The paper presents a new calculation method of upper bounds of critical values for the semirelativistic Coulomb problem with the trial pseudo-Columbian wave functions.

Keywords: critical value, Coulomb potential, trial wave functions, Salpeter equation.

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

E.S. Chebotareva – I.G. Petrovsky Bryansk State University, Russia

The problem of normal incidence of a plane electromagnetic wave on a system of biisotropic layers is solved in general case using the multiple reflection method as well as the matrix method. The resulting formulas are applied in order to numerically calculate periodic structures of biisotropic layers. Periodically repeating peaks and troughs for the transmission coefficient modulus with the changing thickness of biisotropic layers are found.

Keywords: constitutive equations, biisotropic medium, layer, transmission and reflection coefficients, periodic structure.

V.N. Kapshai – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus

A.A. Shamyna – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus

Peculiarities of eigenwaves in absorbing low symmetry crystals were investigated. As it was shown by F.I. Fedorov and A.M. Goncharenko, there are substantial differences in monoclinic crystals. Six variants of existence of optical axes in such crystals were considered in details. Changes in ellipticity of eigenwaves were investigated. Substantial difference between these cases is shown. This difference can be clearly seen on dependencies of ellipticity and intensity of the transmitted light from the angle of incidence in the cases when the incident light has right or left circular polarization.

Keywords: low symmetry crystals, monoclinic crystals, absorption, eigenwaves.

A.F. Konstantinova – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia

T.G. Golovina – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia

E.A. Evdischenko – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia

B.V. Nabatov – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia

K.K. Konstantinov – A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russia

Simulation results of semiconductor laser dynamics using finite-differences time domain (FDTD) method of solving Maxwell-Bloch equations are presented. The ~ 100 fs pulse train regimes under continuous pumping were found to be possible for GaAs vertical cavity surface emitting lasers in the 628 nm wavelength region.

Keywords: finite-difference time domain method, semiconductor laser, femtosecond pulses, coherent interaction.

V.V. Makarevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

Y.O. Katsiashou – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

This paper presents the characteristics of photovoltaic structures Al-Ni/ZnO:Er/Si, obtained by magnetron sputtering, and structures Al-Ni/ZnO:Tb/Si, obtained by the combined method using electrochemical deposition and magnetron sputtering.

Keywords: sol-gel, ZnO, photoelectric characteristics, electrochemical deposition, magnetron sputtering.

V.V. Malyutina-Bronskaya – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

V.B. Zalesskiy – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

T.R. Leonova – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

A.M. Polikanin – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

V.A. Mudryy – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

A.V. Semchenko – F. Scorina Gomel State University, Gomel, Belarus

V.V. Sidsky – F. Scorina Gomel State University, Gomel, Belarus

The method of transmission of light fluxes based on the birefringent elements and the polarization transformations is considered. The method allows to exclude the effect of destabilizing influence, since, light beams of the interferometer pass through the same optical elements. This method allows to combine two probing channels.

Keywords: interference, polarization, birefringent element, phase difference, the rotational polarization, anisotropy.

V.A. Pilipovich – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

V.B. Zalesski – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

A.I. Konojko – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

N.A. Malevich – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

A.M. Polikanin – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

R.G. Sednev – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

The authors investigated the kinetics of hardening of the surface layer of nickel at friction by the method of ferromagnetic resonance (FMR), electron microscopy and X-ray analysis. The cyclical changes in the dislocation density with time trials were determined. The characteristic stages of hardening at friction were defined. The processes that cause cycling of the material strength properties of the surface layer were studied. The basic mechanisms of hardening and destruction were determined. The interrelation of the kinetics of the strength characteristics and wear of metal at friction were investigated. The radar-cyclical nature of the wear layer by layer was determined.

Keywords: effective slipping zones (areas), shear deformation, cellular structure, zone stratification, transcrystalline and intercrystalline destruction.

V.G. Pinchuk – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus

S.V. Korotkevich – Republican Unitary Enterprise of Power Industy, Gomel, Belarus

S.O. Bobovich – Republican Unitary Enterprise of Power Industy, Gomel, Belarus

V.N. Morozov – Department of Physics, F. Scorina Gomel State University, Gomel, Belarus

The conujgate vector-matrix and spacematrix are defined and studied in this paper.

Keywords: matrix, vector-matrix, spacematrix.

