### Automata and events

↓ Abstract

Ukr. Mat. Zh. - 1962νmber=4. - 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.

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

↓ Abstract

Ukr. Mat. Zh. - 1962νmber=4. - 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.

### Classes of conjugate elements in topological groups

↓ Abstract

Ukr. Mat. Zh. - 1962νmber=4. - 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.

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

↓ Abstract

Ukr. Mat. Zh. - 1962νmber=4. - 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.

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

↓ Abstract

Ukr. Mat. Zh. - 1962νmber=4. - 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.

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

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

### Analytical variant of Melentiev's method

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

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

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

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

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

### 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. - 1962νmber=4. - 14, № 4. - pp. 411-417

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

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

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

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

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

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

### On a method of visualizing equipotential lines

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

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

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

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

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

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

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

### First All-Union conference on geometry

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

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

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

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

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