arXiv subjects

D. Prokhorov

Publications and source records attributed to D. Prokhorov.

4 recordsLinked to original sources

arXiv2014

Approximation of sgn(x) on two symmetric intervals by rational functions with fixed poles

Recently A. Eremenko and P. Yuditskii found explicit solutions of the best polynomial approximation problems of sgn(x) over two intervals in terms of conformal mappings onto special comb domains. We give analogous solutions for the best approximation problems of sgn(x) over two symmetric intervals by odd rational functions with fixed poles. Here the existence of the related conformal mapping is proved by using convexity of the comb domains along the imaginary axis.

math.CV↗

arXiv2012

Asymptotic formulas for integer partitions within the approach of microcanonical ensemble

The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary (one-dimensional) partitions, the correction to the leading asymptotic is obtained. The estimate for the number of two-dimensional (plane) partitions coincides with known asymptotic results.

cond-mat.stat-mech↗

arXiv2012

Fermi LAT Search for Dark Matter in Gamma-ray Lines and the Inclusive Photon Spectrum

Dark matter particle annihilation or decay can produce monochromatic gamma-ray lines and contribute to the diffuse gamma-ray background. Flux upper limits are presented for gamma-ray spectral lines from 7 to 200 GeV and for the diffuse gamma-ray background from 4.8 GeV to 264 GeV obtained from two years of Fermi Large Area Telescope data integrated over most of the sky. We give cross section upper limits and decay lifetime lower limits for dark matter models that produce gamma-ray lines or contribute to the diffuse spectrum, including models proposed as explanations of the PAMELA and Fermi cosmic-ray data.

astro-ph.HE↗

arXiv2009

Studying the leptonic structure of galaxy cluster atmospheres from the spectral properties of the SZ effect

We study the energetics of galaxy cluster atmospheres by analyzing the SZ effect spectra around the crossover frequency. We calculated analytically the expressions of both the crossover frequency and the spectral slope of the SZE around the crossover frequency in various cases: a thermal electron population; a power-law, non-thermal electron population; and a population of electrons experiencing a stochastic acceleration. We find that the value of the crossover frequency X_0 of the SZE depends significantly on the cluster peculiar velocity V_r (which determines the amplitude of the kinematic SZE), while the value of the slope of the SZE does not depend on the kinematic SZE spectrum in the optimal frequency range around the crossover frequency of the thermal SZE, i.e. in the (a-dimensional) frequency range x = 3.5 - 4.5. Thus, while the amplitude of the kinematic SZE produces a systematic bias in the position of the crossover frequency, it does not affect significantly the spectral slope of the SZE. We therefore propose to use measurements of the spectral slope of the SZE to obtain unbiased information about the specific properties of various electron distributions in galaxy clusters as well as in other cosmic structures in which a SZE can be produced.

astro-ph.CO↗