Volume 51, № 3, 1999
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 291–304
We investigate extensions of divisible Abelianp-groups with minimality condition by means of a finitep-groupH and establish the conditions under which the problem of describing all nonisomorphic extensions of this sort is wild. All the nonisomorphic Chernikovp-groups are described whose factor-group with respect to the maximum divisible Abelian subgroup is a cyclic group of orderp s ,s≤2.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 305–313
We reduce problems with continual derivatives in boundary conditions for a parabolic equation to a system of two singular integral Volterra equations of the second order.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 314–327
We present a brief review of new directions in the theory of approximation which are associated with the information approach to the problems of optimum recovery of mathematical objects on the basis of discrete information. Within the framework of this approach, we formulate three problems of recovery of operators and their values. In the case of integral operator, we obtain some estimates of the error.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 328–337
We consider a nonlinear pseudoparabolic variational inequality in a tube domain semibounded in variablet. Under certain conditions imposed on coefficients of the inequality, we prove the theorems of existence and uniqueness of a solution without any restriction on its behavior ast→−∞.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 338–348
For dynamical systems which are described by systems of differential or difference equations dependent on a finite-valued Markov process, we suggest a new form of equations for moments of their random solution. We derive equations for a correlation matrix of random solutions.
On conditions of technical stability of solutions of a nonlinear boundary-value problem describing processes under parametric excitation in a Hilbert space
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 349–363
Sufficient conditions for technical stability are obtained for solutions of a nonlinear boundary-value problem which describes distributed parametric processes in a Hilbert space.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 364–375
We constructively prove the theorem of existence of an interpolation integral chain fraction for a nonlinear functionalF:Q[0,1]→R 1.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 376–382
We apply the method of successive approximations to abstract Volterra equations of the formx=f+a*Ax, whereA is a closed linear operator. The assumption is made that a kernela is continuous but is not necessarily of bounded variation.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 383–388
We introduce the notion of CDN[)-groups:G is a CDN[)-group if, for any pair of its subgroupsA andB such thatA is a proper nonmaximum subgroup, ofB, there exists a normal subgroupN which belongs toG and satisfies the inequalitiesA≤N. Fifteen types of nilpotent non-Dedekind groups and nine types of nonnilpotent locally graded groups of this kind are obtained.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 389–397
We establish a criterion of instability for the equilibrium state of nonholonomic systems, in which gyroscopic forces may dominate over potential forces. We show that, similarly to the case of holonomic systems, the evident domination of gyroscopic forces over potential ones is not sufficient to ensure the equilibrium stability of nonholonomic systems.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 398–409
We prove that a topological Abelian locally compact group with generalized minimality condition for closed subgroups is a group of one of the following types: 1) a group with minimality condition for closed subgroups, 2) an additive group of theJ p -ring of integerp-adic numbers, 3) an additive groupR p of the field ofp-adic numbers (p is a prime number).
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 410–412
We prove that every group factorizable into a product of finitely many pairwise permutable central-by-finite minimax subgroups is a soluble-by-finite group.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 413–417
We obtain the decomposition of systems of quasidifferential equations with rapid and slow variables.
A modified projection-iterative method for solution of a singular integral equation with parameters and small nonlinearity
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 418–422
We suggest a modified version of the projection-iterative method of solving a singular integral equation with parameters and small nonlinearity.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 423–427
We present a method of solving for the nonlinear equationf(U(x),Δ L 2 U(x)) = Δ L U(x) (Δ L is an infinite-dimensional Laplacian) unresolved with respect to an iterated infinite-dimensional Laplacian and for the Riquier problem for this equation.
Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 428–431
For systems of difference equations with rational functions on the right-hand sides represented in a unified vector matrix form, we obtain stability conditions and calculate a value of the radius of a disk for the domain of asymptotic stability on the basis of the second Lyapunov method.