661501407623,
0.004792083520442247,
-0.025588711723685265,
0.006350289564579725,
-0.011698806658387184,
-0.03656598553061485,
0.005223988555371761,
0.002466000383719802,
0.044050343334674835,
-0.012764046899974346,
-0.03156137466430664,
0.015604695305228233,
-0.06377257406711578,
0.024215811863541603,
-0.015826569870114326,
0.03182253614068031,
0.023993583396077156,
0.011034592054784298,
-0.06621477752923965,
-0.010033465921878815,
-0.03835807740688324,
-0.054976850748062134,
0.034301403909921646,
0.020712414756417274,
-0.04813070595264435,
-0.026183895766735077,
-0.025322366505861282,
-0.004392010625451803,
0.05119242146611214,
0.007748125120997429,
0.005415707360953093,
-0.04332992061972618,
0.03050895780324936,
0.010484266094863415,
0.01804383285343647,
0.002872573211789131,
0.03758041560649872,
0.04100633040070534,
0.03432931751012802,
-0.008303370326757431,
-0.012053404003381729,
-0.011790608987212181,
0.007055825088173151,
0.07281645387411118,
0.01137254387140274,
0.005946793127804995,
0.007889597676694393,
0.008168645203113556
] |
[
6.032179355621338,
4.498028755187988
] |
Probability
|
Mathematics
|
math-PR
|
na
|
na
|
2007-04-01T13:44:50
|
Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic
spaces of dimensional $m$ and $n$ corresponding, and given a Holder function
$f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries
of $H^m$ and $H^n$. Then for each $\epsilon >0$ there exists a harmonic map
$u:H^m\to H^n$ which is continuous up to the boundary (in the sense of
Euclidean) and $u|_{\partial H^m}=(f^1,...,f^{n-1},\epsilon)$.
|
Approximate solutions to the Dirichlet problem for harmonic maps between
hyperbolic spaces
|
math.DG
|
0704.0087
| 2,007
|
[
0.023763274773955345,
-0.00493727857246995,
-0.0036742857191711664,
0.013952391222119331,
0.04082602635025978,
0.021941596642136574,
0.00904844794422388,
0.014543900266289711,
-0.08489619195461273,
-0.0145108075812459,
-0.03233214467763901,
-0.006718674208968878,
-0.001275225542485714,
0.024309653788805008,
0.007534387055784464,
-0.06938867270946503,
0.06259702146053314,
-0.017604511231184006,
-0.043850693851709366,
0.008049191907048225,
-0.054036203771829605,
-0.005571397021412849,
-0.01730576902627945,
-0.049004413187503815,
0.057006899267435074,
0.0010392070980742574,
0.049426279962062836,
-0.027631454169750214,
-0.024255964905023575,
-0.049379702657461166,
-0.006886097602546215,
-0.0643475130200386,
0.024055996909737587,
-0.03892016410827637,
-0.05613454058766365,
0.009731950238347054,
0.07392054796218872,
0.013802731409668922,
0.04349998012185097,
0.02012179233133793,
0.09440218657255173,
-0.03002636507153511,
0.00675998954102397,
-0.002537158550694585,
0.02424788475036621,
0.008190000429749489,
-0.022203724831342697,
0.046722229570150375,
0.04819503054022789,
0.05033000558614731,
-0.012749189510941505,
0.025987394154071808,
-0.04353688657283783,
-0.05342966318130493,
-0.033263999968767166,
0.00021301531523931772,
0.025627754628658295,
-0.033082980662584305,
0.0326337032020092,
-0.04350046068429947,
-0.00725207244977355,
0.03581290319561958,
-0.03071419894695282,
0.034754373133182526,
0.0001772386021912098,
-0.03403456136584282,
-0.0351526252925396,
-0.017204005271196365,
0.01237171608954668,
-0.07106610387563705,
0.03192776441574097,
0.004766263999044895,
0.07017315924167633,
0.021231340244412422,
-0.048086781054735184,
-0.02311372384428978,
0.026569023728370667,
-0.03260010853409767,
-0.008382914587855339,
0.021025400608778,
0.030393138527870178,
0.018278827890753746,
0.030819794163107872,
0.0061660935170948505,
0.04331241175532341,
0.051895152777433395,
0.05776095762848854,
0.025935586541891098,
-0.06648503988981247,
0.020597539842128754,
-0.015196512453258038,
-0.03341090306639671,
0.0011191141093149781,
0.07486201822757721,
-0.004173691384494305,
-0.007762860972434282,
-0.0305109191685915,
-0.004648169502615929,
-0.004017848055809736,
-0.10165958106517792,
-0.003909552004188299,
0.0004810522950720042,
0.03666596859693527,
0.017205877229571342,
0.05261730030179024,
-0.004831216763705015,
0.05417316034436226,
0.007899263873696327,
-0.011265839450061321,
-0.03531155735254288,
-0.03110894374549389,
-0.0020610790234059095,
0.02058076672255993,
-0.06339827924966812,
0.0007293227827176452,
-0.055774956941604614,
0.053891364485025406,
-0.057910382747650146,
-0.007297322154045105,
0.09828601032495499,
0.040017545223236084,
0.020231647416949272,
0.016542470082640648,
0.01931975595653057,
0.05435295030474663,
0.0582471564412117,
-0.06114080548286438,
-0.04041479155421257,
0.016878165304660797,
-0.014032451435923576,
0.01036912016570568,
0.04123016074299812,
0.03338206186890602,
-0.006563103757798672,
0.03708167374134064,
0.02748323231935501,
-0.008519548922777176,
-0.0352352075278759,
0.007553029805421829,
0.004366183653473854,
-0.005307819694280624,
-0.0411575548350811,
0.04634541645646095,
0.00034766754833981395,
-0.02319338358938694,
0.003407929325476289,
0.05331231281161308,
-0.09375383704900742,
-0.05257657542824745,
0.012016710825264454,
0.009996612556278706,
0.07054081559181213,
0.03183571621775627,
0.07049839943647385,
-0.03049652837216854,
0.039018772542476654,
0.032141637057065964,
-0.0019457435701042414,
0.0244947150349617,
-0.028290916234254837,
-0.016277942806482315,
0.037244763225317,
-0.006947564892470837,
-0.003969565033912659,
-0.025512685999274254,
-0.023607058450579643,
-0.03941711038351059,
-0.007001007907092571,
-0.025473210960626602,
0.038043197244405746,
-0.06271950900554657,
0.00720905652269721,
-0.006307165138423443,
0.03188757970929146,
0.05459596589207649,
-0.004931617062538862,
-0.00040763558354228735,
-0.036271050572395325,
0.037733957171440125,
0.017161209136247635,
0.03822354972362518,
-0.028400490060448647,
0.04289380833506584,
0.021022286266088486,
0.03906157985329628,
0.06892676651477814,
-0.007921326905488968,
-0.05546555668115616,
-0.04298591613769531,
0.0026415216270834208,
-0.007421586662530899,
0.03509030491113663,
-0.014488630928099155,
-0.03523387759923935,
0.01939990557730198,
0.026336150243878365,
0.030565014109015465,
-0.04720939323306084,
0.005718071945011616,
-0.008271325379610062,
0.010972242802381516,
-0.018184810876846313,
0.031508516520261765,
-0.01581963151693344,
0.001982502406463027,
0.07000041753053665,
0.010714990086853504,
-0.024798976257443428,
0.01977263204753399,
-0.023142706602811813,
0.05726393684744835,
-0.020927470177412033,
-0.012588152661919594,
-0.011435842141509056,
-0.021764034405350685,
-0.03602122515439987,
-0.024668479338288307,
-0.031743232160806656,
-0.01764674112200737,
0.02128714695572853,
0.022038040682673454,
-0.02268807403743267,
-0.015766650438308716,
-0.006957561243325472,
-0.01998075284063816,
-0.015608138404786587,
-0.030293092131614685,
0.01566116139292717,
-0.051094166934490204,
0.02787063829600811,
-0.008196595124900341,
-0.09354918450117111,
0.08468926697969437,
-0.001055743545293808,
-0.032833583652973175,
-0.001712258905172348,
-0.004323422908782959,
0.013195551000535488,
-0.020475203171372414,
0.057462502270936966,
0.036850642412900925,
-0.016426943242549896,
0.032685499638319016,
0.03296138718724251,
-0.0350002646446228,
0.026610977947711945,
0.03043319657444954,
-0.010392602533102036,
0.0019135355250909925,
0.01687602885067463,
-0.009722370654344559,
0.008072719909250736,
0.06511611491441727,
0.03320518508553505,
0.010498320683836937,
-0.025354871526360512,
-0.05411393940448761,
0.0515730194747448,
-0.012723472900688648,
-0.07311761379241943,
-0.012110314331948757,
-0.011293962597846985,
0.012334268540143967,
-0.04020500183105469,
-0.05520836263895035,
-0.02604302205145359,
0.010434441268444061,
-0.012324435636401176,
0.0092239985242486,
-0.03427816182374954,
0.07388926297426224,
0.039027053862810135,
0.0719965323805809,
0.05581284314393997,
-0.061793722212314606,
-0.01172110065817833,
0.029745781794190407,
-0.03142530471086502,
0.0032132307533174753,
-0.006141357123851776,
-0.01837410405278206,
-0.034619588404893875,
-0.03276132419705391,
-0.048496875911951065,
0.0020682187750935555,
-0.004913758486509323,
-0.011519567109644413,
0.02759718894958496,
0.026750581339001656,
0.0030017634853720665,
-0.07648652791976929,
-0.04360498860478401,
0.015578566119074821,
0.07572663575410843,
0.021476633846759796,
0.041509076952934265,
0.04435093328356743,
-0.03310537338256836,
-0.021022731438279152,
-0.02962052822113037,
-0.030202491208910942,
0.010629264637827873,
-0.015682993456721306,
0.027504004538059235,
0.045894816517829895,
0.025328077375888824,
0.018500888720154762,
-0.03831928223371506,
0.029300471767783165,
0.07732807099819183,
0.0324886329472065,
-0.036993496119976044,
-0.050111107528209686,
-0.015188593417406082,
-0.03497589752078056,
0.05764899030327797,
0.017196401953697205,
-0.01486312597990036,
-0.01148021500557661,
0.025175374001264572,
0.01297002099454403,
-0.09292023628950119,
-0.03745575621724129,
-0.05077468231320381,
0.01876717060804367,
0.040883868932724,
-0.01763851009309292,
-0.0005332280416041613,
-0.07593951374292374,
-0.04148668050765991,
-0.0002872357435990125,
0.034652188420295715,
0.013460705056786537,
-0.04771263152360916,
0.027416974306106567,
0.020631881430745125,
-0.023067748174071312,
0.04660487174987793,
0.06287576258182526,
0.0013263876317068934,
0.010244349017739296,
-0.01158821675926447,
-0.006106231827288866,
-0.06318537145853043,
0.0065244510769844055,
0.003297247225418687,
-0.04041442647576332,
0.043372612446546555,
-0.01790565997362137,
-0.027129000052809715,
-0.04255152493715286,
-0.02421138621866703,
0.045568790286779404,
0.004732559435069561,
0.005115509033203125,
0.02180579863488674,
0.02382592111825943,
-0.005795478820800781,
0.06397287547588348,
0.0441947877407074,
0.07537118345499039,
-0.002329782349988818,
0.023111382499337196,
0.011879161931574345,
0.058596450835466385,
0.05126471072435379,
0.03918687626719475,
0.07124050706624985,
0.004787010606378317,
-0.012378220446407795,
0.005730513483285904,
-0.06799166649580002,
0.004916990175843239,
0.04076479747891426,
0.05162694677710533,
-0.037530042231082916,
-0.046974532306194305,
0.00973233487457037,
-0.007667034864425659,
-0.009310855530202389,
0.01930518075823784,
0.05781013146042824,
0.02910633198916912,
0.018024558201432228,
0.03585098311305046,
0.008422666229307652,
-0.03491868078708649,
-0.01128285564482212,
0.009632990695536137,
-0.000814326573163271,
0.05491471663117409,
-0.06672380119562149,
-0.029714245349168777,
0.043683573603630066,
-0.04304192215204239,
-0.06388156861066818,
0.034526314586400986,
0.01252617035061121,
0.001756788813509047,
0.006572117563337088,
0.0031892682891339064,
-0.04438069835305214,
-0.03604881465435028,
-0.0017579265404492617,
-0.04823010414838791,
-0.008805775083601475,
-0.0013184312265366316,
-0.03122350201010704,
0.040867194533348083,
-0.032278407365083694,
-0.007647184655070305,
-0.014677928760647774,
-0.010089288465678692,
-0.051190223544836044,
0.061276186257600784,
0.02170489728450775,
0.012480100616812706,
0.0102268997579813,
0.015266269445419312,
0.00609350623562932,
-0.04312605410814285,
0.03018835000693798,
-0.08816906809806824,
0.01164938323199749,
-0.06210484355688095,
0.0004802680341526866,
0.03146729618310928,
0.018984641879796982,
0.03038567677140236,
-0.032935917377471924,
-0.020296167582273483,
0.025854235514998436,
0.015168990008533001,
0.026931822299957275,
-0.05051378905773163,
-0.03919624164700508,
-0.001039838301949203,
-0.0193504448980093,
-0.024865012615919113,
-0.01025119423866272,
0.011596227996051311,
-0.05377655476331711,
0.008348939940333366,
0.005327126011252403,
0.04001714289188385,
0.07968533039093018,
0.025288818404078484,
-0.021399859338998795,
0.026215704157948494,
-0.06273861974477768,
0.01633553020656109,
-0.004210222512483597,
0.04419371858239174,
0.049873508512973785,
0.018883848562836647,
-0.013254174031317234,
0.013981766998767853,
-0.026562243700027466,
0.05897577479481697,
0.04806089401245117,
0.059774454683065414,
0.027199093252420425,
0.0021412884816527367,
-0.018235918134450912,
0.06330718100070953,
-0.036878712475299835,
-0.020189594477415085,
0.03642130643129349,
0.03565869480371475,
0.06426456570625305,
0.02839718386530876,
0.0621676929295063,
0.03570866212248802,
0.010240486823022366,
-0.0135616110637784,
-0.030207786709070206,
-0.023253867402672768,
-0.02497025951743126,
-0.02815225161612034,
-0.015353040769696236,
0.01714596524834633,
0.014800197444856167,
0.0007365134079009295,
0.015428371727466583,
0.005134868901222944,
0.02974010817706585,
-0.0148615762591362,
-0.018420828506350517,
0.013211176730692387,
0.03831922635436058,
-0.0019917793106287718,
0.03732449933886528,
0.005063433200120926,
0.044595059007406235,
-0.02922385185956955,
-0.06292366981506348,
-0.021715769544243813,
-0.015079643577337265,
-0.03137783333659172,
0.0026115907821804285,
-0.002264457754790783,
-0.0003066364151891321,
0.044272322207689285,
-0.03466857597231865,
0.06489048898220062,
0.03163323178887367,
-0.04033071547746658,
-0.03342043235898018,
0.020573796704411507,
0.014338260516524315,
-0.007984298281371593,
0.006214202381670475,
-0.0010637588566169143,
0.09083987772464752,
0.006361489184200764,
0.008755759336054325,
0.009985547512769699,
0.014043478295207024,
-0.1002785786986351,
-0.020653391256928444,
0.055122192949056625,
-0.026777982711791992,
0.026806360110640526,
0.017597896978259087,
0.02219967357814312,
-0.023825282230973244,
-0.034389082342386246,
-0.053761836141347885,
0.006344153545796871,
0.02263980731368065,
0.05000875145196915,
-0.0032244364265352488,
0.013861759565770626,
-0.04806999862194061,
0.001651328639127314,
-0.03598010912537575,
0.015692075714468956,
0.0020364958327263594,
0.030272550880908966,
0.04138829559087753,
0.011150610633194447,
0.001826642663218081,
0.012296094559133053,
0.025153031572699547,
0.03386611118912697,
-0.03176023066043854,
-0.09340158849954605,
0.009883129969239235,
0.009699990041553974,
-0.01804860308766365,
0.03533264622092247,
-0.03815494477748871,
0.019332213327288628,
-0.04567322880029678,
0.002206722041592002,
-0.014396500773727894,
0.021304573863744736,
-0.023182369768619537,
-0.053424447774887085,
-0.03442315012216568,
0.03547146916389465,
0.008627929724752903,
-0.022747177630662918,
0.013757721520960331,
0.002036827616393566,
-0.06431622058153152,
-0.05106375366449356,
0.04538823291659355,
0.08352446556091309,
-0.05466098710894585,
-0.03500779718160629,
-0.06037507951259613,
-0.011878602206707,
0.030082210898399353,
0.013766573742032051,
-0.028542209416627884,
0.019776122644543648,
-0.05382149666547775,
-0.04735483229160309,
-0.0023626317270100117,
-0.05271231010556221,
-0.05686861276626587,
0.02385570853948593,
0.01250087283551693,
-0.09898561984300613,
0.033107396215200424,
-0.005363695323467255,
-0.06483505666255951,
0.1152333915233612,
0.008053798228502274,
0.029598558321595192,
-0.04770730063319206,
-0.06283313781023026,
-0.0025025855284184217,
-0.025156961753964424,
0.0018866428872570395,
0.03611161932349205,
-0.005885439459234476,
-0.036911491304636,
0.0005199234001338482,
0.03140752390027046,
0.039682235568761826,
0.09551959484815598,
-0.04404968023300171,
0.036992397159338,
0.04225078970193863,
0.0006076694116927683,
0.01285865344107151,
-0.030732151120901108,
0.011679152026772499,
0.011089202016592026,
0.008243540301918983,
-0.02715815044939518,
-0.006966015789657831,
-0.011894428171217442,
-0.053133998066186905,
0.004493513610213995,
-0.031434282660484314,
-0.006662204395979643,
-0.016219206154346466,
-0.0016719544073566794,
-0.012520468793809414,
0.043090078979730606,
0.00790379662066698,
0.02985225059092045,
-0.03516963869333267,
-0.015324665233492851,
-0.03764715418219566,
0.008906811475753784,
0.04890036955475807,
0.0800522118806839,
-0.04859702289104462,
-0.04656769335269928,
-0.05478375777602196,
-0.002776229288429022,
-0.020354175940155983,
0.027124103158712387,
0.005387904122471809,
-0.016575593501329422,
0.059365756809711456,
0.025806138291954994,
-0.06808219105005264,
0.0365184023976326,
0.016212008893489838,
0.0315968319773674,
-0.04690633714199066,
0.01844794675707817,
-0.013818544335663319,
-0.05697575956583023,
-0.0025300083216279745,
0.0762212947010994,
0.03317905217409134,
-0.05571049079298973,
-0.000626088643912226,
-0.02322199195623398,
0.03403865918517113,
0.021495811641216278,
-0.0034656624775379896,
-0.042865950614213943,
-0.0050885495729744434,
0.00009902722376864403,
0.02244390919804573,
0.027461007237434387,
-0.007084836717694998,
0.010621302761137486,
-0.04228942096233368,
-0.032120924443006516,
-0.03996172174811363,
-0.060422495007514954,
0.0057015628553926945,
0.028405558317899704,
0.006422180216759443,
-0.009843365289270878,
-0.0021405587904155254,
-0.041782982647418976,
0.0375206433236599,
0.028327608481049538,
0.028865929692983627,
-0.024220263585448265,
-0.050535570830106735,
-0.024022268131375313,
-0.02063628099858761,
-0.015803324058651924,
0.013428619131445885,
-0.010695954784750938,
-0.05055180937051773,
0.004930802620947361,
-0.059297144412994385,
-0.01857561059296131,
-0.0005268965614959598,
0.010113811120390892,
0.0427563413977623,
-0.029409259557724,
-0.07931602746248245,
0.012660019099712372,
-0.006113386247307062,
-0.009304865263402462,
0.020476510748267174,
-0.01819377765059471,
0.02763780765235424,
-0.006109416484832764,
0.04064704105257988,
0.052592724561691284,
-0.00449320999905467,
-0.028954962268471718,
-0.03376049920916557,
-0.014026889577507973,
-0.0014586907345801592,
0.001305482815951109,
0.02732956036925316,
0.01546909287571907,
0.039322253316640854,
0.014194605872035027,
0.0177084319293499,
0.043107058852910995,
-0.03747263178229332,
-0.04404868930578232,
-0.0816667228937149,
0.040072742849588394,
-0.07646328955888748,
-0.0023063081316649914,
0.029759999364614487,
-0.01127403974533081,
-0.033365003764629364,
-0.0282732006162405,
-0.02908983640372753,
0.007408636622130871,
-0.044197823852300644,
0.01753041334450245,
-0.012781213037669659,
0.02838445082306862,
-0.024406274780631065,
-0.00937665905803442,
0.014189193956553936,
-0.030676575377583504,
-0.0692419707775116,
-0.011710860766470432,
0.008415733464062214,
0.025689981877803802,
-0.03349055349826813,
-0.0860450342297554,
-0.0869472324848175,
0.019556649029254913,
0.021281348541378975,
0.04057318717241287,
-0.005000781733542681,
-0.03376404941082001,
0.010129301808774471,
0.05431143939495087,
-0.020078586414456367,
-0.04651891067624092,
-0.0013121439842507243,
0.032176438719034195,
0.058571815490722656,
0.020719267427921295,
-0.0035162908025085926,
-0.0067964522168040276,
0.021177301183342934,
0.05391937121748924,
-0.04044536128640175,
0.04078809171915054,
0.030502542853355408,
-0.010194615460932255,
0.07290554791688919,
0.011778398416936398,
0.028076844289898872,
-0.014454176649451256,
0.006760910619050264
] |
[
3.101862668991089,
2.6736583709716797
] |
Differential Geometry
|
Mathematics
|
math-DG
|
na
|
na
|
2007-04-01T14:10:51
|
The results of the spectral, energetical and temporal characteristics of
radiation in the presence of the photonic flame effect are presented.
Artificial opal posed on Cu plate at the temperature of liquid nitrogen boiling
point (77 K) being irradiated by nanosecond ruby laser pulse produces long-
term luminiscence with a duration till ten seconds with a finely structured
spectrum in the the antistocks part of the spectrum. Analogous visible
luminescence manifesting time delay appeared in other samples of the artificial
opals posed on the same plate. In the case of the opal infiltrated with
different nonlinear liquids the threshold of the luminiscence is reduced and
the spatial disribution of the bright emmiting area on the opal surface is
being changed. In the case of the putting the frozen nonlinear liquids on the
Cu plate long-term blue bright luminiscence took place in the frozen species of
the liquids. Temporal characteristics of this luminiscence are nearly the same
as in opal matrixes.
|
Some new experimental photonic flame effect features
|
physics.optics
|
0704.0088
| 2,007
|
[
0.0352964922785759,
-0.002163228578865528,
0.01154005341231823,
-0.05233415961265564,
0.02747935988008976,
0.010927191935479641,
-0.03779607266187668,
0.02376439794898033,
-0.023777993395924568,
-0.017167823389172554,
-0.03835756331682205,
0.10780343413352966,
0.0019323264714330435,
0.026833344250917435,
-0.0023830162826925516,
-0.037591129541397095,
0.06181333586573601,
0.01563476398587227,
-0.013599430210888386,
0.03440966084599495,
-0.03041049838066101,
-0.037962548434734344,
-0.02653169073164463,
-0.040184877812862396,
0.006666186731308699,
-0.0010386179201304913,
0.03349266201257706,
0.01326144952327013,
-0.012537525035440922,
-0.006906147580593824,
0.044688351452350616,
-0.06592435389757156,
0.01459612138569355,
-0.0005701511399820447,
-0.022295428439974785,
-0.028226712718605995,
0.042757973074913025,
0.004763668868690729,
0.03313016518950462,
0.08307970315217972,
0.016030428931117058,
0.02215888351202011,
0.04589451104402542,
-0.006446498911827803,
0.010064185597002506,
0.021731914952397346,
0.02146172896027565,
-0.01555594988167286,
0.035870831459760666,
-0.005321514327079058,
0.01742030493915081,
0.049075208604335785,
-0.032344669103622437,
-0.012466196902096272,
0.02627020888030529,
-0.014401406981050968,
-0.02139429748058319,
0.015113928355276585,
0.06470364332199097,
-0.002191877691075206,
0.012047315016388893,
0.0431470051407814,
-0.03158481419086456,
0.03355375677347183,
0.05589235946536064,
-0.07160218060016632,
-0.03643881902098656,
-0.002621317747980356,
0.007995554246008396,
-0.008636570535600185,
0.0324227549135685,
0.026982970535755157,
-0.07571519166231155,
0.011235256679356098,
0.03321489319205284,
-0.01073650922626257,
-0.010887691751122475,
0.024433577433228493,
-0.0345834419131279,
0.04130450263619423,
-0.0021798766683787107,
-0.023777179419994354,
0.024222448468208313,
0.049648482352495193,
0.043359577655792236,
-0.003558482974767685,
0.01967770978808403,
0.021669454872608185,
-0.05807428061962128,
0.02634672075510025,
0.03487951308488846,
-0.045214880257844925,
0.05764114484190941,
0.04757481440901756,
-0.004853852093219757,
0.029863106086850166,
-0.008340743370354176,
0.058504365384578705,
-0.02981158159673214,
-0.006975220981985331,
-0.025235053151845932,
0.017610883340239525,
0.013526374474167824,
0.00830262340605259,
0.037647418677806854,
-0.009428484365344048,
-0.006512782070785761,
-0.026949673891067505,
-0.008920656517148018,
-0.02238118276000023,
-0.08291872590780258,
-0.04016554355621338,
-0.03773219510912895,
0.0069992635399103165,
-0.042525794357061386,
-0.0463603176176548,
0.019792601466178894,
-0.09298794716596603,
0.003321873489767313,
0.025217721238732338,
0.033177152276039124,
-0.00006817383837187663,
0.037495385855436325,
0.05675845220685005,
0.06645026803016663,
0.04072520509362221,
-0.007620548363775015,
0.002764455508440733,
-0.009185399860143661,
-0.0036353636533021927,
-0.02455756440758705,
0.04678381234407425,
-0.10224726051092148,
0.007864627055823803,
0.04788165166974068,
0.032772496342659,
0.01242607831954956,
-0.04517460614442825,
0.035126570612192154,
-0.0325867123901844,
0.05316277593374252,
-0.03856348246335983,
-0.02797388844192028,
-0.02706390619277954,
-0.007591433823108673,
-0.06376533210277557,
0.007052408065646887,
-0.038836609572172165,
-0.0014721566112712026,
0.003643222851678729,
0.014540242031216621,
0.048437170684337616,
0.022524889558553696,
0.012459180317819118,
-0.022927988320589066,
0.00732575124129653,
-0.0401303768157959,
-0.034033823758363724,
-0.010936778038740158,
0.01781323179602623,
-0.03059215657413006,
0.017973415553569794,
-0.055504072457551956,
0.0073796408250927925,
-0.09761054813861847,
-0.015315690077841282,
0.05440777540206909,
-0.015364177525043488,
0.052431803196668625,
0.024831179529428482,
0.018195824697613716,
-0.013540090061724186,
-0.044438403099775314,
-0.0379507839679718,
0.038731012493371964,
0.0021691827569156885,
0.05313681811094284,
-0.04319528490304947,
0.03599238395690918,
-0.0030405784491449594,
-0.010515350848436356,
-0.04585922881960869,
-0.06320305168628693,
-0.041789863258600235,
0.05754528194665909,
0.028683021664619446,
0.04384575039148331,
-0.057695455849170685,
-0.0247562937438488,
0.014630977064371109,
-0.016735877841711044,
-0.0254337377846241,
-0.06444652378559113,
-0.06812063604593277,
-0.03532383218407631,
-0.06930452585220337,
0.039113886654376984,
-0.03508369252085686,
-0.05086444690823555,
-0.020213931798934937,
-0.0018029834609478712,
-0.02578224427998066,
-0.026515504345297813,
0.008898857980966568,
-0.030609529465436935,
0.07766588032245636,
0.028263263404369354,
0.025081533938646317,
-0.0167077649384737,
0.015703625977039337,
0.06525571644306183,
0.048172637820243835,
0.00031112952274270356,
-0.016976715996861458,
-0.008763236925005913,
0.03825230151414871,
-0.004193102940917015,
-0.058272261172533035,
0.009721202775835991,
0.023588210344314575,
0.038238879293203354,
0.037177588790655136,
0.005134327337145805,
-0.016341298818588257,
0.0671444684267044,
0.011926059611141682,
-0.02896944060921669,
0.01335905957967043,
-0.027931151911616325,
-0.002307008719071746,
-0.054536521434783936,
-0.01934933103621006,
0.033469632267951965,
-0.013956655748188496,
0.021185308694839478,
0.007851013913750648,
-0.027805183082818985,
0.001028617611154914,
0.020347144454717636,
0.057571325451135635,
0.019353333860635757,
-0.030569076538085938,
-0.01910172402858734,
-0.010446082800626755,
-0.06047656387090683,
-0.04346529394388199,
-0.02903416007757187,
0.0012238010531291366,
-0.03306310996413231,
-0.004818988963961601,
0.01563219353556633,
-0.011846445500850677,
0.01168879959732294,
0.06529052555561066,
-0.009177944622933865,
-0.011371261440217495,
-0.06403309851884842,
0.06797286868095398,
-0.05248524993658066,
-0.018760139122605324,
0.015461040660738945,
-0.028213640674948692,
-0.019977860152721405,
-0.09108015149831772,
-0.02404913678765297,
0.01092302892357111,
-0.03498178347945213,
-0.019992824643850327,
-0.0394802987575531,
-0.01329709216952324,
-0.01592586375772953,
-0.033927369862794876,
0.05773642659187317,
0.0509512796998024,
0.02221738174557686,
0.07682497054338455,
-0.0058512301184237,
0.00009934575791703537,
-0.007782490458339453,
-0.0679604634642601,
-0.06225234642624855,
-0.033445049077272415,
-0.07444177567958832,
0.03311696648597717,
-0.03294806554913521,
-0.023206958547234535,
0.0060084061697125435,
0.016416292637586594,
0.006259841378778219,
-0.013896925374865532,
-0.044221192598342896,
-0.028688056394457817,
0.02708735689520836,
0.025945845991373062,
-0.0669052004814148,
0.0579393096268177,
0.08488096296787262,
0.02010619267821312,
-0.0157727412879467,
0.0336870476603508,
0.08629155904054642,
-0.03285793587565422,
-0.013796423561871052,
0.0041601094417274,
0.01724630780518055,
0.015434548258781433,
-0.03983064740896225,
0.013695836998522282,
0.057452041655778885,
0.034031663089990616,
-0.008839043788611889,
0.02977726235985756,
-0.047443687915802,
-0.015527474693953991,
-0.029613392427563667,
-0.013443024829030037,
0.018327001482248306,
0.0044035036116838455,
0.05031881853938103,
0.023612331598997116,
0.030692722648382187,
-0.028959525749087334,
-0.0013441670453175902,
-0.04242679476737976,
0.04097262769937515,
0.00725297536700964,
-0.01459672674536705,
-0.02749386616051197,
-0.007706733886152506,
0.009833716787397861,
-0.006981978192925453,
0.06430166214704514,
-0.06124083697795868,
-0.03692743554711342,
0.025037191808223724,
0.00305288122035563,
-0.06096646934747696,
0.05172840878367424,
-0.0372948981821537,
0.008015134371817112,
0.045890334993600845,
-0.04081493243575096,
-0.014586485922336578,
-0.03789927065372467,
0.012944204732775688,
-0.022129539400339127,
-0.04169883951544762,
-0.013385530561208725,
-0.0019190468592569232,
0.024484537541866302,
0.008974606171250343,
-0.0002889755996875465,
0.005332758650183678,
-0.033207934349775314,
-0.031205758452415466,
0.040979381650686264,
0.06023615971207619,
-0.02653699740767479,
0.0935274064540863,
-0.022216198965907097,
-0.021874630823731422,
-0.024707777425646782,
0.07441353052854538,
-0.03200910985469818,
0.006164770107716322,
0.06039122864603996,
0.0631072074174881,
0.03616759553551674,
0.024443702772259712,
-0.012183086015284061,
-0.0289455559104681,
-0.030146542936563492,
0.009138442575931549,
-0.017260832712054253,
0.047496259212493896,
0.030575066804885864,
-0.03953569009900093,
-0.006992544513195753,
-0.027549387887120247,
0.05199730023741722,
0.02101556397974491,
-0.03128771483898163,
0.06260372698307037,
0.018875332549214363,
0.023307228460907936,
0.053082168102264404,
-0.0033876001834869385,
-0.033432457596063614,
-0.008573970757424831,
-0.06383362412452698,
0.038987014442682266,
-0.05033722147345543,
-0.03342321887612343,
-0.03183060139417648,
-0.02234070375561714,
-0.014864601194858551,
0.03494501858949661,
-0.011668884195387363,
0.03355531021952629,
-0.02165721356868744,
-0.004499244038015604,
-0.04765860736370087,
-0.034893106669187546,
-0.000912441813852638,
-0.04348497837781906,
-0.014097843319177628,
0.001349191414192319,
-0.03690014034509659,
0.037085019052028656,
0.022212127223610878,
-0.0019217722583562136,
-0.00039889290928840637,
-0.03406353294849396,
-0.08548608422279358,
-0.0005050995969213545,
0.02342391200363636,
0.0634784996509552,
-0.0011359178461134434,
0.029342196881771088,
0.0004448154359124601,
-0.007502371445298195,
0.04600706696510315,
-0.002702580066397786,
0.0010723830200731754,
-0.0258280448615551,
-0.02062862366437912,
-0.011566679924726486,
-0.019170006737113,
0.013105207122862339,
-0.015778077766299248,
0.0692288801074028,
-0.026723593473434448,
-0.025028793141245842,
0.030042197555303574,
-0.004044927190989256,
0.0268276147544384,
0.019852716475725174,
0.02099701203405857,
0.025813063606619835,
0.05691654235124588,
0.05496406927704811,
-0.01838068477809429,
0.06137679144740105,
0.0045688580721616745,
0.0687195286154747,
0.07628139853477478,
0.052939239889383316,
0.009703516028821468,
-0.0598415806889534,
-0.0017661950550973415,
0.025131652131676674,
0.028146866708993912,
0.008669639937579632,
-0.015374728478491306,
0.08870367705821991,
-0.06893474608659744,
-0.0040254672057926655,
0.03011127933859825,
0.03644704446196556,
0.04439535737037659,
0.013795129954814911,
0.030177054926753044,
-0.04489140957593918,
-0.014186114072799683,
0.017995130270719528,
0.009359579533338547,
-0.02347099781036377,
-0.030134955421090126,
-0.0026494001504033804,
0.022013220936059952,
0.0052287462167441845,
-0.023085007444024086,
0.0611187107861042,
0.03647272288799286,
-0.04625023901462555,
-0.07568879425525665,
0.04012226685881615,
-0.052439406514167786,
0.035252686589956284,
0.042392879724502563,
-0.013222403824329376,
0.01358695887029171,
0.03343807905912399,
-0.05535642057657242,
-0.00462594348937273,
0.023453155532479286,
-0.01805037446320057,
0.06302358210086823,
0.02615070715546608,
-0.009480783715844154,
0.005756919737905264,
0.07537192851305008,
0.01420875545591116,
-0.0002921714913100004,
-0.007704843766987324,
-0.020860034972429276,
0.021421965211629868,
0.05582726001739502,
0.06970174610614777,
0.028405891731381416,
0.0069696297869086266,
0.02385387383401394,
0.00202113832347095,
-0.023477135226130486,
-0.006031600758433342,
0.005834165494889021,
-0.029327547177672386,
-0.05696294456720352,
-0.03925545513629913,
0.010591010563075542,
-0.002259286353364587,
0.032884031534194946,
-0.0013148540165275335,
0.03237805515527725,
0.03384947404265404,
-0.07566271722316742,
0.02213766984641552,
-0.014590062201023102,
-0.04976058751344681,
0.021929815411567688,
-0.0120066674426198,
0.01920979470014572,
0.016108587384223938,
0.05087760090827942,
0.005897865630686283,
0.034607794135808945,
0.009010623209178448,
0.003597535891458392,
0.02640841342508793,
-0.03372122719883919,
0.01203412190079689,
0.036012522876262665,
0.01197363156825304,
-0.006331955548375845,
-0.010053354315459728,
0.007495722267776728,
-0.002510480582714081,
0.022721534594893456,
-0.012606242671608925,
0.0317234992980957,
-0.01444705855101347,
-0.0073739467188715935,
0.0042808824218809605,
0.048674046993255615,
0.05204566940665245,
-0.023610498756170273,
-0.04709857329726219,
0.014688238501548767,
0.0026232327800244093,
-0.022127723321318626,
0.07342789322137833,
-0.0607525072991848,
0.08214601874351501,
-0.008962573483586311,
0.09961088001728058,
0.005728718359023333,
-0.04884287342429161,
-0.042452991008758545,
-0.061485372483730316,
0.007258363533765078,
-0.0016405282076448202,
0.01012716069817543,
0.05321814864873886,
-0.06184494122862816,
0.04952207952737808,
-0.1014927327632904,
0.01391114667057991,
-0.01001217495650053,
0.02760244905948639,
-0.022297529503703117,
0.010290190577507019,
-0.020765777677297592,
-0.0029845573008060455,
-0.012455668300390244,
0.0220840722322464,
-0.027572713792324066,
0.0688818171620369,
0.02149013988673687,
-0.05274393409490585,
0.02542257495224476,
-0.031305789947509766,
-0.025365041568875313,
0.028609436005353928,
0.03323699161410332,
-0.016876375302672386,
-0.00898179691284895,
0.02518388256430626,
0.042171940207481384,
0.029406694695353508,
-0.051650211215019226,
-0.016740571707487106,
-0.05053307116031647,
-0.02995247393846512,
-0.027790946885943413,
-0.020833225920796394,
0.010240490548312664,
-0.051377952098846436,
-0.03786890208721161,
-0.03803152218461037,
-0.0020934659987688065,
-0.05158416926860809,
-0.004946277476847172,
0.05725196376442909,
-0.05380367487668991,
0.006212911568582058,
0.03853707015514374,
0.012201541103422642,
0.023888934403657913,
0.02198897860944271,
0.0763281062245369,
-0.016612956300377846,
0.019006013870239258,
-0.033864762634038925,
-0.05626378580927849,
-0.027874909341335297,
-0.04591214656829834,
0.06998982280492783,
-0.023302894085645676,
0.029569102451205254,
-0.010488079860806465,
-0.03755602613091469,
-0.06118582561612129,
0.015276246704161167,
-0.043353836983442307,
0.03452039510011673,
0.005875975359231234,
-0.06021856516599655,
-0.055211327970027924,
-0.021537238731980324,
0.0428788848221302,
0.005851757247000933,
-0.02117747627198696,
0.005137924570590258,
-0.008675136603415012,
0.003274566261097789,
0.010983534157276154,
-0.051379211246967316,
0.014500843361020088,
-0.015396380797028542,
-0.010401262901723385,
0.05776270851492882,
-0.0045908354222774506,
0.036348070949316025,
-0.002843643305823207,
0.035751841962337494,
0.06248980388045311,
-0.02415444888174534,
0.035672325640916824,
0.011612214148044586,
-0.012682110071182251,
0.06322149187326431,
-0.012993195094168186,
0.01879429817199707,
0.04487655311822891,
0.029578030109405518,
0.027462251484394073,
0.016347717493772507,
-0.01812177523970604,
-0.0346861369907856,
-0.008489012718200684,
-0.03730078414082527,
-0.04639679938554764,
-0.056434519588947296,
-0.04297664389014244,
0.01776270940899849,
-0.01983347162604332,
-0.001041893381625414,
-0.08342134207487106,
-0.02007073163986206,
0.015725623816251755,
-0.02080005221068859,
-0.023436391726136208,
0.021281728520989418,
-0.051915742456912994,
-0.036835744976997375,
0.01293432991951704,
-0.01129382848739624,
0.06676574051380157,
0.05396587401628494,
-0.023601623252034187,
-0.03675753250718117,
0.01721123792231083,
0.01225072331726551,
-0.041562970727682114,
-0.010473405942320824,
-0.027101514860987663,
-0.052996858954429626,
0.004175984766334295,
-0.019979670643806458,
-0.06977280974388123,
0.01093900017440319,
-0.010861960239708424,
-0.007145237643271685,
-0.06704936921596527,
0.07549839466810226,
-0.040976524353027344,
-0.008216590620577335,
-0.010639358311891556,
0.014252640306949615,
0.016160326078534126,
-0.04425264149904251,
0.04204614832997322,
-0.010573990643024445,
-0.004123372957110405,
-0.014829938299953938,
-0.004380968865007162,
0.026559004560112953,
0.024712741374969482,
-0.01491463277488947,
-0.0005298000760376453,
-0.015729181468486786,
-0.01594247668981552,
0.05509823188185692,
0.018257565796375275,
0.05619938671588898,
-0.009266067296266556,
0.004305457230657339,
-0.009044401347637177,
-0.01880568452179432,
0.03260022774338722,
-0.03994326665997505,
-0.005775492638349533,
-0.08580359816551208,
0.057057250291109085,
0.006435271818190813,
-0.012081797234714031,
0.0052146753296256065,
-0.023246748372912407,
0.06506270915269852,
-0.028491724282503128,
0.01785511150956154,
0.001980298664420843,
-0.03485168516635895,
-0.03134547919034958,
-0.05664937198162079,
0.003634479595348239,
0.006102630402892828,
0.03774362429976463,
-0.010595505125820637,
0.029569773003458977,
0.05944565683603287,
-0.06101386994123459,
-0.01956959068775177,
0.02339336834847927,
0.0054418593645095825,
-0.048174142837524414,
-0.07003926485776901,
0.014158450998365879,
0.04660645127296448,
-0.005464226473122835,
-0.030495930463075638,
-0.014739464037120342,
0.013289077207446098,
-0.03584695979952812,
0.03996526077389717,
-0.0029385718517005444,
-0.05775994062423706,
0.03503050282597542,
0.0790436863899231,
-0.029050350189208984,
0.002745834644883871,
-0.05042935535311699,
0.006082756910473108,
0.011976353824138641,
0.005112621933221817,
0.03713918849825859,
-0.005801452789455652,
-0.02929934486746788
] |
[
8.988959312438965,
0.958880603313446
] |
Optics
|
General Physics
|
physics-optics
|
na
|
na
|
2007-04-01T14:29:57
|
Statistical modeling of experimental physical laws is based on the
probability density function of measured variables. It is expressed by
experimental data via a kernel estimator. The kernel is determined objectively
by the scattering of data during calibration of experimental setup. A physical
law, which relates measured variables, is optimally extracted from experimental
data by the conditional average estimator. It is derived directly from the
kernel estimator and corresponds to a general nonparametric regression. The
proposed method is demonstrated by the modeling of a return map of noisy
chaotic data. In this example, the nonparametric regression is used to predict
a future value of chaotic time series from the present one. The mean predictor
error is used in the definition of predictor quality, while the redundancy is
expressed by the mean square distance between data points. Both statistics are
used in a new definition of predictor cost function. From the minimum of the
predictor cost function, a proper number of data in the model is estimated.
