
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (44) 2020
PHYSICS
Al’Kamali M.F.S.H., Alexeenko A.A., Titenkov O.A. Structure formation of SiO_{2}xerogels containing copper compounds of different phase composition
Technological methods of formation of pure and composite materials of composition
SiO_{2},
SiO_{2}:Cu(NO_{3})2*3H_{2}O, SiO_{2}:CuO
and
SiO_{2}:Cu^{o},
obtained on the basis of an aqueous dispersion of pyrogenic silica (aerosil) grade A300, are considered. The method of scanning electron microscopy (SEM) was used to study the structural transformations occurring in the synthesized xerogel blanks during their heat treatment in air and in an environment of dried hydrogen (up to Ò = 800^{o} Ñ). By the method of uniaxial pressing on the basis of xerogels of the developed composition, tableted samples were formed in the form of disks with an initial diameter of about 13 mm, for which the arising linear shrinkage and weight loss were established in the temperature range of 25–1200^{o} Ñ.
Keywords: aerosil, aqueous dispersion, solgel technology, structuring heat treatment, surface morphology, micropowders.
M.F.S.H. Al’Kamali – P.O. Sukhoi Gomel State Technical University
A.A. Alexeenko – P.O. Sukhoi Gomel State Technical University
O.A. Titenkov – P.O. Sukhoi Gomel State Technical University
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Girgel S.S. Solutions of the wave equation in parabolic rotary coordinates. I. 3D Kummer –Kummer light beams with the continuous angular index
Analytical expressions in the closed form for nonparaxial and paraxial 3D Kummer – Kummer (KK) beams with continuous angular index m in parabolic rotary coordinates are offered and analyzed. Physical restrictions on possible values of the free parameters of such beams are formulated.
Keywords: nonparaxial beams, paraxial beams, parabolic beams, Kummer – Kummer beams.
S.S. Girgel – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Grishechkin Yu.A., Paulenko A.V. Approximate analytical method for solving the Schrodinger equation with the Gaussian potential in the momentum representation
The approximate analytical method is proposed for solving the Schrodinger equation with the Gaussian potential in the momentum representation. The idea of the method is to represent the desired wave function in the form of a superposition of wave functions of the threedimensional harmonic oscillator in the momentum representation. Solutions are found in the case of coupled states.
Keywords: Schrodinger equation, wave function, Gaussian potential, harmonic oscillator, coupled states.
Yu.A. Grishechkin – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.V. Paulenka – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Zalessky V.B., Kalinovsky V.S., Khodin A.A. Semiconductor photoelectric solar energy
converters metrology
The main characteristics of solar radiation for conversion into electrical energy using semiconductor photoelectric converters (PEC), including the conditions of the Republic of Belarus, are considered. The regulatory framework for preparation and testing of PEC is presented. The principle of operation and the main characteristics of a hardwaremeasuring complex for testing PEC in a pulse mode are presented.
Keywords: photoelectric converter, metrology, solar simulator, AM1.5.
V.B. Zalessky – “Optics, Optoelectronics and Laser Techniques” SSPA, National Academy of Sciences of Belarus
V.S. Kalinovsky – Ioffe PhysicalTechnical Institute, Russian Academy of Sciences, Saint Petersburg
A.A. Khodin – “Optics, Optoelectronics and Laser Techniques” SSPA, National Academy of Sciences of Belarus
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Yiming Liu, Wang Jicheng, Rogachev A.V., Sarkisov O.A., Yarmolenko M.A., Rudenkov A.S. Formation of composite coatings by electron beam dispersion of a mixture of iron, aluminum and PTFE in the conditions of exothermal interaction
The features of the structure and chemical composition of coatings deposited from the volatile products of electron beam dispersion of a mechanical mixture of PTFE, iron nitrate, and aluminum are determined. It is shown that under such conditions of generation of the gas phase, coatings are formed consisting of a polymer matrix and containing particles of oxide, a free metal, and a certain amount of the initial undecomposed salt. The result of exothermic reactions in the crucible is partial defluorination and increased defectiveness of the molecular structure of the fluoroplastic matrix. It is noted that the morphology of the composite layer in comparison with the morphology of PTFE is more “loose” and porous, containing a significant number of dispersed formations that form larger structures. The composite coating is heterogeneous in terms of chemical composition and during its annealing, continuity is violated.
