The SAW device with the electroinduced controllable structure was investigated theoretically and experimentally. The innovative SAW device on a LiTaO3 single crystal with the volume existed and controllable domain structure was proposed. The parameters of the electroinduced structure as well as the acoustic wave interaction have ability to control. The theoretical and experimental results of the acoustic wave interaction in the ferroelectric waveguide with the electroinduced periodical structures were discussed.

Keywords: surface acoustic wave (SAW), ferroelectric domain, phonic crystal, acoustic metamaterials.

S.D. Barsukou – Optics department of F. Skorina Gomel State University

S.A. Khakhomov – Rector of F. Skorina Gomel State University

Kondoh Jun – professor of faculty of optoelectronics and nanomaterial science, Shizuoka University, Japan

Analytical expressions in the closed shape for optical Weber – Gauss (W-G) beams are found and analyzed. Physical restrictions on possible values of the free parameters of such beams are discovered. Pictorial modelling of W-G beams is fulfilled and it is shown that complex values of the free parameter a are physically comprehensible.

Keywords: beams, Weber – Gauss beams, parabolic Gauss beam, Helmholtz – Gauss beams.

S.S. Girgel – Faculty of Physics and Information Technology, F. Skorina Gomel State University

In the framework of the thermodynamic method of investigation based on various two-parameter equations of state the explicit forms for calculation of boundary parameters determining the occurrence of stretched fluid state are obtained. The numerical values of the upper temperature limit and the corresponding volume for the state of the stretched fluid in the reduced variables are determined.

Keywords: boundary parameters, stretched fluid, reduced variables, two-parameter equation of state.

E.A. Dey – Faculty of Physics and Information Technology, F. Skorina Gomel State University

G.Yu. Tyumenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

À sol-gel method for producing protective coatings based on silicon, titanium and zirconium oxides containing reinforcing additives: carbon powder and titanium oxide is resented. The optimal synthesis conditions are determined and the main regime of formation of the obtained materials is described. The investigation of the adhesion of the obtained coatings and studying the effect of adding reinforcing additives on the hardness and impact strength of the formed protective sol-gel coatings are presented.

Keywords: sol-gel technology, protective coatings, adhesion, hardness, hydrophobic properties.

D.L. Kovalenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.Å. Gaishun – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.V. Vaskevich – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.S. Rusykin – Faculty of Physics and Information Technology, F. Skorina Gomel State University

M.I. Moskvichev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.A. Cherchuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University

S. Mhin – Korea Institute of Industrial Technology, Seoul

In the process of chemical-mechanical polishing (CMP) of monocrystalline silicon wafers, suspensions based on nanosized silica dioxide are used. The quality of the surface of semiconductor substrates is characterized by roughness and depth of structural damaged layer. The damaged layer and the effect of surface roughness on the intensity of spectral lines are investigated by Raman spectroscopy. It is shown that the intensity of the main Raman mode of silicon strongly depends on the surface roughness.

Keywords: raman spectroscopy, surface roughness, nanosized particles, damaged layer, chemical-mechanical polishing.

Ya.À. Kosenok – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.E. Gaishun – Faculty of Physics and Information Technology, F. Skorina Gomel State University

O.I. Tyulenkova – Faculty of Physics and Information Technology, F. Skorina Gomel State University

The collinear acousto-optic filtration of quasi-nondiffracting Bessel light beams of o- and e-types in uniaxial crystals has been investigated. Using the method of overlap integrals the expression for the diffraction efficiency depending on the parameters of acoustooptical interacting of Bessel beams and the value of overlap integral is founded. It is shown that for zero order Bessel light beams in the trans-versal phase-matching conditions of the diffracted waves in the range of optical spectrum of 0,4–0,7 μm for lithium niobate crystals the transmission bandwidth of ~0,2 nm is reached; with evaluation of Bessel beam order of m ≥ 1 the bandwidth of transmission is not so significantly big, than ~0,23-0,24 nm.