|
A general approach to statistical modeling of physical laws:
nonparametric regression
|
physics.data-an physics.gen-ph
|
0704.0089
| 2,007
|
[
-0.0008773472509346902,
-0.003138088621199131,
-0.013813100755214691,
-0.017112135887145996,
0.04265045374631882,
0.007402721326798201,
0.021225223317742348,
0.016532646492123604,
-0.05081680044531822,
-0.014514286071062088,
-0.014945274218916893,
0.01722221076488495,
0.05965263396501541,
0.002271752106025815,
-0.018990669399499893,
-0.016407625749707222,
0.03786391019821167,
-0.0023791396524757147,
0.004514799918979406,
-0.008631816133856773,
0.008912813849747181,
-0.034893229603767395,
0.01614796370267868,
-0.05978468433022499,
0.06423763185739517,
-0.010907618328928947,
-0.01385535579174757,
0.03654245659708977,
-0.019847093150019646,
0.033244259655475616,
0.026009559631347656,
-0.08422182500362396,
0.02748413197696209,
-0.03777982294559479,
-0.08220330625772476,
-0.024478351697325706,
0.03153008967638016,
0.01206552516669035,
0.02777261845767498,
0.02798048034310341,
0.06315582990646362,
-0.011722416616976261,
-0.011143410578370094,
-0.014919106848537922,
0.02980264462530613,
0.00688075041398406,
0.01004487369209528,
-0.020436003804206848,
0.0007567947614006698,
0.03780200704932213,
-0.02531946450471878,
0.0400247797369957,
-0.007414781954139471,
-0.00039106825715862215,
-0.003244997002184391,
0.011893861927092075,
0.0577051118016243,
-0.018537336960434914,
0.05320361256599426,
-0.045250535011291504,
0.03392786532640457,
0.033811792731285095,
-0.04679643362760544,
0.00882069580256939,
0.05941096693277359,
-0.06324616074562073,
-0.04325202479958534,
-0.03673731908202171,
0.010935118421912193,
-0.001302223070524633,
0.04718809202313423,
0.04035740718245506,
0.03686858341097832,
-0.005477620754390955,
-0.038709983229637146,
-0.008016100153326988,
0.02852366678416729,
-0.018706072121858597,
0.033017199486494064,
0.04829011857509613,
0.0036958372220396996,
0.01995129883289337,
0.052952852100133896,
0.05085662379860878,
0.06852492690086365,
0.016378404572606087,
-0.019005097448825836,
0.031476013362407684,
-0.027946481481194496,
0.025992222130298615,
-0.012795143760740757,
0.011257560923695564,
0.06504889577627182,
0.05463684722781181,
-0.02357049658894539,
-0.005771426483988762,
-0.0627148374915123,
0.009158352389931679,
0.016580313444137573,
0.03938530012965202,
-0.017682941630482674,
0.06722696125507355,
0.011820069514214993,
-0.000942314334679395,
0.036127056926488876,
0.01872357353568077,
0.01983538083732128,
0.025746246799826622,
-0.003565914463251829,
-0.04940146580338478,
-0.09129248559474945,
0.024845900014042854,
0.02825677953660488,
-0.012561114504933357,
-0.0263291634619236,
-0.07726000249385834,
0.04991411417722702,
-0.08165194094181061,
-0.010721512138843536,
0.07236402481794357,
0.03841829299926758,
-0.014942132867872715,
-0.000570220232475549,
0.04720054194331169,
-0.0035963652189821005,
0.029511762782931328,
-0.03767555579543114,
0.033036552369594574,
0.04134056717157364,
0.027411920949816704,
0.04665271192789078,
0.022769037634134293,
-0.051780711859464645,
0.04350223019719124,
0.05565529316663742,
0.06147252395749092,
-0.0046838014386594296,
-0.027002308517694473,
0.024035435169935226,
0.010060375556349754,
0.008753976784646511,
-0.015021081082522869,
0.011096564121544361,
-0.01704549416899681,
0.003970544785261154,
-0.030102767050266266,
0.0033553889952600002,
-0.02458765357732773,
-0.06176504120230675,
-0.0033938847482204437,
-0.0020414560567587614,
0.050517722964286804,
0.004681918304413557,
0.045533668249845505,
-0.009856084361672401,
-0.04598646238446236,
-0.028426460921764374,
0.017281707376241684,
0.04721074923872948,
-0.03637763857841492,
0.004500646144151688,
-0.01223067194223404,
-0.01622653752565384,
0.08519662916660309,
-0.02785700187087059,
-0.03538963943719864,
0.05342123284935951,
-0.001731251715682447,
0.022421428933739662,
0.050855278968811035,
-0.03043023683130741,
-0.03965571150183678,
0.011250493116676807,
-0.024326743558049202,
0.0102570541203022,
0.007096550893038511,
0.0010527512058615685,
0.011662621982395649,
0.010907231830060482,
-0.05147884041070938,
0.07472428679466248,
-0.018724139779806137,
0.06513549387454987,
-0.026080122217535973,
-0.03209678456187248,
0.023437345400452614,
0.025235822424292564,
-0.007345050107687712,
-0.05952969565987587,
-0.04886624589562416,
0.03614895045757294,
0.008143379352986813,
-0.06670695543289185,
-0.0888223946094513,
-0.019384587183594704,
-0.04224875196814537,
0.07619472593069077,
-0.004637053236365318,
0.011055786162614822,
-0.04041498154401779,
-0.0041785649955272675,
-0.02261684089899063,
-0.026855695992708206,
0.0291750505566597,
0.002729958388954401,
0.008156324736773968,
-0.01739257201552391,
0.011025174520909786,
0.0010177554795518517,
0.022312426939606667,
0.06163498014211655,
0.015573947690427303,
-0.016364146023988724,
0.0664362832903862,
-0.011233069002628326,
-0.029406500980257988,
-0.006705685518682003,
-0.05460429936647415,
-0.013669691048562527,
0.018735449761152267,
-0.019941141828894615,
-0.019290631636977196,
0.021066762506961823,
0.048381734639406204,
0.06293678283691406,
0.025327034294605255,
0.0008677112055011094,
0.013815383426845074,
-0.05539871007204056,
-0.027697404846549034,
-0.025400662794709206,
-0.07682900875806808,
0.009871072135865688,
-0.010600610636174679,
0.009061776101589203,
0.04651285335421562,
0.008634266443550587,
0.01727045513689518,
0.03277171030640602,
0.0359417088329792,
-0.0001759529986884445,
0.010894964449107647,
0.036700278520584106,
-0.03836735710501671,
-0.08188857138156891,
-0.03859390690922737,
-0.021891098469495773,
0.00047842360800132155,
-0.014829101040959358,
0.03129502385854721,
0.024628067389130592,
0.046783484518527985,
0.029076041653752327,
0.0035573667846620083,
0.05301664024591446,
-0.055583350360393524,
-0.023358125239610672,
0.03074956312775612,
-0.03310144320130348,
-0.03677601367235184,
0.041350312530994415,
-0.01840972900390625,
-0.007185769733041525,
-0.03578086569905281,
-0.03594028949737549,
0.01609361544251442,
-0.005590121261775494,
-0.01787799596786499,
-0.0253163930028677,
0.020829031243920326,
-0.022087497636675835,
0.00438027223572135,
0.07781306654214859,
0.05763325095176697,
0.04230267181992531,
0.02264513447880745,
0.07017644494771957,
-0.006292305421084166,
0.010002185590565205,
-0.04275768622756004,
-0.07036750018596649,
-0.032772161066532135,
-0.047861892729997635,
-0.02973107248544693,
-0.03424598276615143,
-0.009484926238656044,
0.05645712837576866,
-0.0109915966168046,
-0.02103080414235592,
0.019657166674733162,
-0.025372225791215897,
-0.00858189258724451,
-0.002127525396645069,
0.066432423889637,
-0.03841777518391609,
0.06929849088191986,
0.04867352917790413,
-0.02658609114587307,
0.049650855362415314,
0.0013147598365321755,
-0.027285754680633545,
-0.004282105714082718,
0.022402789443731308,
-0.011229808442294598,
0.013236005790531635,
0.02306387387216091,
0.007927757687866688,
-0.0017804857343435287,
0.016443535685539246,
0.011461258865892887,
-0.012757807038724422,
0.04076385498046875,
-0.0014481841353699565,
-0.005079417955130339,
-0.06354645639657974,
-0.009317483752965927,
0.0054922751151025295,
0.03920549154281616,
0.09299953281879425,
0.014470319263637066,
0.028810735791921616,
-0.1198764443397522,
0.013652047142386436,
-0.05532903969287872,
-0.004012413788586855,
0.040796518325805664,
-0.025650091469287872,
-0.012675177305936813,
-0.0278764795511961,
-0.007115147542208433,
0.043699320405721664,
0.04841606691479683,
-0.019957348704338074,
-0.03317740559577942,
-0.04077538475394249,
-0.028163829818367958,
0.015102261677384377,
0.03262445330619812,
-0.03135287016630173,
0.04763508960604668,
0.02542705088853836,
-0.06459381431341171,
-0.022975292056798935,
-0.05669756606221199,
-0.05895751342177391,
-0.000900854473002255,
-0.03524235263466835,
-0.008229303173720837,
0.032304294407367706,
-0.02248413860797882,
-0.01146015990525484,
-0.016724076122045517,
0.01302286610007286,
-0.025604231283068657,
-0.0028480645269155502,
0.055835120379924774,
0.0607018806040287,
-0.07414044439792633,
0.08577261865139008,
0.017717458307743073,
0.013398444280028343,
-0.044582683593034744,
0.05355340614914894,
-0.008254818618297577,
0.009637871757149696,
0.04149976745247841,
0.060971494764089584,
0.05761883780360222,
-0.007065104320645332,
-0.03250846266746521,
-0.03817449137568474,
-0.03239619731903076,
0.031852055341005325,
0.03945634514093399,
0.022373300045728683,
0.002683731960132718,
-0.013795685023069382,
0.006959008052945137,
-0.0434504933655262,
0.026138242334127426,
0.040941402316093445,
0.01603061519563198,
0.015885675325989723,
0.0013078054180368781,
-0.0015335192438215017,
-0.0027921521104872227,
-0.03763027861714363,
0.0255503561347723,
0.02678384818136692,
-0.024338874965906143,
0.011332450434565544,
-0.06808852404356003,
-0.035523347556591034,
0.04489006847143173,
0.012429849244654179,
-0.03507031127810478,
0.014393286779522896,
-0.02257598750293255,
0.02782285213470459,
0.010702202096581459,
-0.025979693979024887,
-0.048754122108221054,
0.0185126680880785,
0.05151582509279251,
0.015862587839365005,
0.019253220409154892,
-0.0015498553402721882,
-0.05322682857513428,
0.024107245728373528,
0.016917390748858452,
-0.03402414545416832,
-0.03632798045873642,
-0.009511479176580906,
-0.10775988548994064,
0.07097360491752625,
0.0018665955867618322,
0.0582234188914299,
-0.0087813725695014,
0.013136082328855991,
0.015501167625188828,
0.02234720066189766,
0.046090248972177505,
-0.0236283540725708,
-0.026565853506326675,
-0.05826900526881218,
0.01140836626291275,
0.002981228521093726,
0.02590874210000038,
-0.011005990207195282,
-0.07941560447216034,
0.06350456923246384,
0.0012689639115706086,
-0.0239194855093956,
0.05609757825732231,
-0.06034545227885246,
-0.01661381497979164,
0.02723580040037632,
0.013560800813138485,
-0.004138056188821793,
-0.011215086095035076,
-0.0124779948964715,
-0.061777230352163315,
0.04397638514637947,
0.012797780334949493,
-0.02936371974647045,
0.08716597408056259,
0.08056133985519409,
-0.017873449251055717,
-0.08551979809999466,
0.018543832004070282,
-0.0030075463000684977,
0.0380423367023468,
-0.014802606776356697,
0.026417981833219528,
0.07079171389341354,
-0.03865501284599304,
0.02457858994603157,
0.04742666706442833,
0.08010797202587128,
0.04911293089389801,
-0.021156232804059982,
0.013686737045645714,
-0.03462604060769081,
-0.004209910519421101,
-0.04429740458726883,
0.00939667597413063,
-0.03354441747069359,
-0.030461587011814117,
-0.00499341357499361,
0.05561688542366028,
-0.028149332851171494,
0.00709538534283638,
0.014874043874442577,
0.009386963210999966,
-0.019412746652960777,
-0.0052474308758974075,
0.026528194546699524,
-0.03360411152243614,
0.02514966018497944,
0.028642185032367706,
0.020245380699634552,
-0.024692120030522346,
-0.020220980048179626,
-0.03126988932490349,
-0.020868681371212006,
0.02256191335618496,
-0.0036109527572989464,
0.0015387693420052528,
-0.01836184598505497,
-0.014219434931874275,
-0.012706400826573372,
0.042492400854825974,
0.03488289564847946,
0.004409709945321083,
-0.03376377001404762,
-0.07192680239677429,
-0.001208642148412764,
-0.010857876390218735,
-0.001874926034361124,
0.009860786609351635,
-0.02150958962738514,
0.009815913625061512,
-0.008518383838236332,
0.01985814981162548,
-0.0225980244576931,
-0.0377688966691494,
-0.038353268057107925,
-0.06244535371661186,
-0.04252413660287857,
0.03731846064329147,
0.03700399771332741,
0.08992816507816315,
0.04666838422417641,
0.010293489322066307,
-0.0311143659055233,
-0.024028511717915535,
0.04343826323747635,
0.03358747065067291,
-0.054139088839292526,
-0.012782467529177666,
0.04720345139503479,
-0.014890183694660664,
0.02034093625843525,
0.029631823301315308,
-0.062276627868413925,
-0.007488860748708248,
-0.03772878646850586,
-0.007308401633054018,
0.049321249127388,
0.011062618345022202,
-0.02280818670988083,
0.00048471399350091815,
-0.0075225019827485085,
0.005765806417912245,
-0.06347498297691345,
-0.03701753914356232,
0.004770364612340927,
0.028256602585315704,
0.013508666306734085,
-0.0069598970003426075,
-0.027210088446736336,
0.03510041907429695,
0.060732342302799225,
-0.06058765947818756,
0.05524877831339836,
-0.0497308187186718,
-0.05769148841500282,
0.07306061685085297,
0.027618318796157837,
-0.06888797134160995,
0.045291535556316376,
-0.02293798141181469,
0.019984114915132523,
-0.08152148872613907,
0.04223337396979332,
-0.027949925512075424,
0.009315051138401031,
-0.04822038859128952,
-0.018133534118533134,
0.027181770652532578,
-0.040394701063632965,
0.012462346814572811,
0.04145185649394989,
0.02612343430519104,
0.03490673378109932,
-0.09076599031686783,
-0.04075782746076584,
0.011489271186292171,
0.003318054135888815,
0.025928447023034096,
0.00609346479177475,
-0.031145146116614342,
-0.027364613488316536,
0.05755111202597618,
-0.007246706634759903,
-0.02944958209991455,
0.05347832292318344,
-0.003870174754410982,
-0.031789764761924744,
-0.011317575350403786,
-0.002065139589831233,
-0.02466849610209465,
0.03867205232381821,
-0.012077189981937408,
-0.035374995321035385,
0.022129030898213387,
-0.004121892154216766,
-0.04526100680232048,
0.009574313648045063,
0.0032652749214321375,
0.02341335080564022,
-0.049272652715444565,
0.01623249612748623,
-0.0866372287273407,
-0.031186655163764954,
0.013886655680835247,
0.028036681935191154,
-0.030642230063676834,
-0.027189556509256363,
-0.04599799960851669,
-0.037644948810338974,
-0.033157143741846085,
0.05121238902211189,
-0.048744816333055496,
0.030824856832623482,
0.014970655553042889,
-0.009061307646334171,
-0.014610647223889828,
-0.0006597183528356254,
-0.031764112412929535,
-0.013936871662735939,
0.011053130030632019,
-0.007229938171803951,
-0.020540719851851463,
0.002017547143623233,
-0.013926797546446323,
0.07140716910362244,
-0.02181783691048622,
0.01964857243001461,
-0.0422133132815361,
-0.007378083188086748,
-0.04968683794140816,
-0.00994395837187767,
-0.07928518950939178,
0.008053160272538662,
0.0035369389224797487,
-0.043907102197408676,
-0.058265767991542816,
0.04740234836935997,
0.037403035908937454,
-0.03861314430832863,
0.0014126214664429426,
-0.01174513716250658,
0.014448292553424835,
-0.04717916622757912,
0.09005331993103027,
-0.05539423227310181,
0.04799371212720871,
0.03880693018436432,
0.03862655907869339,
0.052668508142232895,
-0.020294586196541786,
0.014786980114877224,
-0.011444616131484509,
-0.011183417402207851,
0.03126184269785881,
0.006897682324051857,
0.026846783235669136,
-0.028166895732283592,
0.01683577336370945,
0.04478722810745239,
0.026251506060361862,
-0.023296840488910675,
0.005463320296257734,
0.014272087253630161,
0.055224206298589706,
0.0666944608092308,
0.00866259541362524,
0.027905207127332687,
-0.01649724878370762,
-0.014665815979242325,
-0.021934689953923225,
-0.005106669384986162,
-0.02731768786907196,
0.09006747603416443,
-0.038731206208467484,
-0.01748378947377205,
-0.09496501833200455,
-0.032984551042318344,
-0.014684269204735756,
0.022019360214471817,
-0.040882084518671036,
-0.03723130375146866,
-0.007903654128313065,
-0.026978375390172005,
-0.0058274827897548676,
0.014224555343389511,
0.009607307612895966,
-0.029813051223754883,
-0.02000325359404087,
0.00034610257716849446,
-0.000969149696175009,
0.03541463986039162,
0.011776254512369633,
-0.0554208979010582,
0.05855843424797058,
-0.02743799239397049,
-0.017810510471463203,
-0.037039369344711304,
-0.056479353457689285,
-0.015402655117213726,
0.00507163954898715,
0.0483822301030159,
-0.07546838372945786,
0.01018244307488203,
0.006820974871516228,
-0.04120693728327751,
-0.021947218105196953,
0.007902448065578938,
0.04746830835938454,
0.0491044744849205,
0.05100175365805626,
-0.03003630042076111,
-0.013437041081488132,
-0.02419479936361313,
-0.031506747007369995,
0.03411006182432175,
-0.01124303974211216,
-0.0319703072309494,
-0.001883197808638215,
-0.028700485825538635,
0.006337106227874756,
-0.0009675645851530135,
0.029512271285057068,
-0.018735185265541077,
0.005513721611350775,
0.014598407782614231,
-0.07142303138971329,
0.010290110483765602,
-0.04122115671634674,
0.011979931965470314,
-0.03344898670911789,
-0.06742456555366516,
0.02968854270875454,
0.0328887514770031,
-0.03487953171133995,
-0.05285964533686638,
0.0033992775715887547,
0.05775390937924385,
0.03965358808636665,
-0.012074403464794159,
-0.01571158692240715,
-0.04661424085497856,
0.01729554682970047,
-0.02178339846432209,
0.02337273582816124,
-0.0006526147481054068,
0.04894256219267845,
-0.054391562938690186,
0.028596876189112663,
-0.021669674664735794,
-0.017073705792427063,
-0.008896026760339737,
-0.010317912325263023,
0.008938414044678211,
-0.027462922036647797,
-0.0864863246679306,
0.03898574411869049,
-0.0003199846833012998,
-0.028245801106095314,
-0.02205306477844715,
0.004979514051228762,
-0.012056051753461361,
0.022185886278748512,
-0.015194570645689964,
0.003089367179200053,
-0.01908479630947113,
0.025351621210575104,
0.04265481233596802,
-0.023519808426499367,
0.03956277295947075,
-0.009464693255722523,
0.048206813633441925,
0.04133927822113037,
-0.01910402812063694,
-0.017300724983215332,
-0.016397306695580482,
0.030626317486166954
] |
[
4.414292812347412,
6.994759559631348
] |
Data Analysis, Statistics and Probability
|
General Physics
|
physics-data-an
|
physics-gen-ph
|
na
|
2007-04-01T14:35:40
|
Real Options for Project Schedules (ROPS) has three recursive
sampling/optimization shells. An outer Adaptive Simulated Annealing (ASA)
optimization shell optimizes parameters of strategic Plans containing multiple
Projects containing ordered Tasks. A middle shell samples probability
distributions of durations of Tasks. An inner shell samples probability
distributions of costs of Tasks. PATHTREE is used to develop options on
schedules.. Algorithms used for Trading in Risk Dimensions (TRD) are applied to
develop a relative risk analysis among projects.
