Nonlinear Diffusion Processes

We study elliptic systems of strongly nonlinear first-order differential equations in complex form on the plane. For such systems we develop the theory of Hilbert boundary value problems which is very much similar to the well-known theory for a holomorphic vector. Systems of nonlinear elliptic equations describe problems of interaction of several nonlinear stationary processes in the diffusive and convective mass and heat transport by hydrodynamic fluid flows.     

Mechanical Properties of Diamond-Like Silicon–Carbon Films Doped with Vanadium

Crystallography Reports - The influence of doping with vanadium on the mechanical properties of nanocomposite films deposited on silicon substrates has been investigated. It is found that the...     

An Analog for the Frattini Factorization of Finite Groups

Using the classification of finite simple groups, we prove that if H is an insoluble normal subgroup of a finite group G, then H contains a maximal soluble subgroup S such that G=HN_G(S). Thereby Problem 14.62 in the Kourovka Notebook is given a positive solution. As a consequence, it is proved that in every finite group, there exists a subgroup that is simultaneously a -projector and a -injector in the class, , of all soluble groups.     

Spatial distribution of a hole localized on acceptor in deformed crystal

The influence of the host-crystal deformation on the acceptor wave-function in a cubic crystal is considered. The calculations are based on the numerical solution of the Luttinger Hamiltonian for a hole in a complex valence band. The deformation is taken into account using Bir-Pikus Hamiltonian for the deformation. The results can be used for the interpretation of the STM images in strained cubic crystals.     

Finite groups with 2-nilpotent subgroups of even index

Finite groups with 2-nilpotent subgroups of even index are described. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 700–705, May, 1997. Translated by A. I. Shtern