Vladikavkaz Mathematical Journal

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January-March, 2014

Volume 16, Issue 1

Approximate solutions for multi-dimensional singular integral equations and fast algorithms for their solving
Vasil'ev A. V., Vasil'ev V. B.

The error estimate for continuous singular integral and the discrete ones in multi-dimensional space is obtained. The use of fast Fourier transform for finding approximate solutions for equations with such operators is suggested.

Article (rus.) - [pdf] [zip-pdf]

Estimates for some potential type operators whose kernels have singularities on spheres
Gurov M. N., Nogin V. A.

Multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in n   are studied on Hardy spaces H p , 0<p< . Necessary and sufficient conditions are obtained for such operators to be bounded from H p into the Holder space Λ s , from H p into the Sobolev space L k  , and from BMO into Λ s .

Article (rus.) - [pdf] [zip-pdf]

Simulation the parameters of turbulent flow when diffraction of a blunt angle
Kochanenko V. N., Fetisov V. G., Mitsik M. F.

This article provides a method of calculation of parameters of a two-dimensional turbulent flow when occurs diffraction of the blunt angle. The main assumptions are conditions of uniform flow in the upper and lower canal ponds.

Article (rus.) - [pdf] [zip-pdf]

Nonlocal combined problem of Bitsadze-Samarski and Samarski-Ionkin type for a system of pseudoparabolic equations
Mamedov I. G.

In this paper we consider a problem with Bitsadze-SamarskI and SamarskI-Ionkin conditions for a system of pseudoparabolic equations of fourth order with discontinuous coefficients. Found an integral representation of functions in the Sobolev space by defining the operators in the investigation of a nonlocal problem. Even, in particular, proved Goursat problem with nonclassical boundary conditions.

Article (rus.) - [pdf] [zip-pdf]

On a nonlocal problem for nonlinear parabolic equation
Takhirov J. O., Turaev R. N.

A boundary problem for nonlinear parabolic equation with nonlocal boundary conditions is considered. Some a priori estimates are derived to establish the global existence of the solution. Uniqueness and existence theorems are proved.

Article (rus.) - [pdf] [zip-pdf]

Subdomains method for solution of a singular first kind integral equation with Cauchy kernel
Hajrullina L. E., Habibullina G.Z.

The method of subdomains solution of a singular integral equation of the first kind with Cauchy kernel is investigated. A pair of weight spaces, which are the narrowing of the space of continuous functions are introduced. The correctness of the equations on this pair of spaces is proved. Sufficient conditions for the convergence of the method of subdomains in the uniform metric are established.

Article (rus.) - [pdf] [zip-pdf]

On the Ricci curvature of three-dimensional metric lie algebras

Chebarikov M. S.

In this paper, we get a classification of possible values of the Ricci curvature signature of left invariant Riemannian metrics on three-dimensional Lie groups, that is a specification of some results of J. Milnor. As an auxiliary problem, we classify three-dimensional nonunimodular metric Lie algebras.

Article (rus.) - [pdf] [zip-pdf]

Construction of the interpolation functor in the category of Freschet spaces with common basis
Shubarin M. A.

A family of interpolating functors in the category of pairs of Frechet spaces with common absolute basis is constructed and its properties are studied. A reiteration type theorem is proved for this family. In terms of this interpolation functor some types of Kothe spaces are described.

Article (rus.) - [pdf] [zip-pdf]

Vladimir Kuzmich Ionin

On March 12, 2014,Vladimir Kuzmich Ionin, the known Russian mathematician, one of leading domestic scientists in the geometry in whole, Doctor of Physics and Mathematics, has died on his 80-th year.

Article (rus.) - [pdf] [zip-pdf]

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