|
Real Options for Project Schedules (ROPS)
|
cs.CE cond-mat.stat-mech cs.MS cs.NA physics.data-an
|
0704.0090
| 2,007
|
[
0.012502472847700119,
0.041740018874406815,
-0.012216690927743912,
-0.008550737984478474,
-0.007444733288139105,
-0.006951142102479935,
0.0011932842899113894,
0.011678818613290787,
-0.04596954211592674,
0.025030752643942833,
-0.02858990989625454,
0.02221653237938881,
0.060532622039318085,
0.010189934633672237,
-0.08856365084648132,
0.019412724301218987,
0.026670826599001884,
-0.029944054782390594,
-0.028075646609067917,
-0.008479723706841469,
0.0599810928106308,
-0.06687311083078384,
-0.01354485284537077,
-0.0036665587686002254,
0.08520001173019409,
0.02617238461971283,
-0.0375358946621418,
0.007726337295025587,
-0.05868806689977646,
0.004518636967986822,
0.023228641599416733,
-0.029091645032167435,
0.001084055402316153,
0.008190099149942398,
-0.04882170259952545,
-0.09455230087041855,
0.0839078426361084,
-0.015519509091973305,
0.004168870393186808,
0.006150614935904741,
-0.03718838840723038,
-0.028312332928180695,
0.03641645610332489,
-0.026246095076203346,
-0.017600588500499725,
-0.03107905201613903,
0.052385617047548294,
0.016240984201431274,
0.05102163180708885,
-0.0149138905107975,
0.0051461937837302685,
0.04410456866025925,
-0.006196595728397369,
-0.023687241598963737,
-0.007995637133717537,
-0.00880773738026619,
0.013572042807936668,
0.03701864182949066,
0.010608809068799019,
-0.029152488335967064,
0.03422155603766441,
0.027193063870072365,
-0.04445080831646919,
0.01026896107941866,
-0.017035119235515594,
-0.014797995798289776,
-0.029840735718607903,
0.0036694458685815334,
-0.016023917123675346,
-0.04490543529391289,
0.006434675771743059,
-0.012912251055240631,
0.0019106677500531077,
-0.008391503244638443,
-0.008777664043009281,
-0.0023064969573169947,
0.02187792956829071,
0.0004952868330292404,
-0.0641556829214096,
0.07160311192274094,
0.010919060558080673,
-0.06611375510692596,
0.035465553402900696,
0.0520998015999794,
0.06376132369041443,
0.00636644009500742,
0.04774820804595947,
0.024165907874703407,
-0.03415847197175026,
0.058233801275491714,
-0.03775466978549957,
0.03824646770954132,
0.03559855744242668,
0.0814564973115921,
-0.0619274377822876,
0.09780257940292358,
-0.09176677465438843,
0.02415759675204754,
0.022164462134242058,
-0.0000884759720065631,
0.003391084959730506,
0.027722397819161415,
0.039218030869960785,
0.003158774459734559,
0.003096978645771742,
-0.017659157514572144,
-0.00478206854313612,
0.005012245383113623,
-0.006583503447473049,
-0.00027461766148917377,
-0.030130548402667046,
-0.01438856404274702,
-0.020635662600398064,
-0.02875720150768757,
0.02451646700501442,
-0.0018381397239863873,
0.043889306485652924,
-0.07714308798313141,
0.023343751206994057,
0.06744075566530228,
0.032212693244218826,
-0.03994155302643776,
-0.009863657876849174,
0.012472771108150482,
0.020938703790307045,
0.06226453185081482,
-0.06759900599718094,
-0.038981180638074875,
-0.002983551239594817,
-0.014302633702754974,
0.028917698189616203,
0.04980882257223129,
-0.07210647314786911,
0.007040584925562143,
0.023278959095478058,
0.021352848038077354,
-0.019862044602632523,
-0.07131503522396088,
0.05319296196103096,
-0.017873186618089676,
-0.01670375093817711,
-0.0004387508670333773,
-0.021147724241018295,
-0.01033388078212738,
0.014428994618356228,
-0.03760426491498947,
0.01269160769879818,
0.004861848894506693,
-0.05381310358643532,
0.011846009641885757,
-0.021305439993739128,
-0.00332279852591455,
0.04766470938920975,
0.10243968665599823,
-0.023211702704429626,
-0.06163949891924858,
-0.05863817408680916,
-0.019265035167336464,
0.020910829305648804,
0.061859119683504105,
0.03669204190373421,
0.03361579403281212,
-0.05603369325399399,
0.0676506981253624,
-0.039892248809337616,
0.032151754945516586,
0.05970453843474388,
0.03032037243247032,
0.0457390733063221,
0.013315495103597641,
0.00013308774214237928,
-0.050720393657684326,
0.015122488141059875,
-0.03753538802266121,
0.006943756714463234,
-0.009896860457956791,
0.05857090279459953,
0.02693828195333481,
0.04780903458595276,
0.028733741492033005,
0.06434251368045807,
-0.016253501176834106,
-0.022223884239792824,
0.022060910239815712,
-0.03829637169837952,
-0.04469943791627884,
0.027923379093408585,
-0.05914582312107086,
-0.007090398576110601,
-0.01478785090148449,
-0.004666320513933897,
0.0024424537550657988,
-0.034442268311977386,
-0.0742892399430275,
-0.027533182874321938,
-0.07711941748857498,
0.060316286981105804,
-0.055962685495615005,
0.0007698129629716277,
-0.03160369396209717,
0.040048930794000626,
0.01279816497117281,
-0.09450557082891464,
0.0055449604988098145,
-0.012511023320257664,
0.07161595672369003,
0.022259026765823364,
-0.0038839203771203756,
0.011833097785711288,
0.022092575207352638,
0.09175481647253036,
0.01649628020823002,
0.021978022530674934,
-0.01852159947156906,
0.005262753926217556,
0.03203333914279938,
0.0066330283880233765,
-0.05396251752972603,
-0.01381852850317955,
0.033462297171354294,
0.00008167388295987621,
-0.07675589621067047,
-0.03642542287707329,
0.003463480854406953,
0.045153118669986725,
0.013699003495275974,
-0.03140125051140785,
0.03566611930727959,
0.01578282192349434,
-0.024597913026809692,
-0.03370035067200661,
-0.05151711776852608,
0.05754410848021507,
-0.0075943805277347565,
0.015814566984772682,
0.02168804034590721,
-0.047543592751026154,
0.011626901105046272,
0.028895901516079903,
0.050365038216114044,
0.034146979451179504,
-0.024407409131526947,
-0.023257629945874214,
0.008004903793334961,
-0.030208872631192207,
0.006514702457934618,
0.04243362322449684,
0.02481304667890072,
-0.01545612420886755,
0.014129875227808952,
0.05848678573966026,
0.010095435194671154,
0.0106848469004035,
0.00406084256246686,
0.05327202007174492,
-0.03168610483407974,
-0.02368202805519104,
0.045322369784116745,
0.028686560690402985,
-0.030340293422341347,
0.052426960319280624,
-0.0049290438182652,
0.026470830664038658,
-0.03528568893671036,
-0.010125997476279736,
0.03086378052830696,
-0.061365678906440735,
-0.02970636822283268,
-0.017446760088205338,
0.006283402908593416,
0.011541330255568027,
-0.003989187069237232,
0.09946379065513611,
0.021038224920630455,
-0.011379328556358814,
0.009166443720459938,
0.03368169441819191,
-0.018844114616513252,
-0.001088251476176083,
0.0032085091806948185,
-0.03125790134072304,
-0.06105593591928482,
-0.004575165919959545,
0.038266707211732864,
-0.02031875215470791,
0.029032405465841293,
0.05435354262590408,
0.0015841375570744276,
-0.004158275201916695,
0.002263007452711463,
-0.013248546980321407,
-0.04750877991318703,
0.030739804729819298,
0.01660660281777382,
-0.02279747650027275,
-0.008992179296910763,
0.045608941465616226,
-0.05556154251098633,
0.021466253325343132,
0.0031655726488679647,
-0.03764066472649574,
0.0669083297252655,
0.012761052697896957,
0.002458638744428754,
0.033327605575323105,
-0.025060242041945457,
-0.0001643841533223167,
0.007715568877756596,
0.04817395284771919,
-0.010999232530593872,
-0.0007415664731524885,
0.024731196463108063,
-0.03369494900107384,
0.03902895748615265,
-0.019441204145550728,
0.00788882840424776,
0.015552389435470104,
0.0027492863591760397,
0.07349321991205215,
-0.025104941800236702,
0.014295031316578388,
-0.040401142090559006,
0.014710679650306702,
-0.0339585617184639,
0.007249425631016493,
0.0677020251750946,
0.005173262674361467,
0.017066070809960365,
0.010383148677647114,
0.016616813838481903,
-0.002034164499491453,
0.05938715487718582,
-0.032282505184412,
0.01536470465362072,
-0.007905632257461548,
-0.04445001855492592,
0.02238532155752182,
0.009798000566661358,
-0.0036879917606711388,
0.011691097170114517,
0.02012350969016552,
-0.03847895562648773,
-0.0012037056731060147,
-0.03112039342522621,
-0.011397082358598709,
-0.016617944464087486,
0.004118225537240505,
-0.024311428889632225,
0.10566118359565735,
-0.037188053131103516,
-0.041877247393131256,
-0.026806926354765892,
-0.004005716647952795,
-0.008818778209388256,
0.020133379846811295,
0.02873365767300129,
0.01961159147322178,
0.00007545625703642145,
0.023255037143826485,
0.044614698737859726,
-0.021231895312666893,
-0.020172040909528732,
-0.04798471927642822,
0.04023068770766258,
0.024485893547534943,
0.007373750675469637,
0.03168544918298721,
0.015231345780193806,
0.03302302956581116,
-0.01741126738488674,
0.005637981928884983,
0.015230636112391949,
0.04520945996046066,
0.06399988383054733,
0.0382843054831028,
0.017048612236976624,
-0.08373638987541199,
0.013648390769958496,
0.059250473976135254,
-0.017815155908465385,
0.06725620478391647,
-0.0008120601414702833,
0.030754821375012398,
-0.031852222979068756,
0.016440751031041145,
0.008110590279102325,
-0.02598985843360424,
0.004213202744722366,
-0.03614647686481476,
-0.0066694761626422405,
-0.003776181722059846,
-0.028550615534186363,
-0.02577037923038006,
-0.022571926936507225,
0.05115475133061409,
-0.026797836646437645,
0.029639992862939835,
-0.008397978730499744,
0.008218959905207157,
0.003933996893465519,
-0.0624166764318943,
-0.07349656522274017,
-0.006979241035878658,
0.021522538736462593,
-0.02470347099006176,
-0.007269945926964283,
-0.02750655822455883,
-0.017959022894501686,
0.010486628860235214,
0.040746040642261505,
0.0123967994004488,
-0.0002574806858319789,
-0.008327704854309559,
-0.010464679449796677,
0.049499377608299255,
-0.05481462553143501,
0.06115761771798134,
0.027126865461468697,
-0.036755215376615524,
0.0015727372374385595,
-0.034202538430690765,
0.011395680718123913,
0.00807144120335579,
0.0002333710581297055,
-0.03710212931036949,
0.0006971205584704876,
0.03030748851597309,
0.00768679566681385,
0.015274195931851864,
-0.01891781948506832,
0.029176291078329086,
0.04273716360330582,
0.0023187496699392796,
0.013367638923227787,
-0.0506080761551857,
-0.022340519353747368,
0.028627468273043633,
-0.03695615008473396,
0.0006396894459612668,
-0.05521086975932121,
-0.031279124319553375,
-0.03888232633471489,
-0.02289176732301712,
-0.03326180949807167,
-0.011922864243388176,
0.06243718042969704,
0.05060968175530434,
-0.01577906310558319,
0.002603325992822647,
-0.01248665526509285,
0.060670431703329086,
0.0007801222382113338,
-0.021693438291549683,
-0.01796678639948368,
0.06907936185598373,
-0.03592032939195633,
-0.01115665677934885,
-0.006549591664224863,
0.06469239294528961,
0.04234141483902931,
0.018445875495672226,
0.020342055708169937,
-0.027230948209762573,
0.00727187329903245,
-0.034043557941913605,
0.026244690641760826,
-0.03720558434724808,
0.00003961598122259602,
-0.015370271168649197,
0.05564747750759125,
-0.02111390233039856,
-0.060401551425457,
0.02396513894200325,
0.016583241522312164,
-0.020917879417538643,
-0.04158514738082886,
0.023639284074306488,
-0.0504678338766098,
0.02245202846825123,
0.07582497596740723,
0.013399924151599407,
0.002239442430436611,
-0.06619752943515778,
0.030333520844578743,
-0.02028677985072136,
-0.007962647825479507,
-0.0063453055918216705,
-0.06044584885239601,
0.015228052623569965,
0.01660296693444252,
0.015232994221150875,
0.01757572405040264,
0.0167799424380064,
0.036005329340696335,
0.0024747683200985193,
0.0009007119806483388,
0.02664310112595558,
0.04753949120640755,
0.012560030445456505,
-0.01294878963381052,
0.03344488516449928,
-0.021610217168927193,
-0.0012768603628501296,
-0.014876129105687141,
0.014689779840409756,
0.011122843250632286,
0.006632061209529638,
-0.01487059611827135,
0.012126447632908821,
-0.023349372670054436,
0.06808488070964813,
0.056916605681180954,
0.0020784565713256598,
-0.012271266430616379,
0.033524759113788605,
-0.0933278277516365,
0.0728989839553833,
-0.018088730052113533,
-0.03732044994831085,
0.005557442549616098,
-0.018121832981705666,
0.03947801515460014,
-0.01850675605237484,
-0.021941669285297394,
-0.018580671399831772,
0.0176541768014431,
-0.01720224879682064,
-0.039923448115587234,
0.0258675254881382,
-0.044636908918619156,
0.008365962654352188,
0.02704404853284359,
-0.03555505350232124,
0.010623638518154621,
-0.04366592317819595,
-0.0014527665916830301,
-0.03873439505696297,
-0.009520034305751324,
0.014055929146707058,
-0.029598699882626534,
0.004686892032623291,
0.023550305515527725,
0.03167199715971947,
0.03360402211546898,
-0.033381324261426926,
-0.06985516846179962,
-0.054937075823545456,
0.02549423836171627,
-0.06650781631469727,
-0.053310591727495193,
0.044304683804512024,
-0.08207771182060242,
0.032851047813892365,
-0.11083078384399414,
0.004888600669801235,
-0.020821459591388702,
0.0046356781385838985,
-0.04913368076086044,
-0.026995431631803513,
-0.022415710613131523,
-0.033692095428705215,
-0.020367905497550964,
-0.0032030073925852776,
0.019841820001602173,
-0.031300898641347885,
-0.07623104751110077,
-0.011160053312778473,
0.003994166851043701,
0.0075840335339307785,
0.020641734823584557,
-0.01671367511153221,
-0.04500728100538254,
-0.00010001561167882755,
0.018990352749824524,
0.0041345530189573765,
-0.06472337245941162,
-0.0003106659569311887,
-0.011763395741581917,
-0.01507013849914074,
-0.029361888766288757,
0.015471412800252438,
-0.03479953855276108,
-0.0025548599660396576,
0.036516446620225906,
-0.0267698522657156,
0.06847451627254486,
-0.018820008262991905,
-0.06754811108112335,
0.002050435170531273,
-0.0021601798944175243,
0.012660074979066849,
0.0056043947115540504,
-0.022208550944924355,
-0.07069740444421768,
-0.04427623376250267,
0.012648840434849262,
-0.0049801538698375225,
0.06835664063692093,
-0.007635983172804117,
-0.012960453517735004,
0.0052112312987446785,
0.033079247921705246,
0.03958263620734215,
-0.07187295705080032,
0.007771074306219816,
0.05269719287753105,
0.0028055908624082804,
0.08358398079872131,
-0.04269363358616829,
0.040601685643196106,
-0.003449204144999385,
-0.003754754550755024,
-0.0005822324310429394,
-0.03353264182806015,
-0.00045286366366781294,
-0.001307253842242062,
0.048995960503816605,
-0.0026635699905455112,
0.004806326702237129,
-0.05092697590589523,
0.03159685805439949,
-0.003339767688885331,
0.04713359475135803,
-0.06325016915798187,
0.004847895819693804,
0.02406931295990944,
-0.01180205587297678,
-0.028663821518421173,
-0.006679263897240162,
0.05556623265147209,
-0.007801578845828772,
-0.04746680706739426,
0.002570902230218053,
-0.013247580267488956,
-0.05405208840966225,
0.07239700853824615,
-0.07802285999059677,
0.018711423501372337,
-0.01578539051115513,
0.05116827413439751,
0.05876871943473816,
-0.0429508350789547,
-0.06911429017782211,
0.017740795388817787,
0.03478532284498215,
-0.05385822057723999,
0.019813453778624535,
-0.018763944506645203,
0.020156268030405045,
-0.016347816213965416,
0.0598808117210865,
0.043333910405635834,
0.011626532301306725,
0.0026666377671062946,
0.020666737109422684,
-0.00294335070066154,
0.04086770489811897,
-0.001294309040531516,
-0.021561194211244583,
-0.007031532470136881,
-0.04731296747922897,
-0.03511103242635727,
-0.0013125474797561765,
0.01878201775252819,
0.019414063543081284,
-0.02078285813331604,
0.004161423537880182,
0.005665939766913652,
-0.05744951590895653,
-0.02285238727927208,
-0.028298066928982735,
0.025438278913497925,
-0.0559333972632885,
0.016553731635212898,
-0.006337368860840797,
-0.036803461611270905,
0.04590238630771637,
0.018151532858610153,
-0.04471631720662117,
-0.008968881331384182,
0.05049881339073181,
0.035516686737537384,
0.01929762214422226,
-0.018418995663523674,
0.007054806221276522,
-0.03934264928102493,
-0.015189729630947113,
-0.017403962090611458,
-0.033381957560777664,
-0.07620644569396973,
0.030890464782714844,
0.06080804765224457,
-0.002847556257620454,
-0.04268290102481842,
0.025774383917450905,
-0.02532077766954899,
-0.05545388534665108,
-0.01379106380045414,
0.026179922744631767,
0.02635357156395912,
0.011667361482977867,
0.07509207725524902,
0.014167317189276218,
0.06824269890785217,
-0.05296117439866066,
-0.007046924903988838,
0.02001526951789856,
0.040052395313978195,
0.01870187744498253,
-0.03570469096302986,
-0.012246607802808285,
-0.0023777750320732594,
0.062133628875017166,
0.0029403804801404476,
-0.08971140533685684,
-0.0035104749258607626,
0.04271306097507477,
-0.020309899002313614,
-0.04531434550881386,
-0.01765958033502102,
0.030430002138018608,
-0.05346932262182236,
-0.07063915580511093,
0.07925062626600266,
0.003952356521040201,
-0.052011869847774506,
-0.021551188081502914,
-0.017431316897273064,
0.008145165629684925,
-0.0015837933169677854,
0.03086203522980213,
-0.03459205850958824,
-0.06060825660824776,
0.07531367242336273,
0.02468911185860634,
0.01109366025775671,
-0.06591921299695969,
0.03375332057476044,
-0.046905890107154846,
-0.00710542406886816,
0.04736051335930824,
-0.013959753327071667,
0.022840233519673347,
0.018704695627093315,
-0.029130976647138596,
-0.008021253161132336,
-0.08153630048036575,
0.03103606402873993,
0.0788087472319603,
0.021057402715086937,
-0.03843114525079727,
0.018273981288075447,
-0.056169576942920685,
-0.0015446379547938704,
0.015750635415315628,
0.006821400951594114,
0.024313239380717278,
0.025853309780359268,
0.06898311525583267,
-0.00850137509405613,
0.055278073996305466,
-0.032063551247119904,
-0.027680780738592148,
0.024474963545799255,
0.0494810976088047,
-0.036652516573667526,
0.013810344971716404,
-0.017018362879753113
] |
[
1.829657793045044,
8.02159309387207
] |
Computational Engineering, Finance, and Science
|
Computer Science
|
cs-CE
|
cond-mat-stat-mech
|
cs-MS
|
2007-04-01T15:17:36
|
We combine classical methods of combinatorial group theory with the theory of
small cancellations over relatively hyperbolic groups to construct finitely
generated torsion-free groups that have only finitely many classes of conjugate
elements. Moreover, we present several results concerning embeddings into such
groups.
As another application of these techniques, we prove that every countable
group $C$ can be realized as a group of outer automorphisms of a group $N$,
where $N$ is a finitely generated group having Kazhdan's property (T) and
containing exactly two conjugacy classes.
|
Groups with finitely many conjugacy classes and their automorphisms
|
math.GR
|
0704.0091
| 2,007
|
[
-0.0018423531437292695,
0.08010877668857574,
-0.016038501635193825,
-0.03001866117119789,
-0.015676410868763924,
-0.016542470082640648,
-0.020588481798768044,
0.031187603250145912,
-0.012355142273008823,
-0.03272341191768646,
-0.07527825236320496,
0.018466198816895485,
-0.0013160313246771693,
0.04101725295186043,
0.0516892746090889,
0.006178584881126881,
0.013745984993875027,
0.0036948625929653645,
0.000011692734915413894,
0.01051049679517746,
0.0015108732040971518,
-0.012773025780916214,
-0.015690336003899574,
-0.03201845660805702,
0.11139187961816788,
0.027717512100934982,
0.04433863237500191,
0.027117418125271797,
-0.014318917877972126,
0.03560858592391014,
0.05775456503033638,
-0.01959872432053089,
0.013518012128770351,
-0.026822641491889954,
-0.04174673557281494,
-0.013478651642799377,
0.04167395085096359,
-0.01749124564230442,
-0.007278867531567812,
-0.007356415968388319,
0.060213007032871246,
0.036103397607803345,
0.03580557927489281,
-0.0431971549987793,
-0.004105547443032265,
0.0049719312228262424,
0.09048905968666077,
0.015322172082960606,
0.003095915075391531,
-0.06283646076917648,
-0.05480228364467621,
-0.001154961995780468,
0.03608211502432823,
-0.06310249865055084,
-0.04859636723995209,
0.018326302990317345,
0.006105636712163687,
-0.029073212295770645,
0.04311375692486763,
0.002133512869477272,
0.010928493924438953,
0.08016329258680344,
-0.06596003472805023,
0.031105583533644676,
0.008989105001091957,
-0.04977356269955635,
-0.054891906678676605,
0.028710396960377693,
0.060760535299777985,
0.0016076945466920733,
0.0318613275885582,
-0.004486674442887306,
0.0324990414083004,
-0.02514825016260147,
-0.036465175449848175,
0.038926735520362854,
0.018719257786870003,
-0.005492852535098791,
0.003807530738413334,
0.005886103492230177,
0.02808947116136551,
-0.0314660482108593,
-0.018336297944188118,
-0.033063702285289764,
-0.000005917740963923279,
-0.015592589974403381,
0.024094929918646812,
0.013955960050225258,
-0.08413005620241165,
0.018063072115182877,
0.044603489339351654,
0.011206792667508125,
0.03579992055892944,
0.061194054782390594,
-0.010597572661936283,
0.02453717403113842,
0.010437579825520515,
0.05826578289270401,
-0.003750490490347147,
-0.08922936022281647,
0.030377039685845375,
0.09377668052911758,
0.041076600551605225,
0.0410877950489521,
0.041223157197237015,
0.009315180592238903,
0.05377751216292381,
-0.008214409463107586,
0.01554900873452425,
-0.019673306494951248,
-0.08961758762598038,
0.020757758989930153,
-0.018464377149939537,
-0.029168471693992615,
0.006393834482878447,
0.029535489156842232,
0.012838717550039291,
-0.0622476227581501,
0.04812733083963394,
0.034365374594926834,
-0.013239914551377296,
-0.05938158184289932,
-0.014776011928915977,
0.050942663103342056,
0.028575066477060318,
0.04185958579182625,
-0.03407541662454605,
-0.01806238293647766,
-0.003322874428704381,
-0.05154598876833916,
0.018231043592095375,
-0.0215873084962368,
0.00946139357984066,
-0.006743303965777159,
0.017786595970392227,
0.021280746906995773,
-0.058382950723171234,
-0.013673648238182068,
0.029496340081095695,
-0.03801852464675903,
-0.028698423877358437,
0.007599474396556616,
-0.010837304405868053,
0.012426819652318954,
0.056592680513858795,
-0.06245976686477661,
-0.017385654151439667,
-0.07939803600311279,
-0.04484628885984421,
0.026513146236538887,
0.02743827924132347,
0.03544941917061806,
0.06190324202179909,
0.008430750109255314,
-0.03968299925327301,
-0.023877963423728943,
-0.006588813848793507,
0.03111451119184494,
0.039845142513513565,
-0.007730057928711176,
0.0425417535007,
0.022187650203704834,
-0.05556030571460724,
0.019935347139835358,
-0.04886237531900406,
0.001864652382209897,
-0.034093257039785385,
-0.009645609185099602,
-0.04149164631962776,
0.04356784746050835,
-0.033766236156225204,
-0.010174150578677654,
-0.012055330909788609,
0.013593102805316448,
0.024296481162309647,
0.009255421347916126,
-0.04864061251282692,
-0.02555129863321781,
0.04268546402454376,
0.024891024455428123,
0.030208980664610863,
0.030101999640464783,
0.027582699432969093,
0.10134481638669968,
0.02028743550181389,
0.0012918140273541212,
0.005451491102576256,
0.00199170783162117,
0.004452617838978767,
-0.018942341208457947,
0.03530304878950119,
0.02674183063209057,
-0.03813658654689789,
-0.05498943850398064,
-0.028238125145435333,
0.015734465792775154,
0.0036297759506851435,
0.007879117503762245,
-0.008638371713459492,
-0.026231549680233,
0.01849617063999176,
0.01977076195180416,
-0.05984535440802574,
-0.034378424286842346,
-0.0416983887553215,
0.06230573356151581,
0.03261352702975273,
0.009450588375329971,
-0.007171731907874346,
-0.04992916062474251,
0.09216149896383286,
0.03184488043189049,
-0.0147910350933671,
0.025719450786709785,
-0.024960238486528397,
-0.01217043399810791,
0.00854717381298542,
-0.06276559084653854,
-0.04787704348564148,
0.014061116613447666,
0.08173666894435883,
-0.019720816984772682,
-0.0054839071817696095,
-0.03353135287761688,
0.04416971281170845,
0.048237938433885574,
-0.04942232370376587,
0.008658562786877155,
-0.041416823863983154,
-0.03884376212954521,
0.012610788457095623,
-0.042331259697675705,
0.01938624680042267,
-0.04037831723690033,
-0.030915291979908943,
0.016993705183267593,
-0.028343673795461655,
0.053342122584581375,
0.03314678370952606,
0.042309656739234924,
0.043495066463947296,
0.01177956536412239,
0.018701180815696716,
-0.03950924798846245,
-0.04832172021269798,
-0.03494633734226227,
-0.05074889212846756,
-0.011165331117808819,
-0.004957371391355991,
0.02440066449344158,
-0.010621684603393078,
0.018166445195674896,
-0.017959360033273697,
0.029049569740891457,
0.016068441793322563,
0.024338610470294952,
-0.03556523472070694,
0.014141148887574673,
0.015670593827962875,
-0.0011831976007670164,
0.025548188015818596,
-0.011690596118569374,
0.02847261168062687,
-0.07615739107131958,
-0.05215328559279442,
-0.039044659584760666,
0.05458909273147583,
-0.043185263872146606,
0.034778494387865067,
-0.011879704892635345,
0.024657687172293663,
0.04330261051654816,
0.08886241167783737,
0.03448699042201042,
-0.021817181259393692,
-0.026673169806599617,
-0.01222898531705141,
-0.026766424998641014,
-0.053165365010499954,
-0.016949215903878212,
0.033183664083480835,
-0.02715911716222763,
-0.05356621742248535,
0.014587106183171272,
-0.026294834911823273,
0.05357383191585541,
0.05713242292404175,
-0.016395218670368195,
0.007821934297680855,
0.05075211822986603,
-0.038405630737543106,
-0.009072457440197468,
0.0445731058716774,
0.022653905674815178,
0.06522327661514282,
0.026028713211417198,
0.011015640571713448,
0.0011713147396221757,
-0.042752087116241455,
-0.0138215571641922,
-0.051452118903398514,
0.022816341370344162,
0.03195013850927353,
-0.012340179644525051,
0.01405672263354063,
-0.008535807952284813,
-0.014106416143476963,
-0.007065630052238703,
0.029737072065472603,
-0.0003401437134016305,
-0.0320596843957901,
0.05172055959701538,
-0.014376499690115452,
0.0008298754110001028,
-0.06472431123256683,
0.06041925773024559,
0.02111842669546604,
-0.008838393725454807,
0.08065192401409149,
-0.02098120003938675,
-0.009830943308770657,
-0.03963322192430496,
0.06386193633079529,
-0.024190744385123253,
0.012728431262075901,
-0.005960124544799328,
-0.06405913084745407,
-0.02316858619451523,
0.015054837800562382,
-0.036353278905153275,
-0.0018148140516132116,
0.042328834533691406,
0.002676053438335657,
-0.019855493679642677,
-0.02707531861960888,
-0.03129539638757706,
-0.030527105554938316,
0.059063754975795746,
0.015905102714896202,
0.0029221964068710804,
-0.008179716765880585,
-0.028496157377958298,
-0.04307558387517929,
-0.04477931931614876,
0.018102210015058517,
0.028292544186115265,
-0.014437147416174412,
0.00952227134257555,
0.04162752255797386,
-0.017084548249840736,
-0.04138262942433357,
-0.005897383205592632,
-0.005991721525788307,
-0.04237902909517288,
-0.03475993871688843,
0.07321371138095856,
0.023101039230823517,
-0.00017145590391010046,
0.04705001041293144,
0.04058888554573059,
0.018931223079562187,
-0.031032348051667213,
-0.008476522751152515,
-0.03131050616502762,
0.0210578553378582,
0.04362049326300621,
0.022398775443434715,
0.02424134500324726,
0.02875351533293724,
-0.04493293538689613,
-0.011266272515058517,
-0.11618153005838394,
-0.013597497716546059,
0.05319821089506149,
0.021120034158229828,
-0.011010474525392056,
-0.029383374378085136,
0.0821448490023613,
-0.001108528464101255,
-0.03256572410464287,
0.0673048347234726,
0.019695738330483437,
0.08359188586473465,
0.025572316721081734,
-0.016678282991051674,
0.048910509794950485,
-0.03491508588194847,
0.036835215985774994,
-0.059554435312747955,
0.007944963872432709,
0.0032407334074378014,
-0.04109175503253937,
-0.006866851355880499,
0.035436417907476425,
-0.021359577775001526,
-0.027019411325454712,
0.001953436993062496,
-0.02700512856245041,
0.06299612671136856,
-0.03543279692530632,
-0.04255996271967888,
-0.050361525267362595,
0.01047609280794859,
-0.0595342218875885,
-0.03826729580760002,
0.009024236351251602,
0.003447231836616993,
-0.051371991634368896,
0.06972626596689224,
0.015371867455542088,
-0.009996505454182625,
-0.027028389275074005,
0.04401497170329094,
-0.10452040284872055,
0.028019830584526062,
0.026474179700016975,
0.03286949545145035,
0.018971266224980354,
0.02339417301118374,
-0.03381887823343277,
-0.047247689217329025,
0.05067167431116104,
-0.037106215953826904,
-0.015092555433511734,
-0.05806929990649223,
0.027863001450896263,
-0.01765667088329792,
-0.008842011913657188,
-0.04053986445069313,
-0.08219172060489655,
0.0290133785456419,
0.0034313220530748367,
0.023080408573150635,
0.0011293449206277728,
-0.06373664736747742,
-0.041436899453401566,
-0.048493389040231705,
0.01802011765539646,
-0.024402538314461708,
0.023189468309283257,
0.03958208113908768,
-0.01629483699798584,
0.018240120261907578,
-0.04878270626068115,
0.0676412582397461,
0.037971366196870804,
0.08892809599637985,
-0.0031022222246974707,
-0.0015109627274796367,
0.0014420743100345135,
0.05977928265929222,
0.0033595634158700705,
-0.004114258103072643,
0.07097750157117844,
0.06277873367071152,
-0.04626961797475815,
-0.05949015915393829,
-0.016617421060800552,
0.029100440442562103,
0.01571214199066162,
0.011807624250650406,
0.015744194388389587,
0.020647544413805008,
0.04473906010389328,
0.005270966328680515,
-0.017581116408109665,
0.027941718697547913,
0.009127588011324406,
0.017244679853320122,
0.055189892649650574,
-0.00743516581133008,
0.0362827405333519,
-0.011119860224425793,
-0.02389140985906124,
-0.043689049780368805,
-0.018666405230760574,
0.027676861733198166,
-0.0015019342536106706,
-0.0038637742400169373,
0.02280961163341999,
0.06441555172204971,
-0.04142346978187561,
-0.03109787032008171,
0.003913747146725655,
-0.0020560165867209435,
0.018449457362294197,
0.024139372631907463,
-0.044315628707408905,
-0.010844314470887184,
-0.009602762758731842,
-0.005620360840111971,
0.028293723240494728,
-0.028391454368829727,
0.027358941733837128,
-0.03698057308793068,
-0.03692443668842316,
0.04127555340528488,
-0.028621217235922813,
0.03093225136399269,
-0.05037041753530502,
-0.02609284594655037,
0.02388397976756096,
0.01518796756863594,
0.04316546022891998,
0.05522589758038521,
-0.02849988266825676,
-0.006396412383764982,
-0.04854433238506317,
-0.01610420271754265,
-0.0005179491126909852,
-0.04513354226946831,
0.038418155163526535,
0.028151845559477806,
0.07657116651535034,
0.031264372169971466,
0.030839374288916588,
-0.026495104655623436,
-0.040752705186605453,
-0.08087120205163956,
0.0024616271257400513,
-0.05058074742555618,
-0.03761490806937218,
0.021715402603149414,
-0.01326675433665514,
-0.044219210743904114,
0.038554344326257706,
-0.006256608292460442,
-0.1237812489271164,
0.00431000767275691,
0.0074788290075957775,
0.010048098862171173,
-0.031867533922195435,
-0.03341231495141983,
-0.059494007378816605,
0.02555869333446026,
-0.007317489944398403,
-0.009707165881991386,
0.013274247758090496,
0.004296985920518637,
0.01509612612426281,
0.018703263252973557,
-0.016352945938706398,
-0.014329303987324238,
-0.034056928008794785,
-0.03137603774666786,
0.003895208705216646,
-0.07656325399875641,
0.007351827807724476,
-0.013149741105735302,
0.008896497078239918,
0.030315445736050606,
-0.05972342938184738,
0.03931952640414238,
-0.0634850561618805,
0.02593732811510563,
-0.005447701085358858,
-0.015409136191010475,
-0.02023359388113022,
0.0010530429426580667,
-0.0024868014734238386,
0.007246722001582384,
0.02193683758378029,
0.029604032635688782,
-0.000871146796271205,
0.01604517363011837,
-0.07427825778722763,
-0.024522846564650536,
-0.00895950011909008,
0.02509974129498005,
-0.02575347013771534,
-0.002432021778076887,
-0.02380436286330223,
0.015128728933632374,
0.05520821735262871,
0.027269253507256508,
-0.05536969006061554,
0.043773360550403595,
0.015120700001716614,
-0.01859564147889614,
0.0066397348418831825,
-0.006918787490576506,
-0.05720265954732895,
0.00622603390365839,
0.00835352297872305,
-0.04566589742898941,
-0.0010486928513273597,
0.011460126377642155,
-0.04455273970961571,
0.016662556678056717,
-0.01926347054541111,
-0.0006568945827893913,
-0.002049644012004137,
-0.0281121414154768,
0.05688556656241417,
-0.004448689054697752,
0.01838061772286892,
0.02519989386200905,
-0.025788798928260803,
-0.011445540003478527,
-0.06898072361946106,
0.029737280681729317,
0.03245682641863823,
0.09577248245477676,
-0.02514493279159069,
0.05434463173151016,
0.06421776860952377,
-0.047326281666755676,
-0.013528694398701191,
0.018632451072335243,
-0.00883239321410656,
-0.014943869784474373,
0.012873897328972816,
-0.012796253897249699,
-0.04266336187720299,
-0.029570547863841057,
-0.03885570541024208,
0.022607170045375824,
-0.0763072520494461,
0.038075923919677734,
-0.009930667467415333,
0.0023357151076197624,
-0.04670898616313934,
0.05274752154946327,
-0.03680221736431122,
0.013651370070874691,
0.035671915858983994,
-0.002162872115150094,
-0.05751316249370575,
0.006180469878017902,
0.07814257591962814,
0.03744718059897423,
-0.040130678564310074,
0.01517810020595789,
-0.02651412971317768,
-0.04615160822868347,
0.014864389784634113,
-0.038823843002319336,
0.0358404815196991,
0.00949328113347292,
0.03565116599202156,
0.04200855270028114,
-0.044047921895980835,
0.0007656156085431576,
0.018946222960948944,
0.05316309258341789,
-0.02228401228785515,
0.02263346128165722,
-0.01892642304301262,
0.016509464010596275,
-0.02747567929327488,
0.06905445456504822,
0.042136985808610916,
0.0017947334563359618,
0.03880245238542557,
-0.04831117019057274,
-0.015177964232861996,
0.06109267473220825,
0.013287466019392014,
-0.04129381477832794,
0.017264453694224358,
-0.020894890651106834,
0.015715423971414566,
-0.013540170155465603,
0.002751389052718878,
0.018012939020991325,
-0.003340424969792366,
-0.01332226675003767,
-0.042609021067619324,
-0.04358493536710739,
0.02537260204553604,
-0.03001607209444046,
-0.015652257949113846,
-0.017839154228568077,
-0.014216539449989796,
-0.05565984547138214,
-0.03294464200735092,
0.035051409155130386,
0.04625111073255539,
0.02137560397386551,
-0.03377499431371689,
-0.03501635789871216,
0.02560395747423172,
0.0005352844018489122,
0.023558160290122032,
0.0004905245150439441,
-0.03890831023454666,
-0.008244129829108715,
0.0025168347638100386,
-0.015247209928929806,
-0.009780306369066238,
0.04599308967590332,
-0.03160594776272774,
0.020546771585941315,
-0.038221169263124466,
0.009654844179749489,
-0.01644361950457096,
-0.015854619443416595,
-0.011793809942901134,
0.004061212297528982,
0.007746940478682518,
0.021822070702910423,
-0.00021922867745161057,
-0.03511325269937515,
0.006537408567965031,
-0.019703639671206474,
0.012338956817984581,
-0.02404937893152237,
0.04233768582344055,
0.009311790578067303,
-0.005325718317180872,
0.028616726398468018,
-0.006009102798998356,
0.038046907633543015,
0.009473225101828575,
0.07031121850013733,
0.020761046558618546,
-0.06579725444316864,
-0.04420190677046776,
0.028273005038499832,
0.022106779739260674,
0.05705922469496727,
-0.06217096373438835,
-0.012125336565077305,
0.014033743180334568,
-0.04807459935545921,
-0.07709971815347672,
0.026829615235328674,
-0.02030796930193901,
0.03446591645479202,
0.08693405240774155,
0.017422879114747047,
-0.012605259194970131,
-0.03253789618611336,
0.03346412628889084,
-0.04098058119416237,
-0.04220554977655411,
-0.04121992737054825,
-0.027421265840530396,
-0.003706506220623851,
-0.010597280226647854,
-0.005107713397592306,
0.03799067437648773,
0.02701244130730629,
0.012911182828247547,
-0.008170804008841515,
0.004549749195575714,
-0.06738150119781494,
0.022787373512983322,
0.04207596927881241,
0.032539986073970795,
-0.03983153775334358,
0.012873649597167969,
0.026584405452013016,
-0.0019859818276017904,
-0.010722489096224308,
0.03093031793832779,
0.031173812225461006,
0.0033674074802547693,
0.03145748749375343,
0.008639045991003513,
0.057333387434482574,
0.03767004981637001,
-0.02340070530772209,
0.038858041167259216,
-0.03073710948228836,
-0.01063796691596508,
-0.0515480674803257,
-0.05421619489789009
] |
[
1.1242073774337769,
2.5382513999938965
] |
Group Theory
|
Mathematics
|
math-GR
|
na
|
na
|
2007-04-01T16:20:10
|
We study a recently proposed formulation of overlap fermions at finite
density. In particular we compute the energy density as a function of the
chemical potential and the temperature. It is shown that overlap fermions with
chemical potential reproduce the correct continuum behavior.
