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• ### Wavelength-dispersive spectroscopy in the hard x-ray regime of a heavy highly-charged ion: The 1s Lamb shift in hydrogen-like gold(1706.08778)

July 5, 2017 physics.atom-ph
Accurate spectroscopy of highly charged high-Z ions in a storage ring is demonstrated to be feasible by the use of specially adapted crystal optics. The method has been applied for the measurement of the 1s Lamb shift in hydrogen-like gold (Au 78+) in a storage ring through spectroscopy of the Lyman x rays. This measurement represents the first result obtained for a high-Z element using high-resolution wavelength-dispersive spectroscopy in the hard x-ray regime, paving the way for sensitivity to higher-order QED effects.
• ### Direct mass measurements of Cd isotopes show strong shell gap at N=82(1507.04470)

July 16, 2015 nucl-ex, nucl-th, astro-ph.HE
A $^{238}$U projectile beam was used to create cadmium isotopes via abrasion-fission at 410 MeV/u in a beryllium target at the entrance of the in-flight separator FRS at GSI. The fission fragments were separated with the FRS and injected into the isochronous storage ring ESR for mass measurements. The Isochronous Mass Spectrometry (IMS) was performed under two different experimental conditions, with and without B$\rho$-tagging at the dispersive central focal plane of the FRS. In the experiment with B$\rho$-tagging the magnetic rigidity of the injected fragments was determined by an accuracy of $2\times 10^{-4}$. A new method of data analysis, using a correlation matrix for the combined data set from both experiments, has provided mass values for 25 different isotopes for the first time. The high selectivity and sensitivity of the experiment and analysis has given access even to rare isotopes detected with a few atoms per week. In this letter we present for the $^{129,130,131}$Cd isotopes mass values directly measured for the first time. The Cd results clearly show a very pronounced shell effect at $N=82$ which is in agreement with the conclusion from $\gamma$-ray spectroscopy of $^{130}$Cd and confirms the assumptions of modern shell-model calculations.
• ### Conceptual design of elliptical cavities for intensity and position sensitive beam measurements in storage rings(1506.00440)

Position sensitive beam monitors are indispensable for the beam diagnostics in storage rings. Apart from their applications in the measurements of beam parameters, they can be used in non-destructive in-ring decay studies of radioactive ion beams as well as enhancing precision in the isochronous mass measurement technique. In this work, we introduce a novel approach based on cavities with elliptical cross-section, in order to compensate for existing limitations in ion storage rings. The design is aimed primarily for future heavy ion storage rings of the FAIR project. The conceptual design is discussed together with simulation results.
• ### Nuclear Physics Experiments with Ion Storage Rings(1312.7476)

Dec. 28, 2013 nucl-ex
In the last two decades a number of nuclear structure and astrophysics experiments were performed at heavy-ion storage rings employing unique experimental conditions offered by such machines. Furthermore, building on the experience gained at the two facilities presently in operation, several new storage ring projects were launched worldwide. This contribution is intended to provide a brief review of the fast growing field of nuclear structure and astrophysics research at storage rings.
• ### High-resolution measurement of the time-modulated orbital electron capture and of the $\beta^+$ decay of hydrogen-like $^{142}$Pm$^{60+}$ ions(1309.7294)

Sept. 27, 2013 nucl-ex, nucl-th
The periodic time modulations, found recently in the two-body orbital electron-capture (EC) decay of both, hydrogen-like $^{140}$Pr$^{58+}$ and $^{142}$Pm$^{60+}$ ions, with periods near to 7s and amplitudes of about 20%, were re-investigated for the case of $^{142}$Pm$^{60+}$ by using a 245 MHz resonator cavity with a much improved sensitivity and time resolution. We observed that the exponential EC decay is modulated with a period $T = 7.11(11)$s, in accordance with a modulation period $T = 7.12(11)$ s as obtained from simultaneous observations with a capacitive pick-up, employed also in the previous experiments. The modulation amplitudes amount to $a_R = 0.107(24)$ and $a_P = 0.134(27)$ for the 245 MHz resonator and the capacitive pick-up, respectively. These new results corroborate for both detectors {\it exactly} our previous findings of modulation periods near to 7s, though with {\it distinctly smaller} amplitudes. Also the three-body $\beta^+$ decays have been analyzed. For a supposed modulation period near to 7s we found an amplitude $a = 0.027(27)$, compatible with $a = 0$ and in agreement with the preliminary result $a = 0.030(30)$ of our previous experiment. These observations could point at weak interaction as origin of the observed 7s-modulation of the EC decay. Furthermore, the data suggest that interference terms occur in the two-body EC decay, although the neutrinos are not directly observed.
• ### Schottky mass measurements of heavy neutron-rich nuclides in the element range $70\leZ \le79$ at the ESR(1308.3135)

Aug. 14, 2013 nucl-ex
Storage-ring mass spectrometry was applied to neutron-rich $^{197}$Au projectile fragments. Masses of $^{181,183}$Lu, $^{185,186}$Hf, $^{187,188}$Ta, $^{191}$W, and $^{192,193}$Re nuclei were measured for the first time. The uncertainty of previously known masses of $^{189,190}$W and $^{195}$Os nuclei was improved. Observed irregularities on the smooth two-neutron separation energies for Hf and W isotopes are linked to the collectivity phenomena in the corresponding nuclei.
• ### Direct observation of long-lived isomers in $^{212}$Bi(1306.0475)

June 3, 2013 nucl-ex
Long-lived isomers in 212Bi have been studied following 238U projectile fragmentation at 670 MeV per nucleon. The fragmentation products were injected as highly charged ions into the GSI storage ring, giving access to masses and half-lives. While the excitation energy of the first isomer of 212Bi was confirmed, the second isomer was observed at 1478(30) keV, in contrast to the previously accepted value of >1910 keV. It was also found to have an extended Lorentz-corrected in-ring halflife >30 min, compared to 7.0(3) min for the neutral atom. Both the energy and half-life differences can be understood as being due a substantial, though previously unrecognised, internal decay branch for neutral atoms. Earlier shell-model calculations are now found to give good agreement with the isomer excitation energy. Furthermore, these and new calculations predict the existence of states at slightly higher energy that could facilitate isomer de-excitation studies.
• ### Comment on the paper "Search for oscillation of the electron-capture decay probability of $^{142}$Pm" at arXiv:0807.0649v1(0807.2308)

July 15, 2008 nucl-ex
It is argued that orbital electron-capture decays of neutral $^{142}$Pm atoms implanted into the lattice of a solid (LBNL experiment) do not fulfil the constraints of true two-body beta decays, since momentum as well as energy of the final state are distributed among three objects, namely the electron neutrino, the recoiling daughter atom and the lattice phonons. To our understanding, this could be a reason for the non-observation of a periodic time modulation in the number of electron-capture decays of implanted neutral $^{142}$Pm atoms.
• ### Isotope shift in the dielectronic recombination of three-electron ^{A}Nd^{57+}(0801.3798)

Jan. 24, 2008 physics.atom-ph
Isotope shifts in dielectronic recombination spectra were studied for Li-like ^{A}Nd^{57+} ions with A=142 and A=150. From the displacement of resonance positions energy shifts \delta E^{142,150}(2s-2p_1/2)= 40.2(3)(6) meV (stat)(sys)) and \delta E^{142,150}(2s-2p_3/2) = 42.3(12)(20) meV of 2s-2p_j transitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of ^{142,150}\delta <r^2> = -1.36(1)(3) fm^2. The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.
• ### Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like $^{140}$Pr and $^{142}$Pm Ions(0801.2079)

