2019
Том 71
№ 8

Всі номери

Том 47, № 6, 1995

Стаття (англійською)

On proper accretive extensions of positive linear relations

Арлинський Ю. М.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 723–730

A linear relation S is called a proper extension of a symmetric linear relation S if S ⊂ S ⊂ S*. As is well known, an arbitrary dissipative extension of a symmetric linear relation is proper. In the present paper, we establish criteria for an accretive extension of a given positive symmetric linear relation to be proper.

Стаття (російською)

Асимптические разложения, связанные с функционалом метода „складного ножа”. II

, Бардадым Т. А., Иванов А. В.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 731–736

This paper is a sequel to part I [Ukr. Mat. Zh.,47, No. 4, 443–452 (1995)]. By using the results of the first part, we obtain the initial terms of the asymptotic expansions of the bias and variance for the jackknife estimator of the variance of the error of observations in a nonlinear regressive model.

Стаття (українською)

Cauchy problem for the essentially infinite-dimensional heat equation on a surface in a Hilbert space

Богданський Ю. В.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 737–746

It is proved that the Cauchy problem for a simple parabolic equation with essentially infinite-dimensional coefficients on bounded level surfaces of smooth functions in a Hilbert space is uniformly well posed.

Стаття (російською)

О необходимых и достаточных условиях, при которых из суммируемости числового ряда следует его сходимость

Давыдов Н. А.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 747–754

On the basis of the concepts of (C) -point and (¯R, p)-point of a sequence of complex numbers introduced by the author and results established earlier, we formulate necessary and sufficient conditions for the summability of a number series by a positive Cesaro method or the Riesz method to imply the convergence of this series. We also present a sufficient condition for summability to imply the convergence of a subsequence of its partial sums.

Стаття (українською)

Скінченні недисперсивні групи, у яких всі підгрупи непримарного індексу метациклічні

Зузук Л. І.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 755–759

We describe the structure of finite nondispersible groups all subgroups of which with nonprimary index are metacyclic.

Стаття (українською)

On a new class of infinite groups

Івко М. Н., Сенашов В. І.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 760–769

The present paper is devoted to the study of properties of a new class of Φ-groups. The class of layer-finite groups is characterized with an accuracy to within this class.

Стаття (англійською)

Multipoint boundary-value problems with pulse effects

Каранджулов Л. І.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 770–774

By using pseudoinverse matrices, we establish conditions for the existence and uniqueness of solutions of linear and weakly linear boundary-value problems for ordinary differential equations with pulse action. We consider the case where the dimension of a differential system does not coincide with the dimension of the boundary conditions.

Стаття (російською)

Редукция основной бигармонической задачи для квадранта к несингулярным интегральным уравнениям

Мельниченко И. П., Плакса С. А.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 775–784

The principal biharmonic problem for a quadrant with piecewise-continuous boundary conditions is reduced to a system of nonsingular integral equations.

Стаття (російською)

О сходимости комплексных степенных рядов с независимыми случайными коэффициентами

Мередов Б.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 785–789

We find the domains of convergence and analyticity of Maclaurin and Laurent random power series.

Стаття (російською)

Об одной нелокальной задаче для параболического уравнения

Березанский Ю. М., Митропольский Ю. А., Шхануков-Лафишев М. Х.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 790–800

We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW 2 1,0 (Q T ), and construct a difference scheme for the second-order approximation.

Стаття (українською)

Метод усереднення в деяких задачах теорії нелінійних коливань

Петришин Р. І.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 801–810

By using the averaging method, we prove the solvability of multipoint problems for nonlinear oscillation systems. The deviation of the solutions of original and averaged problems is estimated.

Стаття (російською)

Асимптотика по параметру фундаментальной системы решений линейного функционально-дифференциального уравнения

Радзиевский Г. В.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 811–836

We study a functional-differential equation , whereF is a linear operator acting from the Hölder spaceH γ into the Sobolev space W p s [0, 1] and ρ is a complex parameter. For large absolute values of ρ, we construct a one-to-one correspondence between the solutionsx(ρ;t) andy(ρ;t) of the equations andy (n)y n=0. We also establish conditions that should be imposed on the operatorF in order that specially selected fundamental systems of solutions of these equationsx j (ρ;t) andy j (ρ;t), j=1,...,n, satisfy the estimate with constantsc, κ>0 for the functional space =W q l [0, 1] or .

Стаття (українською)

Дослідження інтеграла функції вздовж траєкторій нільпотентного потоку

Парасюк І. О., Самойленко А. М.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 837–847

We establish conditions under which the integral of a function along a nilpotent flow on the Heisenberg-Iwasawa manifold increases not faster than \(|t|^{{1 \mathord{\left/ {\vphantom {1 {2 + \varepsilon }}} \right. \kern-0em} {2 + \varepsilon }}} ,0< \varepsilon<< 1\) and indicate cases where this integral can be represented as a superposition of a function defined on a nilmanifold and a nilpotent flow.

Коротке повідомлення (англійською)

On the monotonicity and constancy of signs of some rational explicit methods for nonlinear systems of ordinary differential equations

Глинський Я. М., Панчишин Ю. Ю.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 848–852

We study one special type of explicit rational numerical methods for the solution nonlinear systems of ordinary differential equations and analyze the so-called property of constancy of signs of integration methods. This means that the inner product of approximate solutions at two adjacent points of the grid is positive for the corresponding differential equation. We establish the unconditional (i.e., for all sizes of steps) monotonicity and constancy of signs of rational methods.

Коротке повідомлення (англійською)

BBGKY hierarchy and its evolution operator for one class of integrable systems

Скрипник В. І.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 853–858

We define the abstract BBGKY hierarchy and its formal evolution operator. The existence of the latter is established in a special Banach space for a system of charged particles with Chern-Simons interaction regularized for small and large distances. An analog of the high-temperature expansion of equilibrium statistical mechanics is applied.

Коротке повідомлення (російською)

Робастная устойчивость систем с запаздыванием

Мустафаева P., Хусаинов Д. Я.

↓ Абстракт

Укр. мат. журн. - 1995. - 47, № 6. - С. 859–863

We consider linear stationary systems of differential equations with delay. The matrices that determine the dynamics of a system vary within a certain interval. We obtain sufficient conditions for the robust stability of systems uniform with respect to delay and depending on the deviation of the argument.