Keywords: iron nitrate, polytetrafluoroethylene, exothermic reactions, electron beam dispersion, molecular structure, morphology.
Liu Yiming – Faculty of Physics and Information Technology, F. Skorina Gomel State University
Jicheng Wang – Jiangnan University, Wuxi, China
A.V. Rogachev – F. Skorina Gomel State University
O.A. Sarkisov – Belarusian State University of Transport, Gomel
M.A. Yarmolenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Kulesh E.A., Rogachev A.V., Piliptsov D.G., Jiang Xiaohong, Fedosenko N.N. Structure and mechanical properties of composite titaniumcarbon coatings formed by the combined method
The features of the structure, phase composition and mechanical properties (nanohardness, Young's modulus, friction and wear coefficients) of composite titaniumcarbon coatings deposited by the ionplasma method in a hydrocarbon gas atmosphere at different pressures are considered. It was found that carbon titaniumcontaining coatings deposited in a hydrocarbon gas environment are characterized by a lower degree of structural ordering and a lower size of Csp^{2} clusters as compared to coatings formed in the absence of hydrocarbon gas. In this case, a significant decrease in roughness and a decrease in microhardness are recorded. It is shown that when Ñ_{3}H_{8} is introduced into the chamber up to pressures not exceeding 6.7x10^{2} Pa, there is a sharp decrease in the coefficient of friction (to values of 0,15) and wear of the counterbody (0,023x10^{13} [m^{3} (Nxm)]). With a further increase in the pressure of the reactive gas, an increase in the coefficient of friction and wear of the counterbody are observed.
Keywords: carbon coatings, titanium, reactive sputtering, nanohardness, wear resistance, coefficient of friction.
E.A. Kulesh – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.V. Rogachev – F. Skorina Gomel State University
D.G. Piliptsov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
Xiaohong Jiang – Nanjing University of Science and Technology
N.N. Fedosenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Nikitjuk Y.V. Investigation of the process of laser splitting of twolayer structures of silicon plates and glass substrates
In this work, a numerical simulation of the process of laser splitting of twolayer structures made of monocrystalline silicon and glass is carried out when the workpiece is exposed to laser beams with wavelengths equal to 1.06 and
10.6 and a refrigerant. The calculation of thermoelastic fields formed in a twolayer plate as a result of laser heating was carried out for three sections of silicon crystals: (100), (110), (111). The analysis of the results obtained was carried out both for the case of processing from the side of the glass layer, and for the case of processing from the side of monocrystalline silicon. The results obtained in this work can be used to optimize the process of precision separation of twolayer structures made of monocrystalline silicon and glass.
Keywords: crack, laser splitting, silicon plate.
Y.V. Nikitjuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Rogachev A.V., Emelyanov V.A., Yiming Liu, Yarmolenko M.A., Rudenkov A.S. Features of the formation of coatings of metal oxides from the active gas phase under conditions of electroninitiated endothermic processes
The features of physicochemical processes initiated by the lowenergy electron flow between the components of the target based on nitrates of metals and metals, their influence on the kinetics of the formation of volatile products, the chemical composition and structure of the deposited coatings are established. When electrons act on a mixture of aluminum nitrate and dispersed aluminum, zinc oxide coatings containing zinc nanorods are formed. The impact of the electron flow on a mechanical mixture of powders of iron nitrate and dispersed aluminum is accompanied by explosive evaporation of the target, and a large number of microdroplet formations deposited at the final stage of exothermic reactions in the surface layers of the target are fixed on the surface of the coating containing oxides and metal nanoparticles.
Keywords: metal, oxide, nitrate, nanorods, nanoparticles.
