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Abstract. The features of forming holograms of periodic structures in noncoherent light using a reference diffraction grating are considered. A device for realizing such recording of holograms is described, and the possibility of forming holograms of periodic structures with arbitrary adjustment of the bands of the holographic structure in the formed hologram is shown. The dependence of the behavior of the grating vector of a holographic structure in the formed hologram on the value of the rotation of the reference grating, as well as on the ratio of the periods of the reference grating and the periodic structure under study, is established.

Keywords: hologram of a periodic structure, incoherent light, reference diffraction grating, grating vector.

For citation: Avlasevich, N.T. Features of forming holograms of periodic structures in noncoherent light with a reference diffraction grating / N.T. Avlasevich, A.M. Lyalikov // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 7-12. – DOI: https://doi.org/10.54341/20778708_2022_3_52_7 (in Russian). – EDN: AJMCSE

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Abstract. New vector solutions of the parabolic equation, featuring Cartesian Light Kummer beams have been offered. The restrictions on parametres at which Kummer beams transfer terminating power have been discovered and physically realised. Pictorial modelling of intensity and crossflows of energy of vector Kummer beams has been fulfilled.

Keywords: cartesian beams, Kummer beams, square intergrability.

For citation: Girgel, S.S. Energy performances of the vector cartesian Kummer beams with transferable terminating power / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 13–17. – DOI: https://doi.org/10.54341/ 20778708_2022_3_52_13 (in Russian). – EDN: ARKFHO

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Abstract. The limited efficiency of the multijunction solar cells using a thermodynamic approach to calculating the efficiency has been estimated. According to the performed studies, the efficiency of single-junction solar cells for the studied materials does not exceed 50%. An increase from one to six in the number of p-n junctions leads to an increase in the efficiency of solar radiation conversation from ~18,2% to ~62,5% (when derating factor is equal to 0,8) and from ~20,2% to ~55,5% (when derating factor is equal to d=0,7 … 0,89). It is shown that the solar cells with six p-n junctions are the most optimal in terms of efficiency.

Keywords: analytical model, Planck distribution, thermodynamic approach, solar spectrum, derating factor, bandgap, p-n junction, limited efficiency.

For citation: Esman, A.K. Multijunction solar cells based on GaInN / GaN / GaInP / GaAs / Si / InGaAsP / A.K. Esman, G.L. Zykov, V.A. Potachits // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 18–21. – DOI: https://doi.org/10.54341/20778708_2022_3_52_18 (in Russian). – EDN: BLXQGP

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Abstract. Within the Wentzel – Kramers – Brillouin approximation, a numerical solution was obtained for the problem of the sum-frequency waves generation in a surface optically nonlinear layer of a dielectric spherical particle placed in a dielectric when it is irradiated with two plane elliptically polarized electromagnetic waves. The dependence of the spatial distribution of the generated radiation on the independent components of the nonlinear dielectric susceptibility tensor of the surface layer and on the particle size is analyzed. The differences and similarities of the results obtained on the basis of the Wentzel – Kramers – Brillouin and Rayleigh – Hans – Debye models are highlighted.

Keywords: sum-frequency generation, Wentzel – Kramers – Brillouin model, Rayleigh – Gans – Debye model, directional patterns.

For citation: Kapshai, V.N. Generation of sum-frequency waves in the surface layer of a spherical particle / V.N. Kapshai, E.D. Golovin, A.A. Shamyna // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 22–27. – DOI: https://doi.org/10.54341/20778708_2022_3_52_22 (in Russian). – EDN: CERJIG

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Abstract. The problem of forced oscillations of a three-layer circular plate with step-variable thickness of the outer layers is presented. The historical review of the theories that have been developed for the straining representation of a three-layer structure is presented. The deformation of the plate follows the zigzag theory. In thin border layers of plate Kirchhoff’s hypotheses are valid. In a relatively thick in thickness medium layer Timoshenko’s hypothesis is fulfilled. The equations of motion are derived from Hamilton’s variational principle. A solution is constructed to determine the displacements during forced vibrations of a plate under impact. Numerical results of the obtained solution are presented. The influence of impact function on the oscillatory character is analyzed.

Keywords: circular three-layer plate, plates with step-variable thickness, forced vibration, stroke.

