Volume 45, № 7, 1993
Symmetrization and initial boundary-value problems for certain classes of nonlinear second order parabolic equations
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 884–892
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 893–897
A class of polynomials generatingq-nary Hamming codes is studied. The criteria for a polynomial to belong to this class are established for the general case and for the case of prime polynomials. The conditions are determined under which reducible polynomials do not belong to the class of polynomials generating theq-nary Hamming codes.
On the uniqueness of solutions to some boundary-value problems for differential equations in a domain with algebraic boundary
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 898–906
Classes of differential equations with constant coefficients admitting unique solutions of Dirichlet and Cauchy boundary-value problems are considered in a bounded domain with algebraic boundary. For the Dirichlet problem in a ball, the necessary and sufficient conditions for the uniqueness of the solution are obtained in the form of a countable sequence of inequalities polynomial in the coefficients of the equation.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 907–914
We obtain the Schrödinger equation for the wave function of a particle interacting with the external field having a potential containing a component of the “white noise” type and the Kolmogorov equations for the distribution of a wave function.
Some properties of polynomials orthogonal in a space with “intermediate” topology. Kernel function and extremal properties
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 915–923
A space of holomorphic functions is considered. A topology in this space is “intermediate” between the topology of uniform convergence and the topology of uniform convergence on compact sets. The properties of systems of orthonormal polynomials are studied in Hilbert spaces with this topology.
The structure of Banach algebras of bounded continuous functions on the open disk that contain H?, the Hoffman algebra, and nontangential limits
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 924–931
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 932–941
A nonautonomous system of ordinary differential equations is considered. If this system admits a uniformly asymptotically stable integral set, then a neighborhood of this set contains a function similar to the Lyapunov function.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 942–947
On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 948–962
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 963–971
Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochastic equation in the case where the powers of a small parameter are inconsistent.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 972–979
A canonical representation is obtained for the logarithm of the likelihood ratio. Limit theorems describing its asymptotic behavior are proved. Using these theorems, we study the rate of decrease of the probability of an error of the second-kind in the Neyman-Pearson test.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 980–981. July
The elastoplastic state of a compressible isotropic plane with a circular hole is studied by the method of a small parameter. An unknown boundary separating the domain of limiting equilibrium and the elastic domain is determined. We construct the complex Kolosov-Muskhelishvili functions that describe the elastic state of a plane and compare these with the solutions of Galin's problem.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 982–991
Quasianalytic classes of functions in a Jordan domainG are defined. We consider classes of functions defined by conditions imposed on the decrease rate of the best uniform polynomial approximations and investigate the dependence of the quasianalyticity of these classes on the geometric structure of a domain.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 992–1008
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 1009–1019
The principal result of the paper is a criterion of compactness for mappings quasiconformal in the mean. The semicontinuity of a deformation of homeomorphisms from the Sobolev class is also proved.
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 1020–1028
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 1029–1038
Estimates of the solutions to the equations of motion for viscous fluid in a moving cavity with a porous damper
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 1039–1044
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 1045–1048
The index of exponential growth is found for the products of random matrices with values on a solvable Lie algebra. The result is expressed via the eigenvalues of the terms.