|
Energy density for chiral lattice fermions with chemical potential
|
hep-lat hep-ph
|
0704.0092
| 2,007
|
[
0.010597224347293377,
0.03931274265050888,
0.003198083257302642,
-0.0500076562166214,
0.02236037515103817,
0.005465228110551834,
-0.05007578432559967,
0.05027471110224724,
-0.038467686623334885,
0.042112190276384354,
-0.04037562012672424,
0.022968580946326256,
-0.012122049927711487,
0.0077755446545779705,
0.0010583458933979273,
0.035287756472826004,
0.030297262594103813,
0.004123760852962732,
0.02203438989818096,
0.02020217850804329,
-0.06671709567308426,
-0.025200748816132545,
0.0011677710572257638,
-0.06984926015138626,
0.09174637496471405,
-0.011250127106904984,
0.0183352530002594,
0.01864425279200077,
-0.05906981974840164,
-0.02072599157691002,
0.029948679730296135,
-0.018125835806131363,
0.017023636028170586,
-0.014235802926123142,
-0.016165729612112045,
-0.005995079409331083,
0.07004144787788391,
-0.0416996143758297,
-0.001961516449227929,
-0.009590836241841316,
0.030463144183158875,
-0.042958978563547134,
0.034848809242248535,
-0.04607356712222099,
-0.030566291883587837,
0.05848468095064163,
-0.01072258222848177,
0.028972437605261803,
0.014634386636316776,
0.022700529545545578,
-0.022768402472138405,
0.06645269691944122,
-0.008209681138396263,
-0.03475042060017586,
0.019447186961770058,
0.018413925543427467,
0.012873929925262928,
-0.020570697262883186,
0.05608602240681648,
-0.010670666582882404,
0.03502897918224335,
0.017643466591835022,
-0.015156889334321022,
0.02586561068892479,
0.0800698772072792,
-0.01709013618528843,
-0.05206030607223511,
0.0351807177066803,
0.02789206989109516,
-0.08459790050983429,
0.012576550245285034,
-0.0013902978971600533,
0.004388837143778801,
0.018110089004039764,
-0.003074351465329528,
-0.04428150877356529,
0.002545507624745369,
-0.010197542607784271,
-0.004716150928288698,
-0.011010914109647274,
-0.03645453602075577,
-0.061310138553380966,
0.040913332253694534,
0.012189884670078754,
0.09862124919891357,
0.004403493832796812,
0.02048683539032936,
0.025415239855647087,
-0.09708263725042343,
0.01560057234019041,
-0.00010833786654984578,
-0.04491448402404785,
0.014042338356375694,
0.025913909077644348,
-0.07896770536899567,
-0.011875712312757969,
0.005394482985138893,
0.0010709544876590371,
0.01652286760509014,
-0.04044041782617569,
-0.03256881237030029,
0.08428885787725449,
0.056131623685359955,
-0.014271914958953857,
-0.008085320703685284,
0.008413528092205524,
-0.006929855793714523,
-0.01152986753731966,
0.006685429252684116,
0.0490296371281147,
-0.06934796273708344,
-0.013139373622834682,
0.037859197705984116,
-0.04390717297792435,
0.018060963600873947,
-0.052054084837436676,
0.07705020159482956,
-0.05963137000799179,
-0.020859304815530777,
0.04420328885316849,
0.0010571310995146632,
0.046541646122932434,
0.034546107053756714,
0.030933907255530357,
0.009234766475856304,
-0.002261136192828417,
-0.06815152615308762,
-0.013114700093865395,
-0.014527049846947193,
-0.04329298064112663,
0.029475349932909012,
0.0009360909461975098,
-0.0555017851293087,
-0.00825361255556345,
0.02381492406129837,
-0.020199211314320564,
-0.03269977122545242,
-0.0023144155275076628,
0.02696058712899685,
0.014428351074457169,
0.024358881637454033,
-0.038531504571437836,
0.0375383161008358,
-0.019649550318717957,
0.013287820853292942,
-0.05898548662662506,
-0.02515583112835884,
-0.062299154698848724,
-0.018175944685935974,
-0.02470775879919529,
0.06073600426316261,
0.05509974807500839,
0.0232878215610981,
0.006242846604436636,
-0.028376398608088493,
-0.03619867190718651,
-0.0012704504188150167,
0.005786191206425428,
0.04539697617292404,
-0.003253529779613018,
0.020298926159739494,
-0.006646444555372,
-0.05773717910051346,
0.02273447997868061,
0.002287576673552394,
0.02995266206562519,
0.03221718594431877,
0.0030819617677479982,
0.007268883287906647,
0.04296140372753143,
-0.03414430096745491,
0.02436857484281063,
-0.05536458641290665,
-0.002106034429743886,
-0.015521778725087643,
-0.00970520731061697,
-0.023613665252923965,
-0.018448296934366226,
0.05215762183070183,
0.033096808940172195,
0.03211640194058418,
-0.014478619210422039,
0.048395171761512756,
0.057838570326566696,
-0.0080074118450284,
0.05023647099733353,
0.028998615220189095,
-0.04469490796327591,
-0.022718606516718864,
-0.013677303679287434,
0.037045374512672424,
0.010507483966648579,
-0.0031384085305035114,
-0.06095065921545029,
0.03436119481921196,
-0.02630600705742836,
0.0946478322148323,
-0.004777065012603998,
-0.007820433005690575,
-0.10615262389183044,
-0.0638868436217308,
0.017036661505699158,
-0.02886335924267769,
0.03079913556575775,
0.0284712053835392,
0.07526513189077377,
-0.007496642880141735,
-0.017824478447437286,
0.05951043590903282,
-0.01757751777768135,
0.017078448086977005,
-0.013626433908939362,
-0.018011918291449547,
0.08708546310663223,
0.01495016273111105,
-0.03197284787893295,
-0.02541024424135685,
-0.02535981312394142,
-0.03552572429180145,
0.03898843005299568,
0.01513480581343174,
-0.037101276218891144,
0.008225328288972378,
0.041058022528886795,
0.01745525561273098,
0.02886124700307846,
0.009054074063897133,
-0.019366374239325523,
0.02398381382226944,
-0.025219321250915527,
-0.008485506288707256,
0.0053143869154155254,
0.04837159812450409,
-0.04873138293623924,
-0.011168991215527058,
0.04610057547688484,
-0.06642182171344757,
0.05825554206967354,
0.01608835719525814,
0.018755754455924034,
-0.024043969810009003,
0.009921375662088394,
-0.006831916514784098,
0.01919206604361534,
-0.006423481740057468,
0.030003590509295464,
-0.010396512225270271,
-0.020525595173239708,
0.023111402988433838,
-0.004242801107466221,
0.07160893827676773,
0.042307231575250626,
-0.0115836001932621,
0.048034388571977615,
0.0012872572988271713,
-0.012114983052015305,
-0.06520934402942657,
0.0459032766520977,
-0.0172137301415205,
-0.09301824122667313,
0.049645934253931046,
-0.05377526953816414,
-0.014657833613455296,
-0.045677028596401215,
-0.021129745990037918,
0.03879666328430176,
0.02361135184764862,
-0.015225157141685486,
-0.013951113447546959,
0.0023564747534692287,
0.03016345202922821,
0.044179756194353104,
0.068658746778965,
0.06072422116994858,
-0.034878797829151154,
-0.009671825915575027,
0.0140709038823843,
-0.040310829877853394,
0.009057268500328064,
-0.039414115250110626,
-0.012698132544755936,
-0.004885867703706026,
-0.04006578400731087,
-0.029458321630954742,
-0.019051918759942055,
-0.01037663221359253,
0.06957607716321945,
-0.033561110496520996,
0.04567159339785576,
0.002072900300845504,
0.040936179459095,
-0.005720649845898151,
-0.004174137953668833,
0.0807957798242569,
-0.040773387998342514,
-0.00384637457318604,
0.07532459497451782,
-0.001945525873452425,
-0.037680838257074356,
0.02346753515303135,
-0.009368976578116417,
0.003962977789342403,
-0.009191270917654037,
0.03102310188114643,
0.03653300181031227,
-0.010804900899529457,
-0.019726552069187164,
0.02462640590965748,
-0.023816192522644997,
-0.03990013152360916,
0.007802282460033894,
0.05103181302547455,
-0.006631175521761179,
0.007669214624911547,
-0.06161026284098625,
0.01686990074813366,
0.005925008561462164,
-0.0034350724890828133,
0.12737137079238892,
-0.03139382228255272,
0.05575751140713692,
0.0009679771610535681,
0.015331992879509926,
-0.04170157387852669,
-0.015181172639131546,
0.0004522494855336845,
0.0017214594408869743,
-0.028714001178741455,
-0.04394322633743286,
-0.0091923912987113,
-0.0296992938965559,
0.05251419544219971,
-0.00860137864947319,
-0.018101448193192482,
-0.0085519477725029,
-0.01613132655620575,
-0.059359584003686905,
0.0011783645022660494,
0.006303845904767513,
0.022186018526554108,
-0.026051491498947144,
-0.00432572141289711,
-0.0030100264120846987,
-0.013209895230829716,
0.0013360247248783708,
-0.01399270910769701,
-0.05024140328168869,
0.03382239118218422,
-0.008535905741155148,
0.010779161006212234,
-0.06208868324756622,
-0.0487341545522213,
0.03030264377593994,
0.03588263317942619,
-0.0037196537014096975,
-0.004062693566083908,
0.024533351883292198,
-0.010408424772322178,
0.0566866509616375,
0.042935844510793686,
0.03891734778881073,
-0.055542584508657455,
0.0539579875767231,
-0.04136801138520241,
0.026047492399811745,
0.036819808185100555,
-0.01950530894100666,
0.009586718864738941,
0.047747690230607986,
0.009391880594193935,
-0.011402242816984653,
-0.07085508108139038,
0.015693150460720062,
0.011989890597760677,
0.06200569123029709,
0.0007093807216733694,
-0.06626219302415848,
-0.009810891933739185,
-0.008762923069298267,
-0.05352870374917984,
0.048842109739780426,
0.03199954330921173,
0.04324715584516525,
0.030165527015924454,
-0.012470082379877567,
-0.02950013242661953,
-0.05110553652048111,
-0.012756085954606533,
-0.004327021539211273,
-0.02083604224026203,
0.01700669713318348,
-0.06850738078355789,
-0.017364269122481346,
0.03973030298948288,
-0.008605157025158405,
-0.04587264358997345,
0.03201965242624283,
-0.017810959368944168,
0.011347606778144836,
0.02954290434718132,
-0.05045187473297119,
-0.06127136945724487,
-0.002381501952186227,
-0.06175374984741211,
-0.0176551453769207,
0.004050379153341055,
0.027193769812583923,
-0.06515747308731079,
0.03432921692728996,
-0.029072701930999756,
0.00485422695055604,
0.03495616838335991,
-0.009315148927271366,
-0.012120326049625874,
0.032867174595594406,
-0.035779453814029694,
0.01915334165096283,
-0.021816518157720566,
-0.0027302480302751064,
0.007996033877134323,
-0.00038697055424563587,
0.06756750494241714,
-0.03944868594408035,
0.015650061890482903,
0.03179539367556572,
-0.018375391140580177,
0.013925979845225811,
0.015415911562740803,
-0.04421557858586311,
-0.07394222915172577,
0.02142295613884926,
0.052413519471883774,
-0.008752796798944473,
0.011468581855297089,
-0.05385129898786545,
0.03547157347202301,
-0.010534703731536865,
-0.022288985550403595,
0.011284437030553818,
0.09793060272932053,
-0.02687135525047779,
-0.020701317116618156,
-0.01965143159031868,
0.02917606569826603,
0.04833623766899109,
0.06094057485461235,
0.011093169450759888,
-0.029894061386585236,
-0.048286646604537964,
-0.014057647436857224,
0.07006969302892685,
0.01193215511739254,
-0.023405613377690315,
0.04671845585107803,
0.07294652611017227,
-0.02697797678411007,
-0.02441626973450184,
-0.007050422020256519,
0.03341076895594597,
0.06994611769914627,
0.02615566924214363,
-0.014245163649320602,
0.018175583332777023,
0.004441415425390005,
-0.009617243893444538,
0.007319966331124306,
0.024795768782496452,
-0.0041935015469789505,
0.03937365114688873,
0.03433588519692421,
-0.021841805428266525,
0.010181864723563194,
0.03397034853696823,
0.0036811281461268663,
-0.02568933181464672,
-0.045664332807064056,
0.004832025617361069,
-0.03678170219063759,
-0.005248802714049816,
0.028225643560290337,
-0.02453448809683323,
-0.003033924149349332,
-0.025355704128742218,
0.023918233811855316,
0.014749708585441113,
0.03651578724384308,
0.010674181394279003,
0.012539577670395374,
0.032720305025577545,
0.005897276569157839,
0.030055193230509758,
0.008204465731978416,
0.041448839008808136,
0.034952763468027115,
0.003346868325024843,
0.008809337392449379,
0.007131416350603104,
0.03558396175503731,
0.03238506242632866,
-0.008629457093775272,
0.01693289913237095,
-0.018212605267763138,
-0.026563022285699844,
-0.0026300845202058554,
0.02906876616179943,
0.059096477925777435,
0.007301873993128538,
-0.09068292379379272,
-0.051785826683044434,
0.02134944498538971,
0.05308006703853607,
0.07069121301174164,
0.11095600575208664,
0.07252578437328339,
0.0032582737039774656,
-0.03700237721204758,
-0.01797313429415226,
-0.03259468451142311,
-0.09417992830276489,
-0.04211242124438286,
-0.0201670303940773,
0.01953987032175064,
-0.019916977733373642,
-0.03552592173218727,
-0.04076419025659561,
0.011743970215320587,
-0.014706183224916458,
-0.07933102548122406,
0.03783746063709259,
0.026556123048067093,
-0.016279377043247223,
0.01004696637392044,
-0.00019853805133607239,
-0.0018355217762291431,
-0.002654291922226548,
-0.032218046486377716,
-0.04518119618296623,
0.055700961500406265,
0.019096916541457176,
0.030890867114067078,
0.01816467195749283,
-0.01803790219128132,
-0.013387060724198818,
-0.0022995579056441784,
-0.017238078638911247,
-0.025631744414567947,
-0.08934930711984634,
0.015639441087841988,
-0.029270801693201065,
-0.05190946161746979,
0.012319332920014858,
-0.006884473841637373,
0.030413836240768433,
-0.0668632984161377,
0.08394579589366913,
-0.009132306091487408,
0.009324677288532257,
-0.003426000941544771,
-0.04322395101189613,
0.027673566713929176,
-0.02832079865038395,
0.015928175300359726,
0.05387125909328461,
-0.0027259266935288906,
0.029964037239551544,
-0.06570642441511154,
-0.057608991861343384,
-0.04240444675087929,
0.0007294112001545727,
-0.0046627395786345005,
0.012399004772305489,
-0.04395751655101776,
0.005613182671368122,
-0.03946547210216522,
-0.011432347819209099,
-0.06506241858005524,
-0.016126001253724098,
-0.037056781351566315,
-0.02053811214864254,
-0.02788584493100643,
-0.03512316569685936,
-0.04798797145485878,
-0.04729558154940605,
0.003926076460629702,
-0.013431627303361893,
0.008425994776189327,
-0.014270404353737831,
-0.0322384350001812,
0.05544957146048546,
-0.035093195736408234,
-0.037225183099508286,
-0.020285800099372864,
-0.022685911506414413,
-0.023686034604907036,
-0.05137386918067932,
-0.030953366309404373,
-0.07606574147939682,
-0.013784102164208889,
-0.0436493456363678,
0.0056144543923437595,
0.04148227348923683,
0.019487086683511734,
0.020217742770910263,
-0.014890255406498909,
0.056372422724962234,
-0.00629557017236948,
0.026477158069610596,
-0.0071642580442130566,
-0.03227018937468529,
-0.005246283020824194,
-0.017389746382832527,
0.019947275519371033,
-0.041831232607364655,
-0.06056823208928108,
0.03326406702399254,
-0.070087730884552,
0.03189271688461304,
0.02863697148859501,
-0.018536293879151344,
-0.012038260698318481,
-0.0025039773900061846,
-0.06531071662902832,
-0.004151342436671257,
-0.07996197789907455,
0.04051916301250458,
-0.007350280415266752,
-0.012021150439977646,
-0.02484969235956669,
0.09739676862955093,
0.003526577027514577,
0.04611476510763168,
-0.0438692606985569,
0.008810310624539852,
0.015868550166487694,
-0.027034398168325424,
-0.016408899798989296,
-0.08145967870950699,
0.033244356513023376,
-0.01242818869650364,
0.055311452597379684,
0.035156212747097015,
-0.06351181119680405,
0.029452817514538765,
0.026096558198332787,
0.027124660089612007,
0.04207553341984749,
0.006066801026463509,
0.000905187742318958,
0.007166907656937838,
-0.016040829941630363,
0.07013995945453644,
0.013896956108510494,
-0.017082294449210167,
0.0239751897752285,
-0.03085639327764511,
-0.022819582372903824,
0.021677477285265923,
0.012621165253221989,
-0.0017847676062956452,
-0.023535829037427902,
-0.010708826594054699,
-0.004543942399322987,
-0.010253842920064926,
0.008088601753115654,
0.036419060081243515,
0.0028032520785927773,
0.04738020524382591,
-0.048824064433574677,
-0.013901026919484138,
-0.003965854179114103,
-0.05603301525115967,
-0.01968124508857727,
-0.009210056625306606,
-0.029234059154987335,
-0.042824722826480865,
0.006005513481795788,
-0.032361578196287155,
0.03619084879755974,
0.021504797041416168,
-0.008496331050992012,
0.01767728477716446,
-0.014366856776177883,
0.023677602410316467,
0.017570652067661285,
0.01952490210533142,
0.004694697912782431,
0.03748904541134834,
-0.004586341790854931,
-0.027572570368647575,
0.0012111784890294075,
0.045040395110845566,
0.015872586518526077,
-0.0010750902583822608,
-0.0532086119055748,
-0.0009108236990869045,
0.01593613252043724,
-0.004909772891551256,
-0.004680192098021507,
0.01731819659471512,
0.09989382326602936,
0.022768385708332062,
-0.007479213643819094,
-0.02208329737186432,
0.005196764133870602,
-0.02652493305504322,
-0.024960750713944435,
0.04488097131252289,
-0.010907506570219994,
-0.005246479995548725,
0.019840305671095848,
0.011094736866652966,
0.014423028565943241,
0.08314229547977448,
0.056993596255779266,
0.06949252635240555,
0.0038729682564735413,
-0.007294477429240942,
-0.031124096363782883,
0.019946616142988205,
0.022894583642482758,
0.023966951295733452,
0.029307546094059944,
-0.0255705788731575,
0.038628485053777695,
-0.010562215000391006,
-0.03447561711072922,
-0.04253498837351799,
-0.03148498758673668,
0.04109453037381172,
0.008850942365825176,
0.012378150597214699,
0.0012772780610248446,
-0.053272221237421036,
0.025743138045072556,
-0.030901841819286346,
0.020109519362449646,
-0.0005025924765504897,
0.05471730977296829,
-0.025425806641578674,
-0.0034137305337935686,
-0.020007161423563957,
-0.026734376326203346,
0.052456147968769073,
-0.024504777044057846,
-0.025112513452768326,
-0.028927965089678764,
-0.1092085987329483,
0.010532313957810402,
0.11223237216472626,
0.046158693730831146,
-0.05557651445269585,
-0.041441190987825394,
-0.018986394628882408,
0.03386847674846649,
0.03265935182571411,
-0.012899050489068031,
0.003356595290824771,
0.06148967891931534,
0.011818045750260353,
0.015081469900906086,
0.008855575695633888,
-0.02960067242383957,
-0.01999754272401333,
0.0019372951937839389,
-0.017288751900196075,
0.018345855176448822,
-0.042106565088033676,
-0.025325389578938484
] |
[
13.282628059387207,
-1.5198650360107422
] |
High Energy Physics - Lattice
|
General Physics
|
hep-lat
|
hep-ph
|
na
|
2007-04-01T16:47:32
|
Lattice contribution to the electronic self-energy in complex correlated
oxides is a fascinating subject that has lately stimulated lively discussions.
Expectations of electron-phonon self-energy effects for simpler materials, such
as Pd and Al, have resulted in several misconceptions in strongly correlated
oxides. Here we analyze a number of arguments claiming that phonons cannot be
the origin of certain self-energy effects seen in high-$T_c$ cuprate
superconductors via angle resolved photoemission experiments (ARPES), including
the temperature dependence, doping dependence of the renormalization effects,
the inter-band scattering in the bilayer systems, and impurity substitution. We
show that in light of experimental evidences and detailed simulations, these
arguments are not well founded.
|
Aspects of Electron-Phonon Self-Energy Revealed from Angle-Resolved
Photoemission Spectroscopy
|
cond-mat.supr-con cond-mat.str-el
|
0704.0093
| 2,007
|
[
0.027757883071899414,
0.07244104892015457,
-0.006239436101168394,
-0.005407537799328566,
0.03846292942762375,
0.004465343430638313,
0.030493412166833878,
0.015067677944898605,
-0.012139523401856422,
0.012528537772595882,
-0.058052562177181244,
0.040516454726457596,
-0.005547687876969576,
-0.011824661865830421,
-0.012138503603637218,
-0.03226594626903534,
0.06589464098215103,
-0.00936193484812975,
0.03906254097819328,
0.049975186586380005,
-0.09994727373123169,
-0.038086678832769394,
-0.05399923399090767,
-0.032174743711948395,
0.07268726080656052,
0.02165769785642624,
-0.004468875005841255,
-0.046875614672899246,
0.009948162361979485,
0.018395772203803062,
0.061998575925827026,
-0.032553937286138535,
0.016866283491253853,
-0.041615426540374756,
-0.04986059293150902,
-0.04270600154995918,
0.10502729564905167,
0.0021297128405421972,
0.048739295452833176,
0.057905878871679306,
-0.02917010523378849,
-0.039617329835891724,
0.03472037985920906,
-0.05310380831360817,
-0.0034222097601741552,
-0.0038056722842156887,
0.0018147064838558435,
-0.016963841393589973,
-0.003994694910943508,
0.019849371165037155,
0.02898435667157173,
0.06771485507488251,
0.08380767703056335,
-0.036349277943372726,
-0.00503323832526803,
-0.019433587789535522,
-0.009532313793897629,
0.03336469456553459,
0.0328279584646225,
-0.002247908851131797,
0.04043615236878395,
0.07387956231832504,
-0.019700996577739716,
0.07300928980112076,
0.07698488235473633,
-0.02723572589457035,
-0.038039397448301315,
-0.013254363089799881,
-0.0655977800488472,
-0.02216542698442936,
0.03666503354907036,
-0.033075395971536636,
-0.032779593020677567,
0.07299615442752838,
-0.0018272659508511424,
-0.00862871203571558,
-0.013246949762105942,
-0.013159139081835747,
0.0019001959590241313,
-0.023561011999845505,
0.002290471689775586,
-0.047908540815114975,
0.03251766040921211,
0.05804505944252014,
0.048827189952135086,
-0.05207446217536926,
0.04423834756016731,
0.030501576140522957,
-0.07122179865837097,
0.05102083832025528,
0.010451256297528744,
-0.01296187937259674,
0.035739604383707047,
0.04198756441473961,
-0.03760077431797981,
0.0390707403421402,
0.007501410320401192,
0.051789455115795135,
-0.011562698520720005,
0.012330136261880398,
-0.08620727062225342,
0.010748675093054771,
-0.029217658564448357,
0.055921051651239395,
0.019121184945106506,
-0.009337377734482288,
-0.030270351096987724,
-0.02865254506468773,
0.0072403266094625,
0.04307633638381958,
-0.05684446543455124,
-0.004059068858623505,
0.007415584288537502,
0.0008869148441590369,
-0.01874312199652195,
-0.011330625042319298,
0.04886070266366005,
-0.049764234572649,
-0.01910431869328022,
0.032137684524059296,
-0.003975897096097469,
0.020907901227474213,
0.004184742923825979,
0.05273110419511795,
0.005978361237794161,
0.05162791907787323,
-0.04597202315926552,
-0.03516462445259094,
-0.004362328443676233,
-0.005379326641559601,
-0.014582916162908077,
-0.007847956381738186,
-0.08207465708255768,
-0.004845861345529556,
0.059781890362501144,
0.034169185906648636,
-0.02876025252044201,
-0.06400994211435318,
0.02098354510962963,
-0.01521533913910389,
-0.023995544761419296,
0.05286195129156113,
0.009915231727063656,
-0.028603726997971535,
-0.014775305055081844,
-0.09177638590335846,
0.015722651034593582,
-0.05738276615738869,
-0.03696916997432709,
0.035707563161849976,
0.020868243649601936,
0.02891780249774456,
0.013045242987573147,
0.04360225051641464,
-0.05168003961443901,
-0.0335097499191761,
-0.006944659166038036,
-0.029363812878727913,
0.021660901606082916,
0.044908180832862854,
0.005004864186048508,
0.038610827177762985,
-0.04601895809173584,
0.03035213053226471,
0.001516031101346016,
-0.0020556270610541105,
0.027744220569729805,
0.03389064595103264,
-0.03211843594908714,
0.06297735869884491,
-0.04768819734454155,
-0.027059704065322876,
-0.011689439415931702,
0.010752719826996326,
-0.015457798726856709,
0.046754222363233566,
0.015654323622584343,
-0.044757142663002014,
0.017504030838608742,
0.018229790031909943,
0.059924785047769547,
0.016607344150543213,
0.009046776220202446,
0.009500552900135517,
0.07106684893369675,
0.035499460995197296,
-0.044586364179849625,
-0.00012408105249051005,
-0.00505452323704958,
0.018648283556103706,
0.01638609543442726,
-0.003422913607209921,
-0.04179242625832558,
-0.09782256931066513,
-0.011556814424693584,
-0.05212921276688576,
0.03563649579882622,
0.011627311818301678,
-0.023819828405976295,
-0.03812894597649574,
-0.053632888942956924,
-0.045802704989910126,
-0.012257837690412998,
0.007147542666643858,
-0.006043249275535345,
0.044962916523218155,
-0.012346960604190826,
0.002656380645930767,
0.00931844487786293,
-0.03752179071307182,
0.05260277912020683,
0.013630119152367115,
-0.02542036771774292,
0.053207240998744965,
-0.0013063376536592841,
-0.00316859339363873,
-0.0031305032316595316,
-0.06002414599061012,
-0.011704251170158386,
0.05823307856917381,
-0.05821331962943077,
-0.04475485160946846,
0.04566996917128563,
-0.010503435507416725,
0.037625882774591446,
0.0001143066692748107,
-0.016262847930192947,
0.017899896949529648,
-0.04752592369914055,
-0.03717494755983353,
-0.026053329929709435,
-0.04361603409051895,
0.030795320868492126,
-0.015481431968510151,
-0.002674342365935445,
-0.009011315181851387,
-0.033596981316804886,
0.030894966796040535,
-0.0033226951491087675,
0.04598793759942055,
0.035869866609573364,
-0.004008193034678698,
-0.013731410726904869,
-0.03858204185962677,
-0.05795621871948242,
-0.005735232029110193,
0.03282399848103523,
-0.010396577417850494,
-0.000625922461040318,
0.006048738956451416,
0.034530267119407654,
-0.007223289925605059,
-0.007195210084319115,
0.04880024865269661,
0.010549940168857574,
-0.011513127014040947,
-0.03655159845948219,
0.04037280008196831,
-0.03941015526652336,
-0.01967783458530903,
0.014628581702709198,
-0.011925091035664082,
0.009016022086143494,
-0.015015593729913235,
-0.01333487406373024,
0.008270131424069405,
-0.02245860919356346,
-0.0604904480278492,
-0.031074773520231247,
-0.03792814165353775,
-0.046955276280641556,
0.09376636147499084,
0.060996852815151215,
0.06741821765899658,
0.03333360701799393,
-0.03156095743179321,
0.04542133957147598,
-0.013569415546953678,
-0.02603510394692421,
-0.014164702035486698,
-0.0567157082259655,
-0.018949108198285103,
-0.018497666344046593,
-0.0011648713843896985,
-0.01137690618634224,
0.026450620964169502,
0.046289198100566864,
-0.035392001271247864,
0.036847881972789764,
0.044783808290958405,
0.020194536074995995,
-0.020562607795000076,
-0.011847654357552528,
0.11122316867113113,
0.015596580691635609,
0.023438429459929466,
0.07334388047456741,
-0.021539056673645973,
-0.0020796663593500853,
0.05407360568642616,
-0.017432231456041336,
0.027300188317894936,
-0.04289934039115906,
0.0290693249553442,
0.03458160161972046,
0.01934928074479103,
0.038893889635801315,
-0.02013563923537731,
0.005140730179846287,
-0.017527488991618156,
0.01093501690775156,
0.020063644275069237,
0.023096807301044464,
-0.016391607001423836,
-0.014039122499525547,
0.055090535432100296,
-0.02329065464437008,
-0.014224382117390633,
0.05532529577612877,
-0.03463201969861984,
-0.022480284795165062,
0.014349334873259068,
-0.0045629539526999,
-0.08518658578395844,
-0.03245102986693382,
0.029095441102981567,
0.004688275512307882,
0.0006057475693523884,
0.010014412924647331,
0.005176580045372248,
0.0021582574117928743,
0.03512374311685562,
-0.03562241792678833,
-0.02575269527733326,
0.021146776154637337,
-0.046063389629125595,
-0.03406272456049919,
0.08169472962617874,
-0.030818484723567963,
0.04065978527069092,
-0.03651115670800209,
-0.02051636576652527,
-0.0526929572224617,
-0.046226952224969864,
0.008400647900998592,
0.009661572054028511,
-0.033185459673404694,
0.014643959701061249,
0.04739503562450409,
0.01194419153034687,
0.023132385686039925,
0.05766044184565544,
0.022210581228137016,
0.05261736363172531,
-0.0626368373632431,
0.02471454069018364,
0.01575488969683647,
0.02871454507112503,
0.0485265776515007,
0.007594494614750147,
0.036505136638879776,
-0.06279128044843674,
0.03954919055104256,
-0.013000715523958206,
-0.0015544331399723887,
0.032146330922842026,
-0.0030714082531630993,
0.04897896200418472,
0.028673700988292694,
-0.05417641997337341,
-0.08443860709667206,
-0.07396043837070465,
0.00803314708173275,
0.02273533307015896,
0.036928772926330566,
0.01639634557068348,
-0.05302892252802849,
0.004494034685194492,
-0.03698461130261421,
0.016402682289481163,
0.05622810497879982,
0.018305029720067978,
0.03342551365494728,
0.006064780987799168,
0.006521319039165974,
-0.0066009098663926125,
-0.08464595675468445,
0.011639458127319813,
-0.08635065704584122,
-0.028500108048319817,
0.003636201610788703,
0.005069684702903032,
-0.04293031617999077,
0.0035522785037755966,
0.0072248829528689384,
-0.09279066324234009,
0.04698110371828079,
-0.0687062218785286,
0.08128897100687027,
-0.007395078428089619,
-0.061286989599466324,
-0.053650349378585815,
0.009249952621757984,
-0.042941078543663025,
-0.02024921588599682,
0.001655415166169405,
-0.016191940754652023,
-0.039492372423410416,
0.023219024762511253,
-0.016054781153798103,
-0.03707721829414368,
0.0459362268447876,
-0.0030086557380855083,
-0.060182079672813416,
0.0007846721564419568,
-0.022037118673324585,
-0.01940268464386463,
-0.031222691759467125,
0.03573725372552872,
-0.030277518555521965,
0.017207708209753036,
0.036963481456041336,
-0.01474638469517231,
-0.0039028713945299387,
-0.02590152807533741,
0.024830155074596405,
-0.022228792309761047,
-0.03725885599851608,
-0.043472763150930405,
-0.06219895929098129,
0.019944338127970695,
0.021551581099629402,
0.004967232700437307,
-0.0029968703165650368,
-0.0426483079791069,
0.01790849305689335,
0.06215762346982956,
0.018383659422397614,
-0.025988899171352386,
0.09395249933004379,
0.04826169088482857,
-0.027554797008633614,
0.015239481814205647,
-0.03289777413010597,
0.044772058725357056,
0.03718381002545357,
0.01015481911599636,
-0.0036305126268416643,
0.025496499612927437,
-0.002360367216169834,
0.021152978762984276,
-0.012311361730098724,
0.037408579140901566,
-0.015208032913506031,
0.06870238482952118,
-0.04185160994529724,
0.00010946861584670842,
-0.004614118952304125,
-0.002325936919078231,
0.03871876746416092,
0.0070364694111049175,
-0.017630204558372498,
-0.034091558307409286,
0.044486839324235916,
-0.011920792050659657,
-0.01523462776094675,
0.003246332285925746,
-0.039016738533973694,
0.00868188589811325,
0.013736249879002571,
-0.006878414656966925,
0.004990863613784313,
0.04188046231865883,
0.05359392240643501,
-0.014940839260816574,
-0.044977977871894836,
0.0025659077800810337,
-0.02292197197675705,
-0.00981275923550129,
0.03322352468967438,
0.039621319621801376,
0.02365569770336151,
-0.001953324768692255,
0.027541514486074448,
0.01977248676121235,
0.01806696690618992,
-0.054602861404418945,
0.012027225457131863,
-0.008090844377875328,
-0.02320554479956627,
0.003400643588975072,
-0.002184838755056262,
-0.02082500047981739,
0.0007261260179802775,
-0.022056562826037407,
-0.0076250480487942696,
0.03232165426015854,
0.02943541668355465,
0.03803123161196709,
0.07082466036081314,
-0.008627548813819885,
0.02755051478743553,
-0.010249964892864227,
-0.029848162084817886,
0.01905764266848564,
0.00017439349903725088,
0.025989172980189323,
-0.09391643106937408,
0.002582578919827938,
-0.019372545182704926,
-0.009349597617983818,
0.052943743765354156,
0.0753730982542038,
0.051551029086112976,
0.0018974191043525934,
-0.018849704414606094,
0.004365109838545322,
-0.027290552854537964,
-0.03922377526760101,
-0.0022285771556198597,
-0.0004657888493966311,
0.017041588202118874,
-0.019229400902986526,
-0.017651831731200218,
-0.07020789384841919,
0.07083772122859955,
-0.0036310371942818165,
-0.051239799708127975,
0.09108182787895203,
-0.015147760510444641,
0.016813691705465317,
0.03339419513940811,
0.0560675747692585,
0.04306592419743538,
0.01806647889316082,
-0.016003534197807312,
-0.02490040473639965,
0.008589616976678371,
-0.028864338994026184,
0.0262510534375906,
0.019756944850087166,
-0.01743633858859539,
0.04403562471270561,
0.03445333614945412,
0.041666317731142044,
-0.018534168601036072,
-0.06170077621936798,
0.0031889856327325106,
-0.0059720356948673725,
-0.05746018886566162,
0.05575886368751526,
0.008883382193744183,
0.020275432616472244,
-0.05606365203857422,
0.05690770223736763,
-0.018261441960930824,
0.019887786358594894,
-0.014568263664841652,
-0.05565640702843666,
-0.01917305588722229,
-0.008171437308192253,
0.009736549109220505,
0.044096820056438446,
0.019519738852977753,
0.009872231632471085,
-0.025363104417920113,
-0.01476321928203106,
-0.0038476979825645685,
0.004117663949728012,
-0.01025497354567051,
0.008290639147162437,
0.0015777512453496456,
-0.00541958212852478,
-0.0472157821059227,
-0.021452646702528,
-0.010758909396827221,
0.04143674671649933,
0.02663717046380043,
-0.010918030515313148,
-0.030515553429722786,
-0.017238596454262733,
-0.03433763608336449,
0.0015065595507621765,
0.07072877138853073,
-0.032452721148729324,
0.023184718564152718,
0.021596215665340424,
0.02981218509376049,
0.09394632279872894,
-0.016700735315680504,
0.013659053482115269,
-0.05888601392507553,
-0.027703426778316498,
-0.0331333726644516,
-0.05138414353132248,
-0.03442304581403732,
-0.04120607301592827,
-0.03322943300008774,
-0.04053710028529167,
0.02251039817929268,
0.05656607076525688,
0.06505008041858673,
0.004800343420356512,
-0.01440977118909359,
0.07572641223669052,
-0.006372921634465456,
0.06165435165166855,
0.06715884804725647,
-0.057034146040678024,
0.02980402112007141,
0.008470379747450352,
0.005872818641364574,
-0.013793905265629292,
-0.060965605080127716,
0.002048410242423415,
-0.05755438283085823,
0.02571863681077957,
0.014471483416855335,
-0.012113107368350029,
0.0026363730430603027,
0.0160815566778183,
-0.03846343979239464,
0.03411566838622093,
-0.01953042484819889,
0.004147202242165804,
-0.014194522053003311,
-0.03953924775123596,
-0.027095606550574303,
0.08328930288553238,
0.015422171913087368,
0.000166210244060494,
0.021405087783932686,
-0.020635094493627548,
-0.022384298965334892,
0.008618518710136414,
0.03454190120100975,
-0.01222936436533928,
-0.02591128833591938,
-0.04441998526453972,
0.008870172314345837,
0.027088040485978127,
-0.00033316193730570376,
-0.011932503432035446,
-0.01792086474597454,
0.029125817120075226,
0.06401346623897552,
-0.01645698770880699,
0.012986451387405396,
0.013441666029393673,
-0.022319363430142403,
0.057563357055187225,
0.029862500727176666,
-0.03559969365596771,
0.005648947320878506,
0.023268939927220345,
-0.015422902069985867,
0.00474909134209156,
0.05263860523700714,
-0.01951638236641884,
-0.025130683556199074,
-0.04679829627275467,
-0.01985495164990425,
0.005042385309934616,
0.02630280889570713,
0.01424210611730814,
-0.020863842219114304,
-0.005447302013635635,
-0.07868547737598419,
0.008856105618178844,
0.014893504790961742,
-0.03090711310505867,
-0.02393500693142414,
0.007114003412425518,
-0.05505383759737015,
-0.05122040584683418,
-0.02745727077126503,
-0.004929767921566963,
0.018121082335710526,
-0.03016798198223114,
-0.009475505910813808,
0.008375467732548714,
0.022734522819519043,
0.05535881593823433,
-0.023159092292189598,
-0.03377708047628403,
-0.02311762236058712,
-0.019441600888967514,
-0.04784436151385307,
-0.053943827748298645,
-0.028038229793310165,
0.019320134073495865,
0.01056668721139431,
-0.036576684564352036,
-0.008431624621152878,
-0.003863212186843157,
-0.024921448901295662,
-0.037190526723861694,
0.02162202075123787,
0.0037762101273983717,
0.029165733605623245,
0.020245522260665894,
0.022633982822299004,
-0.05510254576802254,
0.031902894377708435,
0.00962193962186575,
0.020520182326436043,
0.08149371296167374,
0.019504977390170097,
-0.015197043307125568,
0.006168201565742493,
-0.015884554013609886,
-0.005368579179048538,
0.06885623931884766,
-0.002612554468214512,
0.04594863951206207,
-0.004624512512236834,
-0.033884625881910324,
-0.06412488222122192,
-0.006571432109922171,
0.03400534391403198,
-0.013021322898566723,
-0.006985109765082598,
-0.057758282870054245,
0.04502510651946068,
0.06383557617664337,
-0.10155370086431503,
0.03321552276611328,
0.00015576671285089105,
0.054009661078453064,
0.01697414740920067,
0.016300372779369354,
0.014869731850922108,
-0.029656626284122467,
-0.031222272664308548,
-0.0331428088247776,
0.03202981501817703,
0.016208713874220848,
0.03535320609807968,
-0.006128177046775818,
0.00013105418474879116,
0.0011518166866153479,
-0.04583841562271118,
0.0020348159596323967,
-0.019719524309039116,
-0.014107302762567997,
-0.03060901165008545,
-0.08286339044570923,
-0.000057685225328896195,
0.041284505277872086,
-0.01218633446842432,
-0.06853054463863373,
-0.04255786910653114,
-0.035915836691856384,
0.010606063529849052,
-0.01309981755912304,
-0.022759011015295982,
-0.007846352644264698,
-0.011382080614566803,
0.041917964816093445,
-0.07420744001865387,
0.03623509034514427,
0.018320666626095772,
0.004307937808334827,
-0.004094329196959734,
0.016045324504375458,
0.03936629369854927,
-0.05743860453367233,
-0.014916800893843174
] |
[
8.705536842346191,
-3.5345046520233154
] |
Superconductivity
|
Condensed-Matter Physics
|
cond-mat-supr-con
|
cond-mat-str-el
|
na
|
2007-04-02T18:30:16
|
We present semi-analytical constraint on the amount of dark matter in the
merging bullet galaxy cluster using the classical Local Group timing arguments.
