Visnyk of Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics

Contents and Abstracts

Volume 542,   Issue 51,   2002


Korobov V.I., Smortsova T.I. The solution of the Bellmann equation for the steering problem and its connection with the moment problem P. 3-12.

In the present paper the natural method to solve the Bellmann equation as the partial differential equation of the first order is proposed. The constructive solution of the mentioned equation for the steering problem for the canonical system of the $n$-th order is presented. The connection of the proposed method to solve the Bellmann equation and the moment problem is obtained. 2000 Mathematics Subject Classification 49L20, 93C05. Top of the page.

Boichuk I.P., Tarapov I.E. Application of a momentum integral model to studying viscous liquid motion through deforming tubes , P. 13-18.

The momentum integral model is applied to research of the unsteady motion of viscid fluids in long pipes of the variable section.It is shown, that this method can be effectively used to study the blood motion along thin vessels for a number of different problems. 2000 Mathematics Subject Classification 9210. Top of the page.

Gassan Y. S. Boundary Equations in Dynamic Problems for Thin the Piecwise Homogeneous Plates , P.19-27.

A contact problem of dynamics for thin elastic plates in the framework of Kirchhoff model is under consideration. With the help of the potential theory this problem is reduced to the systems of boundary equations. The unique solvability of these systems is proved in one-parameter scale of Sobolev-type function spaces. 2000 Mathematics Subject Classification 42A70, 35M05. Top of the page.

Grishin A.F., Poedintseva I.V. The integrals with kernels including logarithms , P. 28-34

There are derived asymptotic formulas for integrals of two types. The first integral has a special kernel being a linear- fractional function of $r^{\pi\alpha}$ in variable r. We obtain an n-terms asymptotic expansion in powers of $\frac{1}{r}$,where n depends of $\alpha$. An asymptotic formula for the second type of integrals is deduced by nonstandard integration by parts. 2000 Mathematics Subject Classification 30E15. Top of the page.

Dyukarev Yu. M. The principle of maximum for Stieltjes pairs of analytical matrix-valued functions , P.35-41.

Solutions of many interpolation problems of Stieltjes matrix-valued functions can be described by a linear fractional transformations of Stieltjes pairs. The main result of the article is the principle of maximum for Stieltjes pairs. This principle of maximum can be used for researching of canonical, N-extremal, and the main solutions of interpolation problems of Stieltjes matrix-valued functions. 2000 Mathematics Subject Classification 47A57, 42A82. Top of the page.

Protcenko V.S., Popova N.A.The Dirichlet problem for the Laplace equation in the semispace with the cylindrical cavity , P.42-51.

By means of the general Fourier method Dirichlet problem for Laplace equation has been considered. The using of the addition theorems for the solutions of the Laplace equation in Cartesian and cylindrical coordinate systems has been allowed to reduce the problem to the infinite system of the linear algebraic equations with a quite continuous operator. This system has been decided by the reduction method. Calculations have been made for the concrete parameter values and the boundary functions. 2000 Mathematics Subject Classification 35J25. Top of the page.

Shahadeh Assadi About some classes of non-stationary curves generated by nonlinear operator equations in Hilbert spaces , P.52-58.

In this paper in terms $ K(t,s)= \langle z_t, z_s\rangle$ are investigation curves in Hilbert space which are formed by Cauchy problem $ \frac {dz_t}{dt}= A(t)z_t, \; z_t\bigl |_{t=0}=z_0,$ where $A(t)$ is a family bounded self-adjoint operators and its spectral function not depended on $t.$ By additional restrictions on $K(t,s)$ we have for received nonlinear operator equations for $A(t)$ which allow to represent the solution of Cauchy problem in obvious form . 2000 Mathematics Subject Classification 30A99. Top of the page.

Varyanitza L.A., Rezunenko V.A. Regularization of the electrostatic problem on the infinite cone and two spherical segments , P.59-68.

The regular solution of the electrostatic problem is obtained. The principal part of the operator problem is selected and found by the method of the contour integration. This part of the operator is inverted with the help of the Abel integral transformation. The system of two coupled integral equations of the second-kind Fredholm is produced. The effective solvability of these equations is mentioned. 2000 Mathematics Subject Classification: 65N12, 35A25, 78A45. Top of the page.

Lysenko Y.V., Ovcharenko I.E., Ugrinovskiy R. To the Problem of Effective Inversion of Positive-Definite Hankel-Hadamar , P.69-72.

We propose a procedure based on the power moment problem techniques. This procedure presents on inversion of positive-definite Hankel-Hadamard matrices. 2000 Mathematics Subject Classification 42A70. Top of the page.

Parfyonova N.D. Meromorphic almost periodic functions and their continuous extension to the Bohr's compactification of the strip , P.73-84.

We introduce the concept of the module for meromorphic almost periodic functions in a strip; their properties and connection with modules zeros and poles divisors are studied. We prove, that a meromorphic almost periodic function is continuously extendedx corresponding module Bohr's compactifications of a strip. 2000 Mathematics Subject Classification 42A74, 30D35. Top of the page.