Keywords: collinear acousto-optic interaction, acousto-optic filtration, Bessel light beams, uniaxial crystal, diffraction efficiency.

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

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

P.I. Ropot – B.I. Stepanov Institute of Physics of NAS Belarus

T.V. Nikolaenko – I.P. Shamyakin Mozyr State Pedagogical University

The dependence of the gain of an object light wave in two-wave interaction on the orientation angle and the thickness of the photorefractive 110-cut Bi₁₂GeO₂₀ crystal using only a single crystal sample with a thickness of 16 mm has been experimentally investigated. The technique of carrying out the experiment and processing the results is described. The decisive role of the inverse piezoelectric and photoelastic effects in the theoretical interpretation of the experimental data is shown. Theoretical optimization of the gain of the object light wave in this crystal is performed.

Keywords: photorefractive crystal, BGO crystal, gain of the object light wave, electro-optical effect, inverse piezoelectric effect, photoelastic effect, optical activity.

A.V. Makarevich – I.P. Shamyakin Mozyr State Pedagogical University

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

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

The effect of additional annealing in vacuum on the structure, electrical and optical properties of ZnO:Al films synthesized by sol-gel method is determined. Additional annealing in vacuum at the temperature of 350^o Ñ leads to the increasing of the content of the crystal-line phase in the films. There significant decreasing of the widths of the forbidden gap is observed, which is in good agreement with the data of previous studies of the structural properties of ZnO:Al films.

Keywords: zinc oxide, sol-gel method, vacuum annealing, silicon solar cells, transmission, absorption, diffraction.

V.V. Sydsky – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.V. Semchenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.E. Gaishun – Faculty of Physics and Information Technology, F. Skorina Gomel State University

D.L. Kovalenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.S. Khanna – Indian Institute of Technology Bombay, Mumbai

A numerical simulation of the processing of diamond crystals when exposed to laser radiation with a wavelength of 532 nm was performed. The calculation of the shape of the hole and temperature fields formed in diamond crystals as a result of laser heating was carried out using three modeling options: I – a three-dimensional analysis when exposed to laser radiation along a second-order symmetry axis (L₂), II – a three-dimensional analysis when exposed laser radiation along the axis of symmetry of the third order (L₃), III – three-dimensional analysis when exposed to laser radiation along the axis of symmetry of the fourth order (L₄). An experimental verification of the obtained results was carried out.

Keywords: laser treatment, diamond, finite element method.

E.B. Shershnev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Y.V. Nikitjuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University

S.I. Sokolov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

S.F. Ermakov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.E. Shershnev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

The different ways of embedding of periodic generalized functions space into the algebra of new generalized functions, or mnemofunctions, have been analyzed. The question on additional properties of embeddings has been investigated. Such properties as rotation invariance, consistency with the multiplication of smooth functions and the locality of multiplication have been considered.

Keywords: space of periodic generalized functions, Colombeau type algebra, embedding into the mnemofunctions algebra.

A.B. Antonevich – Belarusian State University, Minsk

T.R. Shahava – Belarusian State University, Minsk

Necessary and sufficient conditions for the system under investigation to belong to the Painleve type system are obtained.

Keywords: system of the ordinary differential equations, Painleve property, movable critical singularities, method of small parameter.

T.N. Vankova – Y. Kupala Grodno State University

L.V. Detchenya – Y. Kupala Grodno State University

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

A.O. Seliverstova – Y. Kupala Grodno State University

Let be a nonempty formation of groups. We call a subgroup H of the group G strongly K--subnormal in G, if N_G(H) is a -subnormal subgroup in G. In this paper we study the question of belonging a finite group in which all Sylow subgroups of strongly K--subnormal, to saturated formation .

Keywords: finite group, Sylow subgroup, formation, K--subnormal subgroup.

