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Abstract. We start with the the multicomponent matrix equation (Γ_μ∂_μ+m)ψ=0, and introduce the concept of the intrinsic symmetry. These symmetries should preserve the form of the basic equation. The relevant Lagrangian should be invariant under the intrinsic symmetry transformation. We will impose one additional requirement on symmetry transformations: such transformations should preserve the Majorana nature of the fields. This means that if the function Ψ_A is real (imaginary) part of the wave function, then after symmetry transformation the function remains real (imaginary). The situation for massless field Γ_μ∂_μψ=0 is substantially different. The Lagrangian invariance with respect to intrinsic symmetry transformation for massless case coincide with that for massive case. The main accent will be done on multicomponent Majorana fields, which can be related to one, two, three and four Dirac fields.

Keywords: generalized Dirac and Majorana fields, Lagrangian formalism, intrinsic symmetry.

For citation: Andrusevich, P.P. Dirac like equations and generalized majorana fields, intrinsic symmetries / P.P. Andrusevich, V.A. Red’kov // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 7-15. – DOI: https://doi.org/ 10.54341/20778708_2024_1_58_7 (in Russian). – EDN: TZLPQY

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Abstract. New vector solutions of the parabolic equation describing vector Cartesian paraxial TM Kummer light beams are proposed. The admissible values of free parameters at which Kummer beams transfer limited power are established and are physically realized. The polarization and energy properties of such beams are investigated. The graphic modeling is executed and the corresponding analysis of the ellipses of polarization, intensity and transverse energy fluxes of vector paraxial TM Kummer light beams is carried out.

Keywords: TM modes, vector beams, Kummer beams, transverse energy fluxes.

For citation: Girgel, S.S. TM modes of vector cartesian Kummer beams with transferable limited power / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 16-21. – DOI: https://doi.org/10.54341/ 20778708_2024_1_58_16 (in Russian). – EDN: ULNKFQ

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Abstract. The results of the studies on numerical modeling, using the finite element method, calculation and analysis of the stress state in a layered body (an isotropic elastic coating on an elastic base) during the interaction of a cylindrical indenter with an elastic coating taking into account friction are presented. The research is aimed at studying the mechanism of wear resistance of high-chromium steels modified with nitrogen ions at different temperatures.

Keywords: stress, coating, contact interaction, finite element method, friction.

For citation: Numerical calculation and analysis of the stress state in a layered body during friction, taken into account the changes in the elastic modules of the coating and base / V.V. Mozharovsky, V.A. Kukareko, S.A. Marjin, A.V. Kushnerou // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 22-28. – DOI: https://doi.org/10.54341/ 20778708_2024_1_58_22 (in Russian). – EDN: THNZPU

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Abstract. This study used finite-element calculations to develop regression and neural network models for the double-beam laser cleaving process of tubular-shaped glass products. A numerical experiment was performed using the central composite design, where the rotation speed of the glass tube, the geometric parameters of an elliptical laser beam with a wavelength of 10.6 μm, and the powers of laser beams with wavelengths of 10.6 μm and 1.06 μm were used as variable factors. The maximum temperatures and maximum thermoelastic tensile stresses in the zone of double-beam processing of glass tubes were determined as responses using finite element modelling with APDL (Ansys Parametric Design Language). The effective architectures for artificial neural networks have been established with TensorFlow in order to determine the maximum temperatures and thermoelastic stresses in the laser-treated area. The comparative analysis of neural network and regression models was carried out. A multi-criteria optimization of the parameters of double-beam laser cleaving of tubular-shaped glass products was performed using MOGA (multi-objective genetic algorithm).

Keywords: laser cutting, crack, ANN, MOGA, ANSYS.

For citation: Optimization of parameters for double-beam laser cleaving of tubular-shaped glass products / Yu.V. Nikityuk, V.A. Emelyanov, E.B. Shershnev, J. Ma, L. Wang, I.Yu. Aushev // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 29-35. – DOI: https://doi.org/10.54341/20778708_2024_1_58_29 (in Russian). – EDN: SWGRMA

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Abstract. The features of the morphology, phase composition and mechanical properties of the carbon coatings deposited from pulsed flows of carbon plasma onto the substrates containing nickel sublayers are determined when its temperature changes to 350°C. It has been established that heat treatment of Ni sublayers has a slight effect on hardness and elasticity modulus, leading to an increase in roughness RMS by 1.75 times and a more than 4-fold increase in grain size. The phase composition of Ni/a-C coatings deposited on heated nickel sublayers is characterized by a higher density of Csp² clusters, and with increasing heating temperature of the substrate, a significant decrease in roughness occurs. Using the method of instrumental nanoindentation, the structural and phase heterogeneity of coatings was established, which manifests itself in a non-monotonic change in the elastic modulus and a significant decrease in hardness with increasing indentation depth.

Keywords: carbon coatings, substrate heating, nickel, structure, mechanical properties.

For citation: Structure and mechanical properties of a-C coatings deposited from pulse carbon plasma on a Ni heated sublayer / D.G. Piliptsou, A.S. Rudenkov, A.V. Rogachev, Zhou Bin, E.A. Kulesh, N.N. Fedosenko // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 36-43. – DOI: https://doi.org/10.54341/20778708_2024_1_58_36 (in Russian). – EDN: RGZSTD

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Abstract. A theoretical analysis of the qualitative behavior of solutions to the Langevin equation for the motion of a spherical dielectric nanoparticle located in an interference field formed by the superposition of oncoming laser beams under the action of a gradient force without taking into account the resistance force of the medium is carried out. It is shown that, depending on the initial conditions, two different modes of movement of nanoparticles are possible – localization of nanoparticles in one of the maxima of the interference pattern of radiation or unlimited distance from the initial position within the interference field.

Keywords: dielectric nanoparticles, radiation forces, light scattering, interference of electromagnetic waves.

For citation: Svistun, A.Ch. Movement and localization of nanoparticles in an ideal liquid under the influence of the gradient force of light pressure / A.Ch. Svistun, E.V. Musafirov, L.S. Gaida, E.V. Matuk // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 44-49. – DOI: https://doi.org/10.54341/20778708_2024_1_58_44 (in Russian). – EDN: SBVDBQ

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Abstract. The features of the molecular structure, chemical composition and antifungicidal properties of the coatings based on clotrimazole, polyurethane (PU), polyvinyl chloride (PVC), formed from the active gas phase formed by electron beam dispersion of compounds in a vacuum, were determined. It was found that the chemical composition of the clotrimazole-based coating almost completely corresponds to the chemical composition of the original drug compound. A slight decrease in chlorine in the coating compared to the original drug compound is explained by the partial destruction of C – Cl bonds under the influence of an electron flow. The high efficiency of regulating the prolonged release of a drug compound by forming composite coatings has been established. It has been shown that the fungicidal activity of composite coatings is largely determined by the properties of the polymer matrix. The coatings based on clotrimazole and graphitized PVC exhibit higher activity.

Keywords: electron beam dispersion, coating, clotrimazole, polyurethane, polyvinyl chloride, molecular structure, properties.

