Technological methods of formation of pure and composite materials of composition SiO₂, SiO₂:Cu(NO₃)2*3H₂O, SiO₂:CuO and SiO₂:Cu^o, obtained on the basis of an aqueous dispersion of pyrogenic silica (aerosil) grade A-300, 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 xe-rogels 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, sol-gel 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

Analytical expressions in the closed form for nonparaxial and paraxial 3D Kummer – Kummer (K-K) beams with continuous angular in-dex 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

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 three-dimensional 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

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 hardware-measuring 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 Physical-Technical Institute, Russian Academy of Sciences, Saint Petersburg

A.A. Khodin – “Optics, Optoelectronics and Laser Techniques” SSPA, National Academy of Sciences of Belarus

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 ini-tial undecomposed salt. The result of exothermic reactions in the crucible is partial defluorination and increased defectiveness of the mo-lecular 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

The features of the structure, phase composition and mechanical properties (nanohardness, Young's modulus, friction and wear coeffi-cients) of composite titanium-carbon coatings deposited by the ion-plasma method in a hydrocarbon gas atmosphere at different pressures are considered. It was found that carbon titanium-containing coatings deposited in a hydrocarbon gas environment are character-ized by a lower degree of structural ordering and a lower size of Csp² clusters as compared to coatings formed in the absence of hydro-carbon gas. In this case, a significant decrease in roughness and a decrease in microhardness are recorded. It is shown that when Ñ₃H₈ 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 [m³ (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

In this work, a numerical simulation of the process of laser splitting of two-layer 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 two-layer 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 two-layer 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

The features of physicochemical processes initiated by the low-energy 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

The article goes on with a study of skew elements in polyadic groups of special form defined by cyclic substitution, that is, in polyadic groups with l-ary operation that is called polyadic operation of special form and is defined on Cartesian power A^k of n-ary group by cyclic substitution satisfying the condition and n-ary operation . As corollaries the results for polyadic groups were obtained. These polyadic groups are of special form with l-ary operation in which is a cycle such that its length devides l–1, in particular, may be cycle of the form (12...k).

Keywords: polyadic operation, n-ary group, skew element, substitution.

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

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 Cauchy-Schwarz, Holder, Minkowski, Mahler, and Muirhead inequalities are obtained.

Keywords: -convex function, Cauchy-Schwarz 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

The finite simple non-abelian groups all the maximal subgroups of which have 3'-index are studied.

Keywords: finite group, maximal subgroup, 3'-index, simple non-abelian group.

S.F. Kamornikov – F. Skorina Gomel State University

V.N. Tyutyanov – Gomel Branch of International University "MITSO", Gomel

An exponential queuing network containing nodes of two types – single-line and multi-line 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 single-line nodes, the routing matrices of the served and non-served customers are, generally speaking, different, and for multi-line nodes they coincide. A sufficient ergodicity condition is established and a stationary distribution is found.

Keywords: open queuing network, single-line and multi-line 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

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 well-known 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

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 well-known 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

The ability of the “Admission committee of F. Skorina Gomel State University” software package to inform applicants during the admis-sion 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, SQL-server, 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

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