Lutsenko A.V., Sklyar E.V. On analytical representation of classes of controls solving the problems of controllability and stabilization , P.85-95.

The possibility investigate for construction of classes of controls solving the problems of controllability and stabilization for linear systems. In explicit form classes of summable controls solving the problems is given. 2000 Mathematics Subject Classification} 93B05. Top of the page.

Udodova O.I. Holomorphic functions in a tube domain, which are almost periodic , P.96-105.

There are series of the theorems confirming, that from holomorphy of a function in a strip and an almost periodicity on one straight line under some conditions are followed almost periodicity in all strip of holomorphy. In this work these theorems are extended to holomorphic functions in a tube domain; besides the uniform metric, we consider Stepanoff's metric. 2000 Mathematics Subject Classification 42A75, 30B50. Top of the page.

Dumina O. A. Boundary equations in the dynamic problem for thermoelastic media with mixed boundary conditions , P.106-117.

The mixed boundary value problem for thermoelastic media with mixed boundary conditions is under consideration. Its solution is represented by the sum of the dynamic analogues of thermoelastic single and double-layer potentials. This representation leads to system of coupled nonstationary boundary equations. The unique solvability of this system is proved in one-parameter scale of Sobolev type function spaces. 2000 Mathematics Subject Classification 42A70, 35M05, 73C25. Top of the page.

Vasyl'kiv Ya.V., Protsyk Yu.S.Canonical Weierstrass integral for subharmonic functions of infinite order , P.118-130.

For any nonegative Borel in $\BR^m\ (m\ge2)$ measures $\mu$ such that $\mu(\{y\in\BR^m:|y|\le r\})r^{2-m}\le\nu(r),\ r>0$, where $\nu$ is a growth function of infinite order, canonical Weierstrass integrals (subharmonic in $\BR^m$ functions $u$ with Riesz measures $\mu_u=\mu$) are constructed and growth majorants $\la(r)$ of functions $B(r,u)=\max\{u(y): |y|\le r\}$ naturally related to functions $\nu(r)$ are founded. As a result, a counterpart of a G.~Skoda's result for entire in $\BC^n$ functions of infinite order is established and explicit representations of subharmonic in $\BR^m\ (m\ge2)$ functions $u$ of infinite order is presented with minimal, in some sense, growth of the function $B(r,u)$. 2000 Mathematics Subject Classification 31A05. Top of the page.

Ievlev I.I. The dynamics of the plate which is interacting with the viscid incompressible liquid , P.131-135.

This work is containing of the solving of the problem about dynamics of the round plate covering the cylindrical capacity which fully filled by the viscid incompressible liquid. The Galerkin's method and the Laplas'es transformation for the variable of a time are applying . The expression of the logarithmic decrement of the fading of a small oscillations was obtained. 2000 Mathematics Subject Classification 76D05,74K20. Top of the page.

Marchenko I.I. On a question of Petrenko for entire functions of two complex variables , P.136-138.

It is constructed the entire function of two complex variables slowly growing on the first of them.The set of defect values of this function coincides with all complex plane. This example gives the answer to a question of V.P.~Petrenko. 2000 Mathematics Subject Classification 30D15, 30D35. Top of the page.

Zheleznyakova E.Yu. The stability of system of two couple stochastic oscillators , P.139-144.

A system of two linear couple oscillators with random Markov finitely valued coefficients is studied in this work. Exact equations for the first and second order solutions based on the transfer to the corresponding of integral Volters equations and averaging of iterations of these equations have been obtained. Analysis of stability in the average or in meansquar is reduced to researching of roots of the corresponding characteristic polynomial. Top of the page.

Gavrylyako V.M., Sokolov A.V. Numerical Solution of Nonsmooth Equations in Optimal Speed Problem , P.145-148.

The main purpose of this paper is to determine the expediency of application of Genetic algorithms to numeric solution of Optimization problems. We discuss the case where functional gradient has discontinuity of the first kind on the set with predefined structure. 2000 Mathematics Subject Classification 93B50. Top of the page.

Sokhin A.S. On some nonlinear system of equations of Burger type , P.149-154.

The paper includes the statement and the method for the solution of a nonlinear two-component system of equation of Burger type. 2000 Mathematics Subject Classification 35Q53. Top of the page.

Bozhydarnyk V.V. The strength of loosed by cracks anisotropic plates with antisym-metric strengthened boundary , P.155-170.

The method of approximative determination of limit elastic equilibrium state for loosed (weaked) by cracks anisotropic plates with antisymmetric strengthened boundary is proposed. Plates are under action of bending and stretching by bending moments, shearing forces, stresses with normal and tangential components in plate's plane. The examples for strengthened by rectan-gular prismatic bar round and elliptic hole in unlimited orthotropic plates and round and elliptic disks are considered. 2000 Mathematics Subject Classification 74K20, 74E10. Top of the page.

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Visnyk Kharkivs'koho natsional'noho universytetu imeni V. N. Karazina, Seriya Matematyka, prykladna matematyka i mekhanika

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