A.V. Rogachev – F. Skorina Gomel State University
V.A. Emelyanov – JSC “Integral”, Minsk
Liu Yiming – Faculty of Physics and Information Technology, F. Skorina Gomel State University
M.A. Yarmolenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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MATHEMATICS
Gal'mak A.M. On skew elements in polyadic groups of special form defined by cyclic substitution
Gorsky S.M., Murashka V.I. Convex functions and generalization of the Holder, Minkowski, and Muirhead inequalities
Let
be any means. Let be a power mean with exponent p. A function f is called convex if for any x and y from the domain of f the inequality holds. In this paper the method of constructing convex functions is proposed. For such functions generalizations of CauchySchwarz, Holder, Minkowski, Mahler, and Muirhead
inequalities are obtained.
Keywords: convex function, CauchySchwarz inequality, Holder inequality, Minkowski inequality, Mahler inequality, Muirhead inequality, Holder mean.
S.M. Gorsky – Saint Petersburg Academic University
V.I. Murashka – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Kamornikov S.F., Tyutyanov V.N. Finite simple groups all the maximal subgroups of which have 3'index
The finite simple nonabelian groups all the maximal subgroups of which have 3'index are studied.
Keywords: finite group, maximal subgroup, 3'index, simple nonabelian group.
S.F. Kamornikov – F. Skorina Gomel State University
V.N. Tyutyanov – Gomel Branch of International University "MITSO", Gomel
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Malinkovskii Yu.V., Niamilastsivaya V.A. Stationary distribution of Jackson networks with an exponential constraint on the sojourn time of claims
An exponential queuing network containing nodes of two types – singleline and multiline is considered. In contrast to Jackson networks, the sojourn time at the nodes of the network is a random variable, the conditional distribution of which is exponential for a fixed number of claims in the node. For singleline nodes, the routing matrices of the served and nonserved customers are, generally speaking, different, and for multiline nodes they coincide. A sufficient ergodicity condition is established and a stationary distribution is found.
Keywords: open queuing network, singleline and multiline nodes, limited sojourn time, ergodicity condition, stationary distribution.
Yu.V. Malinkovskii – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
V.A. Niamilastsivaya – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Sel'kin V.M., Blisnets I.V. Finite groups with restrictions on the Schmidt subgroups
Throughout the article, all groups are finite and G always denotes a finite group. A subgroup H of the group G is called normal in G if every chief factor of the group G between H^{G} and H_{G} is cyclic. In this article, it is proved that if each Schmidt subgroup of the group G is either subnormal or normal in G, then the derived subgroup G' is nilpotent. Some wellknown results are generalized.
Keywords: finite group, nilpotent group, subnormal subgroup, normal subgroup, Schmidt group.
V.M. Selkin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
I.V. Blisnets – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Starovoitov A.P., Ryabchenko N.V., Drapeza A.A. A criterion for the existence and uniqueness of polyorthogonal polynomials of the first type
A criterion for the uniqueness of polyorthogonal polynomials of type I associated with an arbitrary system of power series of the Laurent type is formulated and proved. An explicit form of these polynomials and an explicit form for the corresponding polynomial of the second kind is found. The proven statements complement wellknown results in the theory of orthogonal and polyorthogonal polynomials.
Keywords: orthogonal polynomials, normal index, perfect system, Hankel determinant, polyorthogonal polynomials.
A.P. Starovoitov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
N.V. Ryabchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
A.A. Drapeza – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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INFORMATION SCIENCE
Korotkevich V.A., Korotkevich L.I., Moiseev A.V. Methods and means of informing applicants in “Admission committee of F. Skorina Gomel State University” software package
The ability of the “Admission committee of F. Skorina Gomel State University” software package to inform applicants during the admission campaign is considered. Informing is performed using a combination of desktop, mobile and Internet applications interacting through a common database on an SQL server.
Keywords: software package, SQLserver, desktop application, web application, mobile application, admission committee.
V.A. Korotkevich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
L.I. Korotkevich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
A.V. Moiseev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Tsimokhin I.V., Osipenko N.B. Automation of headline generation for news articles
The approach for automation of headline generation, using the seq2seq method with the Attention mechanism is considered. The steps from dataset gathering to final model verification are described.
Keywords: headline generation, natural language processing, artificial neural networks, text summarisation.
I.V. Tsimokhin – F. Skorina Gomel State University
N.B. Osipenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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