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] [zippdf]
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 nonsplit maximal torus associated with the radical extension
of the basic field
k[x]
.
Article (rus.)  [pdf] [zippdf]
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] [zippdf]
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] [zippdf]
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
nonnegative 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] [zippdf]
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
,
i≠j
, 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 offdiagonal positions) we have
ω
σ
⊆σ⊆
Ω
σ
.
Article (rus.)  [pdf] [zippdf]
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] [zippdf]
On automorphisms of strongly regular graphs with parameters (243,66,9,21)
Makhnev A. A., Tokbaeva A. A.
Orders and fixedpoint 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] [zippdf]
Intermediate subgroups of the steinberg groups over
the field of fractions of a principal ideal ring
Moiseenkova T. V., Nuzhin Ya. N. УДК 512.544.2
It is described Intermediate subgroups of the Steinberg groups of type
2
A
2m−1
,
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] [zippdf]
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 anе
M
e
distance as well as using some contractive conditions.
Our results generalize, extend and improve some earlier results.
Article (eng.)  [pdf] [zippdf]
On integral representation to solutions for a differential
equation with singular coefficients
Sitnik S. M. УДК 517.926.4+517.968.25
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 wellknown 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] [zippdf]
Odinets Vladimir Petrovich (on his 65's anniversary)
Article (rus.)  [pdf] [zippdf]
A Tribute to the Philanthropist and Geometer
(the 90th anniversary of V. A. Zalgaller)
Article (rus.)  [pdf] [zippdf]
Letter to the editor
Article (rus.)  [pdf] [zippdf]
