Nonisothermal relaxation and electromigration in single crystals of Ca3Ga2Ge4O14

The photoconductivity and electrical conductivity, the thermally stimulated polarization and depolarization currents, the permittivity, and the dielectric losses of noncentrosymmetric Ca₃Ga₂Ge₄O₁₄ crystals of a structural type of trigonal calcium gallogermanate (CGG) have been studied for the first time in the temperature interval 100–700 K in air and in vacuum. The features of the temperature behavior of CGG are associated, in particular, with the effect of electrically active defects and partial disordering of the cation sublattice of the crystal structure, which generates polar formations (dipoles) of several kinds. Certain parameters of the electromigration and of the electrically active defects that cause charge-relaxation and polarization effects are determined. It is concluded that dipole relaxation in CGG makes it a new representative of a class of materials in which reorientation of the dipoles as a system of mobile local distortions of the structure has a substantial effect on the physical properties. Fiz. Tverd. Tela (St. Petersburg) 39, 871–876 (May 1997)     

Inversion of the density gradient and the diffusion “gate” in isothermal mixing of gases

The stable quasistationary mixing of ternary gas mixtures in a system of two chambers connected by a capillary is described by a theoretical model which predicts the density distribution of the mixture along the length of the diffusion channel. It is demonstrated that inversion of the density gradient can occur due to a nonlinear concentration distribution of the heavy component in a diffusion “gate” effect. The results obtained using this model are compared with the experimental data. Zh. Tekh. Fiz. 68, 14–17 (May 1998)     

Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.     

The dynamics of a two-component fluid in the presence of capillary forces

In the present paper we study the qualitative behavior ast→∞ of the solution of the Cauchy problem for a system of equations describing a dynamics of a two-component viscous fluid. The model under consideration takes into account the mutual diffusion of the fluid components as well as their capillary interaction. We describe the ω-limit set of trajectories of the dynamical system generated by the problem. It is proved that the stationary solution of the problem, is a homogeneous stationary distribution of one of the components, is asymptotically stable. Any other stationary solution is not asymptotically stable and is even unstable if there are no close stationary solutions corresponding to a smaller energy level. Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 293–305, August, 1997. Translated by A. M. Chebotarev     

The influence of a medium on the rate of the reaction between N,N′-dioctylurea and <Emphasis Type="Italic">n</Emphasis>-octanol

The kinetics and mechanism of alcoholysis of symmetrical dioctylurea in inert solvents were studied. The reaction was found to follow two parallel pathways, one involving the destruction of initial urea and the other, bimolecular interaction. For the reaction series under consideration, the influence of the nature of solvents on the rate of the reaction was studied.     

Convergence of Metropolis-type algorithms for a large canonical ensemble

In this paper, we study the convergence of Metropolis-type algorithms used in modeling statistical systems with a fluctuating number of particles located in a finite volume. We justify the use of Metropolis algorithms for a particular class of such statistical systems. We prove a theorem on the geometric ergodicity of the Markov process modeling the behavior of an ensemble with a fluctuating number of particles in a finite volume whose interaction is described by a potential bounded below and decreasing according to the law r ^?3?α, α ≥ 0, as r → 0.     

On a new class of function systems of Faber-Schauder type

In this paper, we introduce a new class of function systems generalizing the classical Faber-Schauder system. Under the condition that the generating sequence is bounded, we show that systems of such a class constitute bases in the space of continuous functions and prove some properties of series expansions of functions in these systems.