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# XIIIth Quark Confinement and the Hadron Spectrum

31 July 2018 to 6 August 2018
Maynooth University
Europe/Dublin timezone

## Nonequilibrium viscous correction to the phase space density and bulk viscosity in the relaxation time approximation

3 Aug 2018, 14:30
30m
Hall F (Arts Bldg.)

### Hall F

#### Arts Bldg.

Talk D: Deconfinement

### Speaker

Alina Czajka (McGill University/Jan Kochanowski University)

### Description

We present the correct form of the nonequilibrium viscous correction to the phase space density in the relaxation time approximation that properly takes into account the space-time dependence of the thermal mass. We also investigate the impact the correction has on the bulk viscosity. This correction automatically satisfies the Landau matching condition and energy-momentum conservation. It also makes the appearance of the Callan-Symanzyk $\beta_\lambda$-function natural in the bulk viscosity calculation. The bulk viscosity has the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case, it is affected by the cut-off of infrared divergences. This may be an indication that the relaxation time approximation is too crude to obtain the correct form of the bulk viscosity for quantum gases.

### Primary author

Alina Czajka (McGill University/Jan Kochanowski University)

### Co-authors

Sigtryggur Hauksson (McGill University) Dr Chun Shen (Brookhaven National Laboratory) Sangyong Jeon (McGill University) Prof. Charles Gale (McGill University)


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# Hamiltonian of the charged current in SM (related to the lorentz invariance)

recently when I was studying the scatterings which involves a vector boson (like W boson) as an intermediate particle, I saw that the propagator is not Lorentz invariant, I read that there is another source of Lorentz non-invariance in the Hamiltonian of the charged current. I mean the Hamiltonian is not simply the minus of the Lagrangian in this case h=-l. the extra term is not Lorentz invariant and, these two source of the Lorentz non-invariance will cancel each other eventually in the S-Matrix. (you can see :The standard Model, A primer written by Burgess chapters 4,5 and problem 5.4). I don't understand this completely, I'll be grateful if anyone can help me and explain it or introducing a reference for it.

I apologize for my bad English writing.

Thanks

-

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# 3.1: Vapor Pressure Curve

From the last module you will recall that the vapor-pressure curve (Figure 2.2.3) and its extremities were examined. That figure is presented in this module in Figure 3.1.1. We concluded that two very important thermodynamic points bound the vapor pressure curve: the Critical Point at its upper end and the Triple Point at its lower end.

Figure $$\PageIndex{1}$$: Vapor pressure curve

Now let us take a second look at this figure. We can better understand the information represented by the vapor pressure curve by looking at the process of isobaric heating. This is illustrated by line ACB in Figure 3.1.2. The term “isobaric” pertains to a constant pressure process. By isobaric heating process, we then mean a “constant pressure addition of heat into a system.”

Figure $$\PageIndex{2}$$: Vapor pressure curve and ACB Path

Such a process can be described as follows. Starting at point A and moving towards point C at constant pressure, we add heat to the system. By adding this heat, we cause a temperature increase in the system (Temperature at C > Temperature at A.). At point C, which lies above the vapor pressure or boiling point curve, we encounter a phase change. To the left of point C, at lower temperatures, exists only liquid. To the right of point C, at higher temperatures, there is only vapor. Therefore, a sharp discontinuity in density exists at point C. During this transition, from liquid to vapor, we will notice that the heat that we add to the system does not cause any temperature increase, and in fact, temperature and pressure conditions remain constant during the transition represented by the vapor curve. In other words, even though we are adding heat, the system remains at the pressure and temperature associated with point C until the whole phase transition has taken place — i.e., until all the vapor is converted to liquid. Instead of working to increase liquid temperature, this heat serves to move liquid molecules apart until all liquid has become vapor.

Up to this point, we saw that the heat added before the system reached the phase transition was used to raise the temperature of the substance. However, the heat that we are adding right now, during the phase transition, is not causing any temperature increase (hence it is said to be hidden heat or latent heat of vaporization). Therefore, we differentiate between two kinds of heat: sensible heat and latent heat.

Sensible Heat: Its main purpose is to cause an increase in temperature of the system.

Latent Heat: It serves only one purpose: to convert the liquid into vapor. It does not cause a temperature increase.

In fact, the name “latent” suggests “hidden.” Here, we are adding heat to the system but are not seeing its effect in terms of temperature increase. The heat that is needed to transform one mole of saturated liquid into vapor is known as the latent molar heat of vaporization: $$(\Delta \tilde{H}_{vap})$$

Once we have converted all the liquid into vapor (i.e., we supplied all the necessary latent heat to accomplish this), we may continue to add more heat. If we do so, the temperature will rise again and we will end at point B (Figure 3.1.2). This heat is also sensible since it is causing the temperature of the system to rise.

It is interesting to note that, in order to reverse the process from point B to point A, we will have to remove the exact amount of heat that we had added before. This is a basic consequence of an energy balance principle. We call such a reverse process an isobaric cooling process. We will have to remove some sensible heat in order to cool the vapor from point B to C, and then we will remove all the latent heat of the vapor to condense it into liquid (transition at point C). Finally, we will also need to remove more sensible heat from the system for the cooling of the liquid from point C to point A.

In the previous two processes, from A to B or vice versa, we had to cross the phase boundary represented by the vapor pressure curve. However, this is not the only thermodynamic path that is available for us to go from A to B. Figure 3.1.3 depicts another possible path.

Figure $$\PageIndex{3}$$: Vapor pressure curve and continuous path above critical point

Instead of doing the whole process isobarically, we may devise a new path that may also accomplish the goal of taking the system from a condition ‘A’ to a condition ‘B.’ Consider the path ADEB that is shown in Figure 3.1.3.

