2017
Том 69
№ 9

All Issues

Volume 53, № 1, 2001

Article (Russian)

On Some Properties of Orthogonal Polynomials over an Area in Domains of the Complex Plane. II

Abdullayev F. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 3-13

We investigate polynomials that are orthonormal with weight over the area of a domain with quasiconformal boundary. We obtain new exact estimates for the growth rate of these polynomials.

Article (Russian)

On the Asymptotics of the Sojourn Probability of a Poisson Process between Two Nonlinear Boundaries That Move Away from One Another

Gasanenko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 14-22

We obtain the complete asymptotic decomposition of the sojourn probability of a homogeneous Poisson process inside a domain with curvilinear boundaries. The coefficients of this decomposition are determined by the solutions of parabolic problems with one and two boundaries.

Article (Ukrainian)

Best Orthogonal Trigonometric Approximations of Classes of Functions of Many Variables $L^{ψ}_{β, p}$

Konsevich N. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 23-29

We obtain order estimates for the best orthogonal trigonometric approximations of classes of functions of many variables L β, p ψ in the space L q, 1 < p < q < ∞, q > 2.

Article (Ukrainian)

Differentiability of Fractional Integrals Whose Kernels Contain Fractional Brownian Motions

Krvavich Yu. V., Mishura Yu. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 30-40

We prove the stochastic Fubini theorem for Wiener integrals with respect to fractional Brownian motions. By using this theorem, we establish conditions for the mean-square and pathwise differentiability of fractional integrals whose kernels contain fractional Brownian motions.

Article (Ukrainian)

Limit Theorems for Random Elements in Ideals of Order-Bounded Elements of Functional Banach Lattices

Matsak I. K., Plichko A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 41-49

For a sequence of independent random elements belonging to an ideal of order-bounded elements of a Banach lattice, we investigate the asymptotic relative stability of extremal values, the law of large numbers for the pth powers, and the central limit theorem.

Article (Russian)

Methods for the Elimination of Unknowns from Systems of Linear Inequalities and Their Applications

Finin G. S., Ostapenko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 50-56

We study methods for the elimination of an unknown or a group of unknowns from systems of linear inequalities. We justify these methods by using the Helly theorem. The methods considered are applied to the calculation of streams in networks with a generalized conservation law.

Article (Ukrainian)

First-Order Equations of Motion in the Supersymmetric Yang–Mills Theory with a Scalar Multiplet

Pavlyuk A. M., Yatsun V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 57-63

We propose a system of first-order equations of motion all solutions of which are solutions of a system of second-order equations of motion for the supersymmetric Yang–Mills theory with a scalar multiplet. We find N = 1 transformations under which the systems of first- and second-order equations of motion are invariant.

Article (Russian)

On the Existence of Local Smooth Solutions of Systems of Nonlinear Functional Equations with Deviations Dependent on Unknown Functions

Pelyukh G. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 64-77

We obtain conditions for the existence of a local differentiable solution of a system of nonlinear functional equations with nonlinear deviations of an argument.

Article (Ukrainian)

On the Stability of Invariant Sets of Discontinuous Dynamical Systems

Chernikova O. S., Perestyuk N. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 78-84

We establish sufficient conditions for the stability, asymptotic stability, and instability of invariant sets of discontinuous dynamical systems.

Article (Russian)

Ultrafilters and Decompositions of Abelian Groups

Protasov I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 85-93

We prove that every PS-ultrafilter on a group without second-order elements is a Ramsey ultrafilter. For an arbitrary PS-ultrafilter ϕ on a countable group G, we construct a mapping f: G → ω such that f(ϕ) is a P-point in the space ω*. We determine a new class of subselective ultrafilters, which is considerably wider than the class of PS-ultrafilters.

Article (Russian)

On the Periods of Periodic Motions in Autonomous Systems

Ronto A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 94-112

We obtain certain estimates for the periods of periodic motions in Lipschitz dynamical systems.

Brief Communications (Russian)

On τ-Closed Formations of n-Ary Group

Al Dababseh Avni Faez

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 113-116

We prove that if G is a nonsingle-element n-ary finite group that belongs to a τ-closed formation \(\mathfrak{F}\) , then \(G/{\text{soc(}}G{\text{)}} \in \Phi _\tau (\mathfrak{F})\) , where \(\Phi _\tau (\mathfrak{F})\) is the intersection of all maximal τ-closed subformations of the τ-closed formation of n-ary groups \(\mathfrak{F}\) .

Article (Ukrainian)

Higher-Order Relations for Derivatives of Nonlinear Diffusion Semigroups

Antoniouk A. Val., Antoniouk A. Vict.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 117-122

We show that a special choice of the Cameron–Martin direction in the characterization of the Wiener measure via the formula of integration by parts leads to a set of natural representations for derivatives of nonlinear diffusion semigroups. In particular, we obtain a final solution of the non-Lipschitz singularities in the Malliavin calculus.

Brief Communications (Ukrainian)

A Mixed Problem for One Pseudoparabolic System in an Unbounded Domain

Domans'ka G. P., Lavrenyuk S. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 123-129

We prove the existence and uniqueness of a solution of a mixed problem for a system of pseudoparabolic equations in an unbounded (with respect to space variables) domain.

Brief Communications (Ukrainian)

On Proximity of Correlation Functions of Homogeneous and Isotropic Random Fields Whose Spectral Functions Coincide on a Certain Set

Pavlov D. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 130-134

We give examples of application of the mean-value theorem to finding various estimates of the proximity of correlation functions in the case where their spectral functions coincide on a certain set.

Article (English)

Expansions for the Fundamental Hermite Interpolation Polynomials in Terms of Chebyshev Polynomials

Rizk M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 135-143

We obtain explicit expansions of the fundamental Hermite interpolation polynomials in terms of Chebyshev polynomials in the case where the nodes considered are either zeros of the (n + 1)th-degree Chebyshev polynomial or extremum points of the nth-degree Chebyshev polynomial.