Mathematics

Problem with Conditions on all Boundary for One 6-th Order Pseudoparabolic Equation

Authors: Utkina E. A.

Here consider characteristic problem with conditions, setting on all boundary, in two order space for 6th order equation with 3-times taken old particular derivative. The existence and uniqueness of the solution are proved.

Optimality Solutions in Games with Preference Relations

Authors: Savina T. F.

For n person games with preference relations some types of optimality solutions are introduced. Elementary properties of their solutions are considered. One sufficient condition for nonempty Cα-core is found.

Parametrization of Bivariate Nonseparable Haar Wavelets

Authors: Krasilnikova M. S.

A parametrization of all orthogonal wavelet bases for Haar multiresolution analysis is derived. The bases generated by three piecewise constant wavelets {ηi(x, y)}, i = 1, 2, 3, supported on [0, 1] × [0, 1], with values aij ∈ R, i = 1, 2, 3, j = 1, 2, 3, 4 are considered.

The Characteristic of Stability of the Solution in the Problem of Convex Compact Set Asphericity

Authors: Dudov S. I., Mesheryakova Е. А.

We consider the problem of stability of the solution in the problem of asphericity of a convex set with respect to the error of defining the compact set. It is shown that the optimal value of the criterion function (an asphericity indicator) is stable. Properties of the setvalued mapping, that puts to a convex compact compact set the centers of its asphericity are also investigated. It is proved that this mapping is semicontinious from above everywhere in the space of convex compact sets.

Λ-Summability and Multiplicators of Holder Classes of Fourierseries with Respect ̈ to Character Systems

Authors: Agafonova N. Y.

Let G be a Vilenkin group of bounded type. We obtain nessesary and sufficient conditions of uniform Λ-summability for all Fourier series of f ∈ C(G) and one of Λ-summability in L 1 (G) for all Fourier series of f ∈ L 1 (G). Also we extend some T. Quek and L. Yap results to the case of general modulus of continuity.

On Explicit and Exact Solutions of the Markushevich Boundary Problem for Circle

Authors: Adukov V. M., Patrushev A. A.

In the article the Markushevich boundary problem on the circle is considered for the case when the first coefficient of the problem is an arbitrary function from the Holder class and the second coefficient  is the boundary value of a function that is meromorphic in the unit disk. An explicit method of solution of the given problem is proposed, the number of linearly independent solutions of the homogeneous problem and the number of solvability conditions are calculated, the general solution of the problem is found.