The paper is obtained that the Schrodinger equation in the momentum representation for a linear confining potential for states with zero orbital angular momentum can be solved with high accuracy (far superior to other methods) using the special quadrature formulas for hypersingular integral.

Keywords: Schrodinger equation, momentum space, hypersingular integral.

V.V. Andreev – Department of Physics, F. Skorina Gomel State University

The influences of light-induced gratings determined by means of cubic optical nonlinearity on the Bragg diffraction by the Bessel light beams on ultrasound in the gyrotropic mediums are investigated. It is shown that under using Bessel light beams the plate of sufficiency display of optical nonlinearity under Bragg diffraction is substantially lowered. It was found that the diffraction efficiency of Stokes regime of the acousto-optical interaction reaches its maximum value under increasing the light intensity and anti-Stokes mode decreases monotonically.

Keywords: ultrasonic wave, gyrotropic crystal, light-induced grating, Bessel light beam, Bragg diffraction, diffraction efficiency.

Belyi V.N. – Institute of Physics of NAS Belarus, Minsk

Kulak G.V. – I.P. Shamyakin Mozyr State Pedagogical University

Krokh G.V. – I.P. Shamyakin Mozyr State Pedagogical University

Ropot P.I. – Institute of Physics of NAS Belarus, Minsk

Shakin O.V. – State University of Aerospace Instrumentation, Saint Petersburg

The general expressions for the energy flux density of an electromagnetic field S vector Gaussian-like beams with homogeneous polarization are found. These results for the standard Hermite – Gauss beams are concretized. It is established that energy flows of light beams of Hermite – Gauss are divided into certain independent areas (domains). In each area energy flows are autonomous and into other areas do not pass.

Keywords: paraxial beams, vector beams, gaussian-like beams, polarizing properties, power properties, polarization.

S.S. Girgel – Department of Physics, F. Skorina Gomel State University

A physical model of polarization processes is proposed for liquid-disperse systems worked out on the example of solutions of butyral resin and dispersed barium ferrite. The experimental and theoretical curves of polarization and isothermal depolarization are given for different polarization parameters (long-term polarization under low polarization current, multiple short-term cyclic polarization, high-current short-term polarization). The depolarization model is based on the relaxation phenomena generated by diffusion processes in the polarized liquid-disperse systems.

Keywords: dispersion medium, current density, polarization, depolarization, near-electrode layer, voltage.

V.A. Goldade – F. Skorina Gomel State University; V.A. Belyi Metal-Polymer Research Institute of NAS of Belarus

E.A. Tsvetkova – F. Skorina Gomel State University

I.V. Shalamov – Limited liability company «VINEX», Minsk

The problems of the temperature effects of thin-film solar cells on the basis of CuIn_1-xGa_xSe₂ compound on their characteristics at the different values of the thickness of the absorbing layer and the gallium concentration are considered. The optimal values of the absorbing layer thickness are determined. The simulation of the current-voltage characteristics of the considered design of the solar cell are carried out. It is shown that the efficiency of the solar cell can reach 22.65% with the fill factor FF=82.31%, open circuit voltage V_OC=0.81%, short circuit current J_SC=33.93 mA/cm2 when the optimal thickness of the absorbing layer is equal to 3 mm.

Keywords: CuIn_1-xGa_xSe₂ thin-film solar cell, transparent conductive layer, buffer layer, absorption layer, gallium concentration, optimization, AMPS-1D, SCAPS-1D, Comsol Multiphysics.

A.K. Esman – Belarusian National State University, Minsk

V.A. Potachits – Belarusian National State University, Minsk

G.L. Zykov – Belarusian National State University, Minsk

The actively developing direction associated with the fashion-lation of optical phenomena in the radio is considered. On the one hand it depends on the possibility of creating artificial environments with interesting features (so-called meta-), which can not be realized at the level of the optical phenomena due to the inability to achieve the required scaling relations between the sizes of the structural elements and the radiation wavelength. On the other hand, the construction of real physical models of media allows finer understanding of the mechanisms and features of the interaction of electromagnetic waves with matter. In addition, advances of nanotechnology suggest the possibility of transferring the principles of constructing discrete area of radio systems for the optical wavelength range.

Keywords: electromagnetic wave, absorbing medium, the dielectric structure.

V.I. Kondratenko – Department of Physics, F. Skorina Gomel State University

The basic patterns of change in the properties, phase composition and mechanical properties of single-component and doped metal (Cr, Ti, Cu) carbon coatings, subjected to ion nitriding are determined. It is shown that ion nitriding is in the surface layers of increasing the share of sp²-phase with a decrease in the size of the clusters. When the ion nitriding carbonaceous coatings established education CNx compounds with predominant content of N–Csp² bonds. Single-carbon coating after ion nitriding are characterized by a more dispersed structure, high content N–Csp³ bonds, in comparison with the structure and composition of the coating formed under ion assisting or in the presence of molecular nitrogen.

Keywords: carbon coatings, alloying, nitriding, phase composition, morphology, hardness, friction.