Sequence of Paths


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# NGC 2575

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 Classifications of the Host Galaxies of Supernovae, Set IIClassifications on the DDO system are given for an additional 231 hostgalaxies of supernovae that have been discovered during the course ofthe Lick Observatory Supernova Search with the Katzman Automatic ImagingTelescope (KAIT). This brings the total number of hosts of supernovae(SNe) discovered (or independently rediscovered) by KAIT, which have sofar been classified on a homogeneous system, to 408. The probabilitythat SNe Ia and SNe II have a different distribution of host-galaxyHubble types is found to be 99.7%. A significant difference is alsofound between the distributions of the host galaxies of SNe Ia and ofSNe Ibc (defined here to include SNe Ib, Ib/c, and Ic). However, nosignificant difference is detected between the frequency distributionsof the host galaxies of SNe II and SNe IIn. This suggests that SNe IInare generally not SNe Ia embedded in circumstellar material that aremasquerading as SNe II. Furthermore, no significant difference is foundbetween the distribution of the Hubble types of the hosts of SNe Ibc andof SNe II. Additionally, SNe II-P and SNe II-L are found to occur amongsimilar stellar populations. The ratio of the number of SNe Ia-pec tonormal SNe Ia appears to be higher in early-type galaxies than it is ingalaxies of later morphological types. This suggests that the ancestorsof SNe Ia-pec may differ systematically in age or composition from theprogenitors of normal SNe Ia. Unexpectedly, five SNe of Types Ib/c, II,and IIn (all of which are thought to have massive progenitors) are foundin host galaxies that are nominally classified as types E and S0.However, in each case the galaxy classification is uncertain, or newlyinspected images show evidence suggesting a later classification. Amongthese five objects, NGC 3720, the host galaxy of SN 2002at, wasapparently misidentified in the Carnegie Atlas of Galaxies. The luminous and dark matter content of disk galaxiesWe have compiled a sample of disk galaxies with available photometry inthe B and K bands, velocity line-widths and HI integral fluxes. Severalparameters that trace the luminous, baryonic and dark matter contentswere inferred. We investigated how these parameters vary with differentgalaxy properties, and compared the results with predictions of galaxyevolutionary models in the context of the Λ Cold Dark Matter(ΛCDM) cosmogony. The ratio of disk-to-total maximum circularvelocity, (Vd,m/Vt,m), depends mainly on thecentral disk surface density Σd,0 (or surfacebrightness, SB), increasing roughly asΣd,00.15. While a fraction of high SBgalaxies have a (Vd,m/Vt,m) ratio corresponding tothe maximum disk solution, the low SB are completely dark matterdominated. The trend is similar for the models, although they haveslightly smaller (Vd,m/Vt,m) ratios thanobservations, in particular at the highest SBs and when small baryonfractions are used. 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The broadagreement between the models and observations presented here regardingthe trends of the dynamical-to-baryon matter and mass-to-light ratioswith several galaxy properties favors the ΛCDM scenario. However,the excess of dark matter inside the optical region of disk galaxiesremains the main difficulty.Appendices A and B are only available in electronic form athttp://www.edpsciences.org. Table 1 is only available at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/412/633 Mass-to-light ratios from the fundamental plane of spiral galaxy discsThe best-fitting two-dimensional plane within the three-dimensionalspace of spiral galaxy disc observables (rotational velocityvrot, central disc surface brightnessμ0=-2.5logI0 and disc scalelength h) has beenconstructed. Applying the three-dimensional bisector method ofregression analysis to a sample of ~100 spiral galaxy discs that spanmore than 4magarcsec-2 in central disc surface brightnessyields vrot\proptoI0.50\pm0.050\,h0.77\pm 0.07 (B band)and vrot\proptoI0.43\pm0.040\,h0.69\pm 0.07 (R band).Contrary to popular belief, these results suggest that in the B band,the dynamical mass-to-light ratio (within four disc scalelengths) islargely independent of the surface brightness, varying as I0.00\pm0.100\,h0.54\pm 0.14. Consistentresults were obtained when the range of the analysis was truncated byexcluding the low-surface-brightness galaxies. Previous claims thatM/LBvaries withI-1/20,Bareshown to be misleading and/or caused by galaxy selection effects - notall low-surface-brightness disc galaxies are dark matter dominated. Thesituation is, however, different in the near-infrared whereLK'~v4 and M/LK' is shown to vary asI-1/20,K\prime. Theoretical studies ofspiral galaxy discs should therefore not assume a constant M/L ratiowithin any given passband. The B-band dynamical mass-to-light ratio(within four disc scalelengths) has no obvious correlation with (B-R)disc colour, while in the K' band it varies as -1.25+/-0.28(B-R).Combining the present observational data with recent galaxy modelpredictions implies that the logarithm of the stellar-to-dynamical massratio is not a constant value, but increases as discs become redder,varying as 1.70+/-0.28(B-R). Supernova 2002an in NGC 2575IAUC 7828 available at Central Bureau for Astronomical Telegrams. Supernova 2002an in NGC 2575IAUC 7818 available at Central Bureau for Astronomical Telegrams. Supernova 2002an in NGC 2575IAUC 7808 available at Central Bureau for Astronomical Telegrams. Supernova 2002an in NGC 2575IAUC 7805 available at Central Bureau for Astronomical Telegrams. An Investigation into the Prominence of Spiral Galaxy BulgesFrom a diameter-limited sample of 86 low-inclination (face-on) spiralgalaxies, the bulge-to-disk size and luminosity ratios and otherquantitative measurements for the prominence of the bulge are derived.The bulge and disk parameters have been estimated using aseeing-convolved Sérsic r1/n bulge and aseeing-convolved exponential disk that were fitted to the optical (B, R,and I) and near-infrared (K) galaxy light profiles. In general,early-type spiral galaxy bulges have Sérsic values of n>1, andlate-type spiral galaxy bulges have values of n<1. In the B band,only eight galaxies have a bulge shape parameter n consistent with theexponential value 1, and only five galaxies do in the K band. Use of theexponential bulge model is shown to restrict the range ofre/h and B/D values by more than a factor of 2. Applicationof the r1/n bulge models, unlike exponential bulge models,results in a larger mean re/h ratio for the early-type spiralgalaxies than for the late-type spiral galaxies, although this result isshown not to be statistically significant. The mean B/D luminosity ratiois, however, significantly larger (>3 σ) for the early-typespirals than for the late-type spirals. Two new parameters areintroduced to measure the prominence of the bulge. The first is thedifference between the central surface brightness of the galaxy and thesurface brightness level at which the bulge and disk contribute equally.The other test uses the radius at which the contribution from the diskand bulge light are equal, normalized for the effect of intrinsicallydifferent galaxy sizes. Both of these parameters reveal that theearly-type spiral galaxies appear'' to have significantly (more than 2σ in all passbands) bigger and brighter bulges than late-typespiral galaxies. This apparent contradiction with the re/hvalues can be explained with an iceberg-like scenario, in which thebulges in late-type spiral galaxies are relatively submerged in theirdisk. This can be achieved by varying the relative stellar density whilemaintaining the same effective bulge-to-disk ratio. The B/D luminosityratio and the concentration index C31, in agreement with paststudies, are positively correlated and decrease as one moves along thespiral Hubble sequence toward later spiral galaxy types, although forgalaxies with large extended bulges the concentration index no longertraces the B/D luminosity ratio in a one-to-one fashion. A strong(Spearman's rank-order correlation coefficient, rs=0.80) andhighly significant positive correlation exists between the shape, n, ofthe bulge light profile and the bulge-to-disk luminosity ratio. Theabsolute bulge magnitude-logn diagram is used as a diagnostic tool forcomparative studies with dwarf elliptical and ordinary ellipticalgalaxies. At least in the B band these objects occupy distinctlydifferent regions of this parameter space. While the dwarf ellipticalgalaxies appear to be the faint extension to the brighter ellipticalgalaxies, the bulges of spiral galaxies do not; for a given luminositythey have a noticeably smaller shape parameter and hence a more dramaticdecline of stellar density at large radii. Arcsecond Positions of UGC GalaxiesWe present accurate B1950 and J2000 positions for all confirmed galaxiesin the Uppsala General Catalog (UGC). The positions were measuredvisually from Digitized Sky Survey images with rms uncertaintiesσ<=[(1.2")2+(θ/100)2]1/2,where θ is the major-axis diameter. We compared each galaxymeasured with the original UGC description to ensure high reliability.The full position list is available in the electronic version only. The I-Band Tully-Fisher Relation for SC Galaxies: Optical Imaging DataProperties derived from the analysis of photometric I-band imagingobservations are presented for 1727 inclined spiral galaxies, mostly oftypes Sbc and Sc. The reduction, parameter extraction, and errorestimation procedures are discussed in detail. The asymptotic behaviorof the magnitude curve of growth and the radial variation in ellipticityand position angle are used in combination with the linearity of thesurface brightness falloff to fit the disk portion of the profile. TotalI-band magnitudes are calculated by extrapolating the detected surfacebrightness profile to a radius of eight disk scale lengths. Errors inthe magnitudes, typically ~0.04 mag, are dominated by uncertainties inthe sky subtraction and disk-fitting procedures. Comparison is made withthe similar imaging database of Mathewson, Ford, & Buchhorn, both aspresented originally by those authors and after reanalyzing theirdigital reduction files using identical disk-fitting procedures. Directcomparison is made of profile details for 292 galaxies observed incommon. Although some differences occur, good agreement is found,proving that the two data sets can be used in combination with onlyminor accommodation of those differences. The compilation of opticalproperties presented here is optimized for use in applications of theTully-Fisher relation as a secondary distance indicator in studies ofthe local peculiar velocity field. Total magnitude, radius, colour indices, colour gradients and photometric type of galaxiesWe present a catalogue of aperture photometry of galaxies, in UBVRI,assembled from three different origins: (i) an update of the catalogueof Buta et al. (1995) (ii) published photometric profiles and (iii)aperture photometry performed on CCD images. We explored different setsof growth curves to fit these data: (i) The Sersic law, (ii) The net ofgrowth curves used for the preparation of the RC3 and (iii) A linearinterpolation between the de Vaucouleurs (r(1/4) ) and exponential laws.Finally we adopted the latter solution. Fitting these growth curves, wederive (1) the total magnitude, (2) the effective radius, (3) the colourindices and (4) gradients and (5) the photometric type of 5169 galaxies.The photometric type is defined to statistically match the revisedmorphologic type and parametrizes the shape of the growth curve. It iscoded from -9, for very concentrated galaxies, to +10, for diffusegalaxies. Based in part on observations collected at the Haute-ProvenceObservatory. Gas Mass Fractions and the Evolution of Spiral GalaxiesWe show that the gas mass fraction of spiral galaxies is stronglycorrelated with luminosity and surface brightness. It is not correlatedwith linear size. Gas fraction varies with luminosity and surfacebrightness at the same rate, indicating evolution at fixed size. Dimgalaxies are clearly less evolved than bright ones, having consumed only~ \frac {1}{2} of their gas. This resolves the gas consumption paradox,since there exist many galaxies with large gas reservoirs. Thesegas-rich galaxies must have formed the bulk of their stellar populationsin the last half of a Hubble time. The existence of such immaturegalaxies at z = 0 indicates that either galaxy formation is a lengthy oreven ongoing process, or the onset of significant star formation can bedelayed for arbitrary periods in tenuous gas disks. 