
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (46) 2021
PHYSICS
Andreev V.V. Method for calculating the cross section of binary reactions with polarized particles
A new technique for calculating the cross sections for binary reactions with polarized particles has been developed. The technique is based on direct calculation of matrix elements in a special form using the method of basis spinors. New analytical formulas for integrating differential cross sections with respect to the scattering angle of a binary reaction are presented.
Keywords: binary reaction, Feynman diagram, bispinor, helicity.
V.V. Andreev – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Girgel S.S. Solutions of the wave equation in parabolic rotary coordinates. III. Spatiotemporal wave packets of Kummer – Kummer and Tricomi – Kummer with the continuous angular index
Analytical expressions in the closed form for spatiotemporal wave packets of KummerKummer and TricomiKummer with continuous angular index m in parabolic rotary coordinates are offered and analyzed. Physical restrictions on possible values of free parameters of such modes that they transfer finite power are formulated.
Keywords: spatiotemporal wave packets, parabolic rotary coordinates, modes Kummer – Kummer, modes Tricomi – Kummer.
S.S. Girgel – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Kulak G.V., Ropot P.I., Bestugin A.R., Shakin O.V. Acoustooptical spectrum analyzer based on Bessel light beams
The features of noncollinear acoustooptical diffraction of quasidiffraction Bessel light beams in uniaxial crystals for creating radio frequency signal spectroanalyzers are theoretically investigated. An expression is found for the diffraction efficiency depending on the parameters of interacting Bessel beams of o and etype, as well as on the values of the overlap integrals and the frequency detuning of the Bragg synchronism. It is shown that the frequency resolution of the acoustooptical spectrum analyzer is ~ 3.5 kHz in the absence of accurate transverse phase synchronism of diffracted Bessel light beams.
Keywords: noncollinear acoustooptical interaction, Bessel light beams, acoustooptical spectrum analyzer, uniaxial crystal, diffraction efficiency, frequency resolution.
G.V. Kulak – I.P. Shamyakin Mozyr State Pedagogical University
P.I. Ropot – B.I. Stepanov Institute of Physics of the NAS of Belarus, Minsk
A.R. Bestugin – State University of Aerospace Instrumentation, Saint Petersburg
O.V. Shakin – State University of Aerospace Instrumentation, SaintPetersburg
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Kulesh E.A., Rogachev A.V., Piliptsou D.G., Jiang Xiaohong, Rudenkov A.S. Structure and properties of aC films containing metals and products of their interaction with nitrogen, carbon
(CuCrN):aC and (AlCrN):aC coatings were deposited using vacuumplasma methods, their chemical and phase composition, mechanical properties were determined. The features of the formation of nitride and carbide compounds with the content of chromium, copper or aluminum in the coating have been established by the XPS method. It was shown that the concentration of nitrogencontaining bonds and the content of the carbide phase in the (AlCrN):aC coating significantly exceed their content in the (CuCrN):aC coating. The tribotechnical properties of coatings during friction against steel ШХ15, Al_{2}O_{3} and Si_{3}N_{4} have been determined. It is shown that a lower value of the friction coefficient is recorded during contact interaction (AlCrN):aC with steel ШХ15 (0.2), and the minimum coefficient of volumetric wear of the counterbody was obtained in the pair of friction with Al2O3 (1.08х10^{10} m^{3}/(N.m)). It was shown by the indentation method that the introduction of copper increases the ductility of the coatings, while their hardness decreases slightly. (AlCrN):aC coatings are characterized by a higher hardness
(14.2 GPa) and the coefficient of elastic recovery is 51.8% at an indentation depth of 500 nm.
Keywords: composite carbon coatings, metal carbides and nitrides, tribotechnical properties, mechanical properties.
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
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Fedosyuk V.M. The mechanism of bismuth films growth at initial stages of electrochemical deposition
The processes of Bi films electrodeposition from perchlorate electrolyte at the initial stages have been investigated. For the first time it has been shown and explained why, with deposition duration of 1 s, the codeposition of Pb and Bi occurs. The correlation between the synthesis conditions and the chemical composition and microstructure of Bi films is discussed. Analysis of microstructural features revealed a change in the growth mechanism of Bi films from a columnar to a layeredgranular form with an increase in the electrodeposition duration. This anomalous behavior is explained by the appearance of a strong Bi texture and the effects of grain coalescence during growth. Porosity studies have shown that Bi films have a closelypacked microstructure.
Keywords: bismuth, lead, electrodeposition, perchlorate electrolyte, microscopy.
V.M. Fedosyuk – Scientific and Practical Materials Research Centre of National Academy of Sciences of Belarus, Minsk
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Yarmolenko M.A., Sarkisov O.A., Liu Yiming, Rogachev A.V. The effect of plasma treatment of coatings based on organosilicon polymers deposited by electron beam dispersion on their structure and morphology
Changes in the composition, molecular structure and morphology of organosilicon coatings and composite layers based on organosilicon and highmolecular fluorocarbon compounds during their plasma treatment were determined by XPS, IR spectroscopy, and AFM microscopy.The plasma treatment of coatings causes destruction of Si – C bonds, elimination of hydrocarbon fragments and the formation of oxygencontaining groups, SiO2like structures, and an increase in the roughness of surface layers is shown. The destruction of the fluorocarbon component occurs during the plasma treatment of the composite coating. An increase in the mass fraction of PTFE in the initial target is not accompanied by a monotonic decrease in the surface energy of the deposited coating.
