Vladikavkaz Mathematical Journal

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January-March, 2013

Volume 15, Issue 5

The Editorial Board Congratulates Professor Anatoly G. Kusraev on the Occasion of His 60th Birthday

On multidimensional integral operators with homogeneous kernels perturbated by one-sided multiplicative shift operators
Avsyankin O. G.

We study the multidimensional integral operators with kernels homogeneous of degree (n)   and invariant under the rotation group, which are perturbated by one-sided multiplicative shift operators. For these operators the invertibility and one-sided invertibility criterions in L p -space are obtained.

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

On extraction of transvections in overgroups of a non-split maximal torus
Dzhusoeva N. A.

Let E( σ A ) , be a subgroup generated by all transvections of the net group G( σ A ) . Then TE( σ A )   is also a group generated by the torus and the root subgroup items in the first column of the elementary group E( σ A ) .

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

Infinitesimals in ordered vector spaces
Emel'yanov E. Yu.

An infinitesimal approach to ordered spaces is proposed. Archimedean property and Dedekind completeness in ordered spaces are discussed from a nonstandard point of view.

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

Some remarks on the Riemann conjecture about the zeros of the zeta-function
Korobeinik Yu. F.

A criterion of validity of the celebrated Riemann conjecture on the zeros of the ζ -function in the strip 0<Re<1   is derived and some aspects of application of this criterion are discussed.

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

Dynamic systems described by two differential equations with derivatives of fractional order
Nazaraliev M. A., Beibalaev V. D.

Dynamic systems described by two differential equations of fractional order are considered. The behavior of phase trajectories in case of real roots of the characteristic equation is investigated. Phase trajectories for various values of parameter are constructed and system transition from one dynamic state to another is established.

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

On Positive invertibility and splittings of operators in ordered Banach spaces
Sivakumar K. C., Weber M. R.

The positive invertibility of operators between Banach spaces, ordered by special closed cones, is characterized by the existence of splittings for the operators into the difference of two operators with appropriate spectral properties. Some results, up to now known only for matrices, are generalized to operators and to order intervals of operators.

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

Explicit solution of the mixed problem in an anisotropic half-space for the Barenblatt-Zheltov-Kochina equation
Umarov Kh. G.

For the Barenblatt-Zheltov-Kochina model of filtering liquids in fissured rocks an explicit solution of the mixed problem in anisotropic half-space with pronounced horizontal permeability is found by reduction to some abstract mixed problem in Banach space.

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

On numerical solution of a scattering problem. Analysis of numerical results
Khubezhty Sh. S., Tsutsaev A. O.

Numerical results for the Lippmann-Schwinger equation obtained with the application of the associated second kind Legendre function are described and analyzed. The effectiveness of the constructed computational scheme is illustrated.

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

Vector additive schemes for certain classes of hyperbolic equations
Shkhanukov-Lafishev M. H., Arhestova S. M., Tkhamokov M. B.

Vector-additive schemes for certain classes of hyperbolic equations arising in the theories of moisture transport and waves in relaxing media are constructed. Stability and convergence of difference schemes in the class of sufficiently smooth solutions are proved.

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

Aleksandr Alexandrov and Vladimir Smirnov, Mathematicians-Enlighteners
Kutateladze S. S.

This is an overview of the contribitions of Aleksandr D. Akexandrov and Vladinit I. Smirnov in the mathematical life of Russia.

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

Symmetrical polynomials and conservation laws
Shabat A. B.

Vector fields with symmetrical polynomials as the first integrals are considered. The connection of these dynamical systems with the theory of multi-phase solutions of the solitonic models of mathematical physics is established.

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

Mazurov Victor Danilovich
(on the occasion of his 70th birthday)

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

Contribution of Anatoly Kusraev to subdifferential calculus and boolean valued analysis
(on the occasion of his 60th birthday)

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