Jan. 14, 2008 hep-ph, nucl-ex, nucl-th
We report on time-modulated two-body weak decays observed in the orbital electron capture of hydrogen-like $^{140}$Pr$^{59+}$ and $^{142}$Pm$^{60+}$ ions coasting in an ion storage ring. Using non-destructive single ion, time-resolved Schottky mass spectrometry we found that the expected exponential decay is modulated in time with a modulation period of about 7 seconds for both systems. Tentatively this observation is attributed to the coherent superposition of finite mass eigenstates of the electron neutrinos from the weak decay into a two-body final state.
• ### Measurement of the $\beta^+$ and orbital electron-capture decay rates in fully-ionized, hydrogen-like, and helium-like $^{140}$Pr ions(0711.3709)

Nov. 23, 2007 nucl-ex
We report on the first measurement of the $\beta^+$- and orbital electron capture decay rates of $^{140}$Pr nuclei with the most simple electron configurations: bare nuclei, hydrogen-like and helium-like ions. The measured electron capture decay constant of hydrogen-like $^{140}$Pr$^{58+}$ ions is about 50% larger than that of helium-like $^{140}$Pr$^{57+}$ ions. Moreover, $^{140}$Pr ions with one bound electron decay faster than neutral $^{140}$Pr$^{0+}$ atoms with 59 electrons. To explain this peculiar observation one has to take into account the conservation of the total angular momentum, since only particular spin orientations of the nucleus and of the captured electron can contribute to the allowed decay.
• ### New Mass and Lifetime Measurements of $^{152}$Sm Projectile Fragments with Time-Resolved Schottky Mass Spectrometry(nucl-ex/0509019)

Sept. 15, 2005 nucl-ex
The FRS-ESR facilities at GSI provide unique conditions for precision measurements with stored exotic nuclei over a large range in the chart of nuclides. In the present experiment the exotic nuclei were produced via fragmentation of $^{152}$Sm projectiles in a thick beryllium target at 500-600 MeV/u, separated in-flight with the fragment separator FRS, and injected into the storage-cooler ring ESR. Mass and lifetime measurements have been performed with bare and few-electron ions. The experiment and first results will be presented in this contribution.
• ### Isospin Dependence in the Odd-Even Staggering of Nuclear Binding Energies(nucl-th/0508003)

Aug. 2, 2005 nucl-ex, nucl-th
The FRS-ESR facility at GSI provides unique conditions for precision measurements of large areas on the nuclear mass surface in a single experiment. Values for masses of 604 neutron-deficient nuclides (30<=Z<=92) were obtained with a typical uncertainty of 30 microunits. The masses of 114 nuclides were determined for the first time. The odd-even staggering (OES) of nuclear masses was systematically investigated for isotopic chains between the proton shell closures at Z=50 and Z=82. The results were compared with predictions of modern nuclear models. The comparison revealed that the measured trend of OES is not reproduced by the theories fitted to masses only. The spectral pairing gaps extracted from models adjusted to both masses, and density related observables of nuclei agree better with the experimental data.


