Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Frequency Dependent Specific Heat from Thermal Effusion in Spherical Geometry

We present a novel method of measuring the frequency dependent specific heat at the glass transition applied to 5-polyphenyl-4-ether. The method employs thermal waves effusing radially out from the surface of a spherical thermistor that acts as both a heat generator and thermometer. It is a merit of the method compared to planar effusion methods that the influence of the mechanical boundary conditions are analytically known. This implies that it is the longitudinal rather than the isobaric specific heat that is measured. As another merit the thermal conductivity and specific heat can be found independently. The method has highest sensitivity at a frequency where the thermal diffusion length is comparable to the radius of the heat generator. This limits in practise the frequency range to 2-3 decades. An account of the 3omega-technique used including higher order terms in the temperature dependency of the thermistor and in the power generated is furthermore given.Comment: 17 pages, 15 figures, Substantially revised versio

On finite-difference approximations for normalized Bellman equations

A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of convergence of finite difference approximations for the optimal reward functions.Comment: 36 pages, ArXiv version updated to the version accepted in Appl. Math. Opti

Laudatores Temporis Acti, or Why Cosmology is Alive and Well - A Reply to Disney

A recent criticism of cosmological methodology and achievements by Disney (2000) is assessed. Some historical and epistemological fallacies in the said article have been highlighted. It is shown that---both empirically and epistemologically---modern cosmology lies on sounder foundations than it is portrayed. A brief historical account demonstrates that this form of unsatisfaction with cosmology has had a long tradition, and rather meagre results in the course of the XX century.Comment: 11 pages, no figures; a criticism of astro-ph/0009020; Gen. Rel. Grav., accepted for publicatio

Intermediate Wakimoto modules for Affine sl(n+1)

We construct certain boson type realizations of affine sl(n+1) that depend on a parameter r. When r=0 we get a Fock space realization of Imaginary Verma modules appearing in the work of the first author and when r=n they are the Wakimoto modules described in the work of Feigin and Frenkel

Dietary determinants of changes in waist circumference adjusted for body mass index - a proxy measure of visceral adiposity

Background Given the recognized health effects of visceral fat, the understanding of how diet can modulate changes in the phenotype “waist circumference for a given body mass index (WCBMI)”, a proxy measure of visceral adiposity, is deemed necessary. Hence, the objective of the present study was to assess the association between dietary factors and prospective changes in visceral adiposity as measured by changes in the phenotype WCBMI. Methods and Findings We analyzed data from 48,631 men and women from 5 countries participating in the European Prospective Investigation into Cancer and Nutrition (EPIC) study. Anthropometric measurements were obtained at baseline and after a median follow-up time of 5.5 years. WCBMI was defined as the residuals of waist circumference regressed on body mass index, and annual change in WCBMI (¿WCBMI, cm/y) was defined as the difference between residuals at follow-up and baseline, divided by follow-up time. The association between energy, energy density (ED), macronutrients, alcohol, glycemic index (GI), glycemic load (GL), fibre and ¿WCBMI was modelled using centre-specific adjusted linear regression, and random-effects meta-analyses to obtain pooled estimates. Men and women with higher ED and GI diets showed significant increases in their WCBMI, compared to those with lower ED and GI [1 kcal/g greater ED predicted a ¿WCBMI of 0.09 cm (95% CI 0.05 to 0.13) in men and 0.15 cm (95% CI 0.09 to 0.21) in women; 10 units greater GI predicted a ¿WCBMI of 0.07 cm (95% CI 0.03 to 0.12) in men and 0.06 cm (95% CI 0.03 to 0.10) in women]. Among women, lower fibre intake, higher GL, and higher alcohol consumption also predicted a higher ¿WCBMI. Conclusions Results of this study suggest that a diet with low GI and ED may prevent visceral adiposity, defined as the prospective changes in WCBMI. Additional effects may be obtained among women of low alcohol, low GL, and high fibre intake

Metal enrichment and evolution in four z > 6.5 quasar sightlines observed with JWST/NIRSpec

We present JWST/NIRSpec R$\approx$2700 spectra of four high-redshift quasars: VDES J0020-3653 (z = 6.860), DELS J0411-0907(z = 6.825), UHS J0439+1634 (z = 6.519) and ULAS J1342+0928 (z = 7.535). The exquisite data quality, signal-to-noise ratio of 50-200, and large $0.86\!~\mu{\rm m}\le \lambda \le 5.5\!~\mu{\rm m}$ spectral coverage allows us to identify between 13 and 17 intervening and proximate metal absorption line systems in each quasar spectrum, with a total number of 61 absorption-line systems detected at $2.42<z<7.48$ including the highest redshift intervening OI $\lambda$1302 and MgII systems at $z=7.37$ and $z=7.44$. We investigate the evolution of the metal enrichment in the epoch of reionization at $z>6$ and find: i) A continued increase of the low-ionization OI, CII, and SiII incidence, ii) Decreasing high-ionization CIV and SiIV incidence with a transition from predominantly high- to low-ionization at $z\approx6.0$, and iii) a constant MgII incidence across all redshifts. The observations support a change in the ionization state of the intergalactic medium in the EoR rather than a change in metallicity. The abundance ratio of [Si/O] in five $z>6$ absorption systems show enrichment signatures produced by low-mass Pop III pair instability supernovae, and possibly Pop III hypernovae. In the Gunn-Peterson troughs we detect transmission spikes where Ly$\alpha$ photons can escape. From 22 absorption systems at $z>5.7$, only a single low-ionization system out of 13 lies within 2000 km s$^{-1}$ from a spike, while four high-ionization systems out of nine lie within $\sim$2000 km s$^{-1}$ from a spike. This confirms that galaxies responsible for the heavy elements that are transported into the circumgalactic medium lie in predominantly in high-density, neutral environments, while lower density environments are ionized without being polluted by metals at $z\approx$ 6-7. [abridged]Comment: 50 pages including 30 pages of appendices. Submitted to A&