We consider particle orbits in potential models which fit the lensing data.
{\it Marginally consistent} CDM models in Newtonian gravity are found with a
total mass M_{CDM} = 1 x 10^{15}Msun of Cold DM: the bullet subhalo can move
with V_{DM}=3000km/s, and the "bullet" X-ray gas can move with
V_{gas}=4200km/s. These are nearly the {\it maximum speeds} that are
accelerable by the gravity of two truncated CDM halos in a Hubble time even
without the ram pressure. Consistency breaks down if one adopts higher end of
the error bars for the bullet gas speed (5000-5400km/s), and the bullet gas
would not be bound by the sub-cluster halo for the Hubble time. Models with
V_{DM}~ 4500km/s ~ V_{gas} would invoke unrealistic large amount M_{CDM}=7x
10^{15}Msun of CDM for a cluster containing only ~ 10^{14}Msun of gas. Our
results are generalisable beyond General Relativity, e.g., a speed of
$4500\kms$ is easily obtained in the relativistic MONDian lensing model of
Angus et al. (2007). However, MONDian model with little hot dark matter
$M_{HDM} \le 0.6\times 10^{15}\msun$ and CDM model with a small halo mass $\le
1\times 10^{15}\msun$ are barely consistent with lensing and velocity data.
|
Timing and Lensing of the Colliding Bullet Clusters: barely enough time
and gravity to accelerate the bullet
|
astro-ph
|
0704.0094
| 2,007
|
[
0.013255728408694267,
0.03524824604392052,
0.01123193558305502,
-0.02120806649327278,
0.028652282431721687,
0.022794535383582115,
-0.013759462162852287,
-0.037607450038194656,
-0.05461627617478371,
0.011518524028360844,
-0.028913453221321106,
0.04143665358424187,
0.0044558122754096985,
0.006136708427220583,
-0.021585220471024513,
-0.027614912018179893,
0.012157321907579899,
-0.010991469025611877,
-0.004771308973431587,
0.08190856128931046,
-0.008240194991230965,
-0.018286777660250664,
-0.01421139296144247,
-0.07370568811893463,
0.09221209585666656,
0.025051606819033623,
0.03540277108550072,
-0.001375085092149675,
-0.04939618334174156,
0.05154049023985863,
0.08091001957654953,
-0.055962689220905304,
-0.025527268648147583,
-0.059764545410871506,
-0.04020663723349571,
-0.05427050590515137,
0.05208326876163483,
-0.047619033604860306,
0.006999290082603693,
0.06687889993190765,
0.059572119265794754,
-0.05306136608123779,
0.018805639818310738,
0.008993574418127537,
0.04093972593545914,
0.05385711044073105,
0.030312279239296913,
-0.025158904492855072,
0.029271816834807396,
-0.03361096233129501,
-0.03949076309800148,
0.046557266265153885,
-0.012776659801602364,
-0.05876798555254936,
-0.028861388564109802,
0.0124741829931736,
0.03131081908941269,
0.03722264990210533,
0.03378807753324509,
-0.02935892529785633,
0.06106630340218544,
0.013103662990033627,
-0.022873885929584503,
-0.012877892702817917,
0.03854590281844139,
-0.04595807567238808,
-0.055003516376018524,
-0.020559774711728096,
0.021147070452570915,
-0.054809629917144775,
0.024019811302423477,
-0.003237743629142642,
-0.014400443993508816,
0.03997097536921501,
-0.047166742384433746,
-0.014457949437201023,
-0.015485509298741817,
-0.01889178156852722,
-0.01608036272227764,
-0.008413605391979218,
0.018496999517083168,
0.02433529682457447,
0.007027155719697475,
0.003873563837260008,
0.04494921863079071,
0.013673395849764347,
-0.028055410832166672,
0.01805625855922699,
-0.04282490536570549,
0.04799911379814148,
0.04499645158648491,
-0.007207901682704687,
0.03287047892808914,
0.025024691596627235,
0.010614139959216118,
0.05497806891798973,
-0.043882131576538086,
0.09280965477228165,
-0.020777229219675064,
-0.020432373508810997,
-0.023961011320352554,
0.039734531193971634,
0.015283606015145779,
0.025465287268161774,
0.05886642634868622,
0.04030586779117584,
-0.021105913445353508,
0.016059035435318947,
0.03667471185326576,
-0.04780146852135658,
-0.09965453296899796,
-0.05927787721157074,
-0.014805685728788376,
-0.037110794335603714,
-0.036584652960300446,
-0.052963417023420334,
0.03989579901099205,
-0.024080906063318253,
-0.04265424236655235,
0.06394043564796448,
0.0007640552939847112,
-0.004542260896414518,
0.004038228653371334,
0.03203119337558746,
-0.003007840132340789,
-0.019694536924362183,
-0.017601378262043,
-0.012914011254906654,
0.009759659878909588,
-0.04246245697140694,
-0.009310882538557053,
0.005364976357668638,
-0.02347698248922825,
0.03028631955385208,
0.01688961498439312,
-0.000789797690231353,
-0.03215431794524193,
-0.031176963821053505,
-0.013014105148613453,
-0.014128567650914192,
0.018492713570594788,
0.0030191477853804827,
0.007920190691947937,
0.009952114894986153,
-0.014438655227422714,
-0.021916799247264862,
-0.04778287187218666,
0.00813881866633892,
-0.01274216827005148,
-0.026694126427173615,
0.03750266507267952,
0.0284653902053833,
0.027036292478442192,
0.04086311534047127,
-0.04442780092358589,
-0.010431733913719654,
0.0032006294932216406,
0.02719760127365589,
0.008123759180307388,
-0.0027876112144440413,
-0.005989118944853544,
-0.011608392931520939,
-0.034632276743650436,
0.04380860924720764,
-0.0891464501619339,
0.014622076414525509,
0.024277150630950928,
0.0389796644449234,
0.05431089922785759,
-0.021871382370591164,
-0.07293412834405899,
-0.019099531695246696,
-0.015228339470922947,
-0.015278171747922897,
0.012369509786367416,
-0.01545148529112339,
0.018074003979563713,
-0.06528307497501373,
-0.06108848750591278,
0.00012395957310218364,
0.07710108160972595,
-0.03271552920341492,
-0.027227627113461494,
0.03927738592028618,
0.051985546946525574,
-0.00871433224529028,
0.05541412904858589,
-0.01453863549977541,
-0.012758319266140461,
-0.03359714895486832,
0.019740616902709007,
-0.006203463301062584,
0.005066421814262867,
-0.06548159569501877,
-0.022132763639092445,
-0.029235273599624634,
0.06468529254198074,
-0.033418115228414536,
-0.0031350329518318176,
-0.01119239442050457,
-0.025867408141493797,
-0.030992763116955757,
-0.04821367934346199,
0.007078151218593121,
0.02074718289077282,
0.054366584867239,
0.000758380105253309,
0.0489361435174942,
0.022974224761128426,
0.025601327419281006,
0.0841023251414299,
0.011328310705721378,
-0.025903083384037018,
0.003258434124290943,
-0.04090446978807449,
-0.004406957421451807,
0.03395453840494156,
-0.014959330670535564,
-0.007539347279816866,
0.04420643672347069,
0.0031488717067986727,
0.006660586688667536,
-0.05815311521291733,
-0.020166926085948944,
0.06664987653493881,
0.003340223804116249,
-0.003171454416587949,
-0.01163032092154026,
-0.04961274564266205,
0.009136947803199291,
-0.03205607086420059,
0.007155677769333124,
0.0011945090955123305,
-0.01773369312286377,
0.025660553947091103,
-0.003382774069905281,
0.02626113034784794,
0.001885954407043755,
0.0729815661907196,
0.08148390799760818,
0.0424218475818634,
-0.011887435801327229,
0.015828104689717293,
-0.040354982018470764,
-0.07523835450410843,
-0.03283728286623955,
0.029259352013468742,
-0.003045279299840331,
-0.04486948624253273,
0.040130965411663055,
-0.0005998163833282888,
-0.016644654795527458,
0.008578039705753326,
-0.01881125010550022,
0.047970183193683624,
-0.038503360003232956,
-0.06602805107831955,
0.09157618880271912,
-0.06337235867977142,
-0.04713037982583046,
0.038056887686252594,
-0.008028321899473667,
-0.007323645520955324,
-0.04770578071475029,
-0.049622245132923126,
0.005063879303634167,
-0.012048822827637196,
-0.03896752744913101,
0.010445591062307358,
-0.0019957278855144978,
0.015238219872117043,
-0.007598017808049917,
0.07163969427347183,
0.058528609573841095,
-0.0005144531605765224,
0.06991112977266312,
0.016714060679078102,
-0.020761638879776,
-0.010830440558493137,
-0.029983241111040115,
-0.08485881239175797,
-0.028549276292324066,
-0.03126388043165207,
-0.023549791425466537,
-0.028403006494045258,
-0.01277018990367651,
-0.007580957841128111,
-0.0008648524526506662,
0.036813728511333466,
0.010850044898688793,
-0.021041160449385643,
0.04834822192788124,
0.027734536677598953,
0.11901023983955383,
0.05002456530928612,
0.09290341287851334,
0.10624860972166061,
-0.0008731247507967055,
0.02069617621600628,
-0.04965490847826004,
-0.011611216701567173,
-0.024517877027392387,
-0.016278551891446114,
-0.006528780795633793,
0.03448212146759033,
-0.01804257556796074,
-0.009839938022196293,
0.00020176489488221705,
-0.013760578818619251,
-0.021473480388522148,
0.08046741783618927,
0.05805431306362152,
-0.010508041828870773,
0.020829830318689346,
-0.033667147159576416,
-0.00251232972368598,
0.007078398019075394,
-0.011923989281058311,
0.06285905838012695,
0.017699243500828743,
0.012061483226716518,
-0.05463804304599762,
-0.029133977368474007,
-0.10459272563457489,
0.02060614340007305,
0.03757061809301376,
0.0008645367925055325,
-0.047794632613658905,
-0.011071418412029743,
0.028637174516916275,
0.010225853882730007,
0.020382827147841454,
-0.04143582656979561,
-0.002598757855594158,
-0.0188091192394495,
-0.016131645068526268,
-0.019487811252474785,
0.050811767578125,
0.04622568190097809,
0.026518583297729492,
-0.006329936441034079,
0.009413440711796284,
-0.043138399720191956,
-0.00028863304760307074,
-0.017607832327485085,
0.014720998704433441,
-0.02522609941661358,
-0.005474982317537069,
0.04660792648792267,
-0.01902884989976883,
-0.07737897336483002,
-0.014462677761912346,
0.002602851949632168,
-0.026292013004422188,
-0.023723097518086433,
0.03407806530594826,
0.03952975198626518,
-0.011929167434573174,
0.05036856606602669,
0.014130049385130405,
0.01596154272556305,
-0.008289742283523083,
-0.017200717702507973,
0.02659924142062664,
0.04216695576906204,
0.017480816692113876,
0.014125275425612926,
0.0060903229750692844,
0.041036926209926605,
-0.06574930995702744,
-0.029632722958922386,
-0.037592556327581406,
0.012828526087105274,
0.0730322077870369,
0.0674440860748291,
-0.0049414485692977905,
-0.03264383599162102,
0.034281570464372635,
-0.026933416724205017,
-0.002717773662880063,
0.04332142695784569,
-0.0066593363881111145,
0.020506294444203377,
0.015866469591856003,
0.02673104777932167,
-0.015108137391507626,
-0.04157034680247307,
-0.023552635684609413,
-0.02243499644100666,
-0.05132686346769333,
0.029407082125544548,
-0.07641426473855972,
-0.019709384068846703,
0.029958007857203484,
0.017836492508649826,
-0.0005007400759495795,
0.03482716530561447,
0.0043311589397490025,
0.057579413056373596,
-0.017735380679368973,
-0.025158582255244255,
-0.027770664542913437,
-0.01030751597136259,
-0.0071672857739031315,
-0.05480603873729706,
0.023556016385555267,
-0.0532173290848732,
-0.05532442778348923,
0.058259349316358566,
-0.015413949266076088,
0.05118155479431152,
0.0240713432431221,
-0.00008487397280987352,
-0.024254482239484787,
0.02121901325881481,
0.012839422561228275,
0.03322932496666908,
0.00009599496843293309,
-0.019857821986079216,
-0.00730891665443778,
0.002741195959970355,
0.06034483760595322,
-0.05065755546092987,
-0.031855273991823196,
-0.01096266694366932,
0.04203776270151138,
-0.0025229882448911667,
0.007765898946672678,
-0.01215702947229147,
-0.053787942975759506,
0.08223182708024979,
-0.033512942492961884,
-0.01464877650141716,
0.05630547180771828,
-0.04429061338305473,
0.02545984461903572,
0.07383743673563004,
0.0021647890098392963,
0.017823509871959686,
0.04313026741147041,
0.04126398637890816,
-0.04015755653381348,
0.02836655080318451,
0.017350442707538605,
0.029955364763736725,
0.12611882388591766,
0.039190586656332016,
-0.0251932330429554,
-0.03928336501121521,
0.007514669094234705,
0.04604906216263771,
0.008268473669886589,
-0.003203714033588767,
0.006924937013536692,
0.023717638105154037,
-0.012807230465114117,
-0.017266789451241493,
0.04572474583983421,
0.02700161561369896,
0.05383625626564026,
-0.050815649330616,
0.052782028913497925,
-0.0003844670718535781,
0.02693786844611168,
0.03820789232850075,
-0.0407261997461319,
-0.00010711841605370864,
-0.018435640260577202,
-0.012269380502402782,
0.0307447612285614,
-0.05150025337934494,
0.011567479930818081,
0.019684914499521255,
-0.002646505832672119,
-0.025611156597733498,
-0.018751464784145355,
0.030602160841226578,
-0.023257538676261902,
0.039933763444423676,
0.0484142042696476,
0.016497774049639702,
0.0027269504498690367,
0.0034799908753484488,
-0.014544675126671791,
-0.008069746196269989,
0.0550190769135952,
-0.029756508767604828,
-0.006882254034280777,
-0.020310930907726288,
-0.0039881495758891106,
0.019865626469254494,
0.03146553784608841,
-0.003119101980701089,
-0.027487462386488914,
0.005691417958587408,
0.021824903786182404,
0.040501292794942856,
0.0010013693245127797,
0.03447229042649269,
0.0010418241145089269,
-0.01586925983428955,
0.024808460846543312,
0.005893742199987173,
-0.05035286024212837,
-0.009719395078718662,
0.03743332251906395,
-0.05681641399860382,
-0.03223913908004761,
-0.023260019719600677,
0.030765241011977196,
-0.008932845667004585,
0.05856628343462944,
0.06761287152767181,
0.06855189055204391,
0.004905834794044495,
-0.06410250067710876,
0.0545799694955349,
0.03680352121591568,
-0.05854529142379761,
-0.026612551882863045,
0.0007570675807073712,
-0.02206689678132534,
0.042856380343437195,
0.01885230280458927,
-0.01875435933470726,
-0.017467891797423363,
-0.02952786162495613,
-0.08021065592765808,
0.043172504752874374,
-0.026513272896409035,
0.00873065646737814,
-0.04890353977680206,
0.010158953256905079,
-0.008739759214222431,
-0.009469646960496902,
-0.02722657285630703,
-0.0028088600374758244,
0.0410151369869709,
-0.0036370386369526386,
-0.0022333015222102404,
-0.05273500084877014,
0.007866385392844677,
0.021237293258309364,
0.01620294153690338,
0.017105521634221077,
-0.008654097095131874,
-0.02574314922094345,
0.007600346580147743,
0.002295820042490959,
-0.07185203582048416,
0.04395418241620064,
-0.022183172404766083,
0.046854980289936066,
-0.04788653552532196,
0.03754656761884689,
-0.047512486577034,
0.013720102608203888,
-0.03250501677393913,
-0.0633547306060791,
-0.019184809178113937,
0.015420569106936455,
0.024038877338171005,
0.028927620500326157,
0.01640978455543518,
0.015714621171355247,
-0.10961874574422836,
-0.05413483828306198,
0.00012102891923859715,
0.0704292580485344,
-0.046907950192689896,
-0.00811439473181963,
-0.029366744682192802,
-0.048207104206085205,
0.04760129377245903,
0.01471475139260292,
-0.04156146198511124,
0.0617901012301445,
0.03392326459288597,
-0.07458122074604034,
-0.014374477788805962,
0.001984217669814825,
-0.03141038119792938,
0.045012108981609344,
-0.00952901877462864,
-0.048334505409002304,
0.0380411334335804,
-0.04417777061462402,
0.008748079650104046,
0.0442032590508461,
-0.04599785804748535,
0.03154386952519417,
-0.04117555171251297,
-0.021901333704590797,
-0.02860398031771183,
-0.08759257197380066,
-0.029449177905917168,
0.02271234430372715,
-0.005226626992225647,
-0.06692294776439667,
-0.04783438518643379,
0.01574714295566082,
0.06239917501807213,
0.027076078578829765,
-0.0030007953755557537,
0.05748283863067627,
0.024230044335126877,
-0.043067965656518936,
0.016645383089780807,
0.03555767610669136,
0.029325680807232857,
0.010209823027253151,
0.0026740324683487415,
-0.02108612284064293,
0.007738360669463873,
-0.0038822288624942303,
0.021007580682635307,
0.025774367153644562,
-0.0441126674413681,
-0.031615953892469406,
-0.024537697434425354,
0.008443966507911682,
-0.010701047256588936,
0.002772533567622304,
-0.09237901866436005,
-0.03751780092716217,
-0.028139781206846237,
-0.028254449367523193,
-0.02515481598675251,
0.012852644547820091,
0.057175468653440475,
0.04229949414730072,
-0.027301916852593422,
-0.03161335736513138,
-0.05005623400211334,
-0.0181624423712492,
-0.00712121045216918,
-0.02073681354522705,
0.06258295476436615,
-0.03142646700143814,
0.012464851140975952,
0.10336446017026901,
-0.09302596747875214,
0.00044534969492815435,
0.02620856836438179,
0.005974713247269392,
0.003833647584542632,
0.012774946168065071,
0.02765631303191185,
0.014747879467904568,
-0.026620950549840927,
0.00312666199170053,
0.022582320496439934,
-0.035878464579582214,
0.03043084405362606,
0.010666178539395332,
0.0057145413011312485,
0.00908636674284935,
0.008418741635978222,
0.014085737988352776,
-0.0006542617920786142,
-0.034868136048316956,
0.0004978741053491831,
0.006320813205093145,
-0.019300373271107674,
0.02795468084514141,
-0.023093318566679955,
-0.02034754864871502,
-0.04363574832677841,
-0.014157476834952831,
-0.03506694734096527,
0.021972423419356346,
0.008326741866767406,
-0.033463772386312485,
-0.051039110869169235,
-0.010436737909913063,
-0.010645761154592037,
0.004644023720175028,
0.011032534763216972,
0.01853228360414505,
0.0032264189794659615,
0.011163284070789814,
-0.0049892510287463665,
0.014453241601586342,
0.04910675436258316,
0.003337110159918666,
0.02208804525434971,
-0.015054798685014248,
-0.032150350511074066,
-0.012770782224833965,
-0.04178810119628906,
0.03334777429699898,
0.0012919420842081308,
0.014356877654790878,
-0.023757975548505783,
0.001235262956470251,
0.0089160967618227,
-0.021779639646410942,
0.03892892226576805,
0.020383359864354134,
0.031812023371458054,
-0.017907971516251564,
0.01717548444867134,
0.014168975874781609,
0.03802450746297836,
-0.03484640270471573,
0.011038473807275295,
-0.006274108309298754,
0.05052824690937996,
0.016715921461582184,
-0.0031691098120063543,
-0.05430949851870537,
0.01759025640785694,
0.01931070350110531,
0.00860617496073246,
0.028502123430371284,
-0.05199596658349037,
-0.022643612697720528,
-0.032145146280527115,
0.07075285166501999,
-0.04167955741286278,
0.03490056097507477,
-0.028919901698827744,
-0.0347253642976284,
-0.013693655841052532,
0.004796091932803392,
-0.07871894538402557,
-0.005141652654856443,
-0.046411581337451935,
0.058211054652929306,
-0.02482561394572258,
-0.006109142210334539,
0.017188498750329018,
-0.037540845572948456,
-0.008428809233009815,
-0.01167859323322773,
-0.007010169327259064,
-0.03704896196722984,
-0.03821062296628952,
-0.08089756220579147,
0.04335365444421768,
-0.011941000819206238,
-0.07388073205947876,
-0.02393791265785694,
0.020022597163915634,
-0.023327412083745003,
-0.03896390274167061,
-0.026577845215797424,
0.039721377193927765,
0.09311246871948242,
0.014104990288615227,
0.01895936392247677,
0.03676325082778931,
0.00925844069570303,
0.0019324223976582289,
0.005211322568356991,
-0.024322474375367165,
0.0036776543129235506,
0.01973031647503376,
0.015020208433270454,
-0.0570744127035141,
0.012806395068764687,
-0.008131447248160839,
0.0629282221198082,
0.041048314422369,
0.05609700456261635,
-0.007203256711363792,
-0.008372209034860134,
-0.012312494218349457
] |
[
15.239638328552246,
5.189820766448975
] |
Astrophysics
|
Astrophysics
|
astro-ph
|
na
|
na
|
2007-04-01T16:59:04
|
We get asymptotics for the volume of large balls in an arbitrary locally
compact group G with polynomial growth. This is done via a study of the
geometry of G and a generalization of P. Pansu's thesis. In particular, we show
that any such G is weakly commensurable to some simply connected solvable Lie
group S, the Lie shadow of G. We also show that large balls in G have an
asymptotic shape, i.e. after a suitable renormalization, they converge to a
limiting compact set which can be interpreted geometrically. We then discuss
the speed of convergence, treat some examples and give an application to
ergodic theory. We also answer a question of Burago about left invariant
metrics and recover some results of Stoll on the irrationality of growth series
of nilpotent groups.
|
Geometry of Locally Compact Groups of Polynomial Growth and Shape of
Large Balls
|
math.GR math.DG
|
0704.0095
| 2,007
|
[
0.029162850230932236,
0.0682157650589943,
-0.01502145268023014,
-0.06141004338860512,
-0.007549096364527941,
0.013522995635867119,
0.03234477341175079,
-0.020731134340167046,
-0.031791988760232925,
0.01989823393523693,
-0.0580870658159256,
0.02255297638475895,
0.0533129908144474,
0.02506471984088421,
-0.01883113756775856,
-0.03560895100235939,
0.02977858856320381,
-0.028206292539834976,
-0.004696562886238098,
0.014538855291903019,
-0.01061271782964468,
0.00007332305540330708,
0.019919762387871742,
-0.010988431982696056,
0.12242797762155533,
0.01793329231441021,
0.06887473165988922,
-0.011675538495182991,
-0.004563560709357262,
0.008069734089076519,
0.08704579621553421,
-0.054240137338638306,
0.0035425820387899876,
-0.07171553373336792,
-0.014840029180049896,
-0.01138586737215519,
0.03567803278565407,
-0.00231392914429307,
0.009433015249669552,
0.04288448393344879,
0.06267309933900833,
-0.003008908126503229,
0.03727227449417114,
0.006743329111486673,
-0.002096605021506548,
0.023625561967492104,
0.020470909774303436,
0.04245183244347572,
0.04659690707921982,
-0.022071488201618195,
-0.007661203388124704,
0.05030335858464241,
-0.009325241670012474,
-0.08840326964855194,
-0.054380662739276886,
0.03696131706237793,
0.02181602641940117,
-0.053993914276361465,
0.048514463007450104,
-0.015547947958111763,
0.03933711722493172,
0.04093645140528679,
-0.09780343621969223,
0.012209394946694374,
0.04409942775964737,
-0.05512712523341179,
-0.010357365012168884,
0.004086035303771496,
-0.0126497782766819,
-0.006469679530709982,
0.0033258802723139524,
-0.006828846875578165,
0.04069845378398895,
0.01738114096224308,
-0.05498073995113373,
0.022755764424800873,
0.04670687019824982,
-0.0020122944843024015,
0.016351452097296715,
0.010961499996483326,
-0.006935221143066883,
-0.050483472645282745,
0.008460563607513905,
0.004466197919100523,
0.04392008110880852,
0.009150219149887562,
0.011102032847702503,
-0.002064300933852792,
-0.041967689990997314,
0.05879046022891998,
0.04408755153417587,
-0.011076339520514011,
0.0605999119579792,
0.0559869110584259,
-0.02998991683125496,
0.02904743142426014,
-0.008146828040480614,
0.0568062923848629,
-0.07615148276090622,
-0.00412355363368988,
-0.006614508107304573,
0.07224589586257935,
0.004502114374190569,
0.024908527731895447,
0.07460174709558487,
0.04374293237924576,
-0.005592495668679476,
0.028082381933927536,
0.02128875069320202,
-0.013999562710523605,
-0.06178378686308861,
-0.021755965426564217,
0.005683119408786297,
-0.03655362129211426,
-0.03637095168232918,
0.014795501716434956,
0.03747410699725151,
-0.04340290278196335,
-0.006584818009287119,
0.06910282373428345,
0.006224576383829117,
-0.024373961612582207,
0.01289607584476471,
0.027976062148809433,
0.03935140371322632,
0.07765114307403564,
-0.0344487689435482,
-0.021740302443504333,
0.031243225559592247,
-0.012017762288451195,
0.015722014009952545,
-0.011301371268928051,
-0.013841950334608555,
0.0011370957363396883,
0.009723958559334278,
0.060880549252033234,
-0.0474788099527359,
0.01742841675877571,
0.04634523764252663,
0.001696682651527226,
-0.0024318848736584187,
-0.03131597489118576,
0.048427484929561615,
-0.019169112667441368,
-0.002088152803480625,
0.00023410104040522128,
0.050813812762498856,
-0.07748401165008545,
0.017265761271119118,
-0.0065851472318172455,
0.026054492220282555,
0.04089392349123955,
0.01043426152318716,
0.017977925017476082,
-0.017885569483041763,
-0.003486305708065629,
-0.014120122417807579,
0.05139897018671036,
0.09946604073047638,
-0.000586730137001723,
-0.038323428481817245,
0.013459287583827972,
-0.05895957723259926,
0.035934723913669586,
-0.05450556054711342,
0.038428567349910736,
0.04931294918060303,
0.036665160208940506,
-0.041989196091890335,
0.00920943170785904,
-0.05489260330796242,
0.027946526184678078,
-0.024116458371281624,
0.009598457254469395,
0.024097010493278503,
-0.01166954729706049,
-0.03403937444090843,
-0.06001519784331322,
0.0064257183112204075,
-0.010689335875213146,
0.02847151830792427,
-0.03913046419620514,
0.046047769486904144,
0.02573179267346859,
0.0047697932459414005,
0.052838850766420364,
0.03855517879128456,
-0.02581685222685337,
-0.000233983009820804,
-0.006352155935019255,
0.0020118223037570715,
0.03569570183753967,
-0.009590123780071735,
0.01836566813290119,
-0.010572653263807297,
0.02819783054292202,
0.0652698427438736,
-0.036532070487737656,
-0.02676175720989704,
-0.028893308714032173,
-0.03773847594857216,
-0.0040350183844566345,
-0.0370078980922699,
0.0072109573520720005,
-0.025805553421378136,
0.0550491064786911,
-0.015071653760969639,
0.023940235376358032,
0.01878107525408268,
0.014820289798080921,
0.063947893679142,
0.006589035969227552,
-0.0004928864073008299,
0.008234578184783459,
-0.017425663769245148,
0.01724187470972538,
-0.00353034189902246,
-0.024653149768710136,
-0.0213813167065382,
0.040695738047361374,
0.04237470403313637,
-0.02241993136703968,
-0.021466508507728577,
-0.01784784533083439,
0.034034550189971924,
-0.007653576321899891,
-0.03708487004041672,
-0.023949606344103813,
-0.022468972951173782,
0.021419500932097435,
-0.07828420400619507,
-0.08514440059661865,
0.03368717059493065,
-0.0161869116127491,
-0.00931861624121666,
0.02107519842684269,
-0.03574264794588089,
0.05477931722998619,
0.059009574353694916,
0.0629681721329689,
0.05035119503736496,
-0.026015629991889,
0.02940811589360237,
-0.029959768056869507,
-0.0738925188779831,
0.00669985543936491,
0.0018551558023318648,
0.020939674228429794,
-0.07013218104839325,
0.06110474467277527,
0.05813900753855705,
0.002894200850278139,
0.05439240485429764,
0.023003043606877327,
0.006202021148055792,
-0.01683150604367256,
-0.029597511515021324,
0.0018529853550717235,
0.035123854875564575,
-0.0707492083311081,
-0.024004720151424408,
-0.030209554359316826,
0.011601805686950684,
-0.057913124561309814,
-0.05104783922433853,
0.011460335925221443,
0.03615104779601097,
-0.02845570258796215,
-0.017125168815255165,
0.005994108039885759,
0.03345680236816406,
0.03017439879477024,
0.12745784223079681,
0.06956876069307327,
-0.025429928675293922,
0.03345907852053642,
-0.031532179564237595,
-0.050422511994838715,
-0.011998704634606838,
-0.040283411741256714,
-0.008929239585995674,
-0.025108689442276955,
-0.06434403359889984,
0.00819157063961029,
-0.0024442854337394238,
0.017154719680547714,
0.01747061125934124,
-0.03516456112265587,
0.05242694169282913,
0.013741515576839447,
-0.02704431302845478,
0.04799159616231918,
0.07153653353452682,
0.07156797498464584,
-0.0003682247770484537,
0.06880874931812286,
0.025910966098308563,
-0.026248320937156677,
0.017235949635505676,
-0.0015504464972764254,
-0.004486013203859329,
-0.027537081390619278,
-0.013416471891105175,
-0.04258778318762779,
0.084566131234169,
-0.0023396119941025972,
0.005686992313712835,
-0.031339798122644424,
-0.003405521856620908,
-0.019636033102869987,
-0.021199332550168037,
0.03312939777970314,
0.019075211137533188,
-0.018361831083893776,
-0.06437487155199051,
0.009555899538099766,
0.02569754794239998,
0.020564168691635132,
0.060167692601680756,
-0.011745625175535679,
0.00938075128942728,
-0.056142184883356094,
0.03183124586939812,
-0.05042767524719238,
-0.01786128245294094,
-0.02117779105901718,
-0.013096426613628864,
-0.009681718423962593,
0.009175012819468975,
-0.05421637371182442,
-0.01907752826809883,
0.03626297414302826,
-0.01234990544617176,
-0.025578368455171585,
-0.025563837960362434,
-0.03974062204360962,
-0.033805977553129196,
0.016393497586250305,
0.002305145375430584,
-0.005078747868537903,
-0.01287570409476757,
-0.06842895597219467,
-0.0298127643764019,
-0.03066684864461422,
-0.02689664252102375,
0.0089177954941988,
-0.05070105195045471,
-0.014581426978111267,
0.03551308065652847,
0.007947033271193504,
-0.024648798629641533,
-0.029302092269062996,
0.01619279943406582,
-0.0838012844324112,
0.017195003107190132,
0.022626444697380066,
0.010846219025552273,
-0.040784336626529694,
0.0029098507948219776,
-0.022013556212186813,
0.02057127095758915,
-0.005215077195316553,
-0.0010060895001515746,
0.03089684061706066,
0.027250882238149643,
0.010974094271659851,
0.030528856441378593,
0.004976525902748108,
0.011085600592195988,
-0.0222411397844553,
-0.005992552265524864,
-0.044271692633628845,
0.0426776222884655,
0.08222614228725433,
0.03352908417582512,
0.048207469284534454,
-0.08888226747512817,
-0.00383099471218884,
-0.029822155833244324,
-0.053171273320913315,
0.09520233422517776,
-0.01995651237666607,
0.04417874291539192,
-0.04525529220700264,
-0.03700373321771622,
0.04283251613378525,
-0.033436764031648636,
-0.014887752942740917,
-0.020966917276382446,
-0.003874230897054076,
-0.010573236271739006,
-0.05721607059240341,
-0.04170649126172066,
0.010031708516180515,
-0.017887206748127937,
-0.04064541682600975,
0.03904224932193756,
-0.00594696681946516,
0.028814997524023056,
0.0010229138424620032,
-0.04438171908259392,
-0.044946931302547455,
0.0030120504088699818,
0.006932375021278858,
-0.01691414602100849,
0.005761558189988136,
0.008702236227691174,
-0.020150013267993927,
0.06059952825307846,
-0.045890409499406815,
-0.011353596113622189,
0.01575184427201748,
0.0061837295070290565,
-0.05966980382800102,
0.0033434894867241383,
-0.012359143234789371,
0.02274894155561924,
0.0058564962819218636,
0.004331170581281185,
-0.005347142927348614,
-0.0037733791396021843,
0.007631366141140461,
-0.043961867690086365,
0.008980757556855679,
-0.04525715485215187,
0.04620380327105522,
-0.03320281207561493,
0.024192169308662415,
-0.022199995815753937,
-0.0908820629119873,
0.05565427616238594,
0.028418811038136482,
0.013814972713589668,
0.03646441921591759,
-0.04538032412528992,
-0.0036800182424485683,
0.06732649356126785,
0.014323912560939789,
0.0014556823298335075,
0.02136729098856449,
0.01809152401983738,
0.008787560276687145,
-0.005621045362204313,
-0.013249795883893967,
0.04103174805641174,
0.06740344315767288,
0.025049395859241486,
0.042107898741960526,
-0.028306353837251663,
-0.013119645416736603,
0.06850414723157883,
0.0028801350854337215,
-0.0019230879843235016,
0.011690019629895687,
0.026715951040387154,
-0.03912551328539848,
-0.04924595355987549,
0.025300875306129456,
0.018530748784542084,
0.0158462505787611,
0.012521347962319851,
-0.021929992362856865,
-0.05389796197414398,
0.024062717333436012,
-0.009179452434182167,
-0.029111886397004128,
-0.04997693747282028,
0.040128156542778015,
0.012424328364431858,
0.05794896185398102,
-0.04980185255408287,
0.03302527219057083,
-0.004961887840181589,
-0.0037167049013078213,
-0.023177506402134895,
-0.04922842979431152,
0.038451019674539566,
-0.009532683528959751,
0.0537027083337307,
0.03444262593984604,
0.043138474225997925,
-0.074899822473526,
-0.04447917267680168,
-0.02564350515604019,
0.002712072804570198,
0.029988029971718788,
0.0036890441551804543,
0.0061049629002809525,
0.013117282651364803,
0.001636726432479918,
-0.016088075935840607,
0.014243345707654953,
-0.03279220685362816,
0.07475978881120682,
-0.03023667074739933,
-0.042793333530426025,
0.02171325869858265,
-0.030345002189278603,
0.06637725979089737,
-0.02417614310979843,
-0.046226415783166885,
0.03856104984879494,
0.03993606939911842,
-0.012556287460029125,
0.03363657742738724,
0.02010468766093254,
0.010695254430174828,
-0.03361284360289574,
0.03574297949671745,
0.04640394449234009,
-0.015328560955822468,
0.05391361936926842,
0.08859189599752426,
0.05607001110911369,
0.0010174569906666875,
-0.05807894468307495,
-0.0051808604039251804,
-0.005700511392205954,
-0.027117202058434486,
0.015703286975622177,
0.024250337854027748,
-0.02353113703429699,
0.005793686490505934,
-0.03017551079392433,
0.01706000603735447,
0.04349712282419205,
-0.04747568815946579,
-0.041167061775922775,
0.0203788373619318,
0.0031950706616044044,
0.006426369305700064,
-0.05797884613275528,
-0.02501007169485092,
-0.04720782861113548,
0.004464283119887114,
0.0026787929236888885,
-0.01651984639465809,
-0.043070368468761444,
-0.03131384029984474,
-0.02726181037724018,
-0.04280409961938858,
0.006632715463638306,
-0.011283976957201958,
0.044620782136917114,
0.008587640710175037,
-0.01501428708434105,
-0.04238239303231239,
-0.011899376288056374,
0.020729806274175644,
0.00638028746470809,
0.05338093638420105,
-0.004919597879052162,
0.02267315797507763,
-0.013617627322673798,
0.00312651670537889,
-0.028260113671422005,
0.04081655293703079,
-0.033083993941545486,
-0.0649653971195221,
-0.016805626451969147,
0.041288722306489944,
-0.03097136691212654,
0.03090948797762394,
-0.03527757152915001,
0.015885619446635246,
-0.07794289290904999,
0.019831478595733643,
-0.00007501753134420142,
0.01760987378656864,
0.002328434493392706,
-0.019012734293937683,
-0.025224998593330383,
0.052916109561920166,
0.07261142134666443,
0.0017191682709380984,
-0.07561659067869186,
0.022990552708506584,
-0.040275439620018005,
-0.046032268553972244,
0.0008794749737717211,
-0.039719950407743454,
-0.015738433226943016,
0.041052307933568954,
0.007282651029527187,
-0.010344907641410828,
0.02074258029460907,
-0.016315747052431107,
-0.025239139795303345,
0.06216878071427345,
-0.004943464882671833,
-0.013411278836429119,
-0.004529678728431463,
-0.024764683097600937,
-0.002999101299792528,
-0.05309172347187996,
-0.039289653301239014,
-0.029458947479724884,
-0.013110144063830376,
-0.04030974581837654,
-0.07376454770565033,
-0.013993228785693645,
0.03587580844759941,
0.044106513261795044,
-0.056748196482658386,
0.029027972370386124,
0.03454325720667839,
-0.009822877123951912,
0.008586721494793892,
0.0031225578859448433,
-0.005320040974766016,
0.028362272307276726,
0.04587849974632263,
-0.022331127896904945,
-0.011696233414113522,
0.004448621533811092,
-0.05773887783288956,
0.0833640918135643,
-0.046118203550577164,
0.003749558236449957,
-0.10306549817323685,
0.003945774398744106,
-0.022821815684437752,
-0.00040049312519840896,
-0.07209816575050354,
0.0013433691347017884,
0.007032654248178005,
-0.052982982248067856,
-0.03556568920612335,
-0.011550498194992542,
0.06243659183382988,
0.05131564661860466,
0.014957619830965996,
-0.026569530367851257,
-0.04763932526111603,
0.011984285898506641,
0.010797292925417423,
-0.045560818165540695,
0.03613321855664253,
0.007914439775049686,
0.013071299530565739,
0.0692557841539383,
-0.01855437457561493,
-0.06452839821577072,
0.00004801111208507791,
0.012068179436028004,
0.008324711583554745,
-0.039084967225790024,
0.07008123397827148,
-0.00559290312230587,
-0.0280972421169281,
0.05587858334183693,
0.0794513002038002,
-0.014837910421192646,
-0.0076974486000835896,
-0.01589895226061344,
-0.011875763535499573,
0.042573146522045135,
-0.021585771813988686,
-0.04116278886795044,
-0.002310265088453889,
-0.02589898370206356,
0.03602254018187523,
0.05346671864390373,
-0.03909923881292343,
-0.004143560770899057,
-0.02653605304658413,
-0.01133483462035656,
-0.05257773399353027,
-0.08806812018156052,
0.0010239221155643463,
-0.0047126347199082375,
-0.06274508684873581,
-0.03237309679389,
-0.0176214762032032,
-0.05641856789588928,
-0.008254161104559898,
0.02147800289094448,
0.06387621909379959,
-0.009194363839924335,
-0.0341850183904171,
0.0024170882534235716,
-0.018942106515169144,
0.050231900066137314,
0.014057082124054432,
-0.011608414351940155,
0.015902314335107803,
-0.031438786536455154,
-0.05084488168358803,
-0.02937108650803566,
-0.039830464869737625,
0.00016370677622035146,
-0.014907506294548512,
0.0049733868800103664,
0.023493802174925804,
0.0018127552466467023,
-0.018686022609472275,
-0.069984570145607,
0.009248383343219757,
-0.0009124079952016473,
0.0224943645298481,
-0.0012984799686819315,
0.0057775541208684444,
-0.04237857833504677,
-0.01672215573489666,
0.02464365027844906,
-0.03188011422753334,
0.016968127340078354,
0.05057724565267563,
-0.019362151622772217,
0.020410453900694847,
-0.006238127127289772,
0.020628605037927628,
0.04226335883140564,
0.004004389047622681,
0.08829518407583237,
0.05640442669391632,
0.0005317284958437085,
-0.06802459806203842,
0.018058987334370613,
-0.016953924670815468,
0.02317635528743267,
-0.011405035853385925,
-0.004511053673923016,
-0.03981829807162285,
-0.02641124092042446,
-0.05635372921824455,
-0.02436654455959797,
-0.045774396508932114,
0.03477374464273453,
0.04353683069348335,
-0.007676383480429649,
0.021753469482064247,
-0.029245689511299133,
0.02236681617796421,
-0.05897926911711693,
-0.025385169312357903,
-0.02263615094125271,
-0.016660772264003754,
-0.014477139338850975,
-0.026433128863573074,
-0.0006574720609933138,
-0.06015288829803467,
0.020717456936836243,
0.0520404689013958,
0.0013655174989253283,
0.006263211835175753,
-0.04244932159781456,
0.0061960904859006405,
0.04663827270269394,
0.010916410014033318,
0.0060533336363732815,
0.029940880835056305,
0.0010221308330073953,
0.04590234532952309,
-0.036138877272605896,
0.003998723346740007,
-0.0016440487233921885,
0.04050038382411003,
0.011908370070159435,
-0.04005216807126999,
0.029669135808944702,
0.00695599103346467,
0.035218361765146255,
0.0507657453417778,
0.020235514268279076,
0.00786214042454958,
-0.04858708009123802,
-0.0033239221666008234
] |
[
1.4276045560836792,
2.8236756324768066
] |
Group Theory
|
Mathematics
|
math-GR
|
math-DG
|
na
|
2007-04-01T17:28:15
|
In this note we present three representations of a 248-dimensional Lie
algebra, namely the algebra of Lie point symmetries admitted by a system of
five trivial ordinary differential equations each of order forty-four, that
admitted by a system of seven trivial ordinary differential equations each of
order twenty-eight and that admitted by one trivial ordinary differential
equation of order two hundred and forty-four.