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 Reliability Checks on the Indo-US Stellar Spectral Library Using Artificial Neural Networks and Principal Component AnalysisThe Indo-US coudé feed stellar spectral library (CFLIB) madeavailable to the astronomical community recently by Valdes et al. (2004,ApJS, 152, 251) contains spectra of 1273 stars in the spectral region3460 to 9464Å at a high resolution of 1Å (FWHM) and a widerange of spectral types. Cross-checking the reliability of this databaseis an important and desirable exercise since a number of stars in thisdatabase have no known spectral types and a considerable fraction ofstars has not so complete coverage in the full wavelength region of3460-9464Å resulting in gaps ranging from a few Å to severaltens of Å. We use an automated classification scheme based onArtificial Neural Networks (ANN) to classify all 1273 stars in thedatabase. In addition, principal component analysis (PCA) is carried outto reduce the dimensionality of the data set before the spectra areclassified by the ANN. Most importantly, we have successfullydemonstrated employment of a variation of the PCA technique to restorethe missing data in a sample of 300 stars out of the CFLIB. Radial Velocities of Late-Type Field Subgiant StarsHigh-dispersion coudé spectra were observed and measured for 43field subgiants of the G and K spectral types, with the intent ofsearching for hitherto undiscovered spectroscopic binaries. Statisticalanalysis of the measurements revealed no definite but two possible newbinaries. We present the data and discuss the statistical analysis usedto test for new binaries. Additionally, we discuss the techniques forhigh precision of radial-velocity measurement, and the systematic errorsthat interfere with that goal. CHARM2: An updated Catalog of High Angular Resolution MeasurementsWe present an update of the Catalog of High Angular ResolutionMeasurements (CHARM, Richichi & Percheron \cite{CHARM}, A&A,386, 492), which includes results available until July 2004. CHARM2 is acompilation of direct measurements by high angular resolution methods,as well as indirect estimates of stellar diameters. Its main goal is toprovide a reference list of sources which can be used for calibrationand verification observations with long-baseline optical and near-IRinterferometers. Single and binary stars are included, as are complexobjects from circumstellar shells to extragalactic sources. The presentupdate provides an increase of almost a factor of two over the previousedition. Additionally, it includes several corrections and improvements,as well as a cross-check with the valuable public release observationsof the ESO Very Large Telescope Interferometer (VLTI). A total of 8231entries for 3238 unique sources are now present in CHARM2. Thisrepresents an increase of a factor of 3.4 and 2.0, respectively, overthe contents of the previous version of CHARM.The catalog is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/431/773 Local kinematics of K and M giants from CORAVEL/Hipparcos/Tycho-2 data. Revisiting the concept of superclustersThe availability of the Hipparcos Catalogue has triggered many kinematicand dynamical studies of the solar neighbourhood. Nevertheless, thosestudies generally lacked the third component of the space velocities,i.e., the radial velocities. This work presents the kinematic analysisof 5952 K and 739 M giants in the solar neighbourhood which includes forthe first time radial velocity data from a large survey performed withthe CORAVEL spectrovelocimeter. It also uses proper motions from theTycho-2 catalogue, which are expected to be more accurate than theHipparcos ones. An important by-product of this study is the observedfraction of only 5.7% of spectroscopic binaries among M giants ascompared to 13.7% for K giants. After excluding the binaries for whichno center-of-mass velocity could be estimated, 5311 K and 719 M giantsremain in the final sample. The UV-plane constructed from these datafor the stars with precise parallaxes (σπ/π≤20%) reveals a rich small-scale structure, with several clumpscorresponding to the Hercules stream, the Sirius moving group, and theHyades and Pleiades superclusters. A maximum-likelihood method, based ona Bayesian approach, has been applied to the data, in order to make fulluse of all the available stars (not only those with precise parallaxes)and to derive the kinematic properties of these subgroups. Isochrones inthe Hertzsprung-Russell diagram reveal a very wide range of ages forstars belonging to these groups. These groups are most probably relatedto the dynamical perturbation by transient spiral waves (as recentlymodelled by De Simone et al. \cite{Simone2004}) rather than to clusterremnants. A possible explanation for the presence of younggroup/clusters in the same area of the UV-plane is that they have beenput there by the spiral wave associated with their formation, while thekinematics of the older stars of our sample has also been disturbed bythe same wave. The emerging picture is thus one of dynamical streamspervading the solar neighbourhood and travelling in the Galaxy withsimilar space velocities. The term dynamical stream is more appropriatethan the traditional term supercluster since it involves stars ofdifferent ages, not born at the same place nor at the same time. Theposition of those streams in the UV-plane is responsible for the vertexdeviation of 16.2o ± 5.6o for the wholesample. Our study suggests that the vertex deviation for youngerpopulations could have the same dynamical origin. The underlyingvelocity ellipsoid, extracted by the maximum-likelihood method afterremoval of the streams, is not centered on the value commonly acceptedfor the radial antisolar motion: it is centered on < U > =-2.78±1.07 km s-1. However, the full data set(including the various streams) does yield the usual value for theradial solar motion, when properly accounting for the biases inherent tothis kind of analysis (namely, < U > = -10.25±0.15 kms-1). This discrepancy clearly raises the essential questionof how to derive the solar motion in the presence of dynamicalperturbations altering the kinematics of the solar neighbourhood: doesthere exist in the solar neighbourhood a subset of stars having no netradial motion which can be used as a reference against which to measurethe solar motion?Based on observations performed at the Swiss 1m-telescope at OHP,France, and on data from the ESA Hipparcos astrometry satellite.Full Table \ref{taba1} is only available in electronic form at the CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/430/165} A near-infrared stellar spectral library: I. H-band spectra.This paper presents the H band near-infrared (NIR) spectral library of135 solar type stars covering spectral types O5-M3 and luminosityclasses I-V as per MK classification. The observations were carried outwith 1.2 meter Gurushikhar Infrared Telescope (GIRT), at Mt. Abu, Indiausing a NICMOS3 HgCdTe 256 x 256 NIR array based spectrometer. Thespectra have a moderate resolution of 1000 (about 16 A) at the H bandand have been continuum shape corrected to their respective effectivetemperatures. This library and the remaining ones in J and K bands oncereleased will serve as an important database for stellar populationsynthesis and other applications in conjunction with the newly formedlarge optical coude feed stellar spectral library of Valdes et al.(2004). The complete H-Band library is available online at: http://vo.iucaa.ernet.in/~voi/NIR_Header.html The Indo-US Library of Coudé Feed Stellar SpectraWe have obtained spectra for 1273 stars using the 0.9 m coudéfeed telescope at Kitt Peak National Observatory. This telescope feedsthe coudé spectrograph of the 2.1 m telescope. The spectra havebeen obtained with the no. 5 camera of the coudé spectrograph anda Loral 3K×1K CCD. Two gratings have been used to provide spectralcoverage from 3460 to 9464 Å, at a resolution of ~1 Å FWHMand at an original dispersion of 0.44 Å pixel-1. For885 stars we have complete spectra over the entire 3460 to 9464 Åwavelength region (neglecting small gaps of less than 50 Å), andpartial spectral coverage for the remaining stars. The 1273 stars havebeen selected to provide broad coverage of the atmospheric parametersTeff, logg, and [Fe/H], as well as spectral type. The goal ofthe project is to provide a comprehensive library of stellar spectra foruse in the automated classification of stellar and galaxy spectra and ingalaxy population synthesis. In this paper we discuss thecharacteristics of the spectral library, viz., details of theobservations, data reduction procedures, and selection of stars. We alsopresent a few illustrations of the quality and information available inthe spectra. The first version of the complete spectral library is nowpublicly available from the National Optical Astronomy Observatory(NOAO) via ftp and http. High-Precision Near-Infrared Photometry of a Large Sample of Bright Stars Visible from the Northern HemisphereWe present the results of 8 yr of infrared photometric monitoring of alarge sample of stars visible from Teide Observatory (Tenerife, CanaryIslands). The final archive is made up of 10,949 photometric measuresthrough a standard InSb single-channel photometer system, principally inJHK, although