Vladikavkaz Mathematical Journal

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April - June, 2012

Volume 14, Issue 2

About invariant tensor fields on low dimensional Lie groups
Voronov D. S., Gladunova O. P., Rodionov E. D., Slavskii V. V.

Complete classification of possible signatures of the one dimensional curvature operator on three dimensional Lie groups with left-invariant Riemannian metric and complete classification of four-dimensional Lie algebras (up to isomorphism) of Lie groups with left-invariant Riemannian metrics and harmonic Weyl tensor are given in this paper.

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

Some isomorphism results on commutative group algebras
Danchev P.

We prove certain results pertaining to some isomorphism properties of commutative modular group algebras and briefly review a paper by pointing out some obvious mistakes and essential incorrectness.

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

About Shunkov's groups, saturated with direct product of groups
Duzh A. A., Shlyopkin A. A.

It is proved that an infinite periodic Shunkov's group, saturated with direct products of cyclic groups of odd orders by two-dimentional projective special linear groups over finite fields of characteristic two is locally finite.

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

On bases in spaces of continuous
n -homogeneous polynomials in nuclear Kothe spaces
Kondakov V. P.

A basis in the space of continuous n -homogeneous polynomials mappings a nuclear Kothe - Frechet space into itself is constructed. The space of polynomials is considered with the compact open topology. Some related problems are also discussed.

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

On the fundamental solution of the Cauchy problem for a hyperbolic operator
Totieva Zh. D.

Under study are the properties of the fundamental solution of the generalized Cauchy problem for some hyperbolic operator.

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

An evaluation of the Ph. Hall function on rank 1 groups of Lie type
Ushakov Yu. Yu.

In 1936 Ph. Hall introduced the generalized n -th Eulerian function on finite groups and the associated function that is called the $n$-th Hall function. The values of the latter are estimated in the article for three of the four series of Lie type groups of rank 1. When n=2 , these evaluations confirm the Wiegold conjecture for the groups.

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

On nontrivial solvability of a nonlinear Hammerstein-Volterra type integral equation
Khachatryan Kh. A., Grigoryan S. A.

The existence is studied of one parametric family of positive bounded solutions for a class of Hammerstein-Volterra type nonlinear homogeneous integral equations. This class of equations has important applications in the kinetic theory of gases.

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

50 years of nonstandard analysis
Kutateladze S. S.

This is a short invitation to nonstandard analysis on the occasion of the publication of the book "Infinitesimal Analysis: Selected Topics" by E. I. Gordon, A. G. Kusraev, and S. S. Kutateladze.

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

Shabat Alexey Borisovich
(on his 70's anniversary)

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

To the memory of Alexander Nikolaevich Kabel'kov

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

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