The influence of an external electric field on the propagation of a one-dimensional odd dark beam in a cubic optically active photorefrac-tive piezocrystal Bi₁₂SiO₂₀ with thickness of 10 mm is studied experimentally and theoretically. It is established that taking into account the piezoelectric effect at numerical modeling leads to better adequacy of the experimental and theoretical results.

Keywords: soliton, the dark beam, photorefractive piezocrystal.

Zh.V. Kolyadko – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

V.V. Shepelevich – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

S.F. Nichiporko – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

S.M. Shandarov – Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia

The principal possibility of occurrence of virtual states of the substance involved in frictional process was analytically investigated. Quantum mechanisms of virtual states development were theoretically described.

Keywords: wave function, decoherence, quasi-particle, virtuality, tribones.

D.N. Lubimov – «Engineering center L&Co» Ltd, Surgut, Russia

K.N. Dolgopolov – «Engineering center L&Co» Ltd, Surgut, Russia

V.A. Goldade – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The morphological features of the formation and optical properties of multilayer coatings based on refractory oxides of SiO₂, ZrO₂, TiO₂, formed by electron beam evaporation, are established. The polarization spectra of the formed coatings and dependence of these spectra on the nature of the substrate material were analyzed. It is shown that the ratio of the transmittance coefficients of p-polarized and s-polarized radiation in the visible spectral region is maximal when the coating is deposited on the surface made of glass K-8C (in com-parison with the substrates made of quartz and polymethylmethacrylate). The morphology of the coatings is characterized by low values of roughness of 1.6...4.1 nm, that determines the prospects of their application as polarization elements.

Keywords: morphology, polarizer, coating, optical properties, transmittance coefficient.

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

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

N.G. Ariko – Institute of Physical Organic Chemistry of the National Academy of Sciences of Belarus, Minsk, Belarus

D.L. Gorbachev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

The aim of this work is the preparation and characterization of the polycrystalline Pb_XSn_1-XTe bulk alloys, which isgrown by synthesis via a reaction of Pb, Sn, Te elements in sealed quartz ampoules. The elemental composition of the obtained samples was determined from energy dispersive X-ray (EDX). The structural characterization was investigated by X-ray diffraction (XRD). The powder of X-ray diffraction of the alloys showed a single phase only, which was found to be cubic. The lattice parameter à is calculated from the peak po-sitions of X-ray diffraction data. The dependence of the lattice constant on composition X exhibits a linear behavior and may be de-scribed by the Vegard’s law.

Keywords: lead tin telluride, X-ray diffraction, energy dispersive X-ray, microstructure, lattice parameter.

Seidi Hassan – Islamic Azad University of Takestan, Takestan, Iran; Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus, Minsk, Belarus

Valery F. Gremenok – - Head of Laboratory of Solid State Physics State Scientific and Production Association «Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus», Minsk, Belarus

V.A. Ivanov – Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus, Minsk, Belarus

The task of acousto-optic interaction of Bessel light beams (BLB) in uniaxial crystal with plane acoustic wave has been solved. The process of isotropic scattering of BLBs without changes of the polarization state has been calculated. The investigated scheme of the acousto-optical interaction is a method for producing polarized Bessel light beams with the ability to change their state of polarization over time.

Keywords: TH- and TE- polarized Bessel beams, anisotropic crystal, acousto-optical interaction.

P.A. Khilo – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

The influence regularities of the thickness of titanium interlayer on the phase composition and mechanical properties of titanium-carbon bilayer coatings have been determined. The strongest catalytic effect of titanium interlayer is presented in its thickness up to 30-45 nm. At the thickness range the bilayer coatings possess the highest concentration of sp³-hybridization carbon, microhardness, transparency and optical bandgap. As the thickness of the interlayer increases the internal stress monotonically decreases and, it is not changed when the thickness exceeds 40 nm.

Keywords: diamond-like carbon, bilayer coating, structure, morphology, hardness, internal stress, optical properties.

Zhou Bing – Nanjing University of Science and Technology, Nanjing, China

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

Jiang Xiaohong – Nanjing University of Science and Technology, Nanjing, China

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

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

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

We construct a free n-dinilpotent dimonoid and characterize the least n-dinilpotent congruence on a free dimonoid.

Keywords: n-dinilpotent dimonoid, free n-dinilpotent dimonoid, dimonoid, semigroup, congruence.

Anatolii V. Zhuchok – Luhansk Taras Shevchenko National Univesity, Luhansk, Ukraine

Let H and X be subgroups of a finite group G. Then we say that H is: X-quasipermutable (respectively, X_s-quasipermutable) in G provided G has a subgroup B such that G=N_G( H)B and H X-permutes with B and with all subgroups (respectively, with all Sylow subgroups) V of B such that (|H|,|V|)=1; X-propermutable (respectively, X_s-propermutable) in G provided G has a subgroup B such that G=N_G( H)B and H X-permutes with B and with all subgroups (respectively, with all Sylow subgroups) of B. In this paper we analyze the influence of X-quasipermutable, X_s-quasipermutable, X-propermutable and X_s-propermutable subgroups on the structure of G.

