2017
Том 69
№ 5

All Issues

Volume 15, № 2, 1963

Article (Russian)

Streamlining by a plane stream of an ideal incompressible liquid of thin beams with large flexure

Borisenko A. I., Myshkis A. D.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 119-134

singular integral equation (3) for a single beam and (5) for a grating of beams. A single parabolic beam is discussed in detail. In this case the equation assumes form (10), and its solution is found in the form of a series (11) with undetermined coefficients, which are found by means of an infinite system of linear equations, the coefficients of which are expressed by double Fourier coefficients (14). A rapidly converging iterational method is indicated for finding the latter; the system of equations is also solved by means of rapidly converging iterations. The method may be extended to polynomial beams higher than the second power and on a grating of beams without essen t i a 1 changes.

Article (Russian)

Approximation mit Nebenbedingungen in linearen normierten Räumen.

Burov V. N.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 135-144

Hier handelt es sich um die Anwendungen der «geometrischen» Sähe aus dem I. Teil unseres Artikels (s. diese Zeitschrift, Bd. XV. N 1, 1963) auf die wichtigsten Funktionalräumen. Im Falle des Raumes aller stetigen Funktionen С ergeben sich Sätze, die jedes Extremalpolynom charakterisieren und dabei die allgemeine Form für alle Extremalpolynome finden lasser. Es ist auch die Existenz der Basis von gemeinsamen Punkten der Maximalabweichung aller Extremalpolynome ermittelt (vgl. [1 6]). Die weitere Ergebnisse des nächsten Paragraphen (§ 5) bringen Verallgemeinerung und Erweiterung des bekannten Satzes von G. Polya [31 — D. Jackson [4]. Zum Schluss wird es aufgezeigt, das Eindeutigkeit oder Mehrdeutigke4 der Lösung des Extremalproblems von des Struktur der «sphärischen» Körper in entsprechenden Räumen und von der Lage der Ansatzelementenmenge abhängig ist.

Article (Russian)

Some problein of the reliability ol systems with a reserve

Maryanovich T. P.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 145-157

The reliability of a system with some kind of reserve is considered in the case when faulty devices may be replaced.

Brief Communications (Russian)

Conformal mapping of given regions by the trigonometric interpolation method. I

Fil'chakov F. P.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 158-172

A method is outlined for trigonometric interpolation which secures any given precision of the mapped function for a fairly wide class of regions encountered when solving practical problems. The contour may be given analytically, graphically oi merely by a discrete series of points.

Article (Russian)

Sur la question de construction effective des meilleures approximations trigonometriques

Shteinberg A. S.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 173-184

Ayant en vue la résolution d'une question d'analyse numérique, analogue à celle considérée récemment par G. Hornecker [1] dans le cas des approximations polynomiales algébriques, nous élaborons ici un procédé de réalisation condensée de la variante trigonométrique du second algorithme de Rémès (cf., par exemple, [3], § 5, 9) pour la meilleure approximation, au sens de Tchebycheff, des fonctions développables en série trigonométrique, assez rapidement convergente. La méthode des abscisses corrigées, qui permet d'obtenir tout d'un coup le résultat approché de la réalisation successive de deux pas (de rang 0 et 1) du processus itératif de Rémès, est développée ici pour le cas général du problème indiqué, ainsi que pour divers cas possibles de symétrie de structure de la fonction qu'on approche. L'application de la méthode est illustrée par deux exemples qui terminent le travail.

Brief Communications (Russian)

On the smoothness up to the boundary of the nuclear region of an elliptical operator resolvent

Berezansky Yu. M., Roitberg Ya. A.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 185-189

Brief Communications (Russian)

On the construction of holomorphicity shells for Hartog's regions

Shirinbekov M., VIadimirov V. S.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 189-192

Brief Communications (Russian)

On the approximation of analytical functions by Faber-Walsh polynomials

Kiselev P. Ya.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 193-199

Brief Communications (Russian)

On a parametric random effect on linear and nonlinear oscillatory systems

Kolomiyets V. G.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 199-205

Brief Communications (Russian)

On the behaviour of a solution of differential equations of higher order

Krasnodembsky A. M.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 205-213

Brief Communications (Russian)

On the numerical solution of the basic bihannonic problem with a large number of net points

Prikhod’ko E. M.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 214-217

Brief Communications (Russian)

Expansion of linear and nonlinear differential operators into real cofactors. I

Skorobogatko V. Y.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 217-223

Brief Communications (Russian)

Investigation of nonstationary processes in an essentially nonlinear oscillatory system

Faizibaev E. F.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 223-227

Brief Communications (Russian)

Analytical properties of the amplitudes of generation in uniparticular approximation as a functicn of two variables

Fushchich V. I.

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Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 227-232