# Mathematics

## Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for Sturm–Liouville Operators with a Nonintegrable Singularity Inside a Finite Interval

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

## About numerical range of semigroup's generator

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

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

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

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.

## Acts and partial acts over semilattices

We consider the acts and the partial acts over semilattices. We obtain a necessary and sufficient condition to be a partially ordered set X an act over a semilattice. The properties of partial acts are investigated and a sufficient condition is found for the expansion of partial act X over a semilattice S to a full S-act.

## Determination of the Boundary in the Local Charzynski–Tammi Conjecture for the Fifth Coefficient

In this article we find the exact value ofM5 such that the symmetrized Pick function PM4(z) is an extreme in the local Charzynski– Tammi conjecture for the fifth Taylor coefficient of the normalized holomorphic bounded univalent functions

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

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.

## Solvability of Poisson's problem for Laplace operator on two dimensional stratified sets in usual sense

Solvability of Poisson's problem for Laplace operator on two dimensional stratified sets is established in usual sense.

## On a necessary condition of at least one quadratic functional with an integral Stieltjes

In this paper is obtained a necessary condition for an extremum of a quadratic functional with a Stieltjes integral.