some stars have measures in L'. The core of this list ofstars is the standard-star list developed for the Carlos SánchezTelescope. A total of 298 stars have been observed on at least twooccasions on a system carefully linked to the zero point defined byVega. We present high-precision photometry for these stars. The medianuncertainty in magnitude for stars with a minimum of four observationsand thus reliable statistics ranges from 0.0038 mag in J to 0.0033 magin K. Many of these stars are faint enough to be observable with arraydetectors (42 are K>8) and thus to permit a linkage of the bright andfaint infrared photometric systems. We also present photometry of anadditional 25 stars for which the original measures are no longeravailable, plus photometry in L' and/or M of 36 stars from the mainlist. We calculate the mean infrared colors of main-sequence stars fromA0 V to K5 V and show that the locus of the H-K color is linearlycorrelated with J-H. The rms dispersion in the correlation between J-Hand H-K is 0.0073 mag. We use the relationship to interpolate colors forall subclasses from A0 V to K5 V. We find that K and M main-sequence andgiant stars can be separated on the color-color diagram withhigh-precision near-infrared photometry and thus that photometry canallow us to identify potential mistakes in luminosity classclassification. Velocity variability of semiregular and irregular variablesWe compare velocities from near infrared lines with center-of-massvelocities for a sample of semiregular and irregular variables to searchfor indications for a convective blueshift. It is shown that a generalblueshift is present but that the light variability is obviously notdominated by convective cells but rather by stellar pulsation. All starsof our sample show a similar shape and amplitude in the velocityvariations. Long secondary periods are a common feature in these objectsand strongly influence the measured velocity shifts. The star V366 Aqlis found to be the first SRV showing line doubling. A catalogue of calibrator stars for long baseline stellar interferometryLong baseline stellar interferometry shares with other techniques theneed for calibrator stars in order to correct for instrumental andatmospheric effects. We present a catalogue of 374 stars carefullyselected to be used for that purpose in the near infrared. Owing toseveral convergent criteria with the work of Cohen et al.(\cite{cohen99}), this catalogue is in essence a subset of theirself-consistent all-sky network of spectro-photometric calibrator stars.For every star, we provide the angular limb-darkened diameter, uniformdisc angular diameters in the J, H and K bands, the Johnson photometryand other useful parameters. Most stars are type III giants withspectral types K or M0, magnitudes V=3-7 and K=0-3. Their angularlimb-darkened diameters range from 1 to 3 mas with a median uncertaintyas low as 1.2%. The median distance from a given point on the sky to theclosest reference is 5.2degr , whereas this distance never exceeds16.4degr for any celestial location. The catalogue is only available inelectronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr(130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/393/183 CHARM: A Catalog of High Angular Resolution MeasurementsThe Catalog of High Angular Resolution Measurements (CHARM) includesmost of the measurements obtained by the techniques of lunaroccultations and long-baseline interferometry at visual and infraredwavelengths, which have appeared in the literature or have otherwisebeen made public until mid-2001. A total of 2432 measurements of 1625sources are included, along with extensive auxiliary information. Inparticular, visual and infrared photometry is included for almost allthe sources. This has been partly extracted from currently availablecatalogs, and partly obtained specifically for CHARM. The main aim is toprovide a compilation of sources which could be used as calibrators orfor science verification purposes by the new generation of largeground-based facilities such as the ESO Very Large Interferometer andthe Keck Interferometer. The Catalog is available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/386/492, and from theauthors on CD-Rom. On the Wilson-Bappu relationship in the Mg II k lineAn investigation is carried out on the Wilson-Bappu effect in the Mg Iik line at 2796.34 Å. The work is based on a selection of 230 starsobserved by both the IUE and HIPPARCOS satellites, covering a wide rangeof spectral types (F to M) and absolute visual magnitudes (-5.4<=MV <=9.0). A semi-automatic procedure is used to measurethe line widths, which applies also in the presence of strong centralabsorption reversal. The Wilson-Bappu relationship here provided isconsidered to represent an improvement over previous recent results forthe considerably larger data sample used, as well as for a properconsideration of the measurement errors. No evidence has been found fora possible dependence of the WB effect on stellar metallicity andeffective temperature. Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statisticsThe Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521 Sixth Catalogue of Fundamental Stars (FK6). Part III. Additional fundamental stars with direct solutionsThe FK6 is a suitable combination of the results of the HIPPARCOSastrometry satellite with ground-based data, measured over a longinterval of time and summarized mainly in the FK5. Part III of the FK6(abbreviated FK6(III)) contains additional fundamental stars with directsolutions. Such direct solutions are appropriate for single stars or forobjects which can be treated like single stars. Part III of the FK6contains in total 3272 stars. Their ground-based data stem from thebright extension of the FK5 (735 stars), from the catalogue of remainingSup stars (RSup, 732 stars), and from the faint extension of the FK5(1805 stars). From the 3272 stars in Part III, we have selected 1928objects as "astrometrically excellent stars", since their instantaneousproper motions and their mean (time-averaged) ones do not differsignificantly. Hence most of the astrometrically excellent stars arewell-behaving "single-star candidates" with good astrometric data. Thesestars are most suited for high-precision astrometry. On the other hand,354 of the stars in Part III are Δμ binaries in the sense ofWielen et al. (1999). Many of them are newly discovered probablebinaries with no other hitherto known indication of binarity. The FK6gives, besides the classical "single-star mode" solutions (SI mode),other solutions which take into account the fact that hidden astrometricbinaries among "apparently single-stars" introduce sizable "cosmicerrors" into the quasi-instantaneously measured HIPPARCOS proper motionsand positions. The FK6 gives, in addition to the SI mode, the "long-termprediction (LTP) mode" and the "short-term prediction (STP) mode". TheseLTP and STP modes are on average the most precise solutions forapparently single stars, depending on the epoch difference with respectto the HIPPARCOS epoch of about 1991. The typical mean error of anFK6(III) proper motion in the single-star mode is 0.59 mas/year. This isa factor of 1.34 better than the typical HIPPARCOS errors for thesestars of 0.79 mas/year. In the long-term prediction mode, in whichcosmic errors are taken into account, the FK6(III) proper motions have atypical mean error of 0.93 mas/year, which is by a factor of about 2better than the corresponding error for the HIPPARCOS values of 1.83mas/year (cosmic errors included). Rotation and lithium in single giant starsIn the present work, we study the link between rotation and lithiumabundance in giant stars of luminosity class III, on the basis of alarge sample of 309 single stars of spectral type F, G and K. We havefound a trend for a link between the discontinuity in rotation at thespectral type G0III and the behavior of lithium abundances around thesame spectral type. The present work also shows that giant starspresenting the highest lithium contents, typically stars earlier thanG0III, are those with the highest rotation rates, pointing for adependence of lithium content on rotation, as observed for otherluminosity classes. Giant stars later than G0III present, as a rule, thelowest rotation rates and lithium contents. A large spread of about fivemagnitudes in lithium abundance is observed for the slow rotators.Finally, single giant stars with masses 1.5 < M/Msun<=2.5 show a clearest trend for a correlation between rotational velocityand lithium abundance. Based on observations collected at theObservatoire de Haute -- Provence (France) and at the European SouthernObservatory, La Silla (Chile). Table 2 is only available electronicallywith the On-Line publication athttp://link.springer.de/link/service/00230/ Spectral Irradiance Calibration in the Infrared. X. A Self-Consistent Radiometric All-Sky Network of Absolutely Calibrated Stellar SpectraWe start from our six absolutely calibrated continuous stellar spectrafrom 1.2 to 35 μm for K0, K1.5, K3, K5, and M0 giants. These wereconstructed as far as possible from actual observed spectral fragmentstaken from the ground, the Kuiper Airborne Observatory, and the IRAS LowResolution Spectrometer, and all have a common calibration pedigree.From these we spawn 