21 CM H1 Line Spectra of Galaxies in Nearby ClustersA compilation of HI line fluxes, systemic velocities and line widths ispresented for \Ndet detected galaxies, mostly in the vicinities of 30nearby rich clusters out to a redshift of z ~ .04, specifically for usein applications of the Tully-Fisher distance method. New 21 cm HI lineprofiles have been obtained for ~ 500 galaxies in 27 Abell clustersvisible from Arecibo. Upper limits are also presented for \Nnod galaxiesfor which HI emission was not detected. In order to provide ahomogeneous line width determination optimized for Tully-Fisher studies,these new data are supplemented by the reanalysis of previouslypublished spectra obtained both at Arecibo and Green Bank that areavailable in a digital archive. Corrections for instrumental broadening,smoothing, signal-to-noise and profile shape are applied, and anestimate of the error on the width is given. When corrected forturbulent broadening and viewing angle, the corrected velocity widthspresented here will provide the appropriate line width parameter neededto derive distances via the Tully-Fisher relation. The I band Tully-Fisher relation for cluster galaxies: data presentation.Observational parameters which can be used for redshift-independentdistance determination using the Tully-Fisher (TF) technique are givenfor \ntot spiral galaxies in the fields of 24 clusters or groups. I bandphotometry for the full sample was either obtained by us or compiledfrom published literature. Rotational velocities are derived either from21 cm spectra or optical emission line long-slit spectra, and convertedto a homogeneous scale. In addition to presenting the data, a discussionof the various sources of error on TF parameters is introduced, and thecriteria for the assignment of membership to each cluster are given. Near-infrared and optical broadband surface photometry of 86 face-on disk dominated galaxies. II. A two-dimensional method to determine bulge and disk parameters.In this Paper I present a new two-dimensional decomposition technique,which models the surface photometry of a galaxy with an exponentiallight profile for both bulge and disk and, when necessary, with aFreeman bar. The new technique was tested for systematic errors on bothartificial and real data and compared with widely used one-dimensionaldecomposition techniques, where the luminosity profile of the galaxy isused. The comparisons indicate that a decomposition of thetwo-dimensional image of the galaxy with an exponential light profilefor both bulge and disk yields the most reproducible and representativebulge and disk parameters. An extensive error analysis was made todetermine the reliability of the model parameters. If the model with anexponential bulge profile is a reasonable description of a galaxy, themaximum errors in the derived model parameters are of order 20%. Theuncertainties in the model parameters will increase, if the exponentialbulge function is replaced by other often used bulge functions as the deVaucouleurs law. All decomposition methods were applied to the opticaland near-infrared data set presented by de Jong & van der Kruit(1994), which comprises 86 galaxies in six passbands. An image database. II. Catalogue between δ=-30deg and δ=70deg.A preliminary list of 68.040 galaxies was built from extraction of35.841 digitized images of the Palomar Sky Survey (Paper I). For eachgalaxy, the basic parameters are obtained: coordinates, diameter, axisratio, total magnitude, position angle. On this preliminary list, weapply severe selection rules to get a catalog of 28.000 galaxies, wellidentified and well documented. For each parameter, a comparison is madewith standard measurements. The accuracy of the raw photometricparameters is quite good despite of the simplicity of the method.Without any local correction, the standard error on the total magnitudeis about 0.5 magnitude up to a total magnitude of B_T_=17. Significantsecondary effects are detected concerning the magnitudes: distance toplate center effect and air-mass effect. Recalibration of the H-0.5 magnitudes of spiral galaxiesThe H-magnitude aperture data published by the Aaronson et al.collaboration over a 10 year period is collected into a homogeneous dataset of 1731 observations of 665 galaxies. Ninety-six percent of thesegalaxies have isophotal diameters and axial ratios determined by theThird Reference Cataloque of Bright Galaxies (RC3; de Vaucouleurs et al.1991), the most self-consistent set of optical data currently available.The precepts governing the optical data in the RC3 are systematicallydifferent from those of the Second Reference Catalogue (de Vaucouleurs,de Vaucouleurs, & Corwin 1976), which were used by Aaronson et al.for their original analyses of galaxy peculiar motions. This in turnleads to systematic differences in growth curves and fiducialH-magnitudes, prompting the present recalibration of the near-infraredTully-Fisher relationship. New optically normalized H-magnitude growthcurves are defined for galaxies of types SO to Im, from which new valuesof fiducial H-magnitudes, Hg-0.5, are measured forthe 665 galaxies. A series of internal tests show that these fourstandard growth curves are defined to an accuracy of 0.05 mag over theinterval -1.5 less than or equal to log (A/Dg) less than orequal to -0.2. Comparisons with the Aaronson et al. values of diameters,axial ratios, and fiducial H-magnitudes show the expected differences,given the different definitions of these parameters. The values ofHg-0.5 are assigned quality indices: a qualityvalue of 1 indicates an accuracy of less than 0.2 mag, quality 2indicates an accuracy of 0.2-0.35 mag, and quality 3 indicates anaccuracy of more than 0.35 mag. Revised values of corrected H I velocitywidths are also given, based on the new set of axial ratios defiend bythe RC3. Near-infrared and optical broadband surface photometry of 86 face-on disk dominated galaxies. I. Selection, observations and data reduction.We present accurate surface photometry in the B, V, R, I, H and Kpassbands of 86 spiral galaxies. The galaxies in this statisticallycomplete sample of undisturbed spirals were selected from the UGC tohave minimum diameters of 2' and minor over major axis ratios largerthan 0.625. This sample has been selected in such a way that it can beused to represent a volume limited sample. The observation and reductiontechniques are described in detail, especially the not often useddriftscan technique for CCDs and the relatively new techniques usingnear-infrared (near-IR) arrays. For each galaxy we present radialprofiles of surface brightness. Using these profiles we calculated theintegrated magnitudes of the galaxies in the different passbands. Weperformed internal and external consistency checks for the magnitudes aswell as the luminosity profiles. The internal consistency is well withinthe estimated errors. Comparisons with other authors indicate thatmeasurements from photographic plates can show large deviations in thezero-point magnitude. Our surface brightness profiles agree within theerrors with other CCD measurements. The comparison of integratedmagnitudes shows a large scatter, but a consistent zero-point. Thesemeasurements will be used in a series of forthcoming papers to discusscentral surface brightnesses, scalelengths, colors and color gradientsof disks of spiral galaxies. I-band CCD surface photometry of spiral galaxies in 16 nearby clustersResults of I-band CCD surface photometry for 284 spiral galaxies in 16clusters in the redshift range from 3000 to 11,000 km/s are presented.Various effects on surface photometry are discussed, and the relevantcorrections are outlined. Groups of galaxies within 80 Mpc. II - The catalogue of groups and group membersThis paper gives a catalog of the groups and associations obtained bymeans of a revised hierarchical algorithm applied to a sample of 4143galaxies with diameters larger than 100 arcsec and redshifts smallerthan 6000 km/s. The 264 groups of galaxies obtained in this way (andwhich contain at least three sample galaxies) are listed, with the looseassociations surrounding them and the individual members of eachaggregate as well; moreover, the location of every entity among 13regions corresponding roughly to superclusters is specified. Finally,1729 galaxies belong to the groups, and 466 to the associations, i.e.,the total fraction of galaxies within the various aggregates amounts to53 percent. The faint end of the Zwicky magnitude scale - CCD isophotal magnitudes versus Zwicky magnitudesZwicky magnitudes are compared to blue isophotal magnitudes derived fromsurface photometry of digital galaxy images to study the isophotalnature of the Zwicky magnitude scale at the faint end. The approximateisophote that corresponds to the magnitude tabulated in the Catalog ofGroups and Clusters of Galaxies (Zwicky et al. 1961-1968). It is foundthat, in the mean, the Zwicky magnitude closely corresponds to the bluemagnitude measured with the B = 26.0 mag/sq arcsec isophote. The scatteris 0.31 mag and the distribution of isophotal surface brightness is verybroad, however, making the Zwicky magnitudes only accurate to about 30percent when used a luminosity indicator. It is shown that relativedifferences in Zwicky magnitude do not provide an accurate gage of thetrue relative luminosities of galaxies. Arm classifications for spiral galaxiesThe spiral arm classes of 762 galaxies are tabulated; 636 galaxies withlow inclinations and radii larger than 1 arcmin were classified on thebasis of their blue images on the Palomar Observatory Sky Survey (POSS),76 SA galaxies in the group catalog of Geller and Huchra were alsoclassified from the POSS, and 253 galaxies in high-resolution atlaseswere classified from their atlas photographs. This spiral armclassification system was previously shown to correlate with thepresence of density waves, and galaxies with such waves were shown tooccur primarily in the densest galactic groups. The present sampleindicates, in addition, that grand design galaxies (i.e., those whichtend to contain prominent density wave modes) are physically larger thanflocculent galaxies (which do not contain such prominent modes) by afactor of about 1.5. A larger group sample confirms the previous resultthat grand design galaxies are preferentially in dense groups. KISO survey for ultraviolet-excess galaxies. IVPresented here are the fourth list and identification charts of theultraviolet-excess galaxies which have been detected on the multicolorplates taken with the Kiso Schmidt telescope for 10 survey fields. Inthe sky area of some 300 square degrees 752 objects are cataloged downto the photographic magnitude of about 18. A study of the large-scale structure in the distribution of galaxies in a region centered about the Cancer cluster. I - Initial observational results. II - Further observational resultsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1986AJ.....91..705B&db_key=AST A catalog of radio, optical, and infrared observations of spiral galaxies in clustersThe results of a major observational program on the luminosities,colors, and gas contents of spiral galaxies in clusters of galaxies arepresented. The data have been used as part of a detailed investigationinto the nature of cluster spirals and for revisions of the distancescale using the infrared Tully-Fisher relation. The observationalstrategies, reduction procedures, and sources or error are brieflydiscussed. The data include 21-cm H I observations, UBVR multiaperturephotometry, and H-band photometry of several hunderd spiral galaxies in10 clusters. Morphology of spiral galaxies. I - General propertiesRed Palomar Sky Survey plates are scanned to characterize a completesample of 605 spiral galaxies north of declination -33 deg havinginclination angle less than 56 deg and blue diameter 2-15 arcmin. Theselection of the data and the reduction and parameter-extractionprocedures are explained, and the data and the results of statisticalanalysis are presented in tables and graphs. Findings reported include alow frequency of occurrence for small inclination angles (suggestingdistortion of outer structures), similar distributions of central diskbrightness for types Sa-Sc but not for types Sd-Sm (where mean valuesare smaller), fewer late-type galaxies with large exponential-disk scalelengths, no galaxies with both high central brightness and large scalelength (indicating a limit on angular momentum in galaxy formation), anda correlation between mean surface brightness and absolute magnitude forlater-type galaxies but not for types Sa-Scd. The Cancer Cluster - an unbound collection of groupsA surface density contour map of the Cancer Cluster derived from galaxycounts in the Zwicky catalog is presented. The contour map shows thatthe galaxy distribution is clumpy. When this spatial distribution iscombined with nearly complete velocity information, the clumps stand outmore clearly; there are significant differences in the mean velocitiesof the clumps which exceed their internal velocity dispersions. TheCancer Cluster is not a proper 'cluster' but is a collection of discretegroups, each with a velocity dispersion of approximately 300 km/s,separating from one another with the cosmological flow. Themass-to-light ratio for galaxies in the main concentration isapproximately 320 solar masses/solar luminosities (H0 = 100km/s Mpc).
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## Differential and Integral Equations