|
Much ado about 248
|
nlin.SI
|
0704.0096
| 2,007
|
[
-0.019621608778834343,
0.02457207627594471,
0.0005811355076730251,
-0.056415341794490814,
0.010564831085503101,
-0.008087532594799995,
0.05239319056272507,
0.009178412146866322,
-0.03644506633281708,
0.03660127520561218,
-0.09315936267375946,
0.03490140289068222,
-0.0038648576010018587,
-0.005802697967737913,
0.006370162591338158,
-0.01774165779352188,
0.04334339499473572,
-0.007068415638059378,
-0.01797993667423725,
-0.042653776705265045,
0.01733429916203022,
0.041022662073373795,
-0.04679133743047714,
-0.05120719224214554,
0.10072950273752213,
0.02429613284766674,
0.022025298327207565,
-0.012383202090859413,
-0.04356878623366356,
0.04591647535562515,
0.07574746757745743,
-0.014030099846422672,
0.03390226140618324,
-0.015436619520187378,
-0.04357706010341644,
-0.03093680925667286,
0.05640634521842003,
0.06220806762576103,
0.011454733088612556,
0.008205544203519821,
0.026717843487858772,
-0.007957295514643192,
-0.019088193774223328,
-0.01917545311152935,
-0.009301981888711452,
-0.016362378373742104,
-0.02436058595776558,
-0.007057223469018936,
0.03269720450043678,
-0.014892172999680042,
0.002384437248110771,
0.004293207079172134,
-0.003557167248800397,
-0.05112137645483017,
-0.04215885326266289,
0.024229075759649277,
0.0023732713889330626,
-0.07936938107013702,
0.021183568984270096,
0.04148683324456215,
0.015144120901823044,
0.04422987997531891,
0.0039015719667077065,
0.050811465829610825,
0.0277971550822258,
-0.007242599502205849,
0.027071861550211906,
-0.004820688161998987,
-0.03305772319436073,
-0.0025207665748894215,
0.02723030559718609,
-0.023298116400837898,
0.027558671310544014,
-0.029141172766685486,
-0.017015932127833366,
0.03304962441325188,
0.043387364596128464,
0.0036791819147765636,
0.002981604775413871,
0.017630301415920258,
-0.026233796030282974,
-0.01627194508910179,
0.04175291955471039,
0.01881781406700611,
0.0067060478031635284,
0.05506419762969017,
0.01589806005358696,
0.06986694037914276,
-0.07626132667064667,
-0.002347690286114812,
0.0331977978348732,
0.029109381139278412,
0.011933795176446438,
0.05454096570611,
-0.05078641325235367,
0.015905527397990227,
0.003247436136007309,
0.03360380232334137,
-0.06381256133317947,
-0.019432324916124344,
-0.06671427190303802,
0.0811820924282074,
-0.008225247263908386,
0.025535443797707558,
0.11424924433231354,
0.023678356781601906,
0.01661117561161518,
0.01632550172507763,
-0.0387822724878788,
0.013292714953422546,
-0.052291881293058395,
-0.011715713888406754,
-0.03255155682563782,
-0.013336277566850185,
-0.014885297045111656,
-0.011818786151707172,
0.02252982184290886,
-0.06253287941217422,
-0.03461766988039017,
0.027785085141658783,
0.018241779878735542,
-0.02986871264874935,
0.05481371283531189,
0.04797779396176338,
0.02936195582151413,
0.016359366476535797,
-0.041495468467473984,
-0.020525280386209488,
0.005046436563134193,
-0.012044982984662056,
-0.03398940712213516,
-0.03848075494170189,
-0.0421980619430542,
-0.012848805636167526,
0.01811993680894375,
0.04438061639666557,
-0.015023698098957539,
-0.048451535403728485,
-0.001676057931035757,
0.03554311767220497,
0.005170026328414679,
-0.007124627474695444,
-0.016651805490255356,
-0.04898461699485779,
0.01232306007295847,
-0.030228624120354652,
0.009364749304950237,
-0.07934629172086716,
-0.03156067803502083,
-0.027792299166321754,
0.004994349088519812,
0.04025997221469879,
0.0589078888297081,
0.031349215656518936,
-0.07102319598197937,
-0.060004256665706635,
-0.01340477354824543,
0.012653011828660965,
0.006851619575172663,
-0.0296004768460989,
0.012818912044167519,
-0.002610588911920786,
-0.022838186472654343,
0.008566230535507202,
-0.08518271148204803,
0.027265269309282303,
-0.011816535145044327,
0.018636438995599747,
0.005520922597497702,
0.0850728452205658,
-0.0027931861113756895,
0.019801195710897446,
-0.01676284894347191,
-0.028389735147356987,
-0.006912653334438801,
0.01913108304142952,
-0.024031203240156174,
-0.0393490269780159,
0.02671969309449196,
-0.021571319550275803,
0.036475565284490585,
-0.025069665163755417,
0.03479618951678276,
0.029087401926517487,
-0.018282903358340263,
-0.009587309323251247,
0.008945567533373833,
-0.029048101976513863,
-0.022547481581568718,
-0.0014537157258018851,
-0.011035008355975151,
0.06967286020517349,
0.013426150195300579,
-0.005718783475458622,
-0.0194444190710783,
0.006118206772953272,
0.04446377232670784,
-0.010482464917004108,
-0.03280022740364075,
-0.009025110863149166,
0.00806864071637392,
0.006776187568902969,
-0.05626150593161583,
-0.02988956868648529,
-0.011691074818372726,
0.033824194222688675,
0.006944327149540186,
0.022561460733413696,
-0.012456920929253101,
-0.004331447184085846,
0.03475648909807205,
-0.03059716522693634,
0.0016419056337326765,
0.020694250240921974,
-0.039359401911497116,
-0.03869176283478737,
0.004549160599708557,
-0.06364090740680695,
-0.01596969924867153,
0.020524129271507263,
0.002837439300492406,
-0.030268386006355286,
0.035092197358608246,
0.0004221909330226481,
0.004538492299616337,
0.018762217834591866,
-0.01297944225370884,
-0.04163482040166855,
-0.023102836683392525,
-0.04835861548781395,
-0.027280833572149277,
-0.04278343543410301,
0.011336435563862324,
-0.03251379728317261,
-0.03867722302675247,
0.03323616832494736,
-0.04761209711432457,
0.01379495207220316,
0.02771107107400894,
0.09854789823293686,
0.011510794050991535,
0.03908345848321915,
0.02911641262471676,
0.0003110826073680073,
-0.05935317277908325,
-0.013053587637841702,
0.00737387640401721,
-0.01776733063161373,
0.002183208940550685,
0.08346845209598541,
-0.0154983876273036,
-0.006023922003805637,
0.0736304447054863,
0.01658855937421322,
0.05316031724214554,
0.00434994837269187,
-0.044961728155612946,
0.019329611212015152,
0.04412533715367317,
-0.03386930003762245,
0.005066143814474344,
0.008030779659748077,
0.027044938877224922,
-0.004976519849151373,
-0.06005733460187912,
0.022654948756098747,
-0.00021676364121958613,
-0.00035895348992198706,
0.00042169762309640646,
-0.02734879031777382,
0.027534358203411102,
0.04976963624358177,
-0.003750935895368457,
0.06114686280488968,
-0.02048182673752308,
-0.01820371299982071,
0.004840797279030085,
-0.025769425556063652,
-0.06359076499938965,
-0.036627396941185,
-0.004891582764685154,
0.010268518701195717,
-0.04815598204731941,
0.05142476037144661,
0.060691237449645996,
0.08742135763168335,
0.005418163724243641,
0.016153890639543533,
0.011335366405546665,
0.04228809103369713,
-0.02590908482670784,
0.017314163967967033,
0.014274307526648045,
0.012365451082587242,
0.02750094048678875,
0.060575176030397415,
0.024357827380299568,
-0.01036128681153059,
-0.030443508177995682,
0.03621385246515274,
0.005194587167352438,
-0.01646718755364418,
0.00023709071683697402,
-0.011454019695520401,
0.020751122385263443,
0.014947104267776012,
0.024444762617349625,
0.013459953479468822,
0.058440789580345154,
-0.024900810793042183,
-0.05354767665266991,
-0.01754334382712841,
-0.010723289102315903,
-0.055758241564035416,
-0.030816808342933655,
0.04344255104660988,
0.02926694042980671,
0.010592651553452015,
0.043558765202760696,
-0.04440201073884964,
0.017267554998397827,
-0.04983454570174217,
0.050323236733675,
-0.04877714440226555,
0.03316780552268028,
0.021536225453019142,
-0.01939917728304863,
0.027668002992868423,
-0.06624813377857208,
-0.045413922518491745,
-0.008804419077932835,
-0.014287141151726246,
-0.03345897048711777,
0.009960087947547436,
-0.006885691080242395,
-0.0248151496052742,
-0.05514484643936157,
0.01861044019460678,
-0.043524693697690964,
-0.07136829197406769,
0.018605871126055717,
-0.055281125009059906,
-0.018951574340462685,
-0.03502631187438965,
-0.012063753791153431,
-0.06247181072831154,
-0.05279522389173508,
0.04255170002579689,
0.03373022750020027,
0.02523575909435749,
-0.058460552245378494,
-0.008768932893872261,
0.00512307183817029,
-0.024468326941132545,
-0.021554745733737946,
0.018495187163352966,
0.043652161955833435,
-0.012773422524333,
0.006417436525225639,
0.0014958814717829227,
0.022615978494286537,
-0.028979018330574036,
0.023854289203882217,
-0.0005260187899693847,
0.048735376447439194,
0.06803242862224579,
-0.0028740994166582823,
0.016873251646757126,
0.024834072217345238,
-0.037928543984889984,
-0.04333491623401642,
-0.07574804127216339,
0.019748542457818985,
0.01949913427233696,
0.04746786877512932,
-0.03438730910420418,
-0.04463478922843933,
-0.022228455170989037,
-0.029847389087080956,
0.0210555512458086,
0.03975210338830948,
0.003143023932352662,
0.06760742515325546,
0.00986571330577135,
0.043153516948223114,
0.010988381691277027,
-0.05146064981818199,
0.020109161734580994,
-0.01860981062054634,
-0.003394913161173463,
0.03903157263994217,
-0.013155779801309109,
-0.02241583913564682,
0.03605624660849571,
-0.017559725791215897,
-0.0410313680768013,
0.01150491088628769,
0.0023054927587509155,
-0.07747787237167358,
-0.0015982991317287087,
-0.03830878436565399,
-0.0531458780169487,
-0.010084868408739567,
0.02211633324623108,
-0.04050229862332344,
0.0547381266951561,
-0.002579066436737776,
-0.07315778732299805,
0.0768934115767479,
-0.006493723951280117,
0.035684313625097275,
0.010365727357566357,
0.024918094277381897,
-0.03975261375308037,
0.002881420310586691,
0.04627102613449097,
0.018488258123397827,
-0.020481346175074577,
0.014990254305303097,
0.03498755022883415,
0.00821952149271965,
0.05665219575166702,
0.008527141995728016,
0.02416580729186535,
0.005460563115775585,
-0.02368880808353424,
0.008058618754148483,
0.04901537299156189,
-0.050011053681373596,
-0.036481644958257675,
0.029690371826291084,
-0.006417351774871349,
0.005046295002102852,
0.061627309769392014,
-0.10434164106845856,
-0.018001534044742584,
0.002650738228112459,
0.053170494735240936,
-0.021143127232789993,
0.057662345468997955,
0.01750042289495468,
-0.04210486635565758,
-0.00022412951511796564,
-0.04826652631163597,
0.02273200824856758,
0.0070687090046703815,
0.046011507511138916,
-0.013580993749201298,
-0.030400747433304787,
0.013363109901547432,
0.062032300978899,
-0.009666627272963524,
0.024948636069893837,
0.02372698299586773,
0.04973641037940979,
-0.006894472520798445,
0.014858916401863098,
0.05507557466626167,
-0.014143254607915878,
0.049261853098869324,
0.018993521109223366,
0.021213777363300323,
-0.02765856869518757,
0.019067930057644844,
0.009529286064207554,
-0.02745889127254486,
0.01144297793507576,
0.013256673701107502,
-0.009473912417888641,
0.01251038908958435,
0.023807529360055923,
-0.007466492708772421,
0.04159128665924072,
-0.005203092470765114,
0.012661763466894627,
-0.0043569826520979404,
-0.009488465264439583,
-0.06142299249768257,
-0.04350503161549568,
0.07902201265096664,
0.050251077860593796,
-0.02185603231191635,
-0.034295953810214996,
0.009644746780395508,
0.011043203063309193,
0.07740762829780579,
-0.017387762665748596,
0.014248919673264027,
-0.010715987533330917,
-0.026720566675066948,
-0.05989314243197441,
-0.03485880419611931,
-0.011881368234753609,
0.02427390217781067,
-0.037491995841264725,
0.010436038486659527,
-0.009901585057377815,
-0.03326810523867607,
0.00432577496394515,
-0.0019848935771733522,
-0.001944120042026043,
0.07634132355451584,
0.0304220262914896,
0.012961815111339092,
0.048333268612623215,
-0.010076592676341534,
0.0024099531583487988,
-0.028540849685668945,
0.028604848310351372,
0.024568093940615654,
-0.011915293522179127,
0.015303611755371094,
0.05049405246973038,
0.040034160017967224,
0.012149921618402004,
0.01506874244660139,
-0.0039481716230511665,
0.04298253357410431,
-0.010618959553539753,
-0.0017858361825346947,
-0.020094633102416992,
-0.0012239426141604781,
0.0488479845225811,
-0.025537360459566116,
-0.04949615150690079,
0.03804672509431839,
-0.042615436017513275,
-0.09633591771125793,
0.04738878831267357,
-0.022663062438368797,
0.007530872244387865,
0.05616770684719086,
0.022615360096096992,
-0.05526101961731911,
0.026058053597807884,
-0.020532771944999695,
0.018689779564738274,
0.016353514045476913,
0.05211857333779335,
0.027240486815571785,
-0.002583910245448351,
-0.035744789987802505,
0.0065687187016010284,
0.07282920926809311,
0.036317598074674606,
-0.06540817767381668,
-0.09145474433898926,
0.010665671899914742,
-0.013089140877127647,
-0.03155228868126869,
-0.048437926918268204,
-0.0045984224416315556,
0.04963657259941101,
-0.02020840533077717,
-0.009393363259732723,
0.015842296183109283,
-0.025068800896406174,
-0.023576637730002403,
-0.015438050962984562,
0.015509582124650478,
-0.003179149003699422,
0.03542600944638252,
0.005698455963283777,
-0.02258412167429924,
-0.015386375598609447,
-0.14468125998973846,
-0.015308803878724575,
-0.0032464133109897375,
0.05455708131194115,
0.012997251935303211,
0.048008158802986145,
-0.01037414837628603,
0.0006036561098881066,
0.04936429485678673,
0.04237974435091019,
-0.034285563975572586,
0.030246088281273842,
-0.01801634021103382,
-0.04610278457403183,
-0.05277587100863457,
-0.06014423444867134,
-0.032584719359874725,
-0.027524054050445557,
-0.03362436965107918,
-0.05655749514698982,
0.042341865599155426,
-0.03364059701561928,
-0.03144073486328125,
0.037957265973091125,
-0.02163582853972912,
0.04076265171170235,
0.006685897707939148,
-0.019320640712976456,
-0.004202975891530514,
-0.014237609691917896,
-0.0162412878125906,
0.03329072892665863,
0.004184948746114969,
-0.03146009147167206,
-0.03477725014090538,
0.0680004209280014,
0.041795339435338974,
0.08511267602443695,
0.008489634841680527,
0.028355108574032784,
0.07885731011629105,
-0.05249954015016556,
0.026396583765745163,
0.0005751827848143876,
-0.026625145226716995,
0.046110186725854874,
0.04457153379917145,
-0.06741902232170105,
-0.002268931595608592,
-0.006392722018063068,
-0.010350544936954975,
0.05078177526593208,
-0.01013506855815649,
0.011671328917145729,
0.011706747114658356,
-0.019400399178266525,
-0.05079655349254608,
-0.021700408309698105,
-0.008734555914998055,
-0.040372226387262344,
0.001496214885264635,
-0.050259049981832504,
-0.02388404868543148,
0.020788589492440224,
0.07992174476385117,
0.026409229263663292,
-0.0611819326877594,
-0.018389955163002014,
-0.041293416172266006,
0.004327806178480387,
0.02555113472044468,
-0.025661541149020195,
-0.0005032231565564871,
-0.012308810837566853,
0.04142449051141739,
-0.005646636709570885,
-0.02616569586098194,
-0.030473308637738228,
0.0356159508228302,
0.056830160319805145,
-0.02714993618428707,
0.009825949557125568,
0.02272285334765911,
0.006284913048148155,
-0.011007499881088734,
0.12027376145124435,
0.06351948529481888,
-0.01968921720981598,
0.04343389719724655,
-0.018429066985845566,
-0.03799689561128616,
0.05348432436585426,
-0.013593877665698528,
0.002892707707360387,
-0.012367554940283298,
-0.02066681534051895,
0.028776083141565323,
-0.0024987768847495317,
-0.039566583931446075,
-0.020875735208392143,
-0.01473931036889553,
-0.0075238547287881374,
-0.058607250452041626,
0.007639738731086254,
0.051556725054979324,
-0.028467699885368347,
-0.013144627213478088,
0.013960338197648525,
-0.03518304601311684,
-0.05574752762913704,
0.011210925877094269,
0.039466310292482376,
-0.0010919005144387484,
0.04900747165083885,
-0.04043673351407051,
0.05405999347567558,
0.011558241210877895,
-0.013516918756067753,
-0.03480497747659683,
-0.04446754232048988,
-0.015991592779755592,
0.016264719888567924,
-0.0003896026173606515,
-0.03567618876695633,
-0.011899081990122795,
0.04925619438290596,
0.006602700334042311,
0.021968070417642593,
-0.05533313751220703,
0.0502367839217186,
0.04144981503486633,
-0.0717385932803154,
0.0033490387722849846,
0.005320060532540083,
0.014309088699519634,
-0.01050650142133236,
0.02033565379679203,
-0.024097030982375145,
0.018887266516685486,
-0.04214314743876457,
-0.025378860533237457,
0.043901797384023666,
0.004906214773654938,
0.04130483418703079,
-0.04631929099559784,
-0.034089893102645874,
-0.030705487355589867,
0.0553845651447773,
0.011695923283696175,
0.04579755291342735,
0.008206051774322987,
0.007387194316834211,
-0.0886426791548729,
-0.021767633035779,
-0.011927474290132523,
0.06582578271627426,
-0.031305551528930664,
-0.03829440101981163,
0.004758076276630163,
-0.006845911033451557,
-0.06213546171784401,
-0.009974456392228603,
-0.0018504676409065723,
0.055166520178318024,
-0.012349524535238743,
-0.055336449295282364,
0.04251617193222046,
-0.037441033869981766,
0.05336994305253029,
-0.09041343629360199,
0.02229148894548416,
-0.08863134682178497,
0.0033250292763113976,
-0.07602840662002563,
0.023005425930023193,
0.01317798625677824,
-0.056704260408878326,
-0.015381665900349617,
0.015462634153664112,
0.01534708309918642,
0.007284977473318577,
-0.07701881974935532,
-0.0007027765386737883,
0.05169481411576271,
0.006200446281582117,
-0.008817368187010288,
0.0378836914896965,
-0.017323603853583336,
0.04218663275241852,
-0.024613453075289726,
0.030789362266659737,
0.03775421157479286,
-0.0033083620946854353,
0.05726532265543938,
-0.029365960508584976,
0.0038748467341065407,
0.024937674403190613,
0.05262374132871628,
0.06245053932070732,
-0.01403719186782837,
-0.030633097514510155,
-0.05496574938297272,
0.004830906167626381
] |
[
3.8414804935455322,
1.7861462831497192
] |
Exactly Solvable and Integrable Systems
|
Nonlinear Sciences
|
nlin-SI
|
na
|
na
|
2007-04-01T18:02:55
|
We review recent progress in operator algebraic approach to conformal quantum
field theory. Our emphasis is on use of representation theory in classification
theory. This is based on a series of joint works with R. Longo.