A.F. Vasil’ev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

The problem of symmetric bending of a three-layer elastic plate with a light compressible filler asymmetrical in thickness is considered. Kirchhoff's hypotheses are accepted for thin bearing layers. In a relatively thick aggregate, the transverse shear, radial displacements and deflection are taken into account, which vary linearly in thickness are taken into account, the work of shear stresses is neglected. The differential equations of equilibrium in the displacements are obtained using the Lagrange variational method. Physical equations of state correspond to the theory of small elastic-plastic deformations of Ilyushin. The formulation and solution of the boundary value problem are given in displacements in a cylindrical coordinate system. Numerical results are presented.

Keywords: three-layer circular plate, light compressible filler, plasticity, iterative solution.

Yu.V. Zakharchuk – Belarusian State University of Transport, Gomel

The formulation of the optimal control problem with phase constraints is given, the formula for the increment of the quality criterion is obtained, and two constructive optimality criteria are formulated (without using measures). The concept of structure and defining elements are introduced. A constructive algorithm for constructing a solution to the problem under study is proposed. An example of solving a problem is given.

Keywords: phase constraints, formula for incrementing the quality criterion, optimality criterion, structure, determining elements, refinement, refinement equations.

G.L. Karaseva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

E.A. Ruzhitskaya – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A study was conducted in the G-network transition mode with positive customers and signals, when they move the customers to another system or destroy a group of positive customers in it, reducing their number by a random amount, which is specified by some probability distribution. A signal arriving at a system in which there are no positive applications does not have any influence on the queuing network and immediately disappears from it. Streams of positive applications and signals coming to each of the network systems are independent. For nonstationary probabilities of network states, a system of Kolmogorov difference-differential equations is derived. A method for finding them is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. The properties of successive approximations are considered.

Keywords: Markov G-network, positive and negative customers, signals, group removal, non-stationary mode, non-stationary state probability.

D.Y. Kopats – Y. Kupala Grodno State University

M.A. Matalytski – Y. Kupala Grodno State University

Let be a non-empty class of finite groups. A Fitting class is said to be -normal or normal in a class of finite groups if and for all an -radical of G is -maximal in G. If is a class of all soluble finite groups, then -normal Fitting class is called normal. In the theory of normal Fitting classes the problem of Doerk and Hawkes is well known. Let be a Fitting class and . Is the intersection of two non-trivial -normal Fitting classes always non-trivial -normal Fitting class? In this paper a positive answer to this question without the requirement that for the case of arbitrary family of non-trivial -normal Fischer classes partially soluble groups, where is a Fischer class such, that for some prime p is given.

Keywords: Fitting class, -normal Fitting class, -radical, intersection of Fitting classes.

A.V. Martsinkevich – P.M. Masherov Vitebsk State University

A function f is called -convex, if for any x and y from the domain of f inequality holds, where and are means. In this paper geometric interpretation of -convexity of a function is obtained, where and are Kolmogorov’s means. For such functions analogies of rearrangement, Popovicu’s, Chebyshev’s sum and Hermite –Hadamar’s inequalities are obtained.

Keywords: convex function, -convex function, rearrangement inequality, Popovicu’s inequality, Chebyshev’s sum inequality, Jen-sen’s inequality, Hermite – Hadamar’s inequality.

V.I. Murashka – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

S.M. Gorsky – Sanct-Peterburg Academic University

Ya.I. Sandryhaila – Belarussian State University

Let G be a finite group and Then G is called -special if We use to denote the class of all finite -special groups. Let be the intersection of the normalizers of the -special residuals of all subgroups of G, that is, We say that is the -special norm of G. We study the basic properties of the -special norm of G. In particular, we prove that is -soluble.

Keywords: finite group, -special group, -soluble group, -special residual of a group, -special norm of a group.

V.M. Selkin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

N.S. Kosenok – Belarusian Trade and Economic University of Consumer Cooperatives

A mathematical model for the synthesis of test messages based on the fusion of communicative fragments is proposed. Formally, the concepts of such fragments, as well as verbal-associative networks, are defined as models of knowledge about the subject area and synthesized texts.

Keywords: verbal associations, communicative fragment, synthesis of text, text message, sentence template.

S.F. Lipnitsky – United Institute of Informatics Problems of the National Academy of Sciences of Belarus