Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves

We study the relationship between the growth and decrease of the sum of the entire Dirichlet series of finite order (in the sense of Ritt) on arbitrary curves going to infinity. For a class of exponents having a regular distribution (in a certain sense), we obtain a test for the logarithm of the maximal term to be equivalent to the logarithm of the absolute value of the sum of the Dirichlet series on at least one unbounded sequence of points of the curve.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 37–51.Original Russian Text Copyright © 2005 by A. M. Gaisin, I. D. Latypov.     

Investigation of Physical Processes in the Gas Discharge Region Between Liquid Electrodes

Electrophysical, hydro-gas-dynamic, and thermal characteristics of a discharge arising between liquid electrodes are considered. Spatial visualization of flow patterns in the gas discharge region is performed by using the schlieren technique.     

Maximal Term of the Modified Dirichlet Series

We establish a criterion for the logarithm of the maximal term of a Dirichlet series absolutely convergent in the half-plane to be equivalent on an asymptotic set to the logarithm of the maximal term of its Hadamard composition with any other Dirichlet series from a certain class.     

<Superscript>1</Superscript>H and <Superscript>31</Superscript>P nuclear spin-lattice relaxation in C-phosphorylated oximes

The ¹H spin-lattice relaxation times of the proton-bearing groups and the ³¹P spin-lattice relaxation times in C-phosphorylated oximes R¹C(=NOH)P(=O)R²R³ (R¹ = Ph, R² = R³ = OMe; R¹ = Ph, R² = OMe, R³ = OCH²CH²Br; R¹ = PhCH², R² = R³ = OCHMe²) and dioxime R²P(=O)C(=NOH)(CH₂)₄C(=NOH)P(=O)R² (R = OMe) in DMSO-d₆ were measured. The characteristic reorientation times of the whole molecules were estimated using the measured values of the ¹H relaxation times and the results of semiempirical PM3 quantum chemical calculations of the molecular geometries. The reorientation times were used to identify the contributions of different relaxation mechanisms to the rate of ³¹P spin-lattice relaxation. The anisotropy of the chemical shielding of ³¹P nuclei was evaluated from the difference between the ³¹P relaxation rates measured at 101.27 and 161.92 MHz.