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

Analytical expressions in the closed form for spatiotemporal wave packets of Kummer-Kummer and Tricomi-Kummer 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

The features of non-collinear acousto-optical diffraction of quasi-diffraction Bessel light beams in uniaxial crystals for creating radio frequency signal spectro-analyzers are theoretically investigated. An expression is found for the diffraction efficiency depending on the parameters of interacting Bessel beams of o- and e-type, 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 acousto-optical spectrum analyzer is ~ 3.5 kHz in the absence of accurate transverse phase synchronism of diffracted Bessel light beams.

Keywords: non-collinear acousto-optical interaction, Bessel light beams, acousto-optical 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, Saint-Petersburg

(Cu-CrN):a-C and (Al-CrN):a-C coatings were deposited using vacuum-plasma 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 nitrogen-containing bonds and the content of the carbide phase in the (Al-CrN):a-C coating significantly exceed their content in the (Cu-CrN):a-C coating. The tribotechnical properties of coatings during friction against steel ШХ15, Al₂O₃ and Si₃N₄ have been determined. It is shown that a lower value of the friction coefficient is recorded during contact interaction (Al-CrN):a-C 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 m³/(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. (Al-CrN):a-C 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

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 co-deposition 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 layered-granular 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 closely-packed 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

Changes in the composition, molecular structure and morphology of organosilicon coatings and composite layers based on organosilicon and high-molecular 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 oxygen-containing groups, SiO2-like 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 «Транспортно-технологические 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, член-корреспондент НАН Беларуси, директор Научно-исследовательского физико-химического института Гомельского государственного университета им. Ф. Скорины

The problem of finding, from a known generating set of the semigroup A, the generating set of the l-ary semigroup with the l-ary operation which is defined on the k-th Cartesian power of an arbitrary groupoid A for any integer and any permutation from the set S_k of all permutations of the set {1, 2, …, k} has been solved.

Keywords: semigroup, l-ary semigroup, set of generators.

A.M. Gal'mak – Mogilev State University of Food Technologies

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

Solutions in the space of generalized functions of a linear first-order 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

Outbound flows are investigated using the reveresе time procedure for an exponential queuing network containing knots of two types - single-line and multi-line. 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 quasi-reversibility of the Markov network process is established.

Keywords: queuing network, single-line and multi-line knots, limited sojourn time, reverse time, quasi-reversibility.

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

It is shown that for the Pade approximants which locally deliver the best rational approximations to the Mittag – Leffler functions , approximate the as uniformly on the compact set at a rate asymptotically equal to the best possible one. In particular, analogues of the well-know results of Braess and Trefethen relating to the approximation of are proved for the Mittag – Leffler functions.

Keywords: Pade approximations, asymptotic equality, Mittag – Leffler functions, rational approximations.

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

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 web-application 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: web-application, 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

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, problem-oriented 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

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 multi-level matrix clusters organized using the infrastructure of distributed computer net-works and the principles of functioning of network-centric information and control systems is proposed and considered in the paradigm of cyber-physical 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