Mathematics

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.

Nonseparable Wavelets of Meyer Type in Besov and Lizorkin – – Triebel Spaces

Authors: Garkovskaya S.

Iti sproved that Fourier transforms of nonseparable wavelets of Meyer type can be used as decomposition of unity in definition of Besov and Lizorkin – Triebel spaces. The result is the first step in the proof of unconditional basisness of above mentioned wavelets in scales under consideration.

About the Solution of Nondegenerate Four-Element Boundary Value Problem of Karleman Type for Bianalytical Functions in Circle

Authors: Bogdanova N. N., Rasulov K. M.

The article is devoted to the investigation of four-element boundary value problem of Karleman type for sectionally bianalytical functions withdiscontinuityline L = {t : |t| = 1}. Aconstructivemethodfor solution of the problem concerned in a socalled nondegenerate case was found. It is established that solution of the investigated problem consists of solution of two generalized and two usualscalar boundary value problems of Riemann for sectionally analytical functions with discontinuity line L.

On Stilties Differential on Time Scales

Authors: Bakhtina Z. I.

In this paper we apply the method of Stilties differentials offered by U.V. Pokornyi to the theory of Dynamic Equations on Time Scales. It’s possibly to put this theory on serious mathematical basis.