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

Contents and Abstracts

Volume 514,   Issue 50,   2001


Gordevsky V. D. Transitional Regime Between Spiral Equilibrium States of a Gas, P. 17 - 33.

The interaction between two spiral flows of a gas of hard spheres isdescribed by the bimodal distribution which has a form of the linearcombination of stationary inhomogeneous Maxwellians. Each of the flowsrotates about its axis and can move translationally along it. Sufficientconditions for infinitesimality of the integral norm of a differencebetween the right-- and the left--hand sides of the Boltzmann equation areobtained. 2000 Mathematics Subject Classification 76P05. Top of the page.

Dyukarev Yu. M. The continual interpolation problem in the Stieltjes class, P. 34 - 40.

In this work the problem of integral representation of one classof hermitian nonnegative functions is studied.This problem is treated as a continual interpolation problemin the Stieltjes class.With the help of the of interpolation problem methods the existenceand unicity of the solution is proved.2000 Mathematics Subject Classification 47A57, 42A82. Top of the page.

Popova E. V. Special solutions of Maxwell's equations in multiply connected area , P. 41 - 52.

The denumerable system of the basic solutions of Maxwell's equations, including a finite subsystem,characteristic of multiply connected area, is created.2000 Mathematics Subject Classification 35Q60. Top of the page.

Rabah R., Bergeon B. On state space representation for linear discrete-time systems in Hilbert spaces, P. 53 - 62.

For a linear continuous-time control system in Hilbert space with state $x(t)$ is associated a discrete-time system where the state variable is $z_k={(x({(k+1)}h)+x(kh)})/{2}$, with small $h$. This allows to introduce a discrete derivative $\Delta z_k=({x({(k+1)}h)-x(kh))}/h$. The obtained discrete-time system has structural properties with a similar formulation as continuous system. Stability is equivalent to the fact that the spectrum of the state operator of discrete-time system is in the left half plane, Lyapunov and Riccati equation are similar.2000 Mathematics Subject Classification 93C25, 93C55. Top of the page.

Sokhin A. S. Identification of the mathematical model for a linear one-dimensional control system, P. 63 - 72.

The paper includes statement and the solution of the identification problem of the mathematical model for a control system describe by anordinary differential equation of arbitrary order by means ofpreassigned impulse controls and observed final states.2000 Mathematics Subject Classification 93B30. Top of the page.

Vorobyov I. V. A scattering scheme for the singular metrical colligation, P. 73 - 90.

In the work the model of the singular metrical colligationfor the nearly normal operators is created. The connection between the characteristic and determining functions of that colligation is obtained. For the colligation with the involutive metrics the unitary dilation of the solution of the linear homogeneous Cauchy problem is created. The properties of the wave operators and scattering operator are studied. 2000 Mathematics Subject Classification 47A20. Top of the page.

Gorr G. V. Melnik A. S. About three invariant parities for the equations of solid body dynamics, P. 91 - 98.

In this work three invariant parities for the G Grioli - M.P.Harlamov'sequations are considered. In the assumption, that are known potentialand gyroscopic functions, the algorithm of research of conditions oftheir existence is specified which is based on use of the first integralsand integration of the equations Poisson.2000 Mathematics Subject Classification 70E17, 70E05. Top of the page.

Olefir E. I. Uniform correctness one Cauchy problem and the matrix Makenhaupt condition, P. 99 - 105.

Class of unbounded non-selfadjoint operators in the space of vectorfunctions $L_2([0,a],C^n)$, for which the conditions to generate the semi group of the class $C_0$ is formulated in the terms of Makenhaupt condition for the special matrix weight is studied. The application of the main results to the theory of periodic in average functions correspondent to the system of functions.2000 Mathematics Subject Classification 30A99. Top of the page.

Dimitrova S. D. Curvilinear integral of abstract almost periodic and Levitan- almost periodic functions, P. 106 - 114.

In the present paper the Bohl-Bohr theorem has been carried over to curvilinear integral under condition of its independence of integration curve. The class of spaces and functions, for which the Bohl-Bohr theorem is correct has been extended. Almost periodic, Levitan-almost periodic and continuous functions in some weaker topology, than initial in Frechet spaces and general locally convex spacesare considered.2000 Mathematics Subject Classification 43A60. Top of the page.

