
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N4 (37) 2018
PHYSICS
Barsukou S.D., Khakhomov S.A., Kondoh Jun. Features of periodical acoustic impedance structure and acoustic wave interaction in novel controllable SAW device
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
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Girgel S.S. Optical Weber – Gauss beams
Analytical expressions in the closed shape for optical Weber – Gauss (WG) beams are found and analyzed. Physical restrictions on possible values of the free parameters of such beams are discovered. Pictorial modelling of WG 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
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Dey E.A., Tyumenkov G.Yu. Boundary parameters for stretched fluid state
In the framework of the thermodynamic method of investigation based on various twoparameter 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, twoparameter 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
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Kovalenko D.L., Gaishun V.Å., Vaskevich V.V., Rusykin A.S., Moskvichev M.I., Cherchuk V.A., Mhin S. Research of structural and mechanical properties of protective solgel coatings based on oxides Si, Ti, Zr and their complexes
À solgel 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 solgel coatings are presented.
Keywords: solgel 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
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Kosenok Ya.À., Gaishun V.E., Tyulenkova O.I. Investigation of the nearsurface damaged layer in monocrystalline silicon wafers after chemicalmechanical polishing
In the process of chemicalmechanical 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, chemicalmechanical 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
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Kulak G.V., Krokh G.V., Ropot P.I., Nikolaenko T.V. The collinear acoustooptical filtration of polychromatic Bessel light beams in uniaxial crystals
The collinear acoustooptic filtration of quasinondiffracting Bessel light beams of o and etypes 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 transversal phasematching 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 ~0,230,24 nm.
Keywords: collinear acoustooptic interaction, acoustooptic 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
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Makarevich A.V., Shepelevich V.V., Shandarov S.M. Effect of spatial orientation and thickness of Bi_{12}GeO_{20} crystal on the gain of the subject light wave: theory and experiment
The dependence of the gain of an object light wave in twowave interaction on the orientation angle and the thickness of the photorefractive 110cut Bi_{12}GeO_{20} 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, electrooptical 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
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Sydsky V.V., Semchenko A.V., Gaishun V.E., Kovalenko D.L., Khanna A.S. Effects of additional vacuum annealing on the structure, electrical and optical properties of ZnO:Al films synthesized by solgel
The effect of additional annealing in vacuum on the structure, electrical and optical properties of ZnO:Al films synthesized by solgel method is determined. Additional annealing in vacuum at the temperature of 350^{o} Ñ leads to the increasing of the content of the crystalline 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, solgel 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
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Shershnev E.B., Nikitjuk Y.V., Sokolov S.I., Ermakov S.F., Shershnev A.E. Processing of synthetic diamond structures laser radiation with a wave length of 532 nm
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 threedimensional analysis when exposed to laser radiation along a secondorder symmetry axis (L_{2}), II – a threedimensional analysis when exposed laser radiation along the axis of symmetry of the third order (L_{3}), III – threedimensional analysis when exposed to laser radiation along the axis of symmetry of the fourth order (L_{4}). 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
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MATHEMATICS
Antonevich A.B., Shahava T.R. The embeddings of distributions into the algebra of mnemofunctions on circle
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
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Vankova T.N., Detchenya L.V., Petsevich V.M., Seliverstova A.O. On a class of systems of second order differential equations without mobile critical features
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
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Vasil’ev A.F. Finite groups with strongly Ksubnormal Sylow subgroups
Zakharchuk Yu.V. The circular threelayer elasticplastic plate with a compressible filler
The problem of symmetric bending of a threelayer 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 elasticplastic 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: threelayer circular plate, light compressible filler, plasticity, iterative solution.
Yu.V. Zakharchuk – Belarusian State University of Transport, Gomel
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Karaseva G.L., Ruzhitskaya E.A. Method of solving the special optimal control problems with phase constraints
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
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Kopats D.Y., Matalytski M.A. Investigation in nonstationary mode of Gnetwork with signal and group removal customers by successive approximation method
A study was conducted in the Gnetwork 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 differencedifferential 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 Gnetwork, positive and negative customers, signals, group removal, nonstationary mode, nonstationary state probability.
D.Y. Kopats – Y. Kupala Grodno State University
M.A. Matalytski – Y. Kupala Grodno State University
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Martsinkevich A.V. On the problem of Doerk and Hawkes for locally normal Fitting classes
Murashka V.I., Gorsky S.M., Sandryhaila Ya.I. convex functions and generalizations of classical inequalities
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, Jensen’s inequality, Hermite – Hadamar’s inequality.
V.I. Murashka – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
S.M. Gorsky – SanctPeterburg Academic University
Ya.I. Sandryhaila – Belarussian State University
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Selkin V.M., Kosenok N.S. On the generalized norm of a finite group
INFORMATION SCIENCE
Lipnitsky S.F. Mathematical model of the synthesis of texts based on merging of communicative fragments
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 verbalassociative 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
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