Mathematics

Mathematical modelling of loss of stability of system of step and homogeneous cores at blow about the rigid barrier Tymoshenko's method

Authors: Bityurin A. A.

Mathematical modeling of longitudinal elastic central blow of system of step and homogeneous cores about a rigid barrier is carried out, at not holding communications by a solution of the wave equation by Dalamber's method. On the basis of the law of conservation of energy by Tymoshenko's method the size of critical compressing loading according to which, the size of critical pretonic speed leading to loss of stability of considered rod system further pays off. 

Oval lines of the hyperbolic plane of positive curvature

Authors: Romakina L. N.

The classification of real nondegenerate second-order lines of the hyperbolic plane 

Lebesgue functions for Haar system on compact zero-dimensional group

Authors: Komissarova N. E.

 In this article we discuss Lebesgue functions for Haar system on compact zero-dimensional group. We find cases when they are constant, also we find two-sided estimates for Lebesgue functions. 

Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system with nondifferentiable potential

Authors: Burlutskaya M. S., Kurdyumov V. P., Khromov A. P.

This paper investigates the Dirac system with the continuous potential. Asymptotic formulas for the eigenvalues (including refined) and eigenfunctions are established. As an application we obtain a theorem P. Dzhakova and B. S. Mityagin on the Riesz bases with brackets. 

The theorem on existence and uniqueness of the solution of one boundary value problem in strip for degenerate elliptic equations of higher order

Authors: Baev A. D., Buneev S. S.

Theorem on the existence and uniqueness of the solution of the boundary value problem in the strip for one degenerate elliptic equations of higher order, which degenerate on one of boundary of the strip in the third-order equation by one variable, is proved.