Andrejtzev A. U. Classification and exact solutions of non-linear evolution equations , P. 115 - 121.

The new method of classification of non-linear evolutionequations of Form $u_t =uu_{xx}+F(u,u_x )$under differential connections$u_{xx}=f(u,u_x )$, which allow reduction to systems of two ordinarydifferential equations ,is suggested in the paper. It is compatibility of input equationsystem is insured if$F(u,u_x )$satisfies parabolic typeequation, which is reduced by classical change to ordinary differentialequation with a parameter.It is proved that when substituting the solution of the additionalequation to input evolution equation, the latter is reducedto the system of two input differential equation. The examplesof reduction and exact solutions of input equation, obtainedby the described method are given.2000 Mathematics Subject Classification 35K10. Top of the page.

Avramenko O. V. Resonanse and form of waves-packets on fluid interface, P. 122 - 128.

The form of wave-packets, direction of distribution, and condition ofthe second harmonic resonance on a interface of fluid layer andhalf-space are investigated. The conditions of wave packets propagationof the various form are submitted, the characteristics of resonantregion are found out, the formation conditions of head-on waves areformulated.2000 Mathematics Subject Classification 354J. Top of the page.

Leibina O. V.Affine classification of points of many-dimensional complex surfaces , P. 129 - 141.

In this article we obtain the affine classification of points ofmany-dimensional regular complex surfaces embedded into the complex space${\bf C}^n$ with arbitrary codimention. It is also found out for which complex surfaces there exists a finite number of classes of affinelyequivalent points.2000 Mathematics Subject Classification 53B25. Top of the page.

Chernyatin V. A. Constructing of asymptotic estimates for eigenvalues of operator Sturm-Lieuvill with arbitrary accuracy, P. 142 - 155.

The paper devoted to constructing of new asymptotic estimates for eigenvaluesof classcal boundary-value problem of Sturm-Lieuvill. On the basis of elementary means of analysis of successive approximations fortranscendence equation, defined eigenvalues, the principle possibility of obtaining for eigenvalues the asymptotic estimates with accuracy up to arbitrary order of smallness is established.2000 Mathematics Subject Classification 34B24, 34L20. Top of the page.

Gandel Yu. V., Polyanskaya T. S. Substantiation of numerical solution of singular integral equation with Hilbert's kernel, P. 156 - 163.

Several problems of wave diffraction give rise to the first kindintegral equation with logarithmic kernel. This equation reduces tosingular integral equation with Hilbert's kernel and additional clause.A discretization with Lifanov's normalization is realized. The estimatedrate of discrete probem solution convergence to exact solution of singularintegral equation with additional clause is substantiated religiously.2000 Mathematics Subject Classification 45E99,65R20. Top of the page.

Milewski J., Popiel K. The eigenproblem of free anyons and anyons in harmonic isotropic oscillator potential , P. 164 - 169.

The eigenproblem for the cases of free anyons and of anyons in harmonicisotropic oscillator potential on a plane is given by means ofanyonic harmonic functions and hipergeometric functions.2000 Mathematics Subject Classification 81Q05. Top of the page.

Melnik T. A. Iterated method of optimal control problem for linear standard form system , P. 170 - 176.

In that work the modification of a known method oftransformation of independent variables on a solution fromthe theory of hyperbolic systems is considered. In offeredalternative, with reference to the systems of two equationsthe transition to a grid of characteristics is guaranteed.2000 Mathematics Subject Classification 34H05. Top of the page.

Vasyl'kiv Ya. V., Tarasyuk S. I. Minimal growth majorants of subharmonic functions in ${\pbf R^m}$ of infinite order , P. 177 - 182.

The minimal growth majorants of subharmonic functions in ${\bf R^m},\ m\ge3$, with restriction on its Riesz measure are found. As corollary, the canonical representation theorem of $\delta$-subharmonic function in ${\bf R^m}$ by difference of subharmonic functions is dedused.2000 Mathematics Subject Classification 31A05. 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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