Mathematics

Inverse problem for Sturm–Liouville operator on the half-line having nonintegrable singularity in an interior point

The inverse problem of recovering Sturm–Liouville operators on the half-line with a nonintegrable Bessel-type singularity in an interior point from the given Weyl function is studied. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions of the solvability of the inverse problem are obtained. 

Necessary and sufficient conditions of belonging to the Besov–Potapov classes and Fourier coefficients with respect to multiplicative systems

Authors: Fadeev R. N.

 In this paper we obtain necessary and sufficient conditions for a function to belong to the Besov–Potapov classes. Using functions with Fourier coefficients with respect to multiplicative systems from the class GM, we show the sharpness of some these results. 

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.