Existence and stability of periodic solutions for chains of connected oscillators

We consider a nonlinear system of difference equations. This system corresponds to chains of N symmetrically connected oscillators with sufficiently general type of connection, which includes, among others, local and global connection. We prove a theorem on the existence and stability of space-time periodic solutions of such systems for sufficiently small values of the parameter of connection ?.     

On the navier-stokes equation with the additional conditionu 1 1 =u 3=0

We study the Navier-Stokes equation with the additional conditionu ₁ ¹ =u ³=0. In certain cases, solutions are represented in a closed form. In other cases, the investigated system reduces to simpler systems of partial differential equations. We study the symmetry properties of these systems and construct classes of their particular solutions.     

A study of the propagation of a quasistationary relativistic electron beam in a dense gas. II. Experimental studies

Results obtained from experimental studies of the interaction between a quasistationary electron beam (300 keV, 20 A, 500 sec, 0.3 cm) and a dense gas are presented. These investigations were carried out in air at atmospheric pressure and, for the purpose of modeling the propagation of a magnetostricted REB, at reduced pressure (3–300 torr). The rarefaction dynamics of a channel heated by the beam are studied and its maximum propagation distances in a dense gas are determined. The results obtained are compared with the theoretical model examined earlier.V. I. Lenin All-Union Institute of Electrical Engineering. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 2, pp. 190–197, February, 1991.     

REACTIONS OF TETRAPHOSPHORUS DECASULFIDE AND LAWESSON'S REAGENT WITH SILANES CONTAINING A FEW Si-O BONDS

Abstract

The reactions of tetraphosphorus decasulfide and Lawesson's reagent with tetra-, tri- and dialkoxysilanes were studied. On the basis of these reactions, new S-silyl esters of phosphorus(V) thioacids have been prepared. The prepared compounds were identified by IR, ¹H, and ³¹P NMR and mass spectra as well as elemental analyses.     

Reactions of S-Silyl Esters of Tetracoordinated Phosphorus Thioacids with Acetals and Ortho Esters

The reactions of S-trimethylsilyl esters of dithiophosphoric, diamidodithiophosphoric, aryldithiophosphonic, aryltrithiophosphonic, and arylamidodithiophosphonic acids with diethyl acetal of benzaldehyde and ortho formiate and acetate were studied. On the basis of these studies, new derivatives of tetracoordinated phosphorus thioacids were obtained.     

Organic Phosphorus-Suflur Compounds Derived from 1,3,2λ5,4λ5-Dithiaphosphetane 2,4-Disulfides. Synthesis and Properties

The results of author's research into the thiophosphorylating ability of 1,3,2⁵,4⁵-dithiadiphosphetane 2,4-disulfides in reactions with Group II, IV, V, and VI p-element derivatives containing E-X bonds (X = O, S, N) are summarized. New syntheses of organic phosphorus-sulfur compounds with P(S)SE (E = B, Al, C, Si, Ge, Sn, Ph, P, As, Sb, Bi, S) structural fragments are developed. Structural peculiarities and spectral and chemical properties of a series of representatives of these classes of organophosphorus compounds are discussed.     

Considerable increase in thermal conductivity of a polycrystalline CVD diamond upon isotope enrichment

We measured the temperature dependence of thermal conductivity of a polycrystalline CVD diamond with natural isotope composition and an isotope enriched (99.96% ¹²C) sample at temperatures from 5 to 420 K. The isotope enriched diamond demonstrates a considerable growth of thermal conductivity at temperatures above 80 K compared to the diamond with natural composition of isotopes. At room temperature the thermal conductivity reaches 24.3 W·cm^?1K^?1, and the isotope effect makes up not less than 34%.