Keywords: organosilicon coatings, plasma treatment, molecular structure, adsorption properties, morphology.
Ярмоленко Максим Анатольевич – доктор технических наук, доцент кафедры радиофизики и электроники, ведущий научный сотрудник НИС Гомельского государственного университета им. Ф. Скорины
Саркисов Олег Армаисович – кандидат технических наук, доцент кафедры «Транспортнотехнологические машины и оборудование» Белорусского государственного университета транспорта
Имин Лю – аспирант факультета физики и информационных технологий Гомельского государственного университета им. Ф. Скорины
Рогачёв Александр Владимирович – доктор химических наук, профессор, членкорреспондент НАН Беларуси, директор Научноисследовательского физикохимического института Гомельского государственного университета им. Ф. Скорины
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MATHEMATICS
Yi X., Kamornikov S.F., Tyutyanov V.N. One property of hereditary saturated formations
Let be a hereditary saturated formation. It is proved that if for every Sylow subgroup P of a finite group G and every maximal subgroup V of P there is a subgroup T such that VT=G, then
Problems 19.87 and 19.88 from the «Kourovka Notebook» are solved in the article.
Keywords: finite group, Sylow subgroup, supplement, formation, generally subnormal subgroup, lattice formation.
X. Yi Zhejiang – SciTech University, Hangzhou, China
S.F. Kamornikov – F. Skorina Gomel State University
V.N. Tyutyanov – Gomel Branch of International University “МIТSО”, Gomel
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Kuzmina E.V. Generalized solutions of the differential firstorder equation with the special rational coefficient
Solutions in the space of generalized functions of a linear firstorder differential equation in which the coefficient is the generalized function generated by the rational function are considered. Conditions for the existence of a generalized solution to the Cauchy problem are found. It is shown that the generalized solution does not exist for all considered coefficients.
Keywords: generalized functions, differential equation with generalized coefficient, analytical representation.
E.V. Kuzmina – Brest State Technical University; A.S. Pushkin Brest State University
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Malinkovskii Yu.V., Niamilastsivaya V.A. Quasireversibility of Jackson's networks with exponential constraint on the sojourn time of claims
Outbound flows are investigated using the reveresе time procedure for an exponential queuing network containing knots of two types  singleline and multiline. The sojourn time at the knots of network is limited by an exponential random variable for a fixed number of claims in the knot. The quasireversibility of the Markov network process is established.
Keywords: queuing network, singleline and multiline knots, limited sojourn time, reverse time, quasireversibility.
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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Ryabchenko N.V., Starovoitov A.P. Rational approximation of the Mittag – Leffler functions
INFORMATION SCIENCE
Аkinshevа I.V., Fhilippova A.A. Implementation of an algorithm for calculation of logistics costs for milk delivery
The algorithm for calculating the cost of the entire range of services provided by a logistics organization for the delivery of dairy products has been implemented with the greatest profit. The algorithm is based on the calculation method, which uses the principle of determining the value of transport costs, taking into account specific exogenous variables, and the modified Dijkstra's algorithm for choosing the “best” way of product delivery. The webapplication allows you to test the calculation of the cost of a logistics service and calculate the profit from a potential list of logistics services for the purchase and delivery of milk by a logistics organization.
Keywords: webapplication, logistics services, milk, modified Dijkstra's algorithm, transportation costs, profit.
I.V. Аkinshevа – Mogilev State University of Food Technology
A.A. Fhilippova – Mogilev State University of Food Technology
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Demidenko O.M. Creation of models of the computational process and operational load on the local area network
The use of a software and technological complex is considered. This complex allows you to automate the main stages of simulation experiments in the design, research and modification of local area networks (LAN), which includes basic software, problemoriented technological support of the simulation experiment, software technology.
Keywords: model of computation process, operational load, local area network.
O.M. Demidenko – F. Skorina Gomel State University
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Krotiouk Y.М., Kuznechik О.О., Tkachenko V.V. Information support for design and technological preparation for additive manufacturing: cyberphysical approach
The content of the processes of design and technological preparation of additive manufacturing, the requirements for the information support system for the adoption and implementation of design and technological decision is analyzed. The concept of forming flexible integrated additive industries in the form of multilevel matrix clusters organized using the infrastructure of distributed computer networks and the principles of functioning of networkcentric information and control systems is proposed and considered in the paradigm of cyberphysical systems.
Keywords:
Y.М. Krotiouk – United Institute of Informatics Problems of the NAS of Belarus, Minsk
О.О. Kuznechik – State Scientific Institution «Powder Metallurgy Institute», Minsk
V.V. Tkachenko – United Institute of Informatics Problems of the NAS of Belarus, Minsk
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