2018
Том 70
№ 11

# Volume 16, № 2, 1964

Article (Russian)

### Concerning the solution of certain boundary problems with discontinuous coefficients of the boundary condition

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 143-156

For a certain class of coefficients a, including $\sigma \in L_p$ ($p$ depending on the number of variables) a generalized solution of (I), (II) is constructed satisfying the boundary condition (II) in a certain «strong» sense.

Brief Communications (Russian)

### Asymptotic formula for the number of classes of isomorphic autonomic automatons with $n$ states

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 145-246

Article (Russian)

### On an integral manifold of nonlinear differential equations containing slow and fast motions

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 157-163

The authors establish the existence and properties of an $s + 1$ -dimensional local integral manifold of a system of $l + m + n$ nonlinear differential equations of the form $$\frac{dx}{dt} = X(y,z)x + \varepsilon X_1(t, x, y, z),$$ $$\frac{dy}{dt} =Y(x, z), y + \varepsilon Y_1 (t, x, y, z),$$ $$\frac{dz}{dt} = \varepsilon Z_1 (t, x, y, z),$$ where $x, y$ characterize the fast, and $z$ the slow motions.

Article (Russian)

### Investigation of a class of methods of summation of interpolational processes

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 164-184

For the class of all continuous $2jt$-periodic functions, two processes are considered for the approximation of the functions of this class by trigonometric polynomials.

Article (Russian)

### On the algebra of commutative events

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 185-195

A certain complete system of identical relations of the algebra of commutative events is indicated in this paper. It is shown that the problem of identity in the algebra of regular commutative events is solvable algorithmically. It is proved that neither in the algebra of commutative events nor in the algebra of events in an arbitrary alphabet does there exist a finite complete system of identical relations.

Article (Russian)

### On continuous mappings of regions in a Euclidian space

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 196-211

The basic assertion of this paper is that a set of branch points in space $R^n$ with $n \geq 3$ cannot be zero-dimensional. The proof is based on applying the very important theorem on continuity, which is also presented in the article.

Article (Russian)

### On groups of finite rank, 1

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 212-219

The present paper deals with the theory of compact topological groups of finite special rank.

Brief Communications (Russian)

### On some characteristic subgroups of a finite group

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 220-225

Brief Communications (Russian)

### Models of Relativistic Fields Theory and Mandelstam's Representation

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 225-232

Brief Communications (Russian)

### On integral representations of Hermito-indefinite nuclei (case of many variables)

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 232-237

Brief Communications (Russian)

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 237-245

Brief Communications (Russian)

### On the existence of a regular solution of a system of ordinary differential equations in the neighbourhood of a stationary special point

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 246-250

Brief Communications (Russian)

### On the index of the integral operator of the corresponding second problem of the plane theory of elasticity

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 250-253

Brief Communications (Russian)

### On thè basic integral representation of $p$-analytical functions with characteristic $p = x$

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 254-259

Brief Communications (Russian)

### Spectral analysis of Volt erra operators given in a vector function space $L^2_m[0, 1]$

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 259-267

Brief Communications (Russian)

### Program quasilinear oscillating processes

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 268-273

Brief Communications (Russian)

### On the continuous dependence of the solutions of differential equations with a delayed argument of the parameter

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 273-279