|
Conformal Field Theory and Operator Algebras
|
math-ph math.MP math.OA
|
0704.0097
| 2,007
|
[
0.0023044999688863754,
0.01733001507818699,
-0.003509233007207513,
-0.023828143253922462,
0.04100896790623665,
-0.03426094353199005,
0.05781366676092148,
0.05376836284995079,
-0.045881204307079315,
0.012737292796373367,
-0.07722772657871246,
0.07254612445831299,
0.025698445737361908,
-0.0027731345035135746,
0.0002662018232513219,
-0.014760336838662624,
0.0271317008882761,
0.016244225203990936,
0.015135816298425198,
-0.04173032566905022,
-0.015787377953529358,
0.04297107458114624,
0.025763291865587234,
-0.03330370411276817,
0.07859557121992111,
-0.006561276502907276,
0.040144309401512146,
-0.043815143406391144,
0.001522246515378356,
-0.010806524194777012,
0.050893109291791916,
0.01960085891187191,
0.04890024662017822,
-0.04470358043909073,
-0.05666331946849823,
-0.04857014864683151,
0.07379457354545593,
0.0168931744992733,
0.06603513658046722,
0.027549155056476593,
0.0361475795507431,
0.007944617420434952,
-0.022809848189353943,
-0.04862546920776367,
-0.03560919314622879,
-0.03974839672446251,
0.004750548861920834,
-0.02206651121377945,
0.01517228502780199,
0.03551051393151283,
-0.0004125080013182014,
0.028835441917181015,
-0.032573994249105453,
-0.03651032596826553,
-0.020415056496858597,
0.041070252656936646,
-0.03132659196853638,
-0.016465118154883385,
0.03879823163151741,
-0.0009826557943597436,
-0.012995315715670586,
0.062418680638074875,
-0.005136735271662474,
0.018745282664895058,
0.0659012496471405,
-0.025569813326001167,
-0.04462065547704697,
0.02165268175303936,
-0.04224294796586037,
-0.01993522420525551,
0.04740183800458908,
-0.02872994728386402,
0.059205155819654465,
0.07924875617027283,
0.025856731459498405,
-0.014452495612204075,
0.050005652010440826,
-0.03721432387828827,
0.007201637141406536,
-0.0033222835045307875,
0.004707919899374247,
-0.059375278651714325,
0.057660866528749466,
0.041479624807834625,
0.022639429196715355,
-0.009203425608575344,
0.0027985794004052877,
0.041223835200071335,
-0.04119469225406647,
0.018677856773138046,
0.01545863039791584,
0.006340777967125177,
0.04305528476834297,
0.10440635681152344,
-0.05064723640680313,
0.015953578054904938,
-0.019065409898757935,
-0.00832031574100256,
-0.05834295228123665,
-0.04713767394423485,
-0.016138367354869843,
0.08910921216011047,
0.05148937553167343,
0.002676506759598851,
0.058753713965415955,
0.035494156181812286,
0.010656342841684818,
0.00313149718567729,
-0.03698117658495903,
0.03377113863825798,
-0.07407765835523605,
0.05736010521650314,
-0.00043175567407161,
-0.002821915317326784,
-0.04867297783493996,
-0.0018855887465178967,
0.027457237243652344,
-0.09282252192497253,
-0.0300554558634758,
0.04217628017067909,
0.0506221242249012,
-0.0004815588181372732,
0.06754685938358307,
-0.007115031126886606,
-0.008044620044529438,
0.025658778846263885,
-0.0539419986307621,
-0.015066604129970074,
0.027690326794981956,
-0.07226002961397171,
0.020947087556123734,
-0.0012607940007001162,
-0.033773187547922134,
0.011169732548296452,
0.028108084574341774,
0.010769244283437729,
-0.04315239191055298,
-0.034346189349889755,
0.03926079347729683,
-0.022409649565815926,
0.04066332057118416,
0.003861218923702836,
-0.011024139821529388,
-0.0075692846439778805,
0.058615442365407944,
-0.08877743035554886,
0.03425676003098488,
-0.06034402549266815,
-0.00782519020140171,
-0.007820230908691883,
0.04188298434019089,
0.1118861511349678,
0.02810060977935791,
-0.0043372586369514465,
-0.01973925530910492,
-0.029948154464364052,
0.00756768137216568,
-0.01625179499387741,
0.005253916140645742,
-0.01919681951403618,
0.05496576428413391,
0.04720937833189964,
0.0008275412255898118,
0.0618559829890728,
-0.03506045788526535,
-0.02664884179830551,
0.0009058596333488822,
-0.007944825105369091,
0.007987914606928825,
-0.0004960780497640371,
-0.020546598359942436,
0.012840780429542065,
0.021293766796588898,
-0.02955259196460247,
0.013895577751100063,
0.04430827498435974,
-0.05360659956932068,
-0.0018362922128289938,
0.02408776246011257,
0.0072040255181491375,
-0.00259311031550169,
-0.044231168925762177,
0.02356482669711113,
0.050936415791511536,
-0.0218237042427063,
0.024789944291114807,
-0.017522336915135384,
-0.02278878726065159,
-0.050350435078144073,
-0.0289186779409647,
-0.01787976175546646,
0.07308007031679153,
-0.017811289057135582,
-0.04746834188699722,
-0.02213127724826336,
0.0010078896302729845,
0.06323244422674179,
-0.062002141028642654,
-0.017341619357466698,
-0.05261831730604172,
0.020513711497187614,
-0.014190614223480225,
-0.06975757330656052,
0.034219153225421906,
-0.006427739281207323,
0.07119026780128479,
0.01358785666525364,
-0.03385457396507263,
0.016728749498724937,
-0.00225615780800581,
0.04308313876390457,
0.012103131040930748,
0.026349620893597603,
0.015963595360517502,
-0.013021528720855713,
0.014785305596888065,
0.014238224364817142,
-0.06167221441864967,
-0.06637326627969742,
0.0323360338807106,
0.015281296335160732,
-0.03306260332465172,
0.033857155591249466,
-0.014172844588756561,
0.002187828766182065,
0.014033534564077854,
-0.03598622605204582,
0.01974869892001152,
-0.03444058820605278,
-0.020971456542611122,
-0.06630311161279678,
0.02831137180328369,
-0.02205827459692955,
0.003454827005043626,
0.024031266570091248,
-0.0038144956342875957,
-0.012023232877254486,
0.05547409877181053,
0.08540134876966476,
0.03859638422727585,
0.016826052218675613,
0.05842435732483864,
0.01799234002828598,
-0.00785376038402319,
-0.03818706423044205,
-0.0035835811868309975,
0.0044523440301418304,
0.005481685511767864,
0.02139260061085224,
0.026679979637265205,
-0.026389554142951965,
-0.04883606359362602,
-0.034331317991018295,
0.050563786178827286,
0.005232165567576885,
-0.007188759278506041,
-0.0180424302816391,
0.018818847835063934,
0.04605664312839508,
-0.03949357196688652,
0.08505960553884506,
-0.00943493191152811,
-0.026851581409573555,
-0.011052576825022697,
-0.061778172850608826,
0.00019256658561062068,
0.02474445104598999,
-0.0003373806248418987,
-0.018671557307243347,
-0.06435935199260712,
-0.041442181915044785,
0.053820282220840454,
0.034725621342659,
0.016142096370458603,
-0.005352985579520464,
-0.04705279320478439,
-0.010703057050704956,
-0.014395606704056263,
-0.05611444264650345,
-0.03348320350050926,
-0.01770777255296707,
-0.05982741713523865,
-0.02337973192334175,
-0.05717872083187103,
-0.022670535370707512,
0.000524328846950084,
0.046445149928331375,
-0.034454260021448135,
0.0566527284681797,
0.02793518453836441,
0.042874597012996674,
-0.0004313974641263485,
0.004387530032545328,
0.03955961763858795,
-0.015069897286593914,
0.05970996245741844,
0.042016685009002686,
-0.007483602501451969,
0.02621597796678543,
0.06745899468660355,
-0.011909392662346363,
-0.028190337121486664,
0.002255643717944622,
0.017905110493302345,
0.07368043065071106,
-0.00853790994733572,
-0.024364599958062172,
0.013559864833950996,
0.027786200866103172,
0.011192118749022484,
-0.06840857118368149,
0.00405063247308135,
0.011739269830286503,
-0.023141052573919296,
-0.028649907559156418,
-0.016881244257092476,
-0.006047249771654606,
0.04359034448862076,
0.07959889620542526,
-0.019811909645795822,
-0.010433212853968143,
-0.03290216252207756,
0.05696906894445419,
-0.04950736463069916,
0.024999000132083893,
0.05569233372807503,
-0.03770622983574867,
0.05272778868675232,
-0.027922172099351883,
-0.04366495460271835,
0.013755075633525848,
-0.011140200309455395,
0.000036153218388790265,
-0.032780591398477554,
-0.02801859937608242,
-0.022690635174512863,
-0.02776952274143696,
-0.0040589976124465466,
-0.04377836734056473,
-0.05423247069120407,
0.03430785983800888,
-0.05833159387111664,
-0.0221602451056242,
-0.04672553390264511,
-0.0008086950401775539,
-0.00639861635863781,
-0.0563201867043972,
-0.02834814228117466,
0.040371909737586975,
-0.006981750950217247,
-0.08964397013187408,
-0.0023319644387811422,
0.03065970353782177,
-0.020287297666072845,
0.0015233401209115982,
0.02955874241888523,
0.06419962644577026,
0.05053727328777313,
0.028481874614953995,
0.034565310925245285,
-0.027398239821195602,
0.025436198338866234,
0.05970163270831108,
0.055050503462553024,
0.016394013538956642,
-0.020821666345000267,
-0.013402845710515976,
0.003967448603361845,
0.01010135654360056,
0.020965494215488434,
-0.0032325272914022207,
-0.02306128665804863,
0.0222901813685894,
0.015156739391386509,
-0.002573123900219798,
-0.03016694262623787,
-0.05311068147420883,
0.016218559816479683,
-0.019304148852825165,
-0.03570058196783066,
0.012710855342447758,
0.025574397295713425,
0.04428005591034889,
0.005138828884810209,
-0.012267298065125942,
0.011039170436561108,
-0.007389351259917021,
0.011247419752180576,
-0.035910122096538544,
0.008838466368615627,
-0.02973777800798416,
-0.03489729389548302,
-0.01036882121115923,
0.019795922562479973,
-0.05475777015089989,
0.01588207297027111,
0.043913740664720535,
0.012932847253978252,
-0.029614975675940514,
0.005511660594493151,
-0.029096050187945366,
-0.09377891570329666,
0.011086431331932545,
-0.0196184441447258,
-0.044765494763851166,
0.013180882669985294,
-0.020136963576078415,
-0.020571306347846985,
0.035214029252529144,
-0.024729320779442787,
0.0011789890704676509,
0.014149968512356281,
-0.0662926509976387,
-0.06151805818080902,
0.04165014252066612,
0.002078218152746558,
0.03650384396314621,
-0.013655540533363819,
0.013682260178029537,
-0.04584715887904167,
0.012599267065525055,
0.0415450818836689,
0.012240301817655563,
-0.015188020654022694,
-0.002182167721912265,
-0.007342247292399406,
-0.002151816850528121,
0.029646286740899086,
0.02308955229818821,
-0.026306690648198128,
0.01422191597521305,
0.0062661790288984776,
0.031274598091840744,
0.043009571731090546,
-0.0911204069852829,
0.014592400752007961,
0.0010926761897280812,
0.05207713320851326,
-0.009592832066118717,
0.02664095349609852,
0.07435150444507599,
-0.03048126772046089,
-0.013019075617194176,
-0.0017238599248230457,
0.0058674984611570835,
0.025276407599449158,
0.013289718888700008,
-0.010055220685899258,
-0.03635799139738083,
-0.008686942048370838,
0.04387008771300316,
0.04356355592608452,
0.04772600904107094,
0.012058430351316929,
0.06095709279179573,
-0.019479338079690933,
0.004871302284300327,
0.009562017396092415,
0.0810685083270073,
0.05043935403227806,
0.003883320838212967,
0.004239620175212622,
-0.05168330296874046,
0.003748399205505848,
-0.007918765768408775,
-0.005554976873099804,
-0.04297606274485588,
0.01836908794939518,
-0.002481217263266444,
0.023761015385389328,
0.03623269870877266,
0.0036792242899537086,
0.009994777850806713,
-0.05420204997062683,
-0.009648636914789677,
0.020686417818069458,
0.010889988392591476,
-0.035975098609924316,
-0.02854367531836033,
0.010871054604649544,
0.023231124505400658,
0.007036199793219566,
0.0038899416103959084,
0.004895116668194532,
-0.009750062599778175,
0.0632113367319107,
0.043900225311517715,
0.02219053916633129,
-0.025086933746933937,
-0.030625388026237488,
0.006560404319316149,
0.0403284877538681,
-0.005338914226740599,
0.01126157958060503,
-0.054780252277851105,
-0.0021737392526119947,
0.0072503117844462395,
0.028088314458727837,
-0.013906403444707394,
-0.028511952608823776,
-0.0006611135904677212,
0.039132025092840195,
-0.016910968348383904,
0.04025101661682129,
-0.004364370834082365,
-0.003382754046469927,
0.03580370545387268,
-0.04955502226948738,
0.013141772709786892,
-0.015601655468344688,
0.022436413913965225,
0.02844882383942604,
0.0705205425620079,
0.036098115146160126,
0.023407181724905968,
-0.04070385918021202,
0.006830459926277399,
-0.02308262139558792,
-0.05568120628595352,
-0.029458604753017426,
-0.014542303048074245,
-0.024691438302397728,
0.022877391427755356,
-0.009640133008360863,
-0.03864283859729767,
0.025639398023486137,
-0.00619926443323493,
-0.11082905530929565,
0.052101388573646545,
-0.008493710309267044,
0.03369739651679993,
0.04853050410747528,
0.032487187534570694,
-0.01815817877650261,
0.016439128667116165,
-0.058833397924900055,
-0.014776314608752728,
0.06382489949464798,
0.021105768159031868,
0.0435609370470047,
-0.03994416818022728,
0.016030743718147278,
-0.021006518974900246,
-0.023171840235590935,
0.0540316179394722,
-0.03825819864869118,
-0.043315909802913666,
-0.017187559977173805,
-0.01544245332479477,
-0.021430766209959984,
-0.01162488479167223,
-0.018044741824269295,
-0.02057693339884281,
-0.07808547466993332,
0.06062167137861252,
-0.052640512585639954,
-0.058837492018938065,
-0.03162554278969765,
-0.04215076565742493,
0.0347818024456501,
-0.03209816291928291,
0.020429816097021103,
-0.012904436327517033,
-0.04670469090342522,
0.020199209451675415,
-0.0628397986292839,
-0.022972967475652695,
-0.014231870882213116,
0.02767360396683216,
0.017806401476264,
0.018982278183102608,
0.009445802308619022,
0.026166802272200584,
0.03959250822663307,
0.00251102726906538,
-0.050985973328351974,
0.06392208486795425,
-0.02572697214782238,
-0.027827586978673935,
0.0001811673864722252,
0.029822325333952904,
-0.027486257255077362,
-0.03510287404060364,
-0.0911514163017273,
-0.06454411149024963,
-0.0062156179919838905,
-0.04994626343250275,
-0.04003685712814331,
0.0501285195350647,
0.021641308441758156,
-0.012078003957867622,
-0.002539408393204212,
0.03295161575078964,
-0.015501860529184341,
0.0008752611465752125,
0.010822650045156479,
0.019151993095874786,
-0.011643022298812866,
-0.018776725977659225,
-0.011526628397405148,
0.00664481520652771,
-0.007719692308455706,
0.09101428091526031,
0.012051522731781006,
0.05517369508743286,
0.1420309692621231,
-0.046177759766578674,
0.019174035638570786,
-0.006447787396609783,
-0.0004393806157168001,
-0.02157612144947052,
-0.007729464676231146,
-0.034514959901571274,
0.013819755055010319,
0.0011102231219410896,
-0.03500744327902794,
0.06415731459856033,
0.012797483243048191,
-0.036353949457407,
-0.02893533743917942,
-0.0001148115043179132,
-0.030534015968441963,
-0.01904030703008175,
-0.009547560475766659,
-0.024519486352801323,
0.05986139178276062,
-0.0057520316913723946,
-0.061348751187324524,
0.0075060357339680195,
0.07144293934106827,
-0.0015656292671337724,
-0.02760905958712101,
0.010191642679274082,
0.017229773104190826,
0.016498493030667305,
0.008713475428521633,
-0.053165990859270096,
-0.010626427829265594,
-0.020249100401997566,
0.04417834058403969,
-0.021861115470528603,
0.0031641514506191015,
-0.0003433374222368002,
0.008681447245180607,
0.019493024796247482,
0.0014525864971801639,
-0.01354911271482706,
0.00415230356156826,
-0.04900774359703064,
0.028697047382593155,
0.07501380890607834,
0.1070559173822403,
-0.0023953174240887165,
0.04977519065141678,
-0.04048670828342438,
-0.0434863306581974,
0.07334662228822708,
0.006158621050417423,
-0.07122882455587387,
0.00950031541287899,
0.02037353441119194,
-0.023417562246322632,
0.004073944874107838,
0.0026970424223691225,
0.0018171747215092182,
-0.014628126285970211,
-0.030743233859539032,
-0.05296361818909645,
0.0038917800411581993,
0.00783280935138464,
-0.03400597721338272,
-0.05413104221224785,
-0.036541104316711426,
-0.046797942370176315,
-0.029058439657092094,
-0.007713810075074434,
0.006117342505604029,
0.028067830950021744,
-0.0021466498728841543,
-0.01563875749707222,
-0.031747616827487946,
0.034356918185949326,
-0.022989410907030106,
-0.0048770303837955,
-0.009311226196587086,
-0.011565177701413631,
0.03018319047987461,
-0.015906475484371185,
-0.031771451234817505,
-0.04125683754682541,
0.05605121701955795,
-0.03668562322854996,
0.014502378180623055,
-0.08056755363941193,
0.00995086133480072,
-0.0011145113967359066,
-0.06559677422046661,
0.007616471033543348,
0.016237137839198112,
0.0794517919421196,
0.020478086546063423,
0.020617276430130005,
-0.03794173523783684,
0.00233151251450181,
0.02136107347905636,
-0.06712806969881058,
0.013108938001096249,
0.030233819037675858,
-0.01645628735423088,
0.008487455546855927,
-0.03846665099263191,
-0.00988107081502676,
0.031084304675459862,
0.005177960265427828,
0.034299008548259735,
-0.01678524725139141,
-0.041877176612615585,
0.0021311710588634014,
-0.020264212042093277,
-0.0636783167719841,
0.038851842284202576,
-0.028778666630387306,
-0.06322135776281357,
0.06198121979832649,
-0.01762750931084156,
-0.023307910189032555,
-0.014562161639332771,
-0.018567759543657303,
0.04287823662161827,
-0.02412540279328823,
0.012426373548805714,
-0.033115413039922714,
-0.07105069607496262,
0.047386284917593,
-0.02638816088438034,
0.039801113307476044,
-0.025329813361167908,
-0.036232635378837585,
0.0027641011402010918,
-0.00799550674855709,
0.03129193186759949,
-0.02064804919064045,
0.007938615046441555,
-0.013666107319295406,
-0.005244252737611532,
-0.08890550583600998,
-0.035212304443120956,
0.01893521472811699,
0.0032599500846117735,
0.006407309323549271,
0.0019356469856575131,
0.026079174131155014,
-0.005721591413021088,
0.020218871533870697,
0.017846936360001564,
0.03937416896224022,
-0.013926231302320957,
0.03753511980175972,
0.08073998987674713,
0.02371188811957836,
0.0020114125218242407,
0.034460291266441345,
0.0623505525290966,
0.007973822765052319,
-0.01620953157544136,
-0.013004614971578121,
-0.04912376031279564,
0.006417630240321159
] |
[
2.5405611991882324,
0.44799262285232544
] |
Mathematical Physics
|
General Physics
|
math-ph
|
math-OA
|
na
|
2007-04-01T18:27:26
|
Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA
method in which the spreading (signature) matrix contains only a relatively
small number of non-zero elements, is presented and analysed using methods of
statistical physics. The analysis provides results on the performance of
maximum likelihood decoding for sparse spreading codes in the large system
limit. We present results for both cases of regular and irregular spreading
matrices for the binary additive white Gaussian noise channel (BIAWGN) with a
comparison to the canonical (dense) random spreading code.
|
Sparsely-spread CDMA - a statistical mechanics based analysis
|
cs.IT math.IT
|
0704.0098
| 2,007
|
[
-0.01792026311159134,
0.019738387316465378,
-0.0005792831070721149,
-0.05214263126254082,
0.010518423281610012,
-0.013151342049241066,
0.03895752504467964,
0.015426108613610268,
-0.0216338150203228,
-0.012695610523223877,
-0.04112669453024864,
0.04998033493757248,
0.03320758789777756,
-0.0045775799080729485,
-0.024155965074896812,
-0.03550765663385391,
0.01010103989392519,
0.024797877296805382,
-0.008971339091658592,
0.021040940657258034,
-0.005532382521778345,
-0.014094514772295952,
0.015553493984043598,
-0.04045181721448898,
0.08781977742910385,
-0.01984412409365177,
0.0021009778138250113,
0.02324906550347805,
-0.05825163051486015,
0.009864119812846184,
0.019000576809048653,
-0.06027299910783768,
0.015563643537461758,
-0.048469122499227524,
-0.05717363581061363,
-0.02233651839196682,
0.017323600128293037,
-0.04834950342774391,
0.005804885178804398,
0.09118235856294632,
0.01854410581290722,
-0.07235943526029587,
0.03207670524716377,
-0.03647974133491516,
0.03649237006902695,
0.01212745625525713,
-0.025712190195918083,
0.0033919354900717735,
0.021752571687102318,
-0.003908810671418905,
-0.045109011232852936,
0.0040682596154510975,
0.038446057587862015,
-0.00014531679335050285,
0.0049460590817034245,
0.02012648805975914,
0.003728272160515189,
0.019230889156460762,
0.029387328773736954,
-0.01374999713152647,
0.045359496027231216,
0.04366341233253479,
-0.06906643509864807,
0.007110847160220146,
-0.00003550706969690509,
-0.056913379579782486,
-0.016488809138536453,
-0.021870383992791176,
0.023997541517019272,
-0.04167044907808304,
0.05837716534733772,
-0.014981502667069435,
-0.020745839923620224,
-0.042542703449726105,
-0.0006145918159745634,
-0.014915762469172478,
0.015203638933598995,
-0.04906625300645828,
-0.011769499629735947,
0.00985285360366106,
-0.045910440385341644,
-0.05414298549294472,
0.017201410606503487,
0.019705550745129585,
0.1016818955540657,
0.03505558893084526,
-0.014001685194671154,
0.04070953652262688,
-0.0264737568795681,
0.016505809500813484,
0.009204564616084099,
-0.01432331558316946,
0.05505712702870369,
0.039974916726350784,
-0.036724597215652466,
0.022177113220095634,
-0.030706016346812248,
0.006382976658642292,
-0.01605355739593506,
-0.04332559183239937,
-0.010609914548695087,
0.07205582410097122,
0.029594028368592262,
0.016587499529123306,
0.047228988260030746,
0.0309118814766407,
-0.023078808560967445,
0.01561818178743124,
-0.0036659573670476675,
0.023839512839913368,
-0.03866235166788101,
-0.029657816514372826,
0.0246625654399395,
-0.027698665857315063,
-0.01985575631260872,
-0.06577415764331818,
0.08172915875911713,
-0.056119270622730255,
-0.00878250040113926,
0.03146804869174957,
0.007065653335303068,
-0.015618142671883106,
0.004902612417936325,
0.028857974335551262,
-0.007372412830591202,
0.03281593695282936,
-0.025721557438373566,
0.015186534263193607,
-0.015905046835541725,
-0.04023444652557373,
-0.005307319574058056,
0.0099319564178586,
-0.040994949638843536,
0.015839794650673866,
0.051579754799604416,
-0.002986122854053974,
-0.07370709627866745,
-0.043821290135383606,
0.04796004667878151,
0.01492148358374834,
0.0021548348013311625,
-0.008517253212630749,
0.03574218228459358,
-0.01965787075459957,
0.0554441474378109,
-0.025237267836928368,
-0.02259439416229725,
-0.034431781619787216,
-0.008426972664892673,
-0.004825877957046032,
0.010926316492259502,
0.04358939826488495,
0.020625337958335876,
-0.00023153217625804245,
-0.06739768385887146,
-0.014255490154027939,
-0.015581670217216015,
-0.03281516954302788,
0.0010668725008144975,
0.02264554053544998,
-0.000974839145783335,
0.011029351502656937,
-0.006749452091753483,
0.0437149852514267,
-0.03854873403906822,
0.020144401118159294,
0.010142250917851925,
0.05257183313369751,
0.025258947163820267,
0.03055865317583084,
-0.014460587874054909,
-0.03180322423577309,
-0.02325938083231449,
0.0037497244775295258,
-0.016548514366149902,
0.016017666086554527,
-0.014110524207353592,
-0.07330392301082611,
0.03117362968623638,
0.002430256921797991,
-0.01293851062655449,
-0.013462324626743793,
0.02972191572189331,
0.012421696446835995,
-0.007824481464922428,
-0.03170894458889961,
0.03798714280128479,
-0.04684139043092728,
-0.020861608907580376,
-0.030926939100027084,
0.0183885358273983,
-0.023063790053129196,
-0.03401067107915878,
-0.06272178143262863,
0.010080375708639622,
-0.039661213755607605,
0.09703575074672699,
0.0026546649169176817,
0.04168742150068283,
-0.08561108261346817,
-0.018786780536174774,
-0.008986315689980984,
-0.052192479372024536,
0.008406810462474823,
0.000773490930441767,
0.03744855150580406,
0.021216869354248047,
-0.0011229361407458782,
0.021912481635808945,
0.008600584231317043,
0.05542518198490143,
-0.0075975023210048676,
-0.011032347567379475,
-0.01681171916425228,
0.027039308100938797,
-0.00022519560297951102,
-0.016434481367468834,
-0.07788441330194473,
-0.04638740047812462,
0.06144881993532181,
0.060856178402900696,
-0.017801273614168167,
-0.008431165479123592,
-0.004999776370823383,
0.011727317236363888,
0.040371477603912354,
-0.037285804748535156,
0.04404804855585098,
-0.05759246274828911,
0.017677858471870422,
-0.04891546815633774,
-0.02355196140706539,
0.019074097275733948,
-0.01936107501387596,
-0.024576861411333084,
0.027077600359916687,
-0.014132865704596043,
0.02554730698466301,
0.012948772870004177,
0.0805455669760704,
-0.006093425210565329,
0.00847785547375679,
0.028472086414694786,
-0.026413191109895706,
-0.045526739209890366,
-0.028105879202485085,
-0.025696616619825363,
-0.029150722548365593,
-0.04512394592165947,
0.011886510998010635,
0.028678396716713905,
-0.01865215227007866,
0.012985248118638992,
-0.013134499080479145,
0.04832039028406143,
-0.026557428762316704,
-0.008470678701996803,
0.02446545660495758,
0.009651031345129013,
-0.029344648122787476,
0.06295076012611389,
-0.02593771368265152,
-0.01132374256849289,
-0.024263398721814156,
0.01166125014424324,
0.04439818859100342,
0.01751525141298771,
-0.002772255102172494,
-0.02116716094315052,
0.027544358745217323,
0.028478657826781273,
0.018990173935890198,
0.07566225528717041,
0.026710284873843193,
0.020715883001685143,
0.010459893383085728,
0.047871313989162445,
-0.04539274424314499,
-0.003912179730832577,
-0.006997537799179554,
-0.10281728208065033,
-0.0002849902375601232,
0.014506947249174118,
-0.05222189798951149,
-0.013413107953965664,
0.014050011523067951,
0.042389165610075,
-0.032051488757133484,
0.050122831016778946,
0.05880087986588478,
0.00840962864458561,
-0.010865806601941586,
0.039024122059345245,
0.05003349483013153,
-0.0033687385730445385,
0.07145661860704422,
0.04987722262740135,
-0.03081466071307659,
0.02183743380010128,
0.01285362895578146,
-0.05263848230242729,
0.046140749007463455,
0.006918658036738634,
-0.01616702787578106,
0.0048591867089271545,
0.04150109365582466,
0.016019325703382492,
0.028846807777881622,
0.038135211914777756,
0.01781071163713932,
0.005311248824000359,
0.041445087641477585,
-0.007364441175013781,
0.005441457033157349,
-0.030049869790673256,
0.0173060093075037,
0.02882348746061325,
-0.020109647884964943,
0.06286711990833282,
-0.012450605630874634,
0.023722419515252113,
-0.07579553872346878,
0.015371968038380146,
-0.09358620643615723,
0.018953751772642136,
0.03478073701262474,
0.023073868826031685,
0.030532820150256157,
-0.012563087977468967,
-0.013507857918739319,
-0.0038380352780222893,
0.0390334352850914,
-0.024250347167253494,
-0.010634548962116241,
-0.07059327512979507,
-0.043430425226688385,
-0.028100304305553436,
0.012298284098505974,
0.012801455333828926,
-0.024630369618535042,
0.013863468542695045,
-0.046476613730192184,
-0.040531810373067856,
-0.04505953937768936,
-0.02370111644268036,
-0.00574721023440361,
0.009241742081940174,
-0.015225657261908054,
0.05781988799571991,
-0.01818508468568325,
-0.08353947103023529,
-0.06069573387503624,
0.020037872716784477,
0.009084121324121952,
-0.021627631038427353,
0.005860650446265936,
0.027775609865784645,
-0.061649519950151443,
0.04049237072467804,
0.030575817450881004,
0.03388042002916336,
-0.047926098108291626,
0.03496067598462105,
0.02623392827808857,
-0.006900676526129246,
0.03747893497347832,
0.05697759613394737,
0.02679610066115856,
0.003402670379728079,
-0.03180670738220215,
-0.018713144585490227,
-0.029679516330361366,
0.03728664666414261,
0.013649329543113708,
0.020968565717339516,
0.04214025288820267,
-0.06944406032562256,
0.003613086650148034,
-0.015379910357296467,
0.03240351006388664,
0.04997824877500534,
-0.00865915697067976,
0.03962668403983116,
0.005702931433916092,
0.01738591678440571,
-0.04736676812171936,
-0.06120064854621887,
-0.00016884543583728373,
-0.019517743960022926,
-0.045419249683618546,
-0.011877880431711674,
-0.08446104824542999,
-0.03422516584396362,
0.05057689547538757,
0.02439318783581257,
-0.04331088811159134,
0.027875127270817757,
0.03260410949587822,
0.042062509804964066,
0.010550610721111298,
-0.030146373435854912,
-0.03474809601902962,
0.01834394596517086,
0.012682817876338959,
0.003098459681496024,
0.02889420837163925,
-0.058695968240499496,
-0.003203995991498232,
0.023624856024980545,
0.004698662552982569,
-0.011072932742536068,
-0.008799140341579914,
-0.04550585895776749,
-0.07340855151414871,
0.0350351519882679,
0.012524318881332874,
0.032046474516391754,
0.006887422408908606,
-0.016030335798859596,
0.003992598969489336,
-0.03305995836853981,
0.03490132465958595,
-0.04867924749851227,
0.015448707155883312,
-0.03482292219996452,
-0.0003737988299690187,
0.07162052392959595,
0.03550420701503754,
0.02384614199399948,
-0.03400378301739693,
-0.007821554318070412,
0.004155760630965233,
-0.03308308869600296,
0.08498115837574005,
-0.05582623556256294,
0.007570581045001745,
0.04136526584625244,
0.01933143474161625,
0.01780221052467823,
0.029214322566986084,
0.037325307726860046,
-0.0759885236620903,
0.04621846601366997,
0.01635081321001053,
0.02437693066895008,
0.10598106682300568,
0.06840042769908905,
-0.01428295485675335,
-0.013209529221057892,
0.05736479535698891,
0.01553006749600172,
-0.012347156181931496,
0.025100672617554665,
-0.007545855827629566,
0.0798698142170906,
-0.009417188353836536,
-0.01909206062555313,
0.027158396318554878,
0.09951531141996384,
0.06302858889102936,
0.003394607687368989,
0.010297305881977081,
-0.06591382622718811,
0.013916372321546078,
-0.025671226903796196,
0.03462822735309601,
0.023091671988368034,
-0.021019471809267998,
0.0014731856063008308,
0.06209650635719299,
-0.019049981608986855,
0.040368158370256424,
0.03777154162526131,
0.02307550422847271,
-0.007348621264100075,
0.008602643385529518,
0.00969888549298048,
-0.023003393784165382,
0.008473454043269157,
0.05368933081626892,
0.05123300850391388,
-0.014369373209774494,
-0.06189059093594551,
-0.05166265368461609,
0.009465401992201805,
0.06438901275396347,
0.00017133755318354815,
0.012907328084111214,
0.009109660983085632,
-0.02813335694372654,
0.051532402634620667,
0.05852751061320305,
0.007033803034573793,
0.03856575861573219,
-0.050925131887197495,
-0.06863725185394287,
0.03220955654978752,
0.011973165906965733,
-0.06875461339950562,
-0.013770373538136482,
-0.008118907921016216,
0.033107221126556396,
-0.02178232930600643,
0.009851587004959583,
0.04365963861346245,
-0.007938516326248646,
-0.016946207731962204,
-0.05591360107064247,
-0.016110040247440338,
0.00034852209500968456,
-0.05258036404848099,
0.06747227162122726,
0.05490214005112648,
0.030964195728302002,
-0.0006906375056132674,
-0.035045843571424484,
0.007943155243992805,
-0.003049828577786684,
-0.060161083936691284,
0.020316826179623604,
-0.03194502368569374,
-0.025594186037778854,
0.008551552891731262,
0.013547636568546295,
-0.04935995861887932,
-0.042746078222990036,
-0.04981604218482971,
-0.07899455726146698,
-0.0006732125766575336,
-0.02479216270148754,
-0.008276747539639473,
0.02712845616042614,
-0.020847510546445847,
-0.05811861902475357,
-0.017660364508628845,
-0.07295085489749908,
-0.022629592567682266,
-0.0062341708689928055,
-0.0052233231253921986,
0.027252038940787315,
0.02411440946161747,
-0.00842126365751028,
0.03865071013569832,
0.027371345087885857,
-0.006694179028272629,
-0.06469893455505371,
-0.05240807309746742,
-0.0002810151781886816,
-0.015138133428990841,
-0.08802463114261627,
0.014277023263275623,
-0.0072688874788582325,
0.024948058649897575,
-0.027489718049764633,
0.0490214079618454,
-0.06903409212827682,
0.010375508107244968,
0.0013969403225928545,
0.03517164662480354,
0.06593427807092667,
-0.03012813627719879,
0.002745506353676319,
0.021492520347237587,
0.013299046084284782,
0.024657199159264565,
-0.10877750813961029,
-0.045714136213064194,
-0.01702028512954712,
0.0061249141581356525,
0.044787727296352386,
-0.01585078239440918,
0.014690078794956207,
-0.010969736613333225,
0.04706215858459473,
-0.019021619111299515,
-0.024328621104359627,
0.06823994219303131,
-0.01254158653318882,
-0.04519656300544739,
-0.03389037400484085,
-0.03721709921956062,
-0.02098242938518524,
0.04260766878724098,
0.03796887770295143,
0.01570288836956024,
0.007905599661171436,
-0.03712248057126999,
-0.02147345431149006,
0.02873544953763485,
-0.016118036583065987,
0.0039559295400977135,
-0.025661498308181763,
0.012541607953608036,
0.02528100460767746,
-0.06319679319858551,
-0.012988724745810032,
-0.009230359457433224,
0.011261011473834515,
-0.046401649713516235,
-0.028057152405381203,
0.04079778119921684,
0.09207170456647873,
0.016240756958723068,
-0.05318015441298485,
0.04405293986201286,
0.03183384984731674,
0.006427929736673832,
0.008551145903766155,
-0.03204648941755295,
0.01661502942442894,
0.035371486097574234,
-0.0055545540526509285,
-0.012130964547395706,
-0.00907867681235075,
0.010459626093506813,
-0.07764073461294174,
0.02382003329694271,
-0.022483116015791893,
0.029010595753788948,
-0.04319741949439049,
-0.009886189363896847,
-0.03487170860171318,
-0.007442815694957972,
-0.05646389350295067,
-0.049739301204681396,
0.040889814496040344,
0.02484951913356781,
-0.049350954592227936,
0.011668349616229534,
0.03631221503019333,
0.04265323281288147,
0.016135068610310555,
-0.005276857875287533,
-0.029182784259319305,
-0.016766294836997986,
0.02096017450094223,
-0.037835493683815,
0.006690339185297489,
0.01657292991876602,
0.07973834127187729,
0.06727245450019836,
-0.005383369512856007,
-0.021811120212078094,
-0.04047608748078346,
0.03669620305299759,
0.05981004610657692,
-0.014750082977116108,
0.06187325716018677,
0.02639136277139187,
0.027488647028803825,
0.043796978890895844,
0.0734662115573883,
-0.023992737755179405,
0.010728835128247738,
-0.01657220721244812,
0.05178189277648926,
0.0660407692193985,
0.023746807128190994,
0.00017195763939525932,
-0.034175723791122437,
-0.004593063145875931,
0.000885896326508373,
0.00172141520306468,
0.008693506009876728,
0.06414781510829926,
0.0063567678444087505,
0.016106614843010902,
-0.08659207820892334,
-0.031757913529872894,
0.012268408201634884,
-0.02767213247716427,
-0.0053947619162499905,
0.0008290088153444231,
-0.01744476705789566,
0.028999237343668938,
-0.008608384057879448,
-0.037039753049612045,
-0.06480187922716141,
-0.02180165983736515,
0.004414172377437353,
0.025101127102971077,
-0.012062226422131062,
-0.019125482067465782,
0.04576960951089859,
0.02556842565536499,
0.04284783825278282,
-0.0023729049134999514,
-0.01877727545797825,
-0.0739067867398262,
-0.039371974766254425,
0.03449643403291702,
-0.02445841394364834,
0.00563928484916687,
-0.017741147428750992,
-0.0023142939899116755,
0.03235294297337532,
-0.08590580523014069,
-0.005400299560278654,
0.02725799009203911,
0.07119593769311905,
-0.012564093805849552,
0.03275622799992561,
-0.01498688105493784,
0.04140232875943184,
0.026074765250086784,
-0.04498808830976486,
0.013648820109665394,
0.039819009602069855,
-0.008070272393524647,
-0.06325051933526993,
0.0009904054459184408,
-0.030072711408138275,
0.028259357437491417,
0.010376699268817902,
-0.012083744630217552,
0.002804698422551155,
-0.021360373124480247,
-0.051576778292655945,
-0.02000153809785843,
-0.03760022670030594,
0.039748094975948334,
0.004164803773164749,
-0.04382772371172905,
0.01652764156460762,
0.005614791065454483,
-0.04644954577088356,
-0.0031693698838353157,
0.024489175528287888,
0.10062578320503235,
0.003876365954056382,
-0.029135722666978836,
-0.032133158296346664,
-0.03981531411409378,
-0.006069459952414036,
-0.054550327360630035,
-0.005830689799040556,
-0.0002917684323620051,
0.01933307945728302,
-0.08572987467050552,
0.016186373308300972,
-0.03842063993215561,
0.01770024374127388,
0.014408418908715248,
-0.01677272468805313,
0.021294815465807915,
-0.024636905640363693,
-0.0794069841504097,
0.007512248121201992,
0.0205607321113348,
0.008876929990947247,
-0.05355162173509598,
-0.014867548830807209,
-0.025379817932844162,
0.02783586084842682,
-0.030281128361821175,
0.07373284548521042,
0.016226768493652344,
0.06671594828367233,
0.07683402299880981,
-0.059356190264225006,
0.01560754980891943,
-0.05446527525782585,
0.012660270556807518,
0.0005355283501558006,
-0.015958687290549278,
0.027552999556064606,
-0.004185247700661421,
-0.009926353581249714
] |
[
-1.5836248397827148,
8.341211318969727
] |
Information Theory
|
Mathematics
|
math-IT
|
na
|
na
|
2007-04-01T18:14:32
|
For positive semidefinite matrices $A$ and $B$, Ando and Zhan proved the
inequalities $||| f(A)+f(B) ||| \ge ||| f(A+B) |||$ and $||| g(A)+g(B) ||| \le
||| g(A+B) |||$, for any unitarily invariant norm, and for any non-negative
operator monotone $f$ on $[0,\infty)$ with inverse function $g$. These
inequalities have very recently been generalised to non-negative concave
functions $f$ and non-negative convex functions $g$, by Bourin and Uchiyama,
and Kosem, respectively.
In this paper we consider the related question whether the inequalities $|||
f(A)-f(B) ||| \le ||| f(|A-B|) |||$, and $||| g(A)-g(B) ||| \ge ||| g(|A-B|)
|||$, obtained by Ando, for operator monotone $f$ with inverse $g$, also have a
similar generalisation to non-negative concave $f$ and convex $g$. We answer
exactly this question, in the negative for general matrices, and affirmatively
in the special case when $A\ge ||B||$.