For citation: Markova, M.V. Forced vibrations of a three-layer step-variable thickness circular plate under impact / M.V. Markova // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 28–36. – DOI: https://doi.org/ 10.54341/20778708_2022_3_52_28 (in Russian). – EDN: CRBKKQ

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Abstract. With the help of artificial neural networks, the process of two-beam laser cleaning of quartz raw materials has been modeled. For the formation of training data sets and data sets for testing neural networks, the ANSYS finite element analysis program was used. The calculations were performed for 500 variants of input parameters, 40 of which were used to test neural networks. The influence of the parameters of neural network models on the accuracy of determining the maximum temperatures in quartz particles formed as a result of two-beam exposure were studied. The parameters of neural networks were determined that provided acceptable results when predicting temperatures in the laser treatment zone. The results obtained can be used in determining the technological parameters of the processes of two-beam laser cleaning of quartz raw materials.

Keywords: neural network, laser cleaning, quartz raw materials, ANSYS.

For citation: Determination of the parameters of two-beam laser cleaning of quartz raw materials using artificial neural networks and the finite element method / Y.V. Nikitjuk, E.B. Shershnev, S.I. Sokolov, I.Y. Aushev // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 37–41. – DOI: https://doi.org/10.54341/20778708_2022_3_52_37 (in Russian). – EDN: EFURGI

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Abstract. The influence of the electrical modes of the controlled microwave magnetron pulsed inverter power supply on the conditions of large-volume microwave discharge plasma (about 9000 cm³) generation in a large-sized chamber of a resonator-type microwave plasmatron has been studied. The influence of anode current parameters in the power supply circuit of the microwave magnetron on the microwave discharge optical characteristics has been researched. A comparative analysis of the optical characteristics of the microwave discharge formed in the pulsed and constant generation modes depending on the power output of the microwave magnetron power supply has been carried out. It has been established that a decrease in the duty factor between pulses of anode current and the subsequent transition to a constant mode leads to a disproportionate increase in the energy input into the microwave discharge plasma.

Keywords: microwave discharge, microwave magnetron, continuous operating mode, optical plasma luminescence.

For citation: Tsikhan, O.I. The study of the microwave magnetron pulse power supply electrical parameters influence on the microwave discharge plasma generation modes / O.I. Tsikhan, S.I. Madveika, S.V. Bordusau // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 42–47. – DOI: https://doi.org/10.54341/20778708_2022_3_52_42 (in Russian). – EDN: EKYZCG

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Abstract. Using numerical simulation for THz waves, a design has been proposed and a parametric analysis of the geometrical parameters of the cylindrical hyperlens has been carried out. The dependences of image formation from two slits with subwavelength resolution on the number of layers, the thickness of the dielectric and metal layers, the radius and thickness of the hyperlens have been studied. The optimal parameters of the hyperlens for the formation of a high-quality image with subwavelength resolution in the near and far fields have been found.

Keywords: hyperlens, parametrization, numerical simulation, THz range.

For citation: Fanyaev, I.A. Parametric analysis of a cylindrical hyperlens with subwavelength resolution for THz waves / I.A. Fanyaev, I.A. Faniayeu, S.A. Khakhomov // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 48–55. – DOI: https://doi.org/10.54341/20778708_2022_3_52_48 (in Russian). – EDN: ELSIUA

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Abstract. On the basis of numerical simulation, the values of the parameters of an absorbing structure consisting of conductive Π-shaped elements which ensure the formation of weakly reflecting structures with simultaneous strong absorption of waves in the microwave range have been determined. Multicriteria optimization of the metamaterial parameters was performed using the MOGA genetic algorithm built into the DesignXplorer module of the ANSYS Workbench program. The period of the structure, the width and thickness of the conductive layer of Π-shaped elements were used as variable factors. The resonant frequency and the corresponding values of the reflection and absorption coefficients of the metamaterial were used as responses. The ANSYS HFSS program was used to design the absorbing structure and determine the response values. The numerical experiment was carried out using a sample obtained by the Latin hypercube method in the DesignXplorer module of the ANSYS Workbench program. The parameters of the metamaterial obtained as a result of optimization and the parameters obtained as a result of finite element modeling in the ANSYS HFSS program were compared. The maximum relative error of the results obtained using the MOGA algorithm did not exceed 1% when determining the resonant frequencies of the incident radiation, 6% when determining the absorption coefficients of the metamaterial, and 13% when determining the reflection coefficients of the metamaterial.

