IKBFU's Vestnik

2016 Issue №1

Strongly associated threefold distributions of projective space

Abstract

Construction of a general theory of a special class (SH -distribution) of the regular threefold distributions (H -distribution) of the projective space Pn consisting of a basic distribution of the 1st kind of r-dimensional planes  r are equipped with the distribution of the 1st kind of m-dimensional planes Mm (m  r) and equip distribution 1st the first kind of hyperplane elements (hyperplanes) Hn-1 with the ratio of the incidence of the corresponding elements in the common center X: X    M  H is considered in this article. In this paper, these three distributions is considered as a immersed manifold. By virtue of the SH -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements (n  1)-dimensional linear elements and hyperband distribution. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately. Research was carried out by G. F. Laptev method. Determinations of the H -distributionand existence theorems are given in the frame of zero order. Requiring that Λ-, L-, E-distribution were mutually associated we introduce a special class of threefold distributions, which we call strongly associated distributions or SH -distribution. Definition of SH -distribution is given in the frame of the 1st order and the existence theorem is proved.

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Use of the Z-scheme in an Rayleigh-Taylor instability model

Abstract

A nonlinear finite-differential scheme for solution of convection-diffusion equation in the field of models of Rayleigh-Taylor instability in the equatorial region of Earth ionosphere is considered. For test tasks monotony of the constructed scheme is in number confirmed. Experimental value of an order of approximation of the offered method of nonlinear correction of the finitedifferential scheme is received.

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A mathematical model of conversion of GaAs substrate into thin GaNxAs1-x films obtained by nitridation of porous GaAs substrate

Abstract

A mathematical model of conversion of GaAS substrate into thin GaNxAs1-x films obtained by nitridation of porous GaAs substrate are presented. The technologic conditions influence on GaNxAs1-x parameters are discussed. The comparative analysis of both experimental and theoretic data was applied for optimization nitridation conditions in order to obtain «soft» substrates for GaN growth. The results will help to decrease mechanical strains in GaN/GaAs semiconductors structures. For solving and analysis of the presented system of differential equation was used mathematical package for partial differential equation FlexPDE.

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