Vladikavkaz Mathematical Journal

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October - December, 2010

Volume 12, Issue 4

Fractional integrals and differentials of variable order in Holder spaces H ω(t,x)
Vakulov B. G., Kochurov E. S.

We consider generalized Holder spaces of functions on the segment of real axis, whose local continuity modulus has a dominant which may vary from a point to point. We establish theorems on the mapping properties of fractional integrals of variable order, from such a variable generalized Holder space to another one with a "better" dominant, and similar mapping properties of fractional differentials of variable order from such a space into the space with "worse" dominant. Variable order can take values between zero and unity.

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

On maximal subgroups of the general linear group over rational functions field
Dzhusoeva N. A., Dzigoeva V. S., Koibaev V. A.

We construct a class of the maximal subgroups of the general linear group GL(n,k(x))   of degree n   over a field of the rational functions k[x]   with coefficients in a field k   of odd characteristic, containing non-split maximal torus associated with the radical extension of the basic field k[x] .

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

On finite groups with independent subgroups
Zhurtov A. H., Tsirkhov A. A.

Represented the rezults of investigation of class of finite groups in which any non abelian group is independent. Formulated and proved the necessary and sufficient condition of independence of non abelian group in the finite group.

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

On the theory of interaction between a moving point charge and a metal
Kesayev V. I., Maliev I. N.

New formulas for the potential and the longitudinal projection of an electric field induced by a metal in vacuum are derived in the case of nonrelativistic point charged particle is uniformly moving above a plane metallic surface parallel to it. Also it is obtained an new expression for the "friction" force between the charge and the metal is also obtained.

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

Riemann and Hilbert boundary value problems in BMO classes for holomorphic functions
Klimentov S. B.

The classical Riemann and Hilbert boundary value problems for analytic functions are under consideration. We search the solution in BMOA class under assumption that the coefficient of the boundary condition belongs to the set of pointwise multipliers of BMO. We constract examples when the problem with non-negative index in the such natural setting has not solution in BMOA. Sufficient conditions on the coefficient are given when we have usual pattern of solvability in BMOA class.

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

Nets associated with the elementary nets
Koibaev V. A.

For an elementary net (i. e. a net without diagonal) σ=( σ ij )   of additive subgroups σ ij , ij , of a commutative ring R with 1 two nets are constructed: the net ω σ   associated with σ and the net Ω σ   associated with the elementary group E(σ) , and (on the off-diagonal positions) we have ω σ σ Ω σ .

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

About the centralizer of an automorphism of order 2 of burnside group B 0 (2,5)
Kuznetsov A. A., Philippov K. A.

The structure of the centralizer of an automorphism of order 2 of a special kind of Burnside group B 0 (2,5)   is investigated. The generators, order, nilpotency class and derived length of of the centralizer are computed. The lower and upper central series of of the centralizer are built.

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

On automorphisms of strongly regular graphs with parameters (243,66,9,21)
Makhnev A. A., Tokbaeva A. A.

Orders and fixed-point subgraphs of automorphisms of strongly regular graphs with parameters (243,66,9,21) are found. These results will be useful for investigations of automorphisms of strongly regular graphs with parameters (640,243,66,108) (in such graph neighborhoods of vertices are strongly regular with parameters (243,66,9,21)).

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

Intermediate subgroups of the steinberg groups over the field of fractions of a principal ideal ring
Moiseenkova T. V., Nuzhin Ya. N.

It is described Intermediate subgroups of the Steinberg groups of type 2 A 2m1 , 2 D m+1 , 2 E 6 , 3 D 4   over the field of fractions of a principal ideal ring are described under some restrictions on the ring.

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

Some stability results for Picard iterative process in uniform space
Olatinwo M. O.

We prove some stability results for Picard iteration in uniform space by introducing the concept of an M e -distance as well as using some contractive conditions. Our results generalize, extend and improve some earlier results.

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

On integral representation to solutions for a differential equation with singular coefficients
Sitnik S. M.

We consider integral representations to solutions for a differential equation with singular coefficients with Bessel operator. An existence of such integral representations is proved by successive approximations using transmutation operators method. Unlike known results we consider potentials with strong singularities at the origin and also slightly improve well-known method of B. M. Levitan by more accurate calculation of Green function in terms of Legendre function. It leads to more precise estimates without unnecessary constants.

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

Odinets Vladimir Petrovich
(on his 65's anniversary)

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

A Tribute to the Philanthropist and Geometer
(the 90th anniversary of V. A. Zalgaller)

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

Letter to the editor

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

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