### On maximum principles and existence of positive solutions for some cooperative elliptic systems

#### Abstract

In this paper, we provide alternative simple proofs for some of the results in [12], with applications to nonlinear systems, and an extension of the necessary and sufficient condition for the Maximum Principle to some cooperative quasi-linear elliptic systems involving the $p$-Laplacian. We also show that under the same conditions, we have existence of positive solutions.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 1 (1995), 69-85.

Dates
First available in Project Euclid: 21 May 2013

https://projecteuclid.org/euclid.die/1369143784

Mathematical Reviews number (MathSciNet)
MR1296110

Zentralblatt MATH identifier
0821.35018

Subjects
Primary: 35J45
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B50: Maximum principles

#### Citation

Fleckinger, J.; Hernández, J.; de Thélin, F. On maximum principles and existence of positive solutions for some cooperative elliptic systems. Differential Integral Equations 8 (1995), no. 1, 69--85. https://projecteuclid.org/euclid.die/1369143784


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Algrebra II

I have a question for finding vertical and horizontal asymptotes! as to finding the intercepts, domain, and graphing it all together...

like y= 6 over (x+3)

I don't quite understand the concepts and things, but if you can give me a hand that'll be great!

y = 6 / (x+3)
Domain: all possible x values.
Range: all possible y values.
Intercepts: the (x,y) coordinates where the graph intersects the x- and y-axes.
Asymptotes: Horizontal and vertical lines representing x- and y-values that the graph approaches, but never reaches.

I assume that you have a graphing calculator. Set your window so that x and y both range from -10 to +10. Then graph y = 1/x. This is the "inverse" or reciprocal function; for any value x, y is its reciprocal. If x=2, then y=1/2; if x=-7, then y=-1/7. X and y are either both positive or both negative. If the absolute value of x is large, then the absolute value of y is small, and vice versa.

There is one value which neither x nor y will ever be: zero. X can't be zero, because that would be dividing by zero. y=1/x can be manipulated to become xy=1 (multiply both sides by x), and then or x=1/y (from xy=1, divide both sides by y).

Therefore the domain (all possible x values) is: x does not = zero. Ditto the range (all possible y values): y does not = zero.

If you look at the graphs, as a positive x value gets smaller and smaller, it approaches zero, but never reaches it. Similarly, a negative x value can increase and get closer and closer to zero, but never reaches it. x=0 is a value that the graph approaches, but never reaches. We call the line x=0 an asymptote of y=1/x.

Similarly, both positive and negative y values can approach, but never reach 0. Thus, the line y=0 is also an asymptote of y=1/x.

The equation y=mx+b represents a whole "family" of linear equations which have similar properties. Similarly, the y=ax^2+bx+c represents a whole family of quadratic equations.

Similarly, y=1/x is the simplest form of a whole family of "inverse" equations: y=k/(x-h), where k and h are any two numbers except zero, represents a whole family of "inverse" functions.

k "multiplies" the y=1/x equation. Graphically, the y=1/x equation is "vertically stretched". Try k=5. y=5/x. Graph it. You'll see the same 2 curves, but they rise much more steeply near the y axis.

h moves the two curves right by h units. If h=3, then y=1/(x-3). Notice that the denominator has a minus sign, not a plus sign. Since the denominator can't be zero, x-3 can't be zero, so x can't be 3. That means the two curves approach the vertical asymptote x=3. This has the effect of moving both y=1/x curves 3 units to the right. If x = -4, then y=1/(x - (-4)) = 1/(x+4). Now x+4 can't be zero, so x can't = -4, so the vertical asymptote is x=-4.

Can you move the horizontal asymptote up or down? Yes, if you define the basic "family" function as y=k/(x-h) + q. Positive q moves the entire graph upwards, negative q moves it downwards, and the horizontal asmymptote becomes y=q.

For your y=6/(x+3), the domain (x) values are x not = -3, and the vertical asymptote is x = -3. The range (y) values are y not = 0, so the vertical asymptote is y = 0.

How about intercepts? Intercepts are the values where the graph inersects the x- and y-axes. For the y-intercept, x = 0. For your equation, when x=0, y=6/(3+0)=2, so the y-intercept is (0,2). For the x-intercept, y=0. But, we just decided that y can't be 0, so there is no x-intercept.

Hope that helps.

Aram

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text:
# Self Doubt

61 views
A polygon has 12 edges , How many diagonals does it have?

How to find the number of diagonals?

For any $n$ side polygon, the number of diagonals are $\frac{n(n-3)}{2}$.

We can prove this as follows:

First, select a vertex from the polygon. This can be done in $n \choose 1$ ways.
To draw diagonals, we can choose any other vertex except the neighbouring vertices, giving us $n -1\choose 1$ ways.

This gives us a total of $n \times (n-3)$ diagonals.

However, we have overcounted by a factor of two here, since diagonal from $AB$ is same as diagonal from $BA$.

Hence, the total number of diagonals are $\frac{n(n-3)}{2}$

## Related questions

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text:
# Revision history [back]

### get current username on the server side

I am writing a code that I will put on the server side of SAGE/notebook (i.e. in the SAGE_PATH, not locally in a sheet or attached to a sheet. I want this code to know the name of the user launching it, how can I have it?

### get current username on the server side

I am writing a code that I will put on the server side of SAGE/notebook (i.e. in the SAGE_PATH, not locally in a sheet or attached to a sheet. sheet). I want this code to know the name of the user launching it, how can I have it?

### get current username on the server side

I am writing a code that I will put on the server side of SAGE/notebook (i.e. in the SAGE_PATH, not locally in a sheet or attached to a sheet). I want this code to know the name of the user launching it, how can I have it?

following this forum, I found an ugly way to do it:

DATA.split('/home/sageservice/nbfiles.sagenb/home/')[0].split('sage_notebook.sagenb/home/')[1].split('/')[0]

tell me if you have better

### get current username on the server side

I am writing a code that I will put on the server side of SAGE/notebook (i.e. in the SAGE_PATH, not locally in a sheet or attached to a sheet). I want this code to know the name of the user launching it, how can I have it?

following this forumhttp://https://groups.google.com/forum/?fromgroups=#!topic/sage-notebook/aBd1ATWFIKc , I found an ugly way to do it:

DATA.split('/home/sageservice/nbfiles.sagenb/home/')[0].split('sage_notebook.sagenb/home/')[1].split('/')[0]

tell me if you have better


text:
Prettifies Python exception output to make it legible.

# pretty-errors

Prettifies Python exception output to make it legible. Install it with

python -m pip install pretty_errors

If you want pretty_errors to be used whenever you run a python script you must add it to your python startup procedure. You can do so easily by running:

python -m pretty_errors

This is the recommended way to use pretty_errors; apart from being simpler and universal, using it will mean SyntaxError exceptions also get formatted prettily (which doesn't work if you are manually importing pretty_errors).

If you have not installed it universally you can use it in your project simply by importing it:

import pretty_errors

Note you need to be running in a terminal capable of colour output in order to get colour output: in Windows this means powershell, cmder, etc. If you must use a monochrome terminal then you can call the helper function pretty_errors.mono(), which will set some config options in a way that is useful for monochrome output.

If you want to configure the output then use pretty_errors.configure(), pretty_errors.whitelist(), pretty_errors.blacklist(), pretty_errors.pathed_config(). For example:

import pretty_errors
pretty_errors.configure(
separator_character = '*',
filename_display    = pretty_errors.FILENAME_EXTENDED,
line_number_first   = True,
lines_before        = 5,
lines_after         = 2,
line_color          = pretty_errors.RED + '> ' + pretty_errors.default_config.line_color,
code_color          = '  ' + pretty_errors.default_config.line_color,
truncate_code       = True,
display_locals      = True
)
pretty_errors.blacklist('c:/python')

##### Scraping STDERR

Sometimes it will be impossible for pretty_errors to utilize sys.excepthook: for instance, if you are using a framework which installs its own logging (such as uvicorn). In such cases, you can make pretty_errors scrape the output to stderr instead, replacing it with its own. To do so simple call:

pretty_errors.replace_stderr()

Note that this will lose some functionality, since pretty_errors will only have access to what is being output on screen, rather then the entire stack trace. A good API will generally have a way to interact with the exception stack, which will allow for using excepthook: replace_stderr should be the last resort. See this comment for an example

##### Whitelist / Blacklist:

You may use the functions whitelist(path) and blacklist(path) to add paths which will be necessary (whitelist) or excluded (blacklist). The top frame of the stack is never excluded.

