2017
Том 69
№ 6

All Issues

Volume 12, № 2, 1960

Article (Russian)

Great Leader and Scientist (on the 90th anniversary of V. I. Lenin's birth)

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 115-117

Article (Russian)

New Method for the Numerical Integration of Ordinary Differential Equations

Bondarenko P. S.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 118-131

The author introduces the concept of an /in-approximate solution of a problem with initial conditions for an ordinary differential equation of the first order and derives the integral equation of the error of this approximate solution. The segment of the existence of a real hn - approximate solution is established. An iterative process is proposed for the solution of the integral equation of the error, and the sufficient conditions for its convergence are established. The author shows that the proposed iterative process of finding the error of the A«-approximate solution of a problem with initial conditions for an ordinary differential equation of the first order makes it possible to find its numerical solution with any given precision and to determine the segment of existence of a solution of this problem with sufficient precision An estimate of the error of the numerical integration was obtained by the methods of. Euler, Runge and Adams.

Article (Russian)

On the Double Spectral Representation of the Fourth- order Feynman Amplitude

VIadimirov V. S.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 132-146

The double spectral representation for the Feynman amplitude corresponding to a fourth-order diagram is proved and the spectral function is explicitly calculated. The conditions for the validity of such representation in the fourth order are obtained.

Article (Russian)

On an Algorithm of Synthesis of Abstract Automats

Glushkov V. M.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 147-156

A simple and practically convenient algorithm of synthesis of finite automats after events represented by them is described in this paper. The term «finite automat» is taken in the sense of Moore; and the term «event», in the sense of Kleene. As distinct from other algorithms, the synthesis algorithm described is composed so as to represent several events at once.

Article (Russian)

Statement and Solution of Boundary Problems for Infinite Systems of Ordinary Differential Equations

Zhautykov O. A.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 157 - 164

The author considers the problem of finding a solution of the infinite system of ordinary differential equations. The stated problem will be called the boundary problem for the infinite system of ordinary differential equations. On the basis of Picard's method of successive approximations, the author proves the theorem of the existence and singularity of the solution of the stated problem. The properties of the solution of the problem are established, as well as the conditions on satisfaction of which the solution of the boundary problem for an infinite system of differential equations (1) is reduced to the solution of such a problem for a finite system of differential equations.

Article (Russian)

On a Supplement to the Theorem of Bogoliubov-Vladimirov

Kolomitsev V. I., Petrina D. Ya.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 165 - 169

A spectral representation is found for one class of functions . The results obtained supplement the known theorem of Bogoliubov-Vladimirov on the analytic continuation of generalized functions.

Article (Russian)

Sur la méthode des interpolations tchebycheviennes successives et sur diverses variantes de sa réalisation

Rémès E. J.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 170 - 180

Résumé Les applications pratiques récentes de la méthode dont il s'agit, basée sur le second algorithme de l'auteur (1934) pour la construction effective des approximations. tchebycheviennes (polynomiales ou généralisées) des fonctions continues, ont mis à l'ordre du jour certaines questions d'actualité concernant la rationalisation possible des procédures correspondantes de réalisation numérique— conformément aux conditions techniques concrètes qui se présentent ainsi qu'aux types concrets des problèmes tchebycheviens à résoudre. Dans cet article un aperçu général des matières essentielles qui s'y rattachent se fait au fond d'une explication plus développée de quelques points de principe et en tenant compte de certaines recherches postérieures— de l'auteur lui-même, de quelques-uns de ses disciples ainsi que d'autres auteurs— parues jusqu'à ce jour. Dans deux notes à paraître prochainement 113, 14] nous traitons quelques questions concernant l'extension efficace de notre méthode aux problèmes tchebycheviens à paramètres entrant non linéairement.

Article (Russian)

Sur l'application de la méthode des corrections fonctionnelles moyennes aux équations du type parabolique linéaires par rapport aux dérivées

Sokolov Yu. D.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 181 - 195

Article (Russian)

On the Residual Terms of Expansions into Fourier's Series by Jacobi Polynomials of Functions, the r-Order Derivative of Which Satisfies Lipschitz's Condition

Yakhnin B. M.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 196 - 204

Anniversaries (Russian)

Nikolai Mitrofanovich Krylov (on the 80tn anniversary of his birth)

Bogoliubov N. N., Mitropolskiy Yu. A.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 205 - 208

Brief Communications (Russian)

Problem of Dispersion for a Schrodinger Equation

Nizhnik L. P.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 209 - 212

Brief Communications (Russian)

On Topological Subgroups on the Integral

Ogurtsov N. I.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 212 - 215

Brief Communications (Russian)

Factorability of a Differential Operator and a Theorem on Differential Inequalities

Skorobogatko V. Y.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 215 - 219

Brief Communications (Russian)

On the Necessary and Sufficient Conditions for Selective Invariantness

Simonov N. I.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 219 - 223

Brief Communications (Russian)

On One Class of Vectorial Isotropic Random Fields

Yadrenko M. I.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 223 - 225

BookReview (Russian)

List of Literature on Mathematics Published in the Ukraine in 1958—1959

Sakovich G. N.

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Ukr. Mat. Zh. - 1960. - 12, № 2. - pp. 226 - 229