A.M. Gal'mak – Mogilev State University of Food Technologies, Mogilev, Belarus

The effect of delay on the dynamical regimes of non-autonomous van der Pol oscillator with an external harmonic influence was investigated. The maps of dynamical regimes for oscillator with delay and without delay were presented.

Keywords: van der Pol oscillator, stationary states, delays, abridged equation, external periodic effect, bifurcation.

R.I. Korzhik – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

S.P. Zhogal – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

This work is devoted to the study of finite groups factorizable by generalized subnormal subgroups.

Keywords: group, formation, coradical, generalized subnormal subgroup, index, Schmidt group.

V.N. Semenchuk – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

V.F. Veliasnitski – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

We consider the queueing system with limited gated service and adaptive vacations of the server: in one cycle of service only a limited number of customers that were presenting in the system at the moment of the vacation completion may be served; the length of the vacation period depends on whether or not the queue was empty at the previous vacation completion epoch. Distribution of the waiting time is computed.

Keywords: queueing system, limited gated service, adaptive vacations, waiting time.

J.V. Sinyugina – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

The author considers a single-server queueing system with batch arrivals and batch service. A server can fail. The failure completely clears the queue of the system if it is not empty. The time of the service and time of regaining are exponentially distributed. Stationary distribution of the states of the process describing the queueing system behavior is found.

Keywords: queueing system, batch arrivals, batch service.

Starovoitov A.N. – Belarusian State University of Transport, Gomel, Belarus

The restrictions on the indices of subgroups play an important role in the study of finite groups. This theme was considered by R. Guralnik, L.S. Kazarin, V.S. Monahov and other authors. Some authors investigated restrictions on the indices in the consideration of the factorization. L.S. Kazarin proved the solubility of a finite group which is the product of two soluble subgroups of odd index. V.S. Monahov studied the structure of a finite group which is factorized by the factors of prime index. He also studied the structure of a finite group which is factorized by soluble factors of odd index with a number of additional restrictions and without using the theorem on the classification of simple non-Abelian groups.

Keywords: finite group, simple nonabelian group, Frobenius group, factorized group.

N.V. Tyutyanov – Gomel Branch of International University, Gomel, Belarus

This paper considers an open queueing network with different types of positive, negative customers and multiregime service strategies. Staying time of negative customers in each node is the random value having exponential distribution. Every node can operate in several regimes answering different degrees of their working capacity. The conditions of multiplicativity and an analytical view of stationary distribution of the network states probabilities are found.

Keywords: queueing network, different types of positive, negative customers, multiregime service, stationary distribution.

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

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

In the paper soil are considered as nonlinear-deformable firm bodies. Law of deformation process corresponds to an approximating curve of parabolic type. Features of approximating function in the present work are used for definition of parameters of the equation of deformation process. The algorithm of construction and research of mathematical model of system of the nonlinear-deformable earth basis are developed on the basis of the principle of a minimum of full energy of a system and a power linearization method.

Keywords: deformations soil, nonlinear mathematical models, algorithm of construction and research of models.

V.E. Bykhautsau – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

V.V. Bondareva – Belarusian Trade and Economic University of Consumer Cooperatives, Gomel, Belarus

D.V. Prokopenko – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

S.V. Torgonskaya – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

Solution of the boundary problem with nonclassical conditions about low-frequency magnetic field through planar thin-walled composite screen is given. A computing experiment was carried out and graphs of the secondary magnetic field intensity which is shielded by a composite screen were drawn.

Keywords: low-frequency magnetic field, composite screen, secondary magnetic field intensity.

V.Т. Erofeenko – Belarusian State University, Minsk, Belarus

G.Ch. Shushkevich – Y. Kupala Grodno State University, Grodno, Belarus

A.I. Kuts – Y. Kupala Grodno State University, Grodno, Belarus

One of the approaches to the estimation of the probability characteristics of the reliability of networks with two inputs and two outputs is considered. The approach is based on the allocation of probability state security networks, developed as part of the apparatus of probability-algebraic simulation and implementing preliminary calculations when assessing the reliability of large-scale networks.

Keywords: structurally-difficult system, network reliability, probabilistic reliability assessment.

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

D.V. Ratobylskaya – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

S.F. Maslovich – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus

Т.Y. Kamornikova – Department of Mathematics, F. Scorina Gomel State University, Gomel, Belarus