2017
Том 69
№ 9

All Issues

Volume 12, № 1, 1960

Article (Russian)

Interpretation of the Plane Axioms of Euclidian Geometry in an Abstract Group. I

Zarovny V. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 3-12

A special lexicon is given for the interpretation in the group (I, II, IV, D)* of the linear axioms of congruence of Euclidian geometry, and a solution is presented of the problem: under which conditions do these axioms hold true in the group under discussion. The concept of «elliptical systems of crts* is introduced.

Article (Russian)

Distributions on a Hilbert Space

Kats G. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 13-24

A general construction is given of systems of distributions on a Hilbert space. Each system is constructed according to a certain operator and the resulting distributions form a normed space. A canonical representation of these systems is obtained. In a note to follow soon, this construction will be used to obtain the spectral expansions of self-adjoint operators.

Article (Russian)

Some Transformations of Multiple Weiner Integrals

Kovalchik I. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 25-31

In the present paper the author determines multiple Wiener integrals using the determination of an ordinary Wiener integral as an abstract Le-besgue integral. Moreover, the author examines the transformation of multiple Wiener integrals under a general class of linear homogeneous transformations (1), transformations (lfi) and combined transformations (18),generalizing corresponding theorems of R. H. Cameron and W.T. Martin. Corresponding transformation formulae are given — (5), (17), (19).

Article (Russian)

Approximate Solution of Fredholm Integral Equations by the Method of Averaged Functional Corrections

Luchka A. Y.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 32-46

Article (Russian)

On an Integro-Differential Equation

Popov G. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 46-54

Article (Russian)

Anwendung der Operationsberechnung zu einigen Problemen der dunnen, zylindrischen Schalen

Schestopal A. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 55-71

Article (Russian)

On the Calculus of Operations

Shtokalo I. Z.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 72-78

Brief Communications (Russian)

On the Motion of a Load on a Depressed Shell

Berezovsky A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 79-87

Brief Communications (Russian)

On Spherical Representation of Curves and Surfaces in a Lobachevsky Space

Vakarchuk B. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 87-92

Brief Communications (Russian)

On the Inverse Problem for Quantum Mechanics Equations

Mal'chenko V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 93-96

Brief Communications (Russian)

On a Non-linear Integral Equation

Rozovsky M. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 96-98

Brief Communications (Russian)

Remarks on the Transformations of Multiple Sequences

Timan M. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 99-100

Brief Communications (Russian)

On Functions of Two Complex Variables Analytical in a Hypersphere

Shafeyev M. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 101-106

BookReview (Russian)

List of Books and Articles on Mathematics Published in the Ukraine in 1956 — 1957 (compiled by G. N. Sakovich)

Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 107-111