Volume 16, № 2, 1964
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.
Asymptotic formula for the number of classes of isomorphic autonomic automatons with $n$ states
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 145-246
On an integral manifold of nonlinear differential equations containing slow and fast motions
Lykova O. B., Mitropolskiy Yu. A.
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.
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.
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.
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.
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.
On some characteristic subgroups of a finite group
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 220-225
Models of Relativistic Fields Theory and Mandelstam's Representation
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 225-232
On integral representations of Hermito-indefinite nuclei (case of many variables)
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 232-237
Contiguous quadratic complex
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 237-245
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
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
On thè basic integral representation of $p$-analytical functions with characteristic $p = x$
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 254-259
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
Program quasilinear oscillating processes
Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 268-273
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