A.S. Rudenkov – Department of Physics, F. Skorina Gomel State University

A.V. Rogachev – Rector of F. Skorina Gomel State University

D.G. Piliptsov – Department of Physics, F. Skorina Gomel State University

N.N. Fedosenko – Department of Physics, F. Skorina Gomel State University

Xiaohong Jiang – Nanjing University of Science and Technology

An inverse boundary value problem for a second-order hyperbolic equation with integral condition of the first kind is investigated. A definition of classical solution is introduced for this problem. The Fourier method is used to reduce the problem to a system of integral equations. The method of contraction mappings is applied to prove the existence and uniqueness of a solution of the system of integral equations. Then, the existence and uniqueness of a classical solution of the initial problem is proved.

Keywords: inverse boundary problem, hyperbolic equation, Fourier method, classic solution.

Y.T. Mechraliyev – Baku State University

Q.N. Isgenderova – Baku State University

Necessary and sufficient conditions of the analysed system belonging to Peinleve type are obtained.

Keywords: system of the ordinary differential equations, Painleve's property, method of small parameter, method of resonances, mobile critical spe-cial point.

V.M. Petsevich – Y. Kupala Grodno State University

D.N. Shauchenia – Y. Kupala Grodno State University

Let G be a finite group and be a partition of the set of all primes that is, and for all Let We say that a subgroup A of G is Ï-subnormal in G if there is a subgroup chain such that either is normal in or is a -group for some for all . In this paper, we discuss properties of Ï-subnormal subgroups and some other -properties of finite groups. The work continues the research in the papers [1]–[5].

Keywords: finite group, Ï-subnormal subgroup, the lattice of the Ï-subnormal subgroups, -supersoluble group, -group.

Skiba A.N. – Department of Mathematics, F. Skorina Gomel State University

A subgroup H of a finite group G is said to be wide if each prime divisor of the order G divides the order H. We obtain the description of finite -soluble groups with no wide maximal subgroups with -number indices. We also investigate groups with -special subgroups.

Keywords: finite groups, -soluble groups, nilpotent groups.

I.L. Sokhor – Department of Mathematics, F. Skorina Gomel State University

The structure of finite group G, in which single subgroup is not -subnormal in G, but -subnormal in any proper subgroup of G, was established.

Keywords: finite group, composition factors, simple non-abelian group, -subnormal subgroup.

V.N. Tyutyanov – Gomel Branch of International University

T.V. Tihonenko – P.O. Sukhoi Gomel State Technical University

An open queueing network with different types of customers and multimode service strategies is considered. Every node can operate in several modes corresponding to different degrees of its working capacity. There are signals in the network, which change the number of operating mode. Staying time of signals in each node is the random value having exponential distribution. The conditions of multiplica-tivity and an analytical view of stationary distribution of the network states probabilities are found.

Keywords: queueing network, different types of customers, multimode service, signals, stationary distribution.

O.V. Yakubovich – Department of Mathematics, F. Skorina Gomel State University

Y.E. Dudovskaya – Department of Mathematics, F. Skorina Gomel State University

The network of public roads as a part of the transport system of Ukraine is studied. As a part of a complex system of network of roads it can be considered the transport system in operation, which aims at to ensure the conditions of continuous, safe and convenient movement of traffic public roadways for the use in Ukraine. To achieve this goal it is necessary to get optimization of the transport control system in the region with the necessary determination management of criteria. It is proved that the indicator “Performance of the highway” fully meets the purpose of the highways network, which is a measure of the efficiency of its operation that best describes the movement of large volumes of traffic with high enough speeds, provided that the required level of road movement. The main advantage of this indicator is a consideration the speed of the traffic flow along the light intensity. It is proved that the transport system of the region is controlled so that the processes that occur in it can be optimized.

Keywords: road network, operation, development and conditions continuous, safe and comfortable traffic flows regional transport system, management functioning network of public roads.

A.T. Lanovyy – National Transport University, Kyiv

The process of restructuring of simulation models of probabilistic technological processes with a control system for solving multicriteria optimization problems in the management structure of the automation of project modeling of new technological facilities is offered. The theoretical substantiation of a way of restructuring and technology of its application on the basis of the adaptation of the structure of the control system of a simulation model to the conditions of functioning of the technological cycle are shown. The ability to use the proposed approach for assessing the quality of project simulation in constructing optimal structure of the control system of the technological cycle of production is justified.

Keywords: automation of project simulation, restructuring simulation model, controlled systems, multicriteria optimization problem.

V.S. Smorodin – Department of Mathematics, F. Skorina Gomel State University

A.V. Klimenko – Department of Mathematics, F. Skorina Gomel State University

E.I. Sukach – Department of Mathematics, F. Skorina Gomel State University

O.A. Shimchik – Department of Mathematics, F. Skorina Gomel State University

The scheme of multi-valued pseudorandom key sequence generator based on the triple sets of bent-functions is proposed. Designed generator has a high level of cryptographic and stochastic quality and can be used in modern telecommunication systems. The full class of 3-bent-sequences is constructed and classified. The concept of the ternary algebraic normal form is introduced and the fast method for its finding is developed.

Keywords: key sequences generator, multi-valued logic, bent-function, stream encryption algorithm.

A.V. Sokolov – Odessa National Polytechnic University

O.N. Zhdanov – M.F. Reshetnev Siberian State Aerospace University, Krasnoyarsk

N.A. Barabanov – Odessa National Polytechnic University