Keywords: metamaterial, absorption, reflection, multi-criteria optimization MOGA, ANSYS.

For citation: Optimization of parameters of absorbing metamaterials based on Π-shaped elements / S.A. Khakhomov, A.L. Samofalov, Y.V. Nikitjuk, I.V. Semchenko, I.Y. Aushev // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 56–60. – DOI: https://doi.org/10.54341/20778708_2022_3_52_56 (in Russian). – EDN: DVNAMK

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Abstract. Analytical description of the process of charging the polymer target surface by electron beam influence under laser assisted conditions is presented. The results were used to interpret the kinetic dependences of the electron beam dispersion of PMMA, PET, PTFE under laser assist influence λ=532 nm and λ=266 nm. The effect of the assist radiation wavelength on the kinetic parameters of dispersion was determined. The conclusion is made about the dominant effect of the photoinitiated electron emission caused by laser radiation influence during the electron beam dispersion of PMMA. The main effect of laser radiation during the electron beam dispersing of PTFE is an additional photochemical effect. The effect of the assist radiation wavelength on the PET dispersion kinetics is explained by the different nature of the effect; the main influence of photoelectron emission under the influence of radiation with λ=266 nm and photochemical changes under the action of radiation with λ=532 nm.

Keywords: polymers, electron beam dispersion, laser assistance, surface charging, photostimulated electron emission.

For citation: Features of the kinetics of polymers electron-beam dispersion under laser assisted conditions / M.A. Yarmolenko, A.V. Rogachev, A.S. Rudenkov, A.M. Mikhalko // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 61–66. – DOI: https://doi.org/10.54341/20778708_2022_3_52_61 (in Russian). – EDN: FXEIMS

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Abstract. The set of elliptic systems of two second-order partial differential equations on the plane with positive characteristic determinant is considered. An oblique derivative type boundary value problem for a system from in a bounded domain Ω with a smooth boundary ∂Ω is to find a solution for given boundary values of the derivatives along the directions l₁ and l₂ nontangential to ∂Ω. It is known that the set has three homotopy connected components. It is also known that if a system from is a system of orthogonal type and l₁, l₂ are vector fields that are noncollinear at each point of the boundary, then the oblique derivative boundary value problem is Fredholm in its classical formulation (regardless of the homotopy class of the system). In this paper, for each component of a representative is given that has the following properties: each component of an arbitrary twice continuously differentiable solution is a biharmonic function, and an oblique derivative type boundary value problem for this representative is not regularizable. Consequently, the regu-larizability of a problem of oblique derivative type boundary value problem for the elliptic systems under consideration is not related to the homotopy class of the system.

Keywords: elliptic system, regularizable boundary value problem, Lopatinski condition, homotopic classification.

For citation: Basik A.I. On the question of regularizability of the oblique derivative type boundary value problem for second-oder elliptic systems on the plane / A.I. Basik, E.V. Gricuk, T.V. Kapaitsava // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 67–71. – DOI: https://doi.org/10.54341/20778708_2022_3_52_67 (in Russian). – EDN: GFUZYC

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Abstract. The paper considers the structure of the subgroup associated with the intersection of kernels maximal A-admissible subgroups that do not simultaneously belong to the formation and do not contain -residuals whose indices have certain restrictions. The main properties of the corresponding generalized Frattini subgroup are established.

Keywords: finite group, formation, -residual.

For citation: Borodich, R.V. On the intersection of functorial non- -subgroups in groups with operators / R.V. Borodich // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 72–75. – DOI: https://doi.org/10.54341/ 20778708_2022_3_52_72 (in Russian). – EDN: GHELYE

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Abstract. The article focuses on identities and their generalizations in polyadic groupoids of special form, i. e. in polyadic groupoids with l-ary operation η_s,σ,k, that is called polyadic operation of special form and is defined on Cartesian power A^k of n-ary groupoid <A,η> by substitution σ∈S_k and n-ary operation η.

Keywords: polyadic operation, n-ary groupoids, identity, substitution.