Keywords: finite group, X-quasipermutable subgroup, X_s-quasipermutable subgroup, X-propermutable subgroup, X_s-propermutable subgroup, Sylow subgroup, Hall subgroup, p-soluble group, p-supersoluble group, maximal subgroup, saturated formation, PST-group, PT-group.

Xiaolan Yi – Zhejiang Sci-Tech University, Hangzhou, China

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

It is established that every soluble hyperradical formation is hereditary. The description of all soluble hyperradical formation is given.

Keywords: formation, hyperradical formation, soluble finite group.

S.F. Kamornikov – Gomel Branch of International University «ÌIÒSλ, Gomel, Belarus

n-Àry analog of affine Dezarg theorem is determined. New method of relaxation to vector equations on n-ary group is received.

Keywords: semiabelian n-ary group, vector of n-ary group.

D.I. Kirilyuk – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

In this work an inverse problem for the hyperbolic equation of second order with periodical boundary conditions is investigated. For this reason, first of all the initial problem reduces to the equivalent problem, for which the theorem of existence and uniqueness is proved. Then using these facts the existence and uniqueness of the classical solution of initial problem is proved.

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

Y.T. Mechraliyev – Baku State University, Baku, Azerbaijan

Let G be a finite group such that every non-cyclic maximal subgroups in its Sylow subgroups are subnormal in G. Suppose that a Sylow 2-subgroup of G is either cyclic or self-normalizing. Under these assumptions, we prove that G has a Sylow tower.

Keywords: finite group, Sylow subgroup, maximal subgroup, cyclic subgroup, subnormal subgroup, normalizer.

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

A.A. Trofimuk – A.S. Pushkin Brest State University, Brest, Belarus

In the article the authors consider the algorithm for dynamic display with variable time intervals to obtain a wide range display bright-ness. The article describes in detail the idea of the method and timing diagrams of the algorithm. The scheme of the algorithm with de-scription of its work is described.

Keywords: adaptive brightness, MCU, dynamic indication, embedded devices.

O.Ì. Demidenko – F. Skorina Gomel State University, Gomel, Belarus

P.L. Chechat – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

We present a system of geometric constructions, which allows us to select an area inside a flat polygon. The form and the location of the area in the polygon are normally defined only by the form of the polygon, and the sizes are defined by the value of the h-constructions' step. When the area degenerates into a point, which is not the centre of inertia of the polygon. It is shown that the particles of dis-persional systems moving under the influence of external powers on the given scheme are concentrated in a local area and coordinates are given by the location of the external power sources. The examples of usage of this principle are given in technology of shaping and processing materials.

Keywords: localization of space, dispersion systems.

A.S. Neverov – Belarusian State University of Transport, Gomel, Belarus

L.S. Pinchuk – V.A. Belyi Metal Polymer Research Institute of National Academy of Sciences of Belarus, Gomel, Belarus

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

D.N. Shevchenko – Belarusian State University of Transport, Gomel, Belarus

In the article the way of step-by-step correction of regression model in the problem of explanation of a person’s life expectancy with the help of factors of his genetic potential is described. For decoding these factors the popular among practicing psychologists method of a square of Pythagoras is used. «Cultivation» of the model is conducted in two directions. The main reasons for incorrect regression constructions are noted during the work with qualitative signs. Interpretation of resultant models allows to look at real priorities of a social system in a new way and develop recommendations about their change for the purpose of increase of life expectancy of the population of Belarus.

Keywords: regression model, social phenomenon, life expectancy, algorithm of Pythagoras, criterion of interpretation plausibility, stages of model «cultivation».

N.B. Osipenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

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

K.A. Osipenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

In the paper the authors propose criteria that take into account the energy parameters of a nonstationary bioelectric signal, and thereby quickly and efficiently analyze the EMG signal. Experimental data of the dependence of the average EMG amplitude and the energy signals on time are presented. It is established that changing of the inter-electrode distance affects the Registered EMG signal. The dependence of the parameters of the total muscle electromyogram of m. gastrocnemius medialis of the area of the electrodes is not revealed.

Keywords: electromyography, surface electrodes, EMG amplitude, EMG energy.

A.N. Osipov – Byelorussian State University of Informatics and Radioelectronics, Minsk, Belarus

V.M. Bondarik – Byelorussian State University of Informatics and Radioelectronics, Minsk, Belarus

D.F. Kuznecov – Byelorussian State University of Informatics and Radioelectronics, Minsk, Belarus

E.P. Ostroukh – Byelorussian State University of Informatics and Radioelectronics, Minsk, Belarus

Õ. Masudian – Byelorussian State University of Informatics and Radioelectronics, Minsk, Belarus

In the given paper the mathematical models of synthesis of locomotion at kinematic and dynamic levels are defined and investigated for the purposeful movement of biomechanical system. Models are divided into two parts: directly operated muscular system and a part re-flecting locomotion of an apparatus, representing itself as an elastic support. Interaction of these parts is shown and the design of the procedure of full models in computing experiment on the COMPUTER is proposed.

Keywords: synthesis, control, locomotion, mathematical model, kinematic level, biomechanical system.

A.E. Pokatilov – Mogilev State University of Food Technologies, Mogilev, Belarus