422 calibrated spectral templates'' for stars withspectral types in the ranges G9.5-K3.5 III and K4.5-M0.5 III. Wenormalize each template by photometry for the individual stars usingpublished and/or newly secured near- and mid-infrared photometryobtained through fully characterized, absolutely calibrated,combinations of filter passband, detector radiance response, and meanterrestrial atmospheric transmission. These templates continue ourongoing effort to provide an all-sky network of absolutely calibrated,spectrally continuous, stellar standards for general infrared usage, allwith a common, traceable calibration heritage. The wavelength coverageis ideal for calibration of many existing and proposed ground-based,airborne, and satellite sensors, particularly low- tomoderate-resolution spectrometers. We analyze the statistics of probableuncertainties, in the normalization of these templates to actualphotometry, that quantify the confidence with which we can assert thatthese templates truly represent the individual stars. Each calibratedtemplate provides an angular diameter for that star. These radiometricangular diameters compare very favorably with those directly observedacross the range from 1.6 to 21 mas. A catalog of rotational and radial velocities for evolved starsRotational and radial velocities have been measured for about 2000evolved stars of luminosity classes IV, III, II and Ib covering thespectral region F, G and K. The survey was carried out with the CORAVELspectrometer. The precision for the radial velocities is better than0.30 km s-1, whereas for the rotational velocity measurementsthe uncertainties are typically 1.0 km s-1 for subgiants andgiants and 2.0 km s-1 for class II giants and Ib supergiants.These data will add constraints to studies of the rotational behaviourof evolved stars as well as solid informations concerning the presenceof external rotational brakes, tidal interactions in evolved binarysystems and on the link between rotation, chemical abundance and stellaractivity. In this paper we present the rotational velocity v sin i andthe mean radial velocity for the stars of luminosity classes IV, III andII. Based on observations collected at the Haute--Provence Observatory,Saint--Michel, France and at the European Southern Observatory, LaSilla, Chile. Table \ref{tab5} also available in electronic form at CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Catalogs of temperatures and [Fe/H] averages for evolved G and K starsA catalog of mean values of [Fe/H] for evolved G and K stars isdescribed. The zero point for the catalog entries has been establishedby using differential analyses. Literature sources for those entries areincluded in the catalog. The mean values are given with rms errors andnumbers of degrees of freedom, and a simple example of the use of thesestatistical data is given. For a number of the stars with entries in thecatalog, temperatures have been determined. A separate catalogcontaining those data is briefly described. Catalog only available atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html A Search for Lithium-Rich Giants among Stars with Infrared ExcessesThe unusual nature of the single, rapidly rotating, lithium-rich K giantHDE 233517, which is currently undergoing significant mass loss,prompted a search for giants with similar properties. High-dispersionspectroscopic observations were obtained of HD 219025, a knownlithium-rich infrared-excess giant, plus 39 stars from a list of G and Kgiants with excess far-infrared emission. The projected rotationalvelocities of the vast majority of infrared-excess giants appear to besimilar to those of normal G and K giants. Six giants have lithiumabundances at or above theoretical upper envelope values. The percentageof such stars in the sample of 39 infrared-excess giants is similar tothat of normal giants. The three giants with the largest lithiumabundances have previously been discovered. None of the sample of 39giants have an Hα line similar to the broadened and veryasymmetric line of HDE 233517. The star with optical properties mostsimilar to HDE 233517 is HD 219025. Infrared standards for ISO. I. A new calibration of mid infrared photometryWe present N, 8.7 mu m, 9.8 mu m 12.5 mu m and Q bolometry of 26 starswhich were observed on the IRTF. These are primarily K giants which havebeen well measured at other wavelengths and are chosen to be single andnon-variable. Hence the data presented provides a new homogeneous set ofmid IR standards. As a test of part of the calibration strategy of ISOover this wavelength range, the zero points have been set using theKurucz model grids (1993) to predict the mid IR magnitudes from near IRdata. An analysis of the errors involved is presented and a comparisonwith more direct methods for the determination of the zero pointssuggest an possible error of 0.015 mags, although the source of thiserror is unclear as it is at the level of the uncertainty in the moredirect methods. The effect of the SiO fundamental on the spectral energydistributions of K giants is discussed. Towards a fundamental calibration of stellar parameters of A, F, G, K dwarfs and giantsI report on the implementation of the empirical surface brightnesstechnique using the near-infrared Johnson broadband { (V-K)} colour assuitable sampling observable aimed at providing accurate effectivetemperatures of 537 dwarfs and giants of A-F-G-K spectral-type selectedfor a flux calibration of the Infrared Space Observatory (ISO). Thesurface brightness-colour correlation is carefully calibrated using aset of high-precision angular diameters measured by moderninterferometry techniques. The stellar sizes predicted by thiscorrelation are then combined with the bolometric flux measurementsavailable for a subset of 327 ISO standard stars in order to determineone-dimensional { (T, V-K)} temperature scales of dwarfs and giants. Theresulting very tight relationships show an intrinsic scatter induced byobservational photometry and bolometric flux measurements well below thetarget accuracy of +/- 1 % required for temperature determinations ofthe ISO standards. Major improvements related to the actual directcalibration are the high-precision broadband { K} magnitudes obtainedfor this purpose and the use of Hipparcos parallaxes for dereddeningphotometric data. The temperature scale of F-G-K dwarfs shows thesmallest random errors closely consistent with those affecting theobservational photometry alone, indicating a negligible contributionfrom the component due to the bolometric flux measurements despite thewide range in metallicity for these stars. A more detailed analysisusing a subset of selected dwarfs with large metallicity gradientsstrongly supports the actual bolometric fluxes as being practicallyunaffected by the metallicity of field stars, in contrast with recentresults claiming somewhat significant effects. The temperature scale ofF-G-K giants is affected by random errors much larger than those ofdwarfs, indicating that most of the relevant component of the scattercomes from the bolometric flux measurements. Since the giants have smallmetallicities, only gravity effects become likely responsible for theincreased level of scatter. The empirical stellar temperatures withsmall model-dependent corrections are compared with the semiempiricaldata by the Infrared Flux Method (IRFM) using the large sample of 327comparison stars. One major achievement is that all empirical andsemiempirical temperature estimates of F-G-K giants and dwarfs are foundto be closely consistent between each other to within +/- 1 %. However,there is also evidence for somewhat significant differential effects.These include an average systematic shift of (2.33 +/- 0.13) % affectingthe A-type stars, the semiempirical estimates being too low by thisamount, and an additional component of scatter as significant as +/- 1 %affecting all the comparison stars. The systematic effect confirms theresults from other investigations and indicates that previousdiscrepancies in applying the IRFM to A-type stars are not yet removedby using new LTE line-blanketed model atmospheres along with the updatedabsolute flux calibration, whereas the additional random component isfound to disappear in a broadband version of the IRFM using an infraredreference flux derived from wide rather than narrow band photometricdata. Table 1 and 2 are only available in the electronic form of thispaper The rotation measurement of 12 late-type binaries.Not Available The Tokyo PMC catalog 90-93: Catalog of positions of 6649 stars observed in 1990 through 1993 with Tokyo photoelectric meridian circleThe sixth annual catalog of the Tokyo Photoelectric Meridian Circle(PMC) is presented for 6649 stars which were observed at least two timesin January 1990 through March 1993. The mean positions of the starsobserved are given in the catalog at the corresponding mean epochs ofobservations of individual stars. The coordinates of the catalog arebased on the FK5 system, and referred to the equinox and equator ofJ2000.0. The mean local deviations of the observed positions from theFK5 catalog positions are constructed for the basic FK5 stars to comparewith those of the Tokyo PMC Catalog 89 and preliminary Hipparcos resultsof H30. Rotational Velocities of Late-Type StarsA