Mathematics

Wiener's theorem for periodic at infinity functions

Authors: Strukova I. I.

 In this article banach algebra of periodic at infinity functions is defined. For this class of functions notions of Fourier series and absolutely convergent Fourier series are introduced. As a result Wiener's theorem analog devoted to absolutely convergent Fourier series for periodic at infinity functions was proved. 

Mathematical model of dynamic chaos

Authors: Podchukaev V. A.

The problem of analytical designing on the set mathematical model of dynamic system in space of states of mathematical model accompanying it in phase space is put and solved. It is shown, that the representing point of any decision of dynamic system of a general view in space of states conditions belongs to hypersphere with the displaced centre in phase space (or to central hypersphere of variable radius equivalent to it).

The conditions of invertibility of a class nonselfadjoint operators

Authors: Maryushenkov S. V.

In this work we obtain the conditions of invertibility of a class of nonselfadjoint operator that are difference between the nonbounded antisymmetric and the normal operator. 

A direct method of stochastic optimization

Authors: Kolbin V. V., Svishchikova M. V.

 A direct method is proposed for stochastic programming. On each step the method uses solving of the linear program which is the linear approximation of input stochastic programs. 

The problem of optimal control for singularly perturbed system with delay with integral quadratic constraints

Authors: Grebennikova I. V.

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and integral quadratic constraints on the control resources according to the minimax criterion is considered. Procedure is proposed for construction initial approximation of control response for minimax problem of control. 

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. 

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