##### Pathed Configurations

You may set up alternate configurations, which are triggered by the path to the code file of the frame. For example, if you were not interested in the system frames (those under 'c:/python') but did not want to hide them completely by using the blacklist you could do this:

meh = pretty_errors.config.copy()
meh.line_color = meh.code_color = meh.filename_color = meh.function_color = meh.line_number_color = (
pretty_errors.GREY
)
pretty_errors.pathed_config(meh, 'c:/python')

##### Environment Variables
• PYTHON_PRETTY_ERRORS
You may disable pretty_errors by setting the environment variable PYTHON_PRETTY_ERRORS to 0. i.e. at a command prompt:
set PYTHON_PRETTY_ERRORS=0

Calling pretty_errors.activate() will override this.

If you wish to selectively utilize pretty_errors, then use the above, and in your code perform your calculation to determine whether or not to call pretty_errors.activate().

• PYTHON_PRETTY_ERRORS_ISATTY_ONLY
It may be desirable to disable pretty_errors when you are redirecting output to a file (to keep error logs, for instance). If you wish to do so, then setting PYTHON_PRETTY_ERRORS_ISATTY_ONLY to non-zero will cause pretty_errors to check if it is running in an interactive terminal, and only activate if so.
set PYTHON_PRETTY_ERRORS_ISATTY_ONLY=1

Setting this will disable replace_stderr() in the same situations, unless you call it with the force parameter: replace_stderr(force=True).

Calling pretty_errors.activate() will override this.

You may check pretty_errors.terminal_is_interactive to see if the terminal is interactive (pretty_errors sets this by checking sys.stderr.isatty()). You can use this to select a different config. For example:

if not pretty_errors.terminal_is_interactive:
pretty_errors.mono()

##### Configuration settings:

Configuration settings are stored in pretty_errors.config, though should be set using pretty_errors.configure(). A reference for the default config is stored in pretty_errors.default_config.

• name
Optional field to store config name in.

• line_length
Output will be wrapped at this point. If set to 0 (which is the default) it will automatically match your console width.

• full_line_newline
Insert a hard newline even if the line is full. If line_length is the same as your console width and this is enabled then you will see double newlines when the line is exactly full, so usually you would only set this if they are different.

• separator_character
Character used to create the header line. Hyphen is used by default. If set to None or '' then header will be disabled.

• display_timestamp
When enabled a timestamp is written in the traceback header.

• timestamp_function
Function called to generate timestamp. Default is time.perf_counter.

• exception_above
When enabled the exception is displayed above the stack trace.

• exception_below
When enabled the exception is displayed below the stack trace.

• stack_depth
The maximum number of entries from the stack trace to display. When 0 will display the entire stack, which is the default.

• top_first
When enabled the stack trace will be reversed, displaying the top of the stack first.

• always_display_bottom
When enabled (which is the default) the bottom frame of the stack trace will always be displayed.

• show_suppressed
When enabled all suppressed exceptions in the stack trace will be shown (typically they are suppressed because an exception above them has replaced them). The normal python behaviour is to hide them.

• filename_display
How the filename is displayed: may be pretty_errors.FILENAME_COMPACT, pretty_errors.FILENAME_EXTENDED, or pretty_errors.FILENAME_FULL

• line_number_first
When enabled the line number will be displayed first, rather than the filename.

• display_link
When enabled a link is written below the error location, which VSCode will allow you to click on.

• lines_after, lines_before
How many lines of code to display for the top frame, before and after the line the exception occurred on.

• trace_lines_after, trace_lines_before
How many lines of code to display for each other frame in the stack trace, before and after the line the exception occurred on.

• truncate_code
When enabled each line of code will be truncated to fit the line length.

• display_locals
When enabled, local variables appearing in the top stack frame code will be displayed with their values.

• display_trace_locals
When enabled, local variables appearing in other stack frame code will be displayed with their values.

• truncate_locals
When enabled the values of displayed local variables will be truncated to fit the line length.

• display_arrow
When enabled an arrow will be displayed for syntax errors, pointing at the offending token.

• arrow_head_character, arrow_tail_character
Characters used to draw the arrow which points at syntax errors.

• inner_exception_message
Message displayed when one exception occurs inside another, between the two exceptions. Default is None, which will simply display the exceptions separated by the header. If you want to emulate the default non-pretty behaviour, use this:

inner_exception_message = pretty_errors.MAGENTA + "\n During handling of the above exception, another exception occurred:\n"

Note that if you use top_first then the order will be reversed, so you should use a message like this instead:

inner_exception_message = pretty_errors.MAGENTA + "\n The above exception occurred during another exception:\n"

• inner_exception_separator
Default is False. When set to True a header will be written before the inner_exception_message.

• prefix
Text string which is displayed at the top of the report, just below the header.

• infix
Text string which is displayed between each frame of the stack.

• postfix
Text string which is displayed at the bottom of the exception report.

• reset_stdout
When enabled the reset escape sequence will be written to stdout as well as stderr; turn this on if your console is being left with the wrong color.

These color strings will be output before the relevant part of the exception message. You may include non-escape sequence strings if you wish; if you do not have a terminal which supports color output, or simply want to include extra demarcation.

• header_color
Escape sequence to set header color.

• timestamp_color
Escape sequence to set timestamp color.

• exception_color
Escape sequence to set exception color.

• exception_arg_color
Escape sequence to set exception arguments color.

• exception_file_color
Escape sequence to set color of filenames in exceptions (for example, in a FileNotFoundError).

• filename_color
Escape sequence to set filename color.

• line_number_color
Escape sequence to set line number color.

• function_color
Escape sequence to set function color.

• link_color
Escape sequence to set link color.

• line_color
Escape sequence to set the color of the line of code which caused the exception.

• code_color
Escape sequence to set the color of other displayed lines of code.

• arrow_head_color, arrow_tail_color
Escape sequence to set the color of the arrow which points at syntax errors.

• syntax_error_color
Escape sequence to set the color of the syntax error token.

• local_name_color
Escape sequence to set the color of local variable names.

• local_value_color
Escape sequence to set the color of local variable values.

• local_len_color
Escape sequence to set the color of local value length when local is truncated.

pretty_errors has some built in escape sequence constants you can use when setting these colors:

• BLACK
• GREY
• RED
• GREEN
• YELLOW
• BLUE
• MAGENTA
• CYAN
• WHITE

For each color there is a matching BRIGHT_ variant (i.e. pretty_errors.BRIGHT_RED), as well as a _BACKGROUND variant to set the background color (i.e. pretty_errors.RED_BACKGROUND).

For example:

pretty_errors.configure(
line_color = pretty_errors.CYAN_BACKGROUND + pretty_errors.BRIGHT_WHITE
)

##### Further customization

For the most extensive customization (short of forking the package) you may override the default ExceptionWriter class, allowing you to tailor the output however you wish. Typically you will only need to override the write_ methods.

For example:

class MyExceptionWriter(pretty_errors.ExceptionWriter):
self.output_text('######## ERROR ########')

pretty_errors.exception_writer = MyExceptionWriter()

Run help(pretty_errors.ExceptionWriter) in the python interpreter for more details.

## Release history Release notifications | RSS feed

Uploaded source
Uploaded py3


text:
# Cyclus Server (cyclus.server)¶

An asyncronous cyclus server that provides as JSON API over websockets.

The webserver has a number of ‘events’ that it may send or recieve. These in turn affect how a cyclus simulation runs.

The server, which operates both asynchronously and in parallel, has five top-level tasks which it manages:

• The cyclus simulation object, run on a separate thread,
• A action consumer, which executes actions that have been queued either by the cyclus simulation or the user,
• A websockets server that sends and recieves JSON-formatted events from the client.
• A heartbeat that sends special events every so often.
• A monitor for presenting data about certain other future actions.

For purposes of this document, the following terminology is used:

event: A JSON object / dictionary that contains behaviour instructions.

message: The string form of an event.

action: A delayed asynchronous coroutine function that carries out the behaviour specified in a cooresponding event. These do the actual work of the event system.

repeating action: An action coroutine function (or event name) or a list of the coroutine function and arguments that is added to the action queue each time step of the simulation. This enables pausing each time step, streaming table data, etc.

task: A future object that results from calling an action. See asyncio for more details.

## Events¶

Events are JSON-formatted strings that represent JSON-objects (dicts) at their top-most level. All events must have an “event” key whose value is the string name that distinguishes the event from all other kinds of events.

Often times, events may have parameters that they send/recieve. These live in the “params” key as a JSON object / dict.

Events may be conceptually divided into server-sent, client-sent events, and bidirectional events which are sent by either the client or the server.

