Mathematics

Integral operator with kernel having jumps on broken lines

Authors: Khromov A. P., Koroleva O. A.

 In this paper we study equiconvergence expansions in trigonometric Fourier series, and in eigenfunctions and associated functions of an integral operator whose kernel suffers jumps at the sides of the square inscribed in the unit square. 

On spectrum of some classes of matrix operators

Authors: Ismailov M. I.

The paper is devoted to investigation of the spectrum of some classes of matrix operators. The relations between the parts of the spectrum of the matrix operators with corresponding parts of its elements are established. 

An Analogue of the Jordan–Dirichlet Theorem for the Integral Operator with Kernel Having Jumps on Broken Lines

Authors: Koroleva O. A.

In this paper the sufficient conditions (conditions such as Jordan–Dirichlet) expansion function f(x) in a uniformly convergent series of eigenfunctions and associated functions of the integral operator whose kernel is suffering jumps on the sides of the square, inscribed in the unit square. As is known, this expansion requires to f(x) is continuous and belong to the closure of the integral values operator. It turns out that if f(x) also is a function of bounded variation, these conditions are also sufficient.

Modification of new approach to solution of the Hilbert boundary value problem for analytic function in multi-connected circular domain

Authors: Salimov R. B.

The author offers a new approach to the Riemann–Hilbert boundary value problem in multiconnected domain. The approach bases on certain construction of solution of corresponding homogeneous problem including determination of analytic function by known boundary values of its argument circular domain. 

About numerical range of semigroup's generator

Authors: Romanova M. Y.

In the article the semigroup is built. The numerical range of its generator covers complex plane. It is provided that such semigroup is bounded. 

Dynamic load allocation in closed queueing networks with batch movements

Authors: Mitrophanov Y. I., Rogachko E. S., Stankevich E. P.

A method of load allocation control in closed queueing networks with batch movements is proposed. When this method is used in queueing networks of considered type, close to given customer allocation among queueing systems is provided. The control is realized by use of different routing matrices during fixed time intervals in process of network operation. Models of evolution and an approximate method of computing a stationary distribution and other stationary characteristics of considered type queueing networks are presented.

 

The intrinsic geometry of almost contact metric manifolds

Authors: Galaev S. V.

In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermition almost contact metric spaces, is introduced. 

Cohomology of Lie algebra of vector fields on S1/Z2

Authors: Volokitina E. Y.

 In the present paper we calculate the diagonal cohomology of Lie algebra of vector fields on S1/Z2 with coefficients in the space of smooth functions and 1-forms, one-dimensional and two-dimensional cohomology with coefficients in R. 

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