2017
Том 69
№ 9

# Volume 14, № 4, 1962

Article (Russian)

### Automata and events

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 351-361

The author introduces the concept of some generalized operation on events, called superposition, and proves the theorem: the superposition of represented events is another represented event. It is shown that many known operations on events are special cases of superposition and, consequently, the corresponding theorems of synthesis are consequences of the theorem of superposition. A language is introduced for describing represented events, which makes it possible to establish a connection between the language of regular expressions and the language proposed by Y. T. Medvedev. This is used for a new interpretation of V. M. Glushkov's algorithm of abstract synthesis.

Article (Russian)

### Application of a semi-inversive method to steady motions under dams

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 362-365

The method given in [1] is applied to steady plane motions under impervious dams. After general considerations, three particular cases are calculated.

Article (Russian)

### Classes of conjugate elements in topological groups

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 366-371

The author considers the classes of conjugate elements in topological groups. Definition. A topological group is called an FC-group, if the closure of every class of conjugate elements is compact, and one locally normal if everyone of its elements is contained in a compact invariant subgroup. Each locally normal group G is obviously a periodic * FC-group. The converse assertion is proved in this paper for groups with an open compact subgroup. The main result is the following. Theorem. Let G be an FC-group with an open compact subgroup. Then the set of all compact elements of G generates an open invariant subgroup P(G); the factor-group G/P(G) is a discrete torsion-free Abe- Han group.

Article (Russian)

### On the theory of a non-autonomous mathematical pendulum

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 372-382

The authors consider the equation of a nonlinear non-autonomous mathematical pendulum in various approximations from the viewpoint of oscillation, increase and damping of the amplitude and stability of the position of equilibrium; a classification of the motions is presented.

Article (Russian)

### Asymptotic behaviour of linear systems in the case of multiple roots of a characteristic equation

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 383-392

The results obtained by the author in 17] are extended. An algorithm is given for the construction of an asymptotic special solution of the system of linear differential equations (1) in the case when one of the roots of the characteristic equation possesses constant $K$-multiplicity, and the external frequency $iv(\tau)$ becomes equal to it at isolated paints of the segment $0 \leq \tau = \varepsilon t \leq L$, where $\varepsilon$ is a small real parameter.

Brief Communications (Russian)

### On the density of probability of a transition for solutions of stochastic equations of higher orders

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 393-397

Brief Communications (Russian)

### Analytical variant of Melentiev's method

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 398-403

Brief Communications (Russian)

### On the phenomenon of parametric resonance in torsional oscillations of crankshafts

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 403-407

Brief Communications (Russian)

### Investigation of nonlinear oscillatory systems with many degrees of freedom in the presence of random perturbations

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 407-411

Brief Communications (Russian)

### Determinaticn of the regions of analyticity of diagram inserts corresponding to the scuttering of nuclcons by nucléons, $\pi$-mesons by nucléons and $K$-mesons by nucléons

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 411-417

Brief Communications (Russian)

### Unilinear system of mass service with an unreliable instrument

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 417-422

Brief Communications (Russian)

### Infinitesimal bends of piecewise regular surfaces of rotation of negative curvature

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 422-425

Brief Communications (Russian)

### Infinitesimal bends of piecewise regular surfaces of rotation of negative curvature

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 426-432

Brief Communications (Russian)

### On a method of visualizing equipotential lines

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 432-434

Brief Communications (Russian)

### On the construction of asymptotic solutions for nonstationary differential equations with a delayed argument and a small parameter

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 435-440

Brief Communications (Russian)

### On infinitesimal sliding hends of spherical segments relative to an arbitrary plana

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 440-446

Brief Communications (Russian)

### Generalized monogenic functions of G. Moisil and generalized conjoint functions of V. S. Fyodorov

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 446-452

Chronicles (Russian)

### First All-Union conference on geometry

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 453-455

BookReview (Russian)

### G. S. Pisarenko, Energy Dissipation of Mechanical Vibrations

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 456-457

Index (Russian)

### Alphabetical index of the Ukrainian Mathematical Journal, vol. XIV, 1962

Ukr. Mat. Zh. - 1962. - 14, № 4. - pp. 458-459