### Server Events¶

Server-sent events are those that the server sends to the client. These are often repsonse to requests for data about the state of the simulation. They typically contain a “data” key which holds data about the simulation state. They may also have a “success” key, whose value is true/false, that specifies whether the data was able to be computed.

heartbeat: A simple event the lets the client know that the server is still alive. The data value is the approximate time of the next heartbeat in seconds:

{"event": "heartbeat", "data": val}

loaded: A simple message that says that a simulation has been loaded.

“params”: {“status”: “ok”}, “data”: null

}

registry: The in-memory backend registy value in its current form:

{"event": "registry",
"params": null,
"data": ["table0", "table1", ...]
}

table_names: The current file system backend table names:

{"event": "table_names",
"params": null,
"data": ["table0", "table1", ...]
}

### Client Events¶

Client events are often requests originating from users. They may either express a request for behaviour (pause the simulation, restart, etc.) or a request for data. These events may or may not have additional parameters, depending on the type of request.

deregister_tables: Remove table names from the in-memory backend registry. A registry event from the server will follow the completion of this event:

{"event": "deregister_tables",
"params": {"tables": ["table0", "table1", ...]}
}

load: Loads the input file in the simulation and starts running the simulation:

{"event": "load"}

pause: Pauses the simulation until it is unpaused:

{"event": "pause"}

register_tables: Add table names to the in-memory backend registry. A registry event from the server will follow the completion of this event:

{"event": "register_tables",
"params": {"tables": ["table0", "table1", ...]}
}

registry_request: A simple reqest for the in-memory backend regsitry:

{"event": "registry_request"}

shutdown: A reqest to shutdown the server:

{"event": "shutdown",
"params": {"when": "empty" or "now"}
}

table_names_request: A simple reqest for the table names present in the file system backend:

{"event": "table_names_request"}

unpause: Unpauses the simulation by canceling the pause task:

{"event": "unpause"}

### Bidirectional Events¶

These are events that may logically originate from either the client or the server. Certian keys in the event may or not be present depending on the sender, but the event name stays the same.

agent_annotations: This event requests and returns the agent annotations for a given agent spec. If the data field is null, this is a request to the server for annotation information. If the data field is a dict, it represents the annotations for the spec:

{"event": "agent_annotations",
"params": {"spec": "<path>:<lib>:<name>"},
"data": null or object
}

echo: Echos back a single string parameter. When requesting an echo, the data key need not be present:

{"event": "table_names",
"params": {"s": value},
"data": value
}

sleep: The requester instructs the reciever to sleep for n seconds:

{"event": "sleep", "params": {"n": value}}

table_data: Data about a table with the conditions and other parameters applied. If the client sends this event without the “data” key, the server will respond with the requested table:

{"event": "table_data",
"params": {"table": "<name of table>",
"conds": ["<list of condition lists, if any>"],
"orient": "<orientation of JSON, see Pandas>"},
"data": {"<keys>": "<values subject to orientation>"}
}

## Command Line Interface¶

You may launch the cyclus server by running:

$python -m cyclus.server input.xml  Most of the arguments are relatively self-explanatory. However, the CLI here also allows you to load initial and repeating actions. The syntax for this is an event name followed by parameter tokens (which must contain an equals sign): $ python -m cyclus.server input.xml --repeating-actions sleep n=1

You may load many actions by repeating the name-params pattern:

\$ python -m cyclus.server input.xml –repeating-actions sleep n=1 table_data table=”TimeSeriesPower”

Note that everything right of an equals sign in a parameter token is passed to Python’s eval() builtin function. It thererfore must be valid Python. For string values, make sure that you properly escape quotation marks as per the syntax of your shell language.

class cyclus.server.EventCLIAction(option_strings, dest, nargs='+', **kwargs)

A basic class for parsing action specs on the command line.

cyclus.server.action_consumer(state)

The basic consumer of actions.

cyclus.server.action_monitor(state)

Consumes actions that have been scheduled for monitoring tasks, such as status reporting, sending signals, or canceling other task. These are awaited in the order recieved.

cyclus.server.get_send_data()

Asynchronously grabs the next data to send from the queue.

cyclus.server.heartbeat(state)

This sends a heartbeat event to the client with a nominal period. This occurs outside of the normal action-consumer event system. The client is then able to detect the lack of a heartbeat and know that the server has been disconected.

cyclus.server.main(args=None)

Main cyclus server entry point.

cyclus.server.make_parser()

Makes the argument parser for the cyclus server.

cyclus.server.queue_message_action(message)
cyclus.server.run_sim(state, loop, executor)

Runs a cyclus simulation in an executor, which should be on another thread.

cyclus.server.websocket_handler(websocket, path)

Sends and recieves data via a websocket.


text:
# QM Value of an infinite sum

1. Nov 17, 2005

### *melinda*

hi,
In the course of doing my quantum homework I ran into a bit of a snag.

In one of my calculations I need to replace the sum from n = 1 to infinity of 1/n^2 (for odd n only) with its number value.

My book instructs me to get the information from a table and actualy gives the value (for odd n) of the infinite series for 1/n^4 = (pi^4)/96.

In calculus the only series I evaluated to get numbers were geometric and telescoping.

I tried to rewrite my own series as a telescoping and run from there, but I feel like I'm wasting time and trying to reinvent the wheel.

A google search gave me little, and I think I'm using the wrong key words in my wikapedia search.

Does anyone know where I can find my missing piece of info?

thanks,
*melinda*

2. Nov 17, 2005

### mathlete

The sum of 1/(2n-1)^2 for 1,2,3,4... is Pi^2/8 :)

3. Nov 17, 2005

### *melinda*

hey, thanks a bunch!

Do you happen to know how it was derived, and if so, was my telescoping series idea correct?

4. Nov 17, 2005

### Physics Monkey

You can break the sum $$\sum^\infty_{n=1} \frac{1}{n^2}$$ into its even and odd terms. The odd series is the one you wanted. Now focus on the even series for second. Since each term is even, it can be written as $$n = 2 m$$ where $$m$$ runs over all the integers. This means that the even sum is actually just
$$\sum^\infty_{n=2m} \frac{1}{n^2} = \sum^\infty_{m=1} \frac{1}{2^2}\frac{1}{m^2} = \frac{1}{4} \sum^\infty_{m=1} \frac{1}{m^2},$$
but the last term is just the full sum over evens and odds. Thus we can say the even sum is one fourth of the full sum. This means that the odd sum is three fourths of the full sum. All you need to know now is the value of the full sum.

You can obtain the value of the full sum by considering the Fourier series for the function $$x^2$$ on the interval $$[-\pi,\pi]$$. It turns out that the fourier coeffecients are related to $$\frac{1}{n^2}$$ which enables you to sum the series. The result, which you can also find in any table, is $$\pi^2/6$$. There are other ways to do it, but this way is one of the easiest in my opinion. That gives the value of the odd sum, the one you wanted, as
$$\frac{3}{4} \frac{\pi^2}{6} = \frac{\pi^2}{8}.$$

Last edited: Nov 17, 2005


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# Lighting InLine Switch

\$39.99

 Application Choose an option2000/SportSpectrumClear

The InLine Switch adds an on/off function to the NOCQUA Lighting Systems. It is designed to simply cut power without needing to unplug the connections. The InLine Switch also features a glowing LED battery gauge that indicates remaining battery power.

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## Our Take

Please note that each standard NOCQUA Light System comes with an InLine switch. If purchasing an additional InLine Switch, be sure to select the corresponding Light System. The connection ports are different between the NOCQUA Spectrum and NOCQUA 2000/Sport.


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#### Activity

• Activity 1

The cross-elasticity of two independent or unrelated goods is equal to zero. A change in the price of product A (coke) does not have any effect on the quantity demanded of product B (tyres).

### Suppose the cross-elasticity of demand between two products, A and B, is negative. If the price of product A increases as a result of a decrease in the number of firms supplying the product, the quantity demanded will _____

Incorrect. Think again.

Correct. The key to the question is given in the first sentence: "The cross-elasticity between two products is negative." If the cross-elasticity is negative, we know that the two products must be complements. An increase in the price of product A decreases the quantity demanded of A and the demand for product B decreases. The markets for motor vehicles and tyres can be used as an example: The market for motor vehicles is represented in figure A. The equilibrium price is Pe and the equilibrium quantity demand and supplied is Qe, as indicated by point E. The market for tyres is represented in figure B. The equilibrium price is Pe and the equilibrium quantity demanded and supplied is Qe, as indicated by point E. A decrease in the number of motor vehicle producers shifts the supply curve for vehicles from S to S1. The equilibrium price for motor vehicles increases from Pe to to P1 and the equilibrium quantity demanded and supplied thus decreases from Qe to Q1.

The increase in the price of motor vehicles and the lower quantity demanded leads to a decrease in the demand for tyres, because people buy fewer motor vehicles and therefore fewer tyres. In the market for tyres, the demand curve for tyres shifts to the left from D to D1. This decrease in the demand for tyres due to the increase in the price of motor vehicles causes a decrease in the quantity of tyres demanded from Qe to Q1 and a decrease in the price from Pe to P1.

Incorrect. Think again.

Incorrect. Think again.

### Suppose the cross-elasticity of demand between two products, A and B, is positive. If there is a fall in the cost of producing good B, the quantity demanded will _____.