calibration based on the results of Gray has been used to determineprojected rotational velocities for 133 bright stars with spectral typesof F, G, or K, most of which appear in {\it The Bright Star Catalogue}.The vast majority have {\it v} sin {\it i} $\leq$ 10 km s$^{-1}$ and,thus, are slow rotators. With the new calibration, projected rotationalvelocities have been determined for a sample of 111 late-type stars,most of which are chromospherically active. Some of the stars have hadtheir rotational velocities measured for the first time. (SECTION:Stars) Classification and Identification of IRAS Sources with Low-Resolution SpectraIRAS low-resolution spectra were extracted for 11,224 IRAS sources.These spectra were classified into astrophysical classes, based on thepresence of emission and absorption features and on the shape of thecontinuum. Counterparts of these IRAS sources in existing optical andinfrared catalogs are identified, and their optical spectral types arelisted if they are known. The correlations between thephotospheric/optical and circumstellar/infrared classification arediscussed. Accurate Two-dimensional Classification of Stellar Spectra with Artificial Neural NetworksWe present a solution to the long-standing problem of automaticallyclassifying stellar spectra of all temperature and luminosity classeswith the accuracy shown by expert human classifiers. We use the 15Angstroms resolution near-infrared spectral classification systemdescribed by Torres-Dodgen & Weaver in 1993. Using the spectrum withno manual intervention except wavelength registration, artificial neuralnetworks (ANNs) can classify these spectra with Morgan-Keenan types withan accuracy comparable to that obtained by human experts using 2Angstroms resolution blue spectra, which is about 0.5 types (subclasses)in temperature and about 0.25 classes in luminosity. Accuratetemperature classification requires a hierarchy of ANNs, whileluminosity classification is most successful with a single ANN. Wepropose an architecture for a fully automatic classification system. A catalogue of [Fe/H] determinations: 1996 editionA fifth Edition of the Catalogue of [Fe/H] determinations is presentedherewith. It contains 5946 determinations for 3247 stars, including 751stars in 84 associations, clusters or galaxies. The literature iscomplete up to December 1995. The 700 bibliographical referencescorrespond to [Fe/H] determinations obtained from high resolutionspectroscopic observations and detailed analyses, most of them carriedout with the help of model-atmospheres. The Catalogue is made up ofthree formatted files: File 1: field stars, File 2: stars in galacticassociations and clusters, and stars in SMC, LMC, M33, File 3: numberedlist of bibliographical references The three files are only available inelectronic form at the Centre de Donnees Stellaires in Strasbourg, viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5), or viahttp://cdsweb.u-strasbg.fr/Abstract.html The photoelectric astrolabe catalogue of Yunnan Observatory (YPAC).The positions of 53 FK5, 70 FK5 Extension and 486 GC stars are given forthe equator and equinox J2000.0 and for the mean observation epoch ofeach star. They are determined with the photoelectric astrolabe ofYunnan Observatory. The internal mean errors in right ascension anddeclination are +/- 0.046" and +/- 0.059", respectively. The meanobservation epoch is 1989.51. Hybrid stars and the reality of "dividing lines" among G to K bright giants and supergiants.We present results of pointed ROSAT PSPC observations of 15 hybridstars/candidates, which have been analyzed in a homogenous way. 7 ofthese stars were observed in X-rays for the first time. 12 out of 15hybrid stars have been detected as X-ray sources, some of them close tothe detection limit. We conclude that essentially all hybrid stars asdefined by the simultaneous presence of transition region line emissionand cool stellar winds are X-ray sources if exposed sufficiently deep.The X-ray luminosities of hybrid stars cover a range between 2x10^27^and ~10^30^erg/s. Their X-ray surface fluxes can be as low as =~20erg/cm^2^/s and thus considerably lower than those of normal luminosityclass (LC) III giants. X-ray spectra of hybrid stars tend to be harderthan that of normal LC III giants, moreover, the X-ray brightest starshave the hardest spectra. We find that for K II giants the normalizedX-ray flux versus C IV flux obeys a power law with an exponent a=2.9,steeper than among normal giants (1.5). Hybrid K II stars are X-rayunderluminous by a factor of 5 to 20 compared to LC III giants at thesame level of normalized CIV flux f_CIV_/f_bol_; hybrid G supergiantsare even more X-ray deficient. We reanalyze the CaII wind dividing lineand find it vertical at B-V=1.45 for LC III giants. It is nearlyhorizontal between B-V=1.45 and 1.0 (at M_bol_=~-2...-3), and not welldefined for supergiants with B-V<1.0. We therefore suggest thatpossibly all LC II and Ib G and K giants are hybrid stars and that the"dividing line" concept in its simplest form is not valid for G/K giantsbrighter than M_bol_=~-2. Hybrid stars are supposed to be evolvedintermediate mass stars and their coronal activity may in principle bedetermined by the individual history of each star. Nine Seasons of Velocity Measurements in the Draco and Ursa Minor Dwarf Spheroidal Galaxies with the MMT EchelleWe have used the Multiple Mirror Telescope echelle spectrograph tomeasure 112 velocities of 42 stars in the Draco and Ursa Minor dwarfspheroidal galaxies and three velocities of three foreground starsbetween 1982 April and 1990 September. We used 11 A resolution spectraobtained with the MX multifiber spectrograph at the Steward 90" to findadditional giant candidates; 5 UMi and 13 Draco stars were then observedat the MMT and added to the original sample of velocity members. Inaddition, the MX spectra were used to eliminate 74 stars in thedirection of UMI and 59 stars in Draco as likely foreground dwarfs. Wedetected 7 velocity variables, defined as those stars whose probabilityof exceeding the measured X^2^ by chance is less than 1.5%. Three ofthese stars are Carbon (C) stars (UMi K and VA 335 and Draco C1); twohave emission lines (Draco CI and UMi M). We show that the C star DracoC4, with a proper motion membership probability of 7%, has a velocityconsistent with membership. It is not surprising that these C (mostlikely CH) stars are binaries because McClure has shown that mostGalactic CH stars are in binary systems. Of the remaining 35 stars, only4 are velocity variables, with measured velocity extrema of 29.1 kms^-1^ (UMi M), 7.2 km s^-1^ (Draco XI-2), 9.0 km s^-1^ (Draco 24), and8.3 km s^-1^ (Draco 473). The velocity dispersions are 10.1 +/- 1.7 kms^-1^ for UMi, and 9.9 +/- 1.4 km s^-1^ for Draco. These dispersionschange to 10.5 +/- 2.0 for UMi, and 8.2 +?- 1.3 for Draco if weeliminate the velocity variables. Our dispersion for UMi differs fromthat of Hargreaves et al. [MNRAS, 271,693 (1994b)] by 1.3σ of thecombined errors. These velocities are combined with the one-componentKing models of Pryor & Kormendy [AJ, 100,127 (1990)] to give M/L =73 for UMi, and 77 for Draco. H-alpha measurements for cool giantsThe H-alpha line in a cool star is usually an indication of theconditions in its chromosphere. I have collected H-alpha spectra of manynorthern G-M stars, which show how the strength and shape of the H-alphaline change with spectral type. These observations detect surprisinglittle variation in absoption-line depth (Rc approximately0.23 +/- 0.08), linewidth (FWHD approximately 1.44 +/- 0.22 A), orequivalent width (EW approximately 1.12 +/- 0.17 A) among G5-M5 IIIgiants. Lines in the more luminous stars tend to be broader and strongerby 30%-40% than in the Class III giants, while the H-alpha absorptiontends to weaken among the cooler M giants. Velocities of H-alpha andnearby photospheric lines are the same to within 1.4 +/- 4.4 km/s forthe whole group. To interpret these observations, I have calculatedH-alpha profiles, Ly-alpha strengths, and (C II) strengths for a seriesof model chromospheres representing a cool giant star like alpha Tau.Results are sensitive to the mass of the chromosphere, to chromospherictemperature, to clumping of the gas, and to the assumed physics of lineformation. The ubiquitous nature of H-alpha in cool giants and the greatdepth of observed lines argue that chromospheres of giants cover theirstellar disks uniformly and are homogeneous on a large scale. This isquite different from conditions on a small scale: To obtain a highenough electron density with the theoretical models, both to explain theexitation of hydrogen and possibly also to give the observed C IImultiplet ratios, the gas is probably clumped. The 6540-6580 A spectraof 240 stars are plotted in an Appendix, which identifies the date ofobservation and marks positions of strong telluric lines on eachspectrum. I assess the effects of telluric lines and estimates that thestrength of scattered light is approximately 5% of the continuum inthese spectra. I give the measurements of H-alpha as well as equivalentwidths of two prominent photospheric lines, Fe I lambda 6546 and Ca Ilambda 6572, which strengthen with advancing spectral type.
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format: plain


