Conditions of Rayleigh-Bénard convection onset and heat transfer in a near-critical medium

Thermal gravity convection in a horizontal layer of compressible perfect gas heated from below and a van der Waals gas near the critical state is investigated. The characteristics of the isentropic equilibrium of a compressible medium with a van der Waals equation of state are considered. The known conditions of convection onset in the perfect and van der Waals gases are checked on the basis of a solution of the complete and linearized equations. The restrictions imposed in deriving the known formulas for the adiabatic temperature gradients used in the conditions of absence and onset of convection are discussed. The characteristics of the convective heat transfer are examined, including the causes of the heat-transfer deterioration in the near-critical medium above the hydrostatic equilibrium threshold.     

Synthesis and proton conductivity of adsorption-saturated and solvated porous hydroxyethylated cyclam layers on the surface of PVC-coated cellulose fabric

Porous layers of associates of adsorption-saturated and benzene- and hexane-solvated chloride and sulfate of hydroxyethylated cyclams with acid aqua complexes were synthesized on the surface of PVC-coated cellulose fabric. The porous structure of the layers includes a system of internal pores connected with the external pores via the diamine rings of the common walls of the hydroxyethylated cyclam nets; the internal pores are filled with the associates; the solvent molecules are adsorbed on the developed surface of the layers or solvate it. The H⁺ motion rate in a layer placed in solvent vapors or liquid solvents was measured; the layers were found to be nonlinear H⁺ conductors. The potential of H⁺ transition from the acid solution into the layer, the H⁺ mobility constant, and the field variation constant of the H⁺ mobility of the layer depend on the layer composition. The adsorption and solvation are accompanied by the formation of host-guest molecular complexes between the diamine rings of the cyclam nets and the benzene or hexane molecules, affecting the resistance of the associates to the incorporation of H⁺ ions and the H⁺ mobility in the associates.     

Alkylation of pyrocatechol in <Emphasis Type="Italic">tert</Emphasis>-butyl alcohol-sulfuric acid-benzene

Alkylation of pyrocatechol with tert-butyl alcohol in benzene in the presence of sulfuric acid gave 3,5-di-tert-butylbenzene-1,2-diol in a higher yield than in analogous reaction with tert-butyl alcohol. This result was rationalized by reduction of inhibitory effect of liberated water, formation of heterogeneous system, and occurrence of the alkylation process in nonpolar organic phase. Intermediate products were identified and found to undergo intra- and intermolecular tert-butyl group transfer with formation of more stable 3,5-di-tertbutylbenzene-1,2-diol. The formation of p-di-tert-butylbenzene indicated participation of benzene in crossalkylation processes.     

Reachability of Optimal Convergence Rate Estimates for High-Order Numerical Convex Optimization Methods

Doklady Mathematics - The Monteiro–Svaiter accelerated hybrid proximal extragradient method (2013) with one step of Newton’s method used at every iteration for the approximate solution...     

On The Statistical Analysis of the Formation of Secondary Radiation Fields in Remote Control Devices Based on Pulsed Neutron Generators

Physics of Atomic Nuclei - The paper is devoted to the study of the influence of pulsed instability of neutron generation on the efficiency of small transportable HMCs. Experimental diagrams of the...     

Kirkwood and Wigner Quantum Densities,Their Properties,and Applications in Radiophysics

Radiophysics and Quantum Electronics - The Wigner and Kirkwood functions are widely used for signal processing. We review their properties and representations. The Wigner function calculation...     

A Generalization of the Hilbert Basis Theorem

A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.     

Determination of the electron energy distribution in a plasma from the first and second derivatives of the probe current

An approach to the reconstruction of the electron energy distribution function (EEDF) as the sum of the second derivative of the electron current to the probe and some value proportional to its first derivative is proposed (hereafter we mean derivatives with respect to voltage). Solutions to model problems for typical electron distributions in a plasma show that this approach lowers the systematic error of EEDF reconstruction by several times in comparison with the conventional techniques using Langmuir and diffusion probes. The approach is applicable in a wide range of the ratio of the probe radius to the free path of electrons. It can be used for the determination of fast nonequilibrium electron distribution in neon discharge afterglow and also for the evaluation of the Maxwellian electron temperature in the low-energy range of nitrogen discharge afterglow.     

A generalization of operator stochastic integrals

We generalize the method for construction of operator stochastic integrals suggested by Berezanskii, Zhernakov, and Us. We extend the class of integrable commutative quantum processes and study properties of corresponding integrals.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 425–429, April, 1994.This work was partially supported by the Ukrainian State Committee on Science and Technology.