Incorrect. Think again.

Incorrect. Think again.

Incorrect. Think again.

Correct. The key to the question is given in the first sentence: "The cross-elasticity between two products is positive." If the cross-elasticity is positive, we know that the two products must be substitutes. An increase in the price of product A decreases the quantity demanded of A and the demand for product B increases. The markets for butter and margarine can be used as an example: The market for butter is represented in figure A. The equilibrium price is R9,00 and the equilibrium quantity demanded and supplied is 250 kg, as indicated by point E. The market for margarine is represented in figure B. The equilibrium price is R9,00 and the equilibrium quantity demanded and supplied is 250 kg, as indicated by point E. An increase in the production cost of butter shifts the supply curve for butter from S to S1. The equilibrium price for butter increases from R9,00 per kg to R15,00 per kg, and the equilibrium quantity demanded thus decreases from 250 kg to 150 kg.

Figure A – butter

Figure B – margarine

The increase in the price of butter and the lower quantity demanded therefore leads to an increase in the demand for margarine, because people buy margarine instead of butter. At each price of margarine, more margarine is demanded when the price of butter increases from R9,00 per kg to R15,00 per kg. In the market for margarine, the demand curve shifts to the right from D to D1. This increase in the demand for margarine due to the increase in the price of butter, causes an increase in the quantity of margarine demanded from 250 kg to 300 kg.

• Activity 2

### a. Write down the formula for cross elasticity.

$$\text{Income elasticity of demand } e_y = {\text{% change in quantity demanded } \over \text{% change in income}}$$

### b. Select the appropriate characteristics for a complement good from the following categories:

 Categories
 The demand of one good decreases when the price of another increases. Cross elasticity is negative. ec < 0 The demand of one good increases when the price of another increases. Cross elasticity if positive. ec > 0 The demand of one good does not change when the price of another increases. ec = 0

Complement

 Categories
 The demand of one good decreases when the price of another increases. Cross elasticity is negative. ec < 0

### c. Select the appropriate characteristics for a substitute good from the following categories:

 Categories
 The demand of one good decreases when the price of another increases. Cross elasticity is negative. ec < 0 The demand of one good increases when the price of another increases. Cross elasticity if positive. ec > 0 The demand of one good does not change when the price of another increases. ec = 0

Substitute

 Categories
 The demand of one good increases when the price of another increases. Cross elasticity is positive. ec > 0

### d. Select the appropriate characteristics for an unrelated good from the following categories:

 Categories
 The demand of one good decreases when the price of another increases. Cross elasticity is negative. ec < 0 The demand of one good increases when the price of another increases. Cross elasticity if positive. ec > 0 The demand of one good does not change when the price of another increases. ec = 0

Unrelated good

 Categories
 The demand of one good does not change when the price of another increases ec = 0


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# How Time Really Passes

We all experience the passage of time. This is not an illusion. We agree on the serial delivery of moments, and it is very hard to dislocate us from this agreement. However, the core of this experience can be located as a feature of our physical theories. These theories do not replace our notion of passage. Rather, physics provides a reliable account of the regularities underlying our common experience of time passing. It does this by providing us with a concrete relationship between any given now, together with its future and past.

1. We Experience Time Passing

We can apprehend the passage of time through the succession of three mental states, in this order:

1. the expectation of an event;
2. the experience of the event; and
3. the memory of the event.

We prepare for lunch, we eat lunch, and we remember how tasty it was afterward. Moreover, we all agree that this is the way it works — the order doesn’t change.

This is an account of passage that John Norton has proposed. As John suggests, this agreement shows all the signs of not being an illusion. There’s no known procedure that eradicates the experience of passage. There’s no obvious underlying mechanism that reduces passage to an artifact of our perception. The best explanation of the reliable succession of these three mental states is that they reflect an objective regularity in the world. Passage is real. It produces the serial delivery of moments to our minds. We become aware of it through the succession of these three identifiable mental states.

2. Physical Theories Describe Passage

In a physical theory, passage appears as a relationship between matter at any given moment (the ‘now’) and its future and past developments. This relationship is determined by Cauchy evolution. The regularities appearing in Cauchy evolution correspond precisely to the regularities we experience with passage. This gives us good reason to suspect they reflect the same objective feature of reality.

We have said that the core feature of passage is the serial delivery of moments: a future event becomes present, and then recedes into the past. Another way to describe this situation is to say that, once a now has been specified, we are guaranteed a definite future and a definite past. These categories never get mixed up: the past cannot arrive after now; the future cannot arrive before now. There is some real regularity that guarantees future, present, and past will be delivered to us in the right order.

The regularity underlying our experience of passage reflects the same reality as the regularity underlying the way physics describes change. In physical theories, this change is called evolution. Here is how the regularity appears.

By specifying a matter configuration ‘now’ (indicated as a gray circle), we determine a local past and a local future.

We can input a configuration of matter representing ‘now’ into a physical theory. These are called (local) initial conditions. Once now has been specified, the theory determines (in the most common physical situations1.) a definite future and past. The equations of motion of our theory determine the moments in the past from which our matter evolved, as well as the moments in the future to which it will evolve soon. This separation into past, present, and future states of matter matches the key feature of passage: the serial delivery of moments is fixed once we specify our ‘now.’

For example, I might input my ‘now’ to be 10am this morning. My matter configuration at 10am is determined (according to some hypothetical theory) to have evolved out of my bed at around 7am, and is determined to evolve to eat lunch at noon. When I set my ‘now’ to be noon, then everything changes in a regular way. I am determined to have evolved from my 10am configuration, and determined to wash my dishes soon. And so on.

This is a striking match of our experience of the serial delivery of moments. At 10am, I am in a state of remembering my bed, and a state of expecting to eat lunch. This is followed by my noon state of remembering my 10am state, enjoying my lunch, and expecting to do the dishes.

Craig Callender (2000) argues that Cauchy evolution is what makes time informative. Here, we have reached a simpler conclusion: Cauchy evolution is how physics reflects time’s passage.

3. Experience and Theory Reflect the Same Thing

The human mind apprehends the passage of time through a change of state: we expect, we experience, and then we remember. This is a fact about our human experience. The steadfastness of this experience suggests it reflects an objective feature of the world.

Physical theory describes passage by describing a state’s evolution: given an initial state, we determine the past states as well as the future ones. This is a fact about our physical theories. The empirical confirmation of these theories suggests that they too reflect something objective about the world.

This does not mean that our apprehension of passage can be reduced to the physical description of passage, or vice versa. Rather, our conclusion should be that both the experience and the physics are very likely reflective of the same phenomenon. Physics is not devoid of passage. It is even more evidence for its existence.

—————–
1. This is not to ignore the difficult problem of specifying, and justifying, the conditions under which the Cauchy problem is well-posed. There are many well-known cases in which initial conditions fail to settle future/past evolution. However, it is sufficient for us to note that in a great many cases, and in almost all common applications, initial conditions can be chosen so as to guarantee a well-posed Cauchy problem.

Soul Physics is authored by Bryan W. Roberts. Thanks for subscribing.
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## 12 thoughts on “How Time Really Passes”

1. Baptiste

Hi there.
It seems to me that the problem consist in the specification of initials conditions. Ok, there is genuine passage in our experience of time. Ok there is passage in physics described by Cauchy evolution. But the passage in physics is derived of a first step : the fixation of “now”. If you have to localise the “now” before you can speak of a passage of time, can you really speak of a passage as an objective feature of the world ?
You can specifies a lot of initials conditions and so a lot of different passages. If there is so different passages can you say it’s objective ?
If i’m preparing for lunch, this lunch is in my future. But I can find initials conditions for it’s in the past of the system.

My idea is more something like that : there is only genuine passage in experience of time. Objectively what there is, are ordered facts, successive facts (what are called B-relations in metaphysics). Subjective passage is constructed by the perspective of on the eternity, the bloc universe described by relativity.

2. Bryan

Thanks for the note Baptiste,

I agree that physical theory apparently does not provide an objective account of ‘now.’ However, in many cases it does give us the universally quantified sentence, ‘for any now, there exists a definite past and future.’ So, if we can think of that proposition as capturing the essential feature of ‘passage,’ and if we take the theory as a whole to be describing reality, then we have an objective account of passage.

I’m sympathetic to what you’re saying, that genuine passage is an artifact of experience. But as John argues (I think rightly), it’s very hard to call our experience that ‘time really passes’ an illusion, or even a feature of the way we perceive.

Kant declared that Euclidean geometry is an artifact of the way we perceive (in the jargon, it is the transcendentally ideal a priori form of sensory intuition). This turned out to be wrong. If we want to avoid making the same mistake twice, we should perhaps take suggestions about what’s ‘built into our perception’ with a grain of salt.

3. Bryan

Noah: I just mean the way the passage of time is made available to our senses.

We seem to apprehend time in a ‘serial’ way — that is, we go through a particular ordered succession of mental states. When this happens, we are picking up on a particular feature of time, which is made available to us (I used the metaphor ‘delivered’) by the real world.

4. Baptiste

Hello again. Please forgive my bad English language but I would like to say one or two things.