text:
# Math Help - Trig. problems.

1. ## Trig. problems.

Hi,

Can someone help me to do these problems?

1).If tan(θ+α)-(3+2√2)tanθ = 0,
Prove that, sin(2θ+α )= √2sinα

2).Prove that, cos⁻¹x-sin⁻¹x= π/6

2. Hello, Malsha!

2) Prove that: cos⁻¹x-sin⁻¹x= π/6
Could that be: . $\cos^{\text{-}1}x - \sin^{\text{-}1}x \:=\:\frac{\pi}{6}\;?\quad\hdots$ This is not true!

$\text{We have: }\;\underbrace{\cos^{\text{-}1}x}_{\alpha} - \underbrace{\sin^{\text{-}1}x}_{\beta}$

That is: . $\begin{array}{ccc}\alpha \:=\:\cos^{-1}x & \Rightarrow & \cos\alpha \:=\:x \\
\beta \:=\:\sin^{-1}x & \Rightarrow & \sin\beta \:=\:x \end{array}$

We have: . $\begin{array}{ccccc}\cos\alpha &=&\dfrac{x}{1} &=& \dfrac{adj}{hyp} \\ \\[-3mm] \sin\beta &=& \dfrac{x}{1} &=& \dfrac{opp}{hyp} \end{array}$

Hence, the two angles are in this triangle.
Code:
                        *
* β*
1   *     *
*        *
*           *
* α            *
*  *  *  *  *  *  *
x

And we see that the two angles are complementary: . $\alpha + \beta \:=\:\frac{\pi}{2}$

So their sum is a constant, but not their difference.


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# How do you graph the quadratic function and identify the vertex and axis of symmetry for y=-1/6x^2+x-3?

Feb 27, 2017

See explanation

#### Explanation:

As the coefficient of ${x}^{2}$ is negative the graph is of general shape $\cap$

There is no stipulation in the question about how you are to determine the information so I chose the following method

$\textcolor{b l u e}{\text{Determine the y-intercept}}$

$\textcolor{g r e e n}{\text{y-intercept is at the same value as the constant ie } y = - 3}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the vertex}}$

Write as $- \frac{1}{6} \left({x}^{2} - 6 x\right) - 3$

$\textcolor{g r e e n}{{x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times \left(- 6\right) = + 3}$

Substitute $x = 3$ and we have

color(green)(y_("vertex") =-1/6( 3^2-(6xx3))-3" "=" "-1.5)

color(green)("Vertex "->(x,y)=(3,-3/2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the x-intercepts}}$

As the graph is of form $\cap$ and ${y}_{\text{vertex}} = - 1.5$

The curve doe NOT cross the x-axis.

So there is no solution to $\text{ } - \frac{1}{6} {x}^{2} + x - 3 = 0$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the axis of symmetry}}$

The axis of symmetry passes through the vertex so it has the x value as the vertex.

$\textcolor{g r e e n}{\text{Axis of symmetry } \to x = 3}$


text:
TITLE

# Effect of Non-Uniform Basic Temperature Gradient on the Onset of Rayleigh-BÃ©nard-Marangoni Electro-Convection in a Micropolar Fluid

AUTHOR(S)
Joseph, Thadathil Varghese; Manjunath, Sree Ramaiah; Pranesh, Subbarama
PUB. DATE
August 2013
SOURCE
Applied Mathematics;Aug2013, Vol. 4 Issue 8, p1180
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-BÃ©nard-Marangoni convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed.
ACCESSION #
91671582

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# Normalized sinc

The normalized sinc function $\mathrm{sinc}_{\pi}$ is defined by $$\mathrm{sinc}_{\pi} = \left\{ \begin{array}{ll} \dfrac{\sin(\pi z)}{z}, & \quad z \neq 0 \\ 1, & \quad z=0. \end{array} \right.$$


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# DPF 2011

8-13 August 2011
Rhode Island Convention Center
US/Eastern timezone

## Triangularity and Dipole Assymetry in Ideal Hydrodynamics

9 Aug 2011, 17:15
20m
552 B (Rhode Island Convention Center)

### 552 B

#### Rhode Island Convention Center

Parallel contribution Heavy Ion Physics/Hot and Dense QCD

### Speaker

li Yan (Stony Brook University)

### Description

We introduce a cummulant expansion to parameterize possible initial conditions in heavy ion collisions. We show that the cummulant expansion converges and can systematically reporduce the results of the Glauber type initial conditions. At third order in the gradient expansion, the cummulants are described with the triangularity $\llangle r^3 \cos3(\phi - \psi_{1,3} ) \rrangle$, and a dipole assymetry, $\llangle r^3 \cos(\phi- \psi_{1,3}) \rrangle$. We show that the orientation angle of the dipole assymetry $\psi_{1,3}$ has a $20\%$ assymetry out of plane for mid-central collisons. This leads to a small net $v_1$ out of plane. In peripheral and mid-central collisions the orientation angles $\psi_{1,3}$ and $\psi_{3,3}$ are strongly correlated, but this correlation disappears towards central collisions. We study the ideal hydrodynamic response to these cummulants and determine the associated $v_1/\epsilon_1$ and $v_3/\epsilon_3$ for a massless ideal gas. The space time development of $v_1$ and $v_3$ is clarified with figures. These figures show that $v_1$ and $v_3$ develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for $v_3$ is provisionally compared to Alver and Roland fit of STAR inclusive two particle correlation functions. Finally, we propose to measure the $v_1$ associated with the dipole assymetry by measuring $\llangle \cos(\phi - 3\Psi_{R3} + 2\Psi_{R2}) \rrangle$ where $\Psi_{R3}$ is an experimental estimate for the triangular event plane while $\Psi_{R2}$ is the usual quadrupole event plane plane estimate. This experimental measurement would provide convincing evidence for the strong correlation between $\psi_{1,3}$ and $\psi_{3,3}$, and by association the hydrodynamic interpretation of two particle correlations at RHIC.

### Primary author

li Yan (Stony Brook University)

 Slides


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# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# polyvalm

Matrix polynomial evaluation

## Syntax

Y = polyvalm(p,X)

## Description

example

Y = polyvalm(p,X) returns the evaluation of polynomial p in a matrix sense. This evaluation is the same as substituting matrix X in the polynomial, p.

## Examples

collapse all

Find the characteristic polynomial of a Pascal Matrix of order 4.

X =  pascal(4)
X =

1     1     1     1
1     2     3     4
1     3     6    10
1     4    10    20

p = poly(X)
p =

1.0000  -29.0000   72.0000  -29.0000    1.0000

The characteristic polynomial is

Pascal matrices have the property that the vector of coefficients of the characteristic polynomial is the same forward and backward (palindromic).

Substitute the matrix, X, into the characteristic equation, p. The result is very close to being a zero matrix. This example is an instance of the Cayley-Hamilton theorem, where a matrix satisfies its own characteristic equation.

Y = polyvalm(p,X)
Y =

1.0e-10 *

-0.0013   -0.0063   -0.0104   -0.0241
-0.0048   -0.0217   -0.0358   -0.0795
-0.0114   -0.0510   -0.0818   -0.1805
-0.0228   -0.0970   -0.1553   -0.3396

## Input Arguments

collapse all

Polynomial coefficients, specified as a vector. For example, the vector [1 0 1] represents the polynomial ${x}^{2}+1$, and the vector [3.13 -2.21 5.99] represents the polynomial $3.13{x}^{2}-2.21x+5.99$.

Data Types: single | double
Complex Number Support: Yes

Input matrix, specified as a square matrix.

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

collapse all

Output polynomial coefficients, returned as a row vector.


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# A Trigonometric Dilemma!

Geometry Level 5

$\large{\sin(x) = \dfrac{x}{100}}$

Let $$A$$ be the number of real roots of the above equation if $$x$$ is measured in degrees.

Let $$B$$ be the number of real roots of the above equation if $$x$$ is measured in radians.

Find the value of $$A+B$$?

×


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>> Home >> Stata News >> Vol 31 No 1 (2016 quarter 1) >> In the spotlight: Bayesian IRT–4PL model

## In the spotlight: Bayesian IRT–4PL model

Item response theory (IRT) is often used for modeling the relationship between the latent abilities of a group of subjects and the examination items used for measuring their abilities. Stata 14 introduced a suite of commands for fitting IRT models using maximum likelihood; see, for example, "In the spotlight: irt" by Rafal Raciborski in Stata News, Volume 30 Number 3 and the [IRT] Item Response Theory Reference Manual for more details. One-parameter logistic (1PL), 2PL, and 3PL IRT models are commonly used to model binary responses. Models beyond 3PL, such as 4PL and 5PL models, have not been as widely used. One of the reasons is the difficulty in estimating the additional parameters introduced by these models using maximum likelihood. In recent years, these models have been reconsidered within the Bayesian framework (Loken and Rulison 2010; Fox 2010; Kim and Bolt 2007). In this article, we demonstrate how to fit a Bayesian 4PL model using bayesmh.

### Data

We will use the abridged version of the mathematics and science data from DeBoeck and Wilson (2004), which contains 800 student responses, y, to 9 test questions (items) intended to measure mathematical ability. To fit IRT models using bayesmh, the data must be in long form with items, item, recorded as multiple observations per subject, id.

### Model

We consider the following 4PL model,

P(Yij = 1) = c + (dc)InvLogit{ai(θjbi)}, c < d < 1

where i = 1, 2, ..., 9 and j = 1, 2, ..., 800. The 4PL model extends the 3PL model by adding an upper asymptote parameter d ≠ 1. The d parameter can be viewed as an upper limit on the probability of correct response to the ith item. The probability of giving correct answers by subjects with very high ability can thus be no greater than d. ai and bi are item-specific discrimination and difficulties. Here we consider a common guessing parameter c and a common upper asymptote parameter d, but they can also be item specific. InvLogit() is an inverse-logit function. The latent abilities θj are assumed to be normally distributed:

θjN(0,1)

A Bayesian formulation also requires prior specifications for all other model parameters. This is an important step in Bayesian modeling and must be considered carefully. For illustration, we consider the following priors.

Discrimination parameters ai's are assumed to be positive and are often modeled in the log scale. Because we have no prior knowledge about the discrimination and difficulty parameters, we assume that the prior distributions of ln(ai) and bi have support on the whole real line and are symmetric. A normal prior distribution is thus a natural choice. To control the impact of the prior on these parameters, we consider a hierarchical Bayesian model specification and introduce hyperparameters to model means and variances of the normal prior distribution.

ln(ai) ∼ N(μa,σ2a)
biN(μb,σ2b)

We use informative priors for the guessing parameter c and the upper asymptote parameter d. We assume that the prior mean of c is about 0.1 and use an inverse-gamma prior with shape 10 and scale 1 for c. We restrict d to the (0.8,1) range and assign it a Uniform(0.8,1) prior.

c ∼ InvGamma(10,1)
d ∼ Uniform(0.8,1)

The mean hyperparameters, μa and μb, and variance hyperparameters, σ2a and σ2b, require informative prior specifications. We assume that the means are centered at 0 with a variation of 0.1. To lower the variability of the ln(ai) and bi parameters, we use an inverse-gamma prior with shape 10 and scale 1 for the variance parameters so that their prior means are about 0.1.

μa,μbN(0,0.1)
σ2a,σ2b ∼ InvGamma(10,1)

### Using bayesmh

We specify the model above using bayesmh as follows:

The first two lines model the probability of success of a Bernoulli outcome as a nonlinear function of model parameters. Subject-specific parameters {subj:} and item-specific parameters {discrim:} and {diff:} are included as "random effects" in the model by using the corresponding redefine() options (available in Stata 14.1) for computational efficiency. The priors for model parameters are specified in the corresponding prior() options. We place model parameters in separate blocks to improve the simulation efficiency and provide more sensible initial values for some of the parameters. Here we treat the abilities {subj:i.id} as nuisance parameters and exclude them from the final results. We use a longer burn-in period, burnin(5000), to allow for longer adaptation of the MCMC sampler, which is needed given the large number of parameters in the model.

bayesmh produces the following results:

The upper asymptote parameter d is estimated to be 0.96 with a 95% credible interval of [0.94, 0.99]. The estimate is fairly close to one, so a simpler 3PL model may be sufficient for these data.

### Comparing models

More formally, we can compare deviance information criteria (DIC) of the 4PL and the 3PL (with d = 1) models.

The DIC of the 3PL model (not shown here) is 8049.4. The 4PL model has a lower DIC value, 8032.7, which suggests that the 4PL model provides a better fit. However, we should not rely solely on the DIC values to make our final model selection. A practitioner may still prefer the simpler 3PL model given that the upper asymptote estimate is close to one.

For more examples of Bayesian binary IRT models and details about model specifications, see our blog entry: "Bayesian binary item response theory models using bayesmh.

—Nikolay Balov
Senior Statistician and Software Developer, StataCorp

—Yulia Marchenko
Executive Director of Statistics, StataCorp

### References

De Boeck, P., and M. Wilson, ed. 2004. Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach. New York: Springer.

Fox, J.-P. 2010. Bayesian Item Response Modeling: Theory and Applications. New York: Springer.

Kim, J.-S., and D. M. Bolt. 2007. Estimating item response theory models using Markov chain Monte Carlo methods. Educational Measurement: Issues and Practice 26: 38–51.

Loken, E., and K. L. Rulison. 2010. Estimation of a four-parameter item response theory model. British Journal of Mathematical and Statistical Psychology 63: 509–525.


text:
For the representation $ho$ of the local unitary (LU) group $G$ on the $N$-fermion Hilbert space $\mathcal{V}=\wedge^N V$ with $M$-dimensional single particle space $V$, a universal subspace $\mathcal{W}\subseteq\mathcal{V}$ is a subspace that meets all $G$-orbits in $\mathcal{V}$. We focus on the case that $\mathcal{W}$ is spanned by Slater determinants $\ket{v_1}\wedge\ket{v_2}\we...\wedge\ket{v_N}$ built from orthonormal local basis ${\ket{v}}$. Hence our discussion is a fermionic analogue of the universal subspace spanned by local basis product states studied in quantum information theory. While the N=2 case has a straightforward solution based on the existence of Slater decomposition, which is an analogue of the Schmidt decomposition, for $N>2$ case the problem is nontrivial due to the lack of a similar decomposition. We introduce a configuration for the Slater determinants called single occupancy, where the single particle states ${\ket{v}}$ are paired and none of such pairs occurs entirely in $\ket{v_1}\wedge\ket{v_2}\we...\wedge\ket{v_N}$. We show that, for N=3 the subspace $\mathcal{S}$ spanned by all the single occupancy states is universal. For $M$ even, we also obtain universal subspaces of $\mathcal{S}$ whose dimensions are minimal. For the smallest non-trivial case of $N=3,M=6$ where $\dim\wedge^3 V=20$, a direct application of our results gives universal subspaces with dimension 5. We further show that it is not the case for $N>3$, i.e. not all fermionic states are LU equivalent to a single occupancy state. For $N$ even, BCS states provide explicit examples for states that are not LU equivalent to any single occupancy state.

Lin Chen obtained the PhD in theoretical physics from Zhejiang University, China in 2008. He was a Postdoctoral Research Fellow with the Centre for Quantum Technologies (CQT), National University of Singapore (NUS) from 2008 to 2011. Since 2011.09, Lin has been working as a Postdoctoral Research Fellow with the Institute for Quantum Computing (IQC), University of Waterloo, Canada. Lin's research interest is on the theoretical and mathematical part of quantum entanglement, quantum information and their relations with physics and computer science.