Constitutional Law—Emergency Rent Control Law Amendment of 1962 Upheld as No Denial Of Due Process Or Equal Protection

Bucho Holding Co. v. Temporary State Housing Rent Comm\u27n, 11 N.Y.2d 469, 184 N.E.2d 569, 230 N.Y.S.2d 977 (1962)

Education Law—Bayer Aspirin Tablets Held to Be a Proprierary Medicine Within the Exception To The New York Education Law

Loblaw, Inc. v. New York State Board of Pharmacy, 11 N.Y.2d 102, 181 N.E.2d 621, 226 N.Y.S.2d 681 (1962)

All the Exact Solutions of Generalized Calogero-Sutherland Models

A collective field method is extended to obtain all the explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of all the classical groups, including the solutions corresponding to spinor representations for $B_N$ and $D_N$ cases.Comment: Latex, 17 pages. Title and abstract slightly changed, plus minor correction

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

The Young Stellar Population of IC1613. I. A New Catalogue of OB Associations

Context: Determining the parameters of massive stars is crucial to understand many processes in galaxies and the Universe, since these objects are important sources of ionization, chemical enrichment and momentum. 10m class telescopes enable us to perform detailed quantitative spectroscopic analyses of massive stars in other galaxies, sampling areas of different metallicity. Relating the stars to their environment is crucial to understand the physical processes ruling their formation and evolution. Aims: In preparation for the GTC, our goal is to build a catalogue of massive star candidates in the metal-poor irregular galaxy IC1613 with high astrometric accuracy, apt for the current generation of multi-object spectrographs. A census of OB associations in this galaxy is also needed, to provide important additional information about age and environment of the candidate OB stars. Methods: From INT-WFC observations, we have built an astrometric and photometric catalogue of stars in IC1613. Candidate blue massive stars are preselected from their colors. A friends-of-friends algorithm is developed to find their clustering in the galaxy. While a common physical origin for all the members of the associations cannot be ensured, this is a necessary first step to place candidate OB stars in a population context. Results: We have produced a deep catalogue of targets in IC1613 that covers a large field of view. To achieve high astrometric accuracy a new astrometric procedure is developed for the INT-WFC data. We have also built a catalogue of OB associations in IC1613. We have found that they concentrate in the central regions, specially in the HII bubbles. The study of extinction confirms that it is patchy, with local values of color-excess above the foreground value.Comment: Accepted for publication in Astronomy and Astrophysics. 16 pages + appendix (14 pages); 20 figure

Cool and warm dust emission from M33 (HerM33es)

We study the far-infrared emission from the nearby spiral galaxy M33 in order to investigate the dust physical properties such as the temperature and the luminosity density across the galaxy. Taking advantage of the unique wavelength coverage (100, 160, 250, 350 and 500 micron) of the Herschel Space Observatory and complementing our dataset with Spitzer-IRAC 5.8 and 8 micron and Spitzer-MIPS 24 and 70 micron data, we construct temperature and luminosity density maps by fitting two modified blackbodies of a fixed emissivity index of 1.5. We find that the 'cool' dust grains are heated at temperatures between 11 and 28 K with the lowest temperatures found in the outskirts of the galaxy and the highest ones in the center and in the bright HII regions. The infrared/submillimeter total luminosity (5 - 1000 micron) is estimated to be 1.9x10^9 Lsun. 59% of the total luminosity of the galaxy is produced by the 'cool' dust grains (~15 K) while the rest 41% is produced by 'warm' dust grains (~55 K). The ratio of the cool-to-warm dust luminosity is close to unity (within the computed uncertainties), throughout the galaxy, with the luminosity of the cool dust being slightly enhanced in the center of the galaxy. Decomposing the emission of the dust into two components (one emitted by the diffuse disk of the galaxy and one emitted by the spiral arms) we find that the fraction of the emission in the disk in the mid-infrared (24 micron) is 21%, while it gradually rises up to 57% in the submillimeter (500 micron). We find that the bulk of the luminosity comes from the spiral arm network that produces 70% of the total luminosity of the galaxy with the rest coming from the diffuse dust disk. The 'cool' dust inside the disk is heated at a narrow range of temperatures between 18 and 15 K (going from the center to the outer parts of the galaxy).Comment: 12 pages, 14 figures, accepted for publication in A&

Two-loop HTL Thermodynamics with Quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.Comment: 33 pages, 6 figure

Risk prediction models with incomplete data with application to prediction of estrogen receptor-positive breast cancer: prospective data from the Nurses' Health Study

Introduction A number of breast cancer risk prediction models have been developed to provide insight into a woman\u27s individual breast cancer risk. Although circulating levels of estradiol in postmenopausal women predict subsequent breast cancer risk, whether the addition of estradiol levels adds significantly to a model\u27s predictive power has not previously been evaluated. Methods Using linear regression, the authors developed an imputed estradiol score using measured estradiol levels (the outcome) and both case status and risk factor data (for example, body mass index) from a nested case-control study conducted within a large prospective cohort study and used multiple imputation methods to develop an overall risk model including both risk factor data from the main cohort and estradiol levels from the nested case-control study. Results The authors evaluated the addition of imputed estradiol level to the previously published Rosner and Colditz log-incidence model for breast cancer risk prediction within the larger Nurses\u27 Health Study cohort. The follow-up was from 1980 to 2000; during this time, 1,559 invasive estrogen receptor-positive breast cancer cases were confirmed. The addition of imputed estradiol levels significantly improved risk prediction; the age-specific concordance statistic increased from 0.635 ± 0.007 to 0.645 ± 0.007 (P \u3c 0.001) after the addition of imputed estradiol. Conclusion Circulating estradiol levels in postmenopausal women appear to add to other lifestyle factors in predicting a woman\u27s individual risk of breast cancer

The Interstellar Environment of our Galaxy

We review the current knowledge and understanding of the interstellar medium of our galaxy. We first present each of the three basic constituents - ordinary matter, cosmic rays, and magnetic fields - of the interstellar medium, laying emphasis on their physical and chemical properties inferred from a broad range of observations. We then position the different interstellar constituents, both with respect to each other and with respect to stars, within the general galactic ecosystem.Comment: 39 pages, 12 figures (including 3 figures in 2 parts