For citation: Gal'mak, A.M. On identities and their generalizations in polyadic groupoids of special form. I / A.M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 76–81. – DOI: https://doi.org/10.54341/ 20778708_2022_3_52_76 (in Russian). – EDN: GSUIIC

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Abstract. A subgroup H is called weakly subnormal in G if H=<A,B> for some subgroup A subnormal in G and seminormal subgroup B of G. Here the subgroup B is called seminormal in G, if there exists a subgroup Y such that G=BY and BX is a subgroup for each subgroup X of Y. Finite non-nilpotent group, whose all proper subgroups are nilpotent are called Schmidt. If in a group with a nilpotent maximal subgroup the derived subgroup of a Sylow 2-subgroup from a maximal subgroup is contained in the center of a Sylow 2-subgroup, then the group is solvable. If the maximal subgroup of a group is non-nilpotent, then in it there is a Schmidt subgroup. The structure of the group itself, in particular, its solvability depends on the properties of Schmidt subgroups from a maximal subgroup of the group. In this paper, we establish the solubility of a finite group under the condition that some Schmidt subgroups from the maximal subgroup groups are weakly subnormal in a group.

Keywords: finite group, solvable group, Schmidt subgroup, weakly subnormal subgroup, maximal subgroup.

For citation: Zubei, E.V. Finite groups with weakly subnormal Schmidt subgroups in some maximal subgroups / E.V. Zubei // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 82–85. – DOI: https://doi.org/10.54341/ 20778708_2022_3_52_82. – EDN: GSZHBR

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Abstract. A non-nilpotent finite group all of whose proper subgroups are nilpotent is called a Schmidt group. A subgroup A is called seminormal in a group G if there exists a subgroup B such that G=AB and AB₁ is a proper subgroup of G for each proper subgroup B₁ of B. If A is either subnormal in G or seminormal in G, then the subgroup A is called semisubnormal in G. We establish the nilpotency of the derived subgroup of a group all of whose Schmidt subgroups are semisubnormal.

Keywords: finite group, Schmidt subgroup, seminormal subgroup, subnormal subgroup.

For citation: Kniahina, V.N. Nilpotency of the derived subgroup of a finite group with semisubnormal Schmidt subgroups / V.N. Kniahina // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 86–89. – DOI: https://doi.org/ 10.54341/20778708_2022_3_52_86 (in Russian). – EDN: HJSCLA

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Abstract. À mathematical model of multicriteria management of the production of finished products with an optimal combination of technological modes (TM) is presented. The problem of determining the optimal combination of TM in the production of a certain type of product according to the criteria of minimizing the cost of resources and time costs, taking into account the maximum possible product quality, was solved using stream programming, as the problem of determining the shortest path or the minimum consumption of resources and time, taking into account the lexicographic ordering of the importance of optimization criteria.

Keywords: technological process, flow model, multicriteria control, Bellman optimality principle, quality.

For citation: Demidenko, O.M. Multi-criterial optimization of resource distribution in the process of finished products / O.M. Demidenko, E.M. Borchik, A.I. Yakimov // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 90–96. – DOI: https://doi.org/10.54341/20778708_2022_3_52_90 (in Russian). – EDN: HPJWKR

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Abstract. The processes of reactive magnetron sputtering of a Ta target in an Ar/O₂ gas mixture have been studied. The dependences of the discharge voltage, deposition rate, electrical and physical characteristics of tantalum oxide films on the method of gases supply and oxygen concentration in the Ar/O₂ gas mixture are established. It has been established that the metallic, transition and reactive modes of the sputtering system operation are determined by the change in the rate of film deposition. Regardless of the method of the working gases supply, the initial formation of dielectric tantalum oxide films with low optical absorption is observed in the transition mode of the system operation.

Keywords: thin films, tantalum oxide, reactive magnetron sputtering, deposition rate, dielectric properties.

For citation: Peculiarity of reactive magnetron deposition of tantalum oxide films with different methods of gas supply into the chamber / H.T. Doan, D.A. Golosov, V.A. Burdovitsin, S.M. Zavadski, S.N. Melnikov // Problems of Physics, Mathematics and Technics. – 2022. – N 3 (52). – P. 97–104. – DOI: https://doi.org/10.54341/20778708_2022_3_52_97 (in Russian). – EDN: HSPOIT

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