In the course of this work, we introduce the novel notion of $Y$-dominated
majorisation between the spectra of two Hermitian matrices, where $Y$ is itself
a Hermitian matrix, and prove a certain property of this relation that allows
to strengthen the results of Bourin-Uchiyama and Kosem, mentioned above.
|
On Ando's inequalities for convex and concave functions
|
math.FA
|
0704.0099
| 2,007
|
[
-0.022629674524068832,
-0.00803929753601551,
-0.0011941742850467563,
0.03377443179488182,
0.014448911882936954,
-0.032977912575006485,
0.05782641842961311,
0.02336559258401394,
-0.02513442002236843,
-0.0025083329528570175,
-0.0993650034070015,
0.02940450981259346,
0.005652803461998701,
-0.001023542950861156,
0.04877753555774689,
-0.019085749983787537,
-0.01215885579586029,
0.03756502643227577,
-0.043535083532333374,
0.023493144661188126,
-0.0700736790895462,
0.02595728076994419,
-0.01992643252015114,
-0.04303106293082237,
0.09580036997795105,
0.04062502831220627,
0.01472039707005024,
0.0108338026329875,
-0.013322662562131882,
0.02039901725947857,
0.05125484615564346,
-0.02311074361205101,
-0.0040322840213775635,
-0.06964945048093796,
-0.042995985597372055,
0.02802269719541073,
0.0936506912112236,
-0.011058308184146881,
0.04084708169102669,
0.03358548879623413,
0.09026363492012024,
-0.006310665979981422,
0.022212395444512367,
-0.015475956723093987,
-0.0019855941645801067,
-0.02230481058359146,
0.012194378301501274,
-0.004779940936714411,
0.026264235377311707,
-0.028745563700795174,
-0.020594434812664986,
0.010107516311109066,
0.03227240592241287,
-0.06109049171209335,
-0.05372089892625809,
0.055762164294719696,
0.030665375292301178,
-0.07078109681606293,
-0.008138610050082207,
-0.014742211438715458,
-0.009823971427977085,
0.00007039247429929674,
-0.008768355473876,
0.021379495039582253,
0.05065399780869484,
-0.07917170226573944,
0.012146693654358387,
0.05140442028641701,
-0.019641300663352013,
-0.009780855849385262,
0.012563878670334816,
0.0032189188059419394,
0.07260214537382126,
0.007113427389413118,
-0.03622669726610184,
-0.016451509669423103,
0.032982148230075836,
-0.0033502476289868355,
-0.006077819038182497,
0.016946997493505478,
0.0240342877805233,
-0.03747449815273285,
0.0497647225856781,
0.03276798874139786,
0.02561916410923004,
0.007911840453743935,
0.0832144245505333,
-0.015802012756466866,
-0.028693078085780144,
0.062317345291376114,
0.03599187731742859,
-0.03445303812623024,
0.019498828798532486,
0.09659116715192795,
-0.019202230498194695,
0.051502227783203125,
0.0017404119716957211,
0.004481468349695206,
-0.009212376549839973,
-0.014037437736988068,
0.020668983459472656,
0.01841653883457184,
0.033391136676073074,
0.03969782963395119,
0.08892536908388138,
0.06874693930149078,
0.05879008024930954,
-0.03571822866797447,
-0.001106671174056828,
-0.018049344420433044,
-0.09579121321439743,
0.026345139369368553,
-0.024683503434062004,
-0.05192269757390022,
-0.00785497110337019,
-0.025783127173781395,
0.03269920498132706,
-0.0649745762348175,
-0.051980819553136826,
0.0683736801147461,
-0.0245218388736248,
0.029892420396208763,
0.0030947376508265734,
0.02075674571096897,
0.02363726682960987,
0.04913190379738808,
-0.04035969823598862,
0.0228415634483099,
0.04246633127331734,
-0.06097150593996048,
0.025390425696969032,
0.0330786295235157,
-0.05502551794052124,
0.0035931726451963186,
0.025532513856887817,
0.06864838302135468,
-0.03172069042921066,
0.00998955313116312,
-0.00793625507503748,
-0.023212391883134842,
0.010136800818145275,
0.05570271611213684,
-0.00008314934530062601,
-0.01304926723241806,
-0.009510970674455166,
-0.05234033614397049,
0.03168029710650444,
-0.00780786108225584,
-0.024756401777267456,
0.0063554379157722,
0.027955876663327217,
0.03787829354405403,
0.014001521281898022,
0.04189054295420647,
-0.011837472207844257,
-0.0479595921933651,
-0.052922751754522324,
-0.006366528104990721,
-0.011396626941859722,
-0.026869410648941994,
-0.013973802328109741,
0.023899519816040993,
-0.009518683888018131,
0.031739410012960434,
-0.041724592447280884,
-0.04836266115307808,
0.057757895439863205,
0.029307693243026733,
0.0020715631544589996,
0.034548595547676086,
-0.04433495178818703,
0.029689021408557892,
0.04080731421709061,
-0.055208563804626465,
0.046370115131139755,
0.011916608549654484,
-0.03436344489455223,
-0.06238102167844772,
0.03859042748808861,
0.03715677186846733,
0.03837186098098755,
-0.012189379893243313,
-0.0016119867796078324,
0.027567187324166298,
0.024361558258533478,
-0.009387749247252941,
-0.0019150205189362168,
-0.03851573169231415,
-0.10935933887958527,
-0.010127333924174309,
0.014550251886248589,
0.008677113801240921,
-0.0017160665011033416,
-0.039159514009952545,
9.732963235364878e-7,
-0.042257800698280334,
0.08055576682090759,
0.008597577922046185,
0.013269780203700066,
-0.03473227471113205,
-0.027657421305775642,
-0.011924638412892818,
-0.0008074069046415389,
0.008807767182588577,
-0.0298925694078207,
0.060089413076639175,
-0.027861474081873894,
-0.00510768499225378,
0.022802377119660378,
-0.041642721742391586,
-0.02936599962413311,
0.004812692292034626,
0.003995147999376059,
0.03185759484767914,
-0.0317002534866333,
0.0060655707493424416,
0.019178956747055054,
-0.03672744333744049,
-0.02125481516122818,
-0.0013024479849264026,
0.01745428703725338,
-0.00014799436030443758,
-0.0485428087413311,
0.014857200905680656,
0.012908835895359516,
0.015339710749685764,
-0.013023264706134796,
-0.016622545197606087,
-0.06745988130569458,
0.002651185030117631,
-0.04636790603399277,
-0.09792536497116089,
0.05546832084655762,
-0.027196872979402542,
-0.0018916887929663062,
0.02799365110695362,
0.027602195739746094,
0.08591484278440475,
0.07128702104091644,
0.07621794939041138,
0.03384996950626373,
-0.004552340134978294,
-0.01401542779058218,
0.02465052343904972,
-0.07267742604017258,
-0.025644322857260704,
-0.05458207055926323,
-0.0324590690433979,
0.018121387809515,
0.04410632699728012,
-0.053316738456487656,
-0.03520429879426956,
0.008314301259815693,
0.06801873445510864,
0.007730708923190832,
-0.016542544588446617,
-0.04768814146518707,
-0.014752236194908619,
-0.04524752497673035,
-0.0239701047539711,
0.04749259725213051,
-0.016319457441568375,
-0.025829993188381195,
-0.029054032638669014,
-0.04032181575894356,
-0.0019408662337809801,
-0.04476872459053993,
-0.014452677220106125,
0.010755732655525208,
0.017377324402332306,
0.049657855182886124,
0.05886625871062279,
0.024584462866187096,
0.027838315814733505,
-0.040378980338573456,
0.008093513548374176,
0.007804540917277336,
-0.11016328632831573,
-0.05112101510167122,
-0.022031404078006744,
-0.055836692452430725,
-0.020556839182972908,
-0.05016987770795822,
-0.008921901695430279,
-0.002222619252279401,
0.057822391390800476,
0.03928152471780777,
-0.04753099009394646,
-0.02333163097500801,
0.03778936341404915,
-0.012829680927097797,
0.021112624555826187,
0.0511191189289093,
0.060690898448228836,
0.004241154529154301,
0.06757642328739166,
0.09427058696746826,
-0.029696691781282425,
-0.020786572247743607,
-0.0020808943081647158,
-0.01171940565109253,
-0.016945086419582367,
0.016425512731075287,
0.0043379939161241055,
0.05436740070581436,
-0.02048150822520256,
0.0011764959199354053,
0.009972645901143551,
0.02017882466316223,
0.048543330281972885,
-0.04359104111790657,
-0.0030378103256225586,
-0.027973713353276253,
0.005165026057511568,
-0.02095673605799675,
0.04490114375948906,
-0.014741066843271255,
0.0172109454870224,
0.03609022498130798,
0.0024411489721387625,
0.026163462549448013,
-0.037607915699481964,
0.018519533798098564,
-0.0349145382642746,
-0.0027373828925192356,
-0.004597619641572237,
-0.04547338932752609,
0.05928774178028107,
0.01781895011663437,
-0.043361932039260864,
0.005419404711574316,
0.06427443027496338,
0.03698117285966873,
0.014077728614211082,
-0.006911978591233492,
0.0016011919360607862,
-0.0016081364592537284,
-0.004327230621129274,
-0.0037110340781509876,
0.02004411816596985,
0.0030292957089841366,
-0.025596899911761284,
-0.038611192256212234,
-0.06424902379512787,
-0.024416359141469002,
-0.019345490261912346,
0.0047553605400025845,
0.03447935730218887,
0.04764936491847038,
0.0371081568300724,
-0.04398820176720619,
0.00723487650975585,
0.04368440806865692,
-0.01933472789824009,
-0.008800744079053402,
0.05762917920947075,
0.07990553975105286,
0.002596537582576275,
-0.0037516322918236256,
-0.01937275379896164,
0.020760394632816315,
-0.017793960869312286,
0.0328088253736496,
-0.02268294245004654,
0.03624992072582245,
0.023117711767554283,
0.0227053165435791,
0.025706589221954346,
-0.03297847509384155,
-0.004793996922671795,
0.01340730395168066,
-0.04422792047262192,
0.056820739060640335,
0.007805658970028162,
0.009639254771173,
-0.031187953427433968,
-0.04562045633792877,
-0.03136899694800377,
0.01765846088528633,
0.009523444809019566,
0.09789660573005676,
-0.01407182402908802,
0.05842418223619461,
0.0067837596870958805,
-0.0053266491740942,
-0.019131898880004883,
-0.031880591064691544,
0.009792388416826725,
0.07553113251924515,
-0.0004959973739460111,
-0.023919004946947098,
-0.046988990157842636,
-0.0017635779222473502,
0.035772159695625305,
0.05292971432209015,
-0.01494556199759245,
0.04258527234196663,
-0.00275729619897902,
-0.016433928161859512,
0.03458140790462494,
-0.04031079262495041,
-0.04694873094558716,
0.03519757464528084,
-0.025761067867279053,
-0.0194588340818882,
-0.006098813842982054,
-0.007504905574023724,
-0.03228982165455818,
0.00562291918322444,
-0.015531955286860466,
-0.018515722826123238,
-0.0058272541500627995,
-0.05487343296408653,
-0.00940799806267023,
0.03052152693271637,
0.020836012437939644,
0.043998852372169495,
-0.03518981114029884,
0.027587106451392174,
-0.06602802872657776,
-0.012371506541967392,
0.039412908256053925,
-0.025463800877332687,
-0.006726280320435762,
0.014591137878596783,
-0.007677177432924509,
-0.019980354234576225,
-0.017642322927713394,
0.039651818573474884,
-0.025847841054201126,
0.021455727517604828,
0.03453657776117325,
0.02743629179894924,
0.0466567687690258,
-0.05491925776004791,
-0.0003851639339700341,
0.03268406540155411,
-0.023266850039362907,
-0.020601682364940643,
0.009375641122460365,
0.0032520368695259094,
-0.04422876983880997,
-0.015103495679795742,
-0.02381855994462967,
0.056048013269901276,
0.026752745732665062,
0.033730752766132355,
-0.014069895260035992,
-0.044772353023290634,
-0.0055579859763383865,
0.04474256560206413,
0.040726639330387115,
0.03172381967306137,
-0.03569288179278374,
0.014969957992434502,
-0.05806224048137665,
-0.014794345013797283,
-0.008907346986234188,
0.045454178005456924,
0.018223604187369347,
0.047632135450839996,
-0.010545206256210804,
-0.006544597912579775,
0.011724361218512058,
-0.014942974783480167,
0.005847470834851265,
-0.024068428203463554,
0.07418640702962875,
-0.056175511330366135,
0.054111845791339874,
0.004428514279425144,
0.014054298400878906,
0.0791999101638794,
0.04152568802237511,
-0.049778733402490616,
-0.0053295474499464035,
0.021707361564040184,
0.03462198004126549,
0.006467895582318306,
0.05866377055644989,
0.003467090893536806,
-0.0006488701328635216,
-0.004392560571432114,
-0.019533060491085052,
-0.011736172251403332,
0.038460541516542435,
0.02966449037194252,
-0.013829494826495647,
0.009430373087525368,
-0.05598212406039238,
-0.014953183941543102,
0.008889018557965755,
0.0032881007064133883,
0.007111427374184132,
-0.062166254967451096,
-0.04536277428269386,
-0.015183542855083942,
-0.0134813217446208,
-0.025245340541005135,
0.014369692653417587,
-0.01826423592865467,
-0.01754513941705227,
0.023943280801177025,
0.0034512653946876526,
0.010153434239327908,
0.004607068374752998,
0.004338621161878109,
-0.06415111571550369,
-0.010182985104620457,
0.02053152769804001,
0.042855117470026016,
0.027093948796391487,
0.0528501532971859,
0.03819243982434273,
-0.012846422381699085,
-0.042913567274808884,
0.03792635723948479,
-0.03506970405578613,
-0.0790274515748024,
0.005855846684426069,
0.03327430039644241,
-0.03781426325440407,
0.007856505922973156,
-0.0020095068030059338,
-0.032669663429260254,
0.0014505170984193683,
-0.019082382321357727,
-0.03517553582787514,
0.04612012207508087,
0.05701342225074768,
0.026577595621347427,
0.047770850360393524,
-0.03487325459718704,
-0.028696853667497635,
0.0032360577024519444,
-0.010453568771481514,
-0.04359201714396477,
0.03146926313638687,
0.006662852130830288,
0.03881775587797165,
0.04641266167163849,
-0.011930076405405998,
0.02393542043864727,
0.047017902135849,
-0.028236297890543938,
-0.03679380193352699,
-0.08920241892337799,
-0.041835956275463104,
-0.06428369134664536,
0.0021555763669312,
0.025758542120456696,
-0.017055874690413475,
-0.020164359360933304,
-0.07411646097898483,
0.04829716682434082,
-0.00967094860970974,
0.0011955663794651628,
-0.014683627523481846,
0.028794245794415474,
0.016954172402620316,
0.06443807482719421,
0.0010799616575241089,
-0.022190749645233154,
-0.019815878942608833,
0.017801601439714432,
-0.05739956349134445,
0.006549956277012825,
0.06255079060792923,
0.005515864118933678,
0.02377515286207199,
0.016479799523949623,
-0.04822495952248573,
-0.002607353962957859,
0.022611765190958977,
-0.0177609845995903,
-0.03866804391145706,
-0.030781792476773262,
-0.05774172767996788,
-0.02028178982436657,
-0.057690560817718506,
-0.01584893837571144,
-0.07614292204380035,
-0.005769960582256317,
-0.016444463282823563,
-0.054958950728178024,
0.04067418351769447,
-0.02137775346636772,
-0.04105798155069351,
0.06150347739458084,
-0.04442371800541878,
0.021034225821495056,
-0.06587578356266022,
-0.059197135269641876,
-0.019488176330924034,
-0.0029894805047661066,
-0.03200790286064148,
-0.005464250687509775,
-0.011350295506417751,
-0.022557027637958527,
-0.04614236578345299,
-0.016605909913778305,
0.03129078075289726,
0.072636179625988,
-0.0027533129323273897,
0.018635230138897896,
0.02984236553311348,
-0.021065350621938705,
0.05491846054792404,
-0.01316395215690136,
0.006919628940522671,
-0.029166599735617638,
0.008095831610262394,
-0.03632263094186783,
-0.001267950632609427,
0.005714699625968933,
-0.012295331805944443,
0.014718983322381973,
0.01995057985186577,
0.018602008000016212,
-0.0065372297540307045,
0.007303718477487564,
-0.05647742748260498,
-0.009598213247954845,
-0.00882048811763525,
0.04440712928771973,
0.014548002742230892,
-0.020178059116005898,
-0.06346996128559113,
-0.02206350490450859,
0.04264632984995842,
0.03573456406593323,
-0.020652715116739273,
-0.02263275347650051,
-0.04906310513615608,
-0.03375795856118202,
-0.011921609751880169,
-0.08007809519767761,
0.027339071035385132,
0.011736579239368439,
0.01558084785938263,
0.016064463183283806,
-0.020360644906759262,
-0.024412158876657486,
-0.004851560574024916,
0.0397418774664402,
-0.004725356586277485,
-0.020193004980683327,
-0.008074763230979443,
-0.005949561949819326,
0.014360046945512295,
0.08132561296224594,
0.0784066691994667,
-0.013342286460101604,
0.017850538715720177,
-0.045039981603622437,
0.009164001792669296,
0.07682846486568451,
-0.0016937481705099344,
-0.011008762754499912,
0.00028753376682288945,
0.02064189314842224,
-0.006303299684077501,
0.03578871488571167,
0.021995455026626587,
0.0028071338310837746,
-0.019662756472826004,
-0.006090071983635426,
-0.04553723707795143,
-0.07081420719623566,
-0.011931175366044044,
-0.0024217066820710897,
-0.029126575216650963,
-0.0024002613499760628,
-0.014560390263795853,
-0.08051740378141403,
0.0015170271508395672,
-0.005831697024405003,
0.03295798599720001,
-0.07128021866083145,
-0.017551865428686142,
0.02364419400691986,
-0.025356806814670563,
0.02146609127521515,
0.007268317975103855,
-0.0091801593080163,
-0.03214479982852936,
-0.0005590947112068534,
-0.04799012467265129,
-0.007679037284106016,
-0.042068641632795334,
-0.008611364290118217,
-0.010397669859230518,
0.05627862736582756,
-0.04505205899477005,
-0.027181994169950485,
-0.017564093694090843,
-0.043439216911792755,
0.06370055675506592,
0.0022973595187067986,
0.02997514046728611,
-0.035560183227062225,
-0.005126011557877064,
-0.04580872878432274,
-0.006474998779594898,
-0.0008995984098874032,
0.001206466113217175,
0.03401132673025131,
0.017739713191986084,
0.012735520489513874,
-0.0493318997323513,
-0.020059125497937202,
-0.0011838236823678017,
0.014466471038758755,
0.0525357648730278,
0.04964505508542061,
-0.015088662505149841,
-0.04368126019835472,
-0.07855013012886047,
0.0052955010905861855,
-0.01021597534418106,
0.04804621636867523,
-0.03583350032567978,
0.006314252503216267,
-0.055635444819927216,
-0.05859432369470596,
-0.04225866496562958,
-0.02684810385107994,
-0.024812737479805946,
0.05966651812195778,
0.08457263559103012,
-0.019434574991464615,
-0.04167574271559715,
-0.07536166906356812,
0.017661381512880325,
-0.013898715376853943,
0.01295910682529211,
0.009620541706681252,
0.021109888330101967,
-0.021295832470059395,
0.04552663862705231,
0.022607209160923958,
-0.06879492104053497,
-0.003533334704115987,
0.033116068691015244,
-0.0026520355604588985,
0.04395495355129242,
-0.031406719237565994,
0.00597801897674799,
0.006765629164874554,
0.04179123416543007,
-0.05118202790617943,
0.021284006536006927,
-0.031468410044908524,
0.06308089196681976,
0.04269803315401077,
-0.03047575242817402,
0.056187015026807785,
-0.004717700649052858,
0.07715876400470734,
-0.004398329183459282,
0.03870617225766182,
0.01753985695540905,
0.02512815035879612,
0.015902897343039513,
-0.009772006422281265,
0.04018617421388626,
-0.021217212080955505,
-0.041188109666109085
] |
[
2.2457306385040283,
3.9877545833587646
] |
Functional Analysis
|
Mathematics
|
math-FA
|
na
|
na
|
2007-04-02T10:11:53
|
The topological structure of the event horizon has been investigated in terms
of the Morse theory. The elementary process of topological evolution can be
understood as a handle attachment. It has been found that there are certain
constraints on the nature of black hole topological evolution: (i) There are n
kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii)
Handles are further classified as either of black or white type, and only black
handles appear in real black hole space-times. (iii) The spatial section of an
exterior of the black hole region is always connected. As a corollary, it is
shown that the formation of a black hole with an S**(n-2) x S**1 horizon from
that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat
space-times.
|
Topology Change of Black Holes
|
gr-qc
|
0704.0100
| 2,007
|
[
0.00527263293042779,
0.026053177192807198,
-0.011468295007944107,
-0.02267368696630001,
0.024084581062197685,
0.02947605960071087,
0.04350665584206581,
0.0015672427834942937,
-0.012630023062229156,
0.02119891718029976,
-0.04131434112787247,
0.024466175585985184,
0.0781618058681488,
0.03541609272360802,
-0.007632561028003693,
-0.02668154053390026,
-0.05760866776108742,
0.022570980712771416,
-0.03394486755132675,
-0.02867984026670456,
0.007020376622676849,
-0.005743155721575022,
-0.0012900236761197448,
-0.03603261336684227,
0.07015927881002426,
-0.009460457600653172,
0.0315302349627018,
0.030925722792744637,
-0.04186219722032547,
0.022839128971099854,
0.06920119374990463,
-0.020201537758111954,
0.0207319688051939,
-0.017717136070132256,
-0.026831233873963356,
-0.05559220165014267,
0.02178739756345749,
0.021781036630272865,
0.030252283439040184,
0.04505283758044243,
0.028886595740914345,
-0.025345826521515846,
-0.030715906992554665,
-0.023436423391103745,
0.015728283673524857,
0.005165838170796633,
-0.0020396350882947445,
0.052316855639219284,
0.053680386394262314,
0.046333085745573044,
0.014969021081924438,
0.06076434999704361,
0.029388386756181717,
-0.04029495641589165,
0.002609597984701395,
0.0240226648747921,
0.03872360661625862,
0.0037811645306646824,
0.08400473743677139,
0.006124862469732761,
-0.06488552689552307,
0.057479359209537506,
-0.00935529824346304,
0.04713111370801926,
0.05080266296863556,
-0.03616112470626831,
-0.01690111868083477,
0.002084926702082157,
-0.02305472455918789,
-0.013156279921531677,
0.024637579917907715,
-0.0007842383929528296,
0.0479305237531662,
0.085102379322052,
-0.055444784462451935,
0.049766749143600464,
-0.014115185476839542,
-0.010519561357796192,
-0.013784606009721756,
0.033050525933504105,
-0.012579504400491714,
-0.014051771722733974,
0.02118200995028019,
-0.018267575651407242,
0.058874234557151794,
-0.016602780669927597,
0.03668372333049774,
-0.021061314269900322,
-0.05368201062083244,
0.04092274233698845,
0.026178814470767975,
-0.012949563562870026,
0.021534280851483345,
0.05070260539650917,
-0.03628813102841377,
0.038947705179452896,
-0.027333321049809456,
0.06441278010606766,
0.014618274755775928,
-0.023371892049908638,
-0.026519885286688805,
0.0387381948530674,
0.031008493155241013,
-0.020351897925138474,
0.07014162838459015,
-0.006842830218374729,
-0.03324733301997185,
0.010736939497292042,
0.046147577464580536,
-0.0007663092692382634,
-0.07679346948862076,
-0.03689761087298393,
0.025339214131236076,
-0.011966003105044365,
-0.018734941259026527,
-0.05261673033237457,
0.029473144561052322,
-0.07854561507701874,
-0.03941342979669571,
0.060202810913324356,
0.011638437397778034,
-0.060768973082304,
-0.014206597581505775,
0.023464201018214226,
0.01658523455262184,
-0.002191506326198578,
-0.041294485330581665,
-0.031311970204114914,
0.06057337298989296,
-0.016816090792417526,
-0.0033037448301911354,
-0.005969285033643246,
-0.019857844337821007,
0.046865470707416534,
0.03715991973876953,
0.007017937488853931,
-0.05267855152487755,
-0.04860551655292511,
0.04390721768140793,
-0.028474148362874985,
0.00003762426786124706,
-0.07164229452610016,
0.016916902735829353,
-0.031277112662792206,
0.0436624176800251,
-0.05049977824091911,
0.04490654543042183,
-0.07890736311674118,
-0.008990893140435219,
-0.011404029093682766,
0.005033776629716158,
0.0792364850640297,
-0.0106003163382411,
0.017954852432012558,
-0.048115309327840805,
0.0073903691954910755,
0.03891962394118309,
0.018467705696821213,
0.06780915707349777,
0.003680436871945858,
0.03591826185584068,
0.02662261575460434,
-0.012783549726009369,
0.06553249806165695,
-0.06148720160126686,
-0.028192188590765,
0.037969790399074554,
-0.0019785002805292606,
0.037415798753499985,
0.029731938615441322,
-0.032908398658037186,
0.021529793739318848,
0.019227253273129463,
0.04845235124230385,
0.023371729999780655,
-0.030554721131920815,
-0.031150726601481438,
-0.023728996515274048,
0.015061738900840282,
-0.0255073644220829,
0.033386390656232834,
-0.050839707255363464,
-0.005891476757824421,
0.026307784020900726,
0.050880610942840576,
0.02151085063815117,
-0.03902193903923035,
-0.012661688029766083,
-0.0016414797864854336,
-0.011898821219801903,
0.017685985192656517,
-0.0010553359752520919,
-0.017777252942323685,
-0.01810598559677601,
0.013728464022278786,
-0.001795692485757172,
0.05821146443486214,
-0.05784599483013153,
0.02920905314385891,
0.026968758553266525,
0.0024973000399768353,
0.002473217900842428,
-0.015221512876451015,
0.040295835584402084,
-0.04814394563436508,
0.03881390020251274,
-0.007232965435832739,
0.018934402614831924,
-0.017741460353136063,
-0.0195095706731081,
0.0682908222079277,
0.02161071076989174,
0.01962827518582344,
-0.03564627096056938,
-0.03989141806960106,
0.026356255635619164,
-0.030820902436971664,
0.005904674530029297,
-0.008877192623913288,
-0.007257107179611921,
0.034684330224990845,
-0.04273266717791557,
0.00829481240361929,
-0.009837543591856956,
0.03472593054175377,
0.02371261827647686,
-0.003656171727925539,
-0.05424167960882187,
-0.013706132769584656,
-0.0171605683863163,
-0.08032578229904175,
-0.06958431005477905,
0.016317840665578842,
-0.015673037618398666,
0.0016783488681539893,
0.01146928034722805,
0.027774624526500702,
-0.0008873812039382756,
0.041292954236269,
0.0266423299908638,
0.015064128674566746,
-0.00024163101625163108,
0.023238593712449074,
-0.027146494016051292,
-0.03192753344774246,
-0.013339107856154442,
0.0068609099835157394,
-0.0234446432441473,
-0.04296991229057312,
0.032443657517433167,
0.03529126197099686,
-0.056222833693027496,
0.018469523638486862,
0.05721444636583328,
0.03324268385767937,
-0.04882879927754402,
-0.0027323442045599222,
0.04309700056910515,
-0.047875531017780304,
-0.061714883893728256,
0.05994550138711929,
-0.02520010992884636,
0.003899528644979,
-0.015070886351168156,
-0.0939074456691742,
-0.021054942160844803,
-0.016395917162299156,
-0.04321491718292236,
-0.03329961374402046,
0.005552677437663078,
-0.03863602876663208,
-0.012562934309244156,
0.05160512030124664,
0.092070572078228,
-0.013585641980171204,
0.016536425799131393,
-0.0011233444092795253,
0.013898824341595173,
-0.06633405387401581,
-0.030512826517224312,
-0.0427602156996727,
-0.00964996125549078,
-0.07584898918867111,
-0.023502180352807045,
-0.03913302719593048,
0.006179661490023136,
0.011535201221704483,
-0.0072294119745492935,
-0.056200698018074036,
0.030032198876142502,
-0.04547891020774841,
-0.02068585343658924,
-0.002574298996478319,
0.034651536494493484,
0.052612293511629105,
0.05052966997027397,
0.04897018522024155,
-0.023906687274575233,
-0.002369303023442626,
-0.015623140148818493,
0.04252833500504494,
0.021975623443722725,
-0.010117621161043644,
0.00832035019993782,
0.05237523466348648,
0.0038897707127034664,
-0.029490306973457336,
-0.037281859666109085,
-0.00492847478017211,
0.009031159803271294,
0.02233952097594738,
0.006578064523637295,
0.019956469535827637,
-0.011307546868920326,
-0.027220601215958595,
0.07098504155874252,
0.05964360386133194,
0.009879565797746181,
0.05876854434609413,
0.02752188965678215,
-0.0014937911182641983,
-0.005172251723706722,
0.0022988931741565466,
-0.04882471263408661,
0.023259209468960762,
0.047827400267124176,
0.007541511673480272,
0.002289124997332692,
0.0039044395089149475,
0.015268724411725998,
0.00016360156587325037,
0.057354263961315155,
-0.007709240075200796,
0.019632527604699135,
-0.0293724462389946,
0.017241118475794792,
-0.044770583510398865,
0.0050249299965798855,
-0.00044180822442285717,
0.009064109064638615,
0.028673555701971054,
-0.0706210508942604,
0.0024500114377588034,
-0.03466076776385307,
-0.002018745057284832,
0.03942164406180382,
-0.0211542509496212,
0.02798803336918354,
0.023828696459531784,
-0.01795090362429619,
-0.035416990518569946,
-0.016716599464416504,
0.03638996183872223,
0.011387960985302925,
-0.005608835723251104,
0.015733955428004265,
0.013183316215872765,
-0.03135528042912483,
0.04819168895483017,
0.00865976419299841,
0.04084126651287079,
-0.02151426300406456,
0.006247618235647678,
-0.00687764398753643,
0.02558298222720623,
0.04470116272568703,
0.0378168486058712,
0.02561722882091999,
0.009819313883781433,
-0.016036197543144226,
-0.02548784576356411,
-0.00048354134196415544,
-0.006254536099731922,
0.04474865645170212,
0.06696460396051407,
0.008749806322157383,
-0.05565418675541878,
0.04345405474305153,
0.023107105866074562,
-0.023963574320077896,
0.0642276480793953,
-0.02249552309513092,
0.014373654499650002,
-0.015738995745778084,
0.007878639735281467,
0.061155471950769424,
-0.0438460111618042,
-0.027583952993154526,
-0.05524442717432976,
-0.0222431942820549,
0.0036215169820934534,
-0.052070602774620056,
-0.006603844463825226,
-0.05282485857605934,
0.009822677820920944,
-0.015145862475037575,
0.009410383179783821,
-0.028673849999904633,
0.016655053943395615,
-0.0033448501490056515,
0.010099061764776707,
-0.0747031643986702,
-0.007972451858222485,
-0.013415588065981865,
0.003855886170640588,
0.039602912962436676,
-0.023405849933624268,
-0.03457598760724068,
0.029464075341820717,
-0.005273886490613222,
0.0319952517747879,
0.027748802676796913,
-0.002125005703419447,
-0.07789310067892075,
0.05051083862781525,
-0.004617863800376654,
0.05678360536694527,
-0.014973461627960205,
0.03515537828207016,
-0.0005953949876129627,
-0.019619056954979897,
0.0575852170586586,
-0.005464022979140282,
0.00468833651393652,
-0.00960618071258068,
-0.0061349389143288136,
-0.032890718430280685,
0.048777658492326736,
-0.020054176449775696,
0.00015344624989666045,
0.012220519594848156,
0.006570783443748951,
-0.032256342470645905,
0.045231468975543976,
-0.10342655330896378,
0.030249878764152527,
0.019790569320321083,
0.017745116725564003,
-0.030989520251750946,
-0.0006578749744221568,
0.08490968495607376,
-0.0500187911093235,
-0.02996201626956463,
-0.03198695927858353,
0.06602560728788376,
0.07412801682949066,
0.03197663649916649,
-0.014380216598510742,
-0.015381239354610443,
-0.005868404638022184,
0.01703588105738163,
0.010372829623520374,
0.02242586761713028,
-0.036907024681568146,
0.07638920843601227,
-0.04609740898013115,
-0.0407734178006649,
0.005538583733141422,
-0.0009480133303441107,
0.0682118833065033,
-0.009706706739962101,
0.026996953412890434,
-0.017933636903762817,
0.04278142377734184,
0.01630139909684658,
0.006063461769372225,
-0.039140425622463226,
0.0018398929387331009,
0.02883925475180149,
0.07501566410064697,
-0.025682274252176285,
0.03141392394900322,
0.010243050754070282,
-0.028964176774024963,
-0.07442742586135864,
0.03901303559541702,
0.038388967514038086,
-0.06233763322234154,
-0.012957874685525894,
0.027901288121938705,
0.03268468752503395,
-0.02799205854535103,
-0.004361866973340511,
-0.0032599156256765127,
-0.011867961846292019,
0.08686050027608871,
-0.019658785313367844,
0.019666854292154312,
0.009733345359563828,
0.03129453584551811,
0.013097994960844517,
-0.013841093517839909,
0.021578889340162277,
0.0524466335773468,
-0.04377062991261482,
-0.09685232490301132,
0.03183326497673988,
0.001976687926799059,
0.011908447369933128,
-0.030665386468172073,
-0.06833549588918686,
-0.02539134956896305,
-0.012059606611728668,
0.005228819325566292,
-0.019184665754437447,
0.014595678076148033,
-0.01588553376495838,
-0.05826129391789436,
0.035605184733867645,
0.012334025464951992,
0.0039398628287017345,
0.05321425944566727,
-0.023045726120471954,
0.059983331710100174,
0.06240085884928703,
-0.05907699838280678,
0.030540473759174347,
0.007590565364807844,
-0.02353372983634472,
0.0074730184860527515,
-0.012627796269953251,
0.018912166357040405,
0.02866147644817829,
-0.00956569705158472,
-0.04552270472049713,
0.06188251078128815,
-0.06848382204771042,
-0.05423326790332794,
0.042023248970508575,
-0.00455244816839695,
0.007789738941937685,
0.014214622788131237,
-0.019249331206083298,
-0.019333716481924057,
0.020273342728614807,
-0.042131610214710236,
0.041677121073007584,
0.023054806515574455,
0.05820751562714577,
-0.01981535367667675,
-0.005413210950791836,
-0.007799841929227114,
0.0027356836944818497,
0.0008088583708740771,
0.032352034002542496,
-0.01497411634773016,
-0.07723911106586456,
0.05956408008933067,
-0.03708728030323982,
-0.05891444906592369,
-0.05553806200623512,
-0.002141558099538088,
0.047918327152729034,
-0.06976669281721115,
-0.013212934136390686,
-0.024391282349824905,
0.02539224736392498,
-0.05941271781921387,
-0.06794285029172897,
-0.060985445976257324,
0.0028966302052140236,
0.02892487309873104,
0.02032190002501011,
-0.00674609886482358,
0.0025720095727592707,
-0.1115899384021759,
-0.04843922704458237,
0.021570606157183647,
0.05364292114973068,
0.0007684267475269735,
-0.005838744342327118,
-0.0574074387550354,
-0.05031481012701988,
0.02686256915330887,
0.005127591080963612,
-0.03684239834547043,
0.03331571817398071,
-0.026599783450365067,
-0.05046665668487549,
0.00004345920751802623,
-0.05479162186384201,
-0.027006274089217186,
0.057969462126493454,
-0.05078576132655144,
-0.018644198775291443,
0.015965403988957405,
-0.04926702752709389,
-0.004310907330363989,
0.022360097616910934,
0.031435269862413406,
0.004537490196526051,
0.01958605833351612,
0.004882956854999065,
-0.005984024610370398,
-0.06102152168750763,
0.03108910284936428,
-0.035997312515974045,
-0.0023158728145062923,
-0.03899151086807251,
-0.061901722103357315,
-0.03964347392320633,
0.007029558066278696,
0.06571290642023087,
-0.020983681082725525,
0.010467073880136013,
0.1037239283323288,
-0.0031345083843916655,
0.01405757199972868,
0.058947425335645676,
-0.017076704651117325,
0.034244269132614136,
0.002860406180843711,
-0.028989579528570175,
-0.02716028317809105,
0.01876993104815483,
-0.018887566402554512,
0.0663762018084526,
-0.07424481213092804,
0.05933353677392006,
-0.049004700034856796,
0.031346142292022705,
-0.05071805417537689,
-0.04615367203950882,
-0.012754328548908234,
0.019641781225800514,
0.011713790707290173,
-0.02380155585706234,
-0.04863261058926582,
-0.001552437781356275,
0.040586918592453,
-0.008570210076868534,
-0.017675962299108505,
-0.08246126025915146,
-0.013001098297536373,
-0.006777890492230654,
0.027496183291077614,
-0.012378986924886703,
0.015053858980536461,
-0.015128162689507008,
0.004856573883444071,
0.049189336597919464,
-0.02883049286901951,
0.01958303339779377,
0.007623337209224701,
0.05671872943639755,
-0.007473660167306662,
-0.002559806453064084,
0.0664905235171318,
0.008837960660457611,
0.021429261192679405,
0.04718753695487976,
0.030444543808698654,
-0.06053648889064789,
0.022745147347450256,
0.010284345597028732,
-0.05625811964273453,
0.0034146939869970083,
-0.05269385129213333,
-0.05054445192217827,
-0.022128818556666374,
0.000698411837220192,
0.021894311532378197,
-0.04071064665913582,
-0.049044907093048096,
0.015922553837299347,
0.0051864502020180225,
0.0370347760617733,
-0.04953368008136749,
-0.04088953509926796,
0.02735413983464241,
-0.056795068085193634,
-0.005853417795151472,
-0.06328374147415161,
-0.040861502289772034,
-0.07739564031362534,
-0.05378149822354317,
0.004042993299663067,
0.01912662759423256,
-0.004018726292997599,
0.011004284955561161,
0.06471272557973862,
-0.010635880753397942,
0.011938631534576416,
-0.006118021439760923,
0.01142171397805214,
0.020579706877470016,
-0.044770192354917526,
-0.0006549084791913629,
-0.05809853971004486,
-0.011680464260280132,
0.03936241194605827,
0.011371488682925701,
-0.04269906133413315,
-0.08830152451992035,
0.03123839758336544,
0.008275813423097134,
-0.030787840485572815,
0.002158354502171278,
-0.00698079215362668,
0.008783021941781044,
0.04345476254820824,
0.03957529366016388,
-0.0351346917450428,
0.015528470277786255,
0.016816655173897743,
-0.011691953055560589,
0.02143351174890995,
0.005525671876966953,
0.002512281062081456,
0.046604037284851074,
-0.010979133658111095,
0.025957942008972168,
0.013056346215307713,
-0.0080223698168993,
0.010380919091403484,
-0.07253692299127579,
0.04156089574098587,
-0.06926164776086807,
0.010840825736522675,
-0.03339984267950058,
-0.00526505708694458,
-0.016942212358117104,
-0.06228742003440857,
-0.004042032640427351,
-0.035854995250701904,
0.03682137280702591,
0.0425446517765522,
-0.04512408375740051,
0.006451609078794718,
0.015778884291648865,
-0.0062950532883405685,
0.010924486443400383,
-0.07383475452661514,
0.02367892861366272,
-0.06158314645290375,
0.010021314024925232,
-0.017704356461763382,
0.028322050347924232,
-0.03437868878245354,
-0.057307589799165726,
0.02023683674633503,
-0.02325350046157837,
0.04421907290816307,
0.0033574653789401054,
-0.04294966906309128,
-0.009814595803618431,
-0.00945553183555603,
0.048300281167030334,
0.07602715492248535,
0.04814022406935692,
-0.025046397000551224,
-0.01097516156733036,
0.006763243582099676,
-0.024342207238078117,
-0.001972432713955641,
0.031109167262911797,
-0.047944847494363785,
-0.0018947420176118612,
0.01725470833480358,
-0.01649315096437931,
0.03937080129981041,
0.013094831258058548,
0.022824682295322418,
0.023970015347003937,
-0.03758229687809944,
0.022777961567044258,
0.0025124072562903166,
0.04590214043855667
] |
[
12.671773910522461,
2.278218984603882
] |
General Relativity and Quantum Cosmology
|
General Physics
|
gr-qc
|
na
|
na
|