Mathematics

Obstructions to Embedding of Matrix Algebra Bundles into a Trivial One

Authors: Ershov A. V.

Topological obstructions to embedding of an Mk(C)-bundle into a trivial Mkl(C)-bundle under the condition (k, l) = 1 are studied. The relation of this problem to the theory of bundles with a structure groupoid is described.

Method for Analysis of Queueing Networks with Dynamic Control of Service Rates

Authors: Dolgov V. I., Rogachko E. S.

Model of evolution and a method for analysis of closed exponential queueing networks with dynamic control of service rates are proposed. A method of computing of the stationary distribution and formulas for calculating of stationary characteristics of the networks are presented. An example of analysis of considered type queueing network is given. According to the results of analysis and simulation of this network the accuracy of this method is sufficient for practical application.

On Varieties of Partially Ordered Semigroups with Operations of Cylindrification

Authors: Bredikhin D. A.

The finite basis of identities of the varieties of the ordered algebras generated by partially ordered semigroups of binary relations with cylindrifications operations is found in this paper.

Recovering Differential Operators on a Bush-Type Graph

Authors: Yurko V. A.

An inverse spectral problem is studied for Sturm–Liouvilleoperators on arbitrary graphs with a cycle. A constructive procedure for the solution is provided and the uniquenness is established.

About Asymptotics of Chebyshev Polynomials Orthogonal on an Uniform Net

Authors: Sultanov E. S.

In this article asymptotic properties of the Chebyshev polynomials Tn(x,N) (0 ≤ n ≤ N − 1) orthogonal on an uniform net ΩN = {0,1,...,N − 1} with the constant weight µ(x) = 2 N (discrete analog of the Legendre polynomials) by n = O(N 1 2 ), N → ∞ were researched. The asymptotic formula that is relating polynomials Tn(x,N) with Legendre polynomials Pn(t) for x = N 2 (1 + t) − 1 2 was determined.

Multiple Non-Completeness for the System of Eigenfunctions of a Class of the Pencils of Ordinary Differential Operators

Authors: Shigaeva O.

A class of the pencils of ordinary differential operators of n-th order with constant coefficients is considered. The roots of the characteristic equation of the pencils from this class is supposed to lie on a straight line coming through the origin. The main condition is such that the generating functions for the system of eigen- and associatedfunctionsarelinearcombinationsofexponentialfunctions.

On the Uniqueness of Series with Respect to Characters of Dyadic Groups

Authors: Polyakova N.

Conditions on series with respect to characters of dyadic groups are specified by which finite or countable set is the set of uniqueness.

Interpolation by the Simplest Fractions

Authors: Kondakova E. N.

The interpolation by means of real simplest fractions is considered. There are offered a different ways of intepolating simpest fractions construction with distinct real nodes. Necessary and sufficient conditions of existence and uniqueness of interpolating simplest fractions are received. Interpolation of constants is in detail investigated; in this case the estimation of an error of interpolation on Chebyshev‘s system of nodes is received.

Two-Mode Branching Extremals of Smooth Functionals with Homogeneous Features of the Sixth Order in Minima Points

Authors: Kolesnikova I. V.

A description of Fredholm functionals extremal distribution, bifurcating from minima points with two-dimensional degeneration and features of the sixth order is given. The main illustrating exampleistheproblemofheterogeneouscrystalferroelectricphases branching (based on helical model). We use modified Lyapunov – Schmidt method ( reduction to key function on Rn), equipped with the elements of singularities theory of smooth functions. Emphasis is put on key function with square symmetry.

On the Diffusionand Slow Convectionin Slightly Compressible Viscous Fluid

Authors: Gritsenko S. A.

We consider diffusion and slow convection of admixture in slightly compressible viscous fluid, described by the Stokes system, where viscous of fluid depends on the concentration of admixture. The Stokes system suppliedby the diffusionequation with the convective term.We prove for this system the correctnes softheinitial-boundary problem in the limited domain with the homogeneous Dirichlet conditions for the fluid velocity and the homogeneous Neuman condition for the concentration of admixture on the boundary of domain.

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