Vladikavkaz Mathematical Journal

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July - September, 2011

Volume 13, Issue 3

On half conformally flat 4-dimensional Lie groups
Gladunova O. P., Rodionov E. D., Slavskii V. V.

Classification of half conformally flat Lie algebras of real four-dimensional Lie groups with left-invariant Riemannian metrics is given.

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

Cyclic subgroups of second degree full linear group over a field of the zero characteristic
Zhemuhova M. Z., Pachev U. M.

A description of cyclic subgroups in a full linear group G L 2 (F)   over any zero characteristic field F   is given.

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

The asimptotics of a periodical solution of differential equation with great high-frequency terms
Ishmeev M. R.

The full asimptotics of a periodical solution for the systems of non-linear differential equations, containing terms proportional to a degrees of frequency is constructed.

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

Closed pairs
Koibaev V. A.

This is a study of closed pairs of abelian groups (closed elementary nets of degree 2). If the elementary group E(σ)   does not contain new elementary transvections, then an elementary net σ   (the net without the diagonal) is called closed. Closed pairs we construct from the subgroup of a polynomial ring. Let R 1 [x]   - the ring of polynomials (of variable x   with coefficients in a domain R ) with zero constant term. We prove the following result.
Theorem. Let A, B - additive subgroups of R 1 [x]  . Then the pair (A,B)   is closed. In other words, if t 12 (β)   or t 21 (α)   is contained in subgroup t 21 (A), t 12 (B) , then βB , αA .

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

On existence of the solution of parabolic problem on the graph with a boundary conditions, containing derivatives on time
Kulaev R. Ch.

The mixed problem for the parabolic equation set on geometrical graph, with boundary conditions containing a derivative on time is considered. The theorem of existence of the solution of the boundary problem giving representation of the solution in the form of circuit integral is established.

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

On representations of yangian of Lie superalgebra sl(1,2)
Stukopin V. A.

The finite-dimensional irreducible representations of Yangian of Lie Superalgebra sl(1,2) . The necessary and sufficiently conditions of irreducibility of finite-dimensional representations are formulated and proved.

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

Maharam extension of a positive orthosymmetric bilinear operator
Tasoev B. B.

Maharam extension of a positive orthosymmetric bilinear operator in vector lattices is constructed.

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

Valentin Vasil'evich Napalkov
(on his 70's anniversary)

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

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