In metaphysics there are two theories about passage. According to theory A there is a genuine passage of things in time. Things are future then they are present and finally they are past. On the contrary theory B says that there is no passage of things in time. Things are what they are for eternity (that’s why theory B go with a perdurantism account of identify throught time).

The point is that you have to choose between A and B theories. There is no middle hybrid solution. Physics seems to give us a B-theory of time because as you say ‘for any now, there exists a definite past and future.’ The expression ‘for any now’ shows that past and future are in physics a question of perspective.
I do not understand why you are saying “it’s very hard to call our experience that ‘time really passes’ an illusion, or even a feature of the way we perceive.”
I agree that passage of time is not an illusion. But it doesn’t imply that passage of time is not a feature of the way we perceive : it’s the only thing it can be in a B theory.
Compare that with experience of space. In B theory “now” is just like “here”. You know that you are here just watching at your desk for example. You could be in another place right ? Just like you could be in another time if you accept a classic B theory of time account. Then you move, you go in other place. Surely you can say that space has passed but intuitively we prefer to say that is it us who have changed of location. It’s the same in time : we change of location (but independently of our will in the case of time).
We pass in the time (or time pass, never mind) between two instants in the sense that our temporal localisation change between that two instants. Passage is profoundly linked to our perspective and in that sense is mind-dependant (always if you accept a B theory).
So I do not understand in a B theory background what could be a genuine physical passage of time, except a change of location from a space-time slice to the successive hypersurface.

Maybe I’m wrong and you will just answer me saying that philosophy of physics do not defend a B theory of time. But if B theory is wrong A theory A is right. In that case physics lacks the specificity of “now”, the fact that present is not a mere perspective on eternity but an ontological feature of the universe. Then you can not say that physics reflects time’s passage : it does not because nothing in physics show the existence of a privilege time, our time, the present as required by A theory.

I know it’s a blog of philosophy of physics so don’t hesitate to tell me if I’m boring you with metaphysical considerations.

5. Bryan

>> The point is that you have to choose between A and B theories. There is no middle hybrid solution.

Come now! Can’t we compromise? ;-)

Actually, I really am arguing for A-series passage here, not B-series. But more importantly, I’m saying that many have been too quick to assume that physics provides us with nothing more than a temporal ordering (which is what B-theorists settle for). I think physics provides us with an A-series as well.

Physics does indeed lack a ‘now’ — I agree that’s provided by one’s personal psychology. But what physics does have is the capacity to take any given ‘now’ as input, and provide a future and a past as output. I argue that this is enough for us to say that physics provides an A-series ordering.

6. Tim Nash

The problem with basing an A-series ordering on given NOWs is that these NOWs are localized just like Time is.

In the famous twin paradox, the faster moving twin (as well as his spaceship) is experiencing a ‘fatter’ NOW. His year is his twins decade, his second is equal to his twin’s entire day, etc. This means that NOW does not extend into infinity, it is localized. It also means that there can be no Universal time line because the localized time Arrows do not necessarily line up.

One more problem is that if you line up a ‘fat’ NOW with a thin one, you have a time arrow being overlaid upon a moment (point vs line). So for any given ‘moment’ for which you want to calculate output there already exists a faster moving particle who has already put such a moment in his rear view mirror.

Julian Barbour has really got me wondering. I’d like to see more understanding of what NOW is.

7. Bryan

Actually, I like the idea that “NOW” should be localized to finite regions of spacetime. After all, our experience of the present is purely local. Shouldn’t our description temporal passage be local as well?

8. Tim

The perception of infinite “NOW”, the collapse of the “wave function of the universe” is more pervasive than any other time experience. And a quantum computing model of the universe also seems to argue for a universe with only one wave function. So even if NOW seems localized, it really cannot be. Where does this NOW end and a different one begin? It is a shifting frame of reference as you travel from point to point. Each point sharing the same instance, the same collapse of the wave function.
All these calculations remind me of the effort that went into adjusting planetary motion to place earth at the center. A lot of effort to preserve our notions of time. If Sean Carroll’s new book represents the current view I think it is too conservative. Here is my favorite line so far. It seems to argue against the main thrust of his book: “the final theory of everything is likely to exhibit non-locality in some very dramatic ways” page 249
This may be a nod to B-series thinking.

9. Bryan

Tim: You’re adopting a very natural assumption about “now”: that if (1) a theory tells us that two events happen at the same time; and (2) one of the events has the property of being “now”; then both events have the property “now”.

However, since I think the property “now” can only be defined in a local region of finite volume, I have to deny this assumption. I think that an event A can count as “now” and not an event B, even though A and B happen at the same time. Yep. It’s unusual. But we local-now types have to bite the bullet here.

10. Tim

I agree that that is a biting of the bullet and a rejection of an important “objective feature of the world”.

I am curious, do you think any of these are equivalent to the other?:
1) simultaneous events A and B
2) “NOW”
3) collapse of wavefuntion of the universe.

On a side note, I hope B- series ideas are a funded area of research.
A- series types won’t care much, but some Series B models bring up the question of why we all share a NOW of the same duration.

11. Bryan

If “simultaneous” means “lying on the same (infinite) Cauchy surface,” then I’m saying: 1 and 2 are not equivalent. I also think 2 and 3 are not equivalent. The reason is, a simultaneity surface and a wavefunction extend all the way to infinity. But there is simply no evidence that “now” extends all the way to infinity, this being quite clearly outside the realm of anyone’s perception.

To put it another way: “now” is a concept that appears in theories of perception. Nothing about these theories suggests that “now” can or should be understood non-locally. Contrast this with “simultaneous,” which is a concept that appears in physics. Spacetime physics suggests the concept “simultaneous” can and should be understood non-locally. Conclusion: “simultaneous” is a non-local concept; “now” is not.


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Question

# p-Nitrophenol is a stronger acid than phenol while p-cresol is a weaker acid. This can be explained as:A.${\text{ - C}}{{\text{H}}_{\text{3}}}$ group decreases the electron density on the oxygen of O-H group making p-cresol a weaker acid.B.${\text{ - N}}{{\text{O}}_{\text{2}}}$ decreases the electron density on the oxygen of O-H group making p-nitrophenol a stronger acid. C.${\text{ - C}}{{\text{H}}_{\text{3}}}$ group increases the electron density on the oxygen of O-H group making the release of ${{\text{H}}^{\text{ + }}}$ easierD.${\text{ - N}}{{\text{O}}_{\text{2}}}$ group increases the electron density on oxygen of O-H group making release of ${{\text{H}}^{\text{ + }}}$easier

Verified
119.1k+ views
Hint:The p-nitrophenol is a nitro group attached to the para position of phenol. Similarly, p-cresol is a methyl group attached to the para position of phenol. An electronegative atom pulls the electrons and has high electron density. The presence of the electron-withdrawing group and electron-donating group affects the acidity of the compounds. Acidity is determined by the ability to release ${{\text{H}}^{\text{ + }}}$ ions.
Let us look at the structure of p-nitrophenol. Phenol is an electron-deficient group.

This is the lewis dot structure of ${\text{N}}{{\text{O}}_{\text{2}}}$.
We can see that Nitrogen in ${\text{N}}{{\text{O}}_{\text{2}}}$ already has a positive charge on it. It is because it gave one of its lone pairs to oxygen (double bond). When this nitrogen is attached to the benzene ring, the nitrogen will pull the electrons from the benzene ring to reduce the positive charge.
Therefore, ${\text{N}}{{\text{O}}_{\text{2}}}$ is an electron-withdrawing group.
In p-nitrophenol, since it is ${\text{N}}{{\text{O}}_{\text{2}}}$ is an electron-withdrawing group, all the electron density will be drifted towards ${\text{N}}{{\text{O}}_{\text{2}}}$
This will result in a decrease in the electron density of oxygen in the O-H bond.
Thus, the release of ${{\text{H}}^{\text{ + }}}$ is easier.
Now, let us look at o-cresol.

The ${\text{ - C}}{{\text{H}}_{\text{3}}}$ is attached to the para position of phenol.
We know that the methyl group in cresol is electron-donating. It gives its electron density to the electron-deficient phenol. Thus, the electron density on the O-H group increases.
Therefore, it cannot give out ${{\text{H}}^{\text{ + }}}$ ions.
Therefore, the correct answer is that the ${\text{ - N}}{{\text{O}}_{\text{2}}}$ decreases the electron density on the oxygen of the O-H group making p-nitrophenol a stronger acid.

Thus, the correct option is (B).

Note: The presence of an electron-donating group will decrease the acidity. This is because the electron-donating group increases the electron density on the electron-deficient species. Thus, it makes it difficult to release ${{\text{H}}^{\text{ + }}}$ ions as the bonds are stronger. The presence of electron-withdrawing groups ${\text{ - N}}{{\text{O}}_{\text{2}}}$ decreases the electron density and facilitates the release of ${{\text{H}}^{\text{ + }}}$ ions. Other examples of electron-donating groups are ${\text{ - N}}{{\text{H}}_{\text{2}}}$, -NR, - etc., and the electron-withdrawing groups are halogen, ${\text{ - N}}{{\text{O}}_{\text{2}}}$, ${\text{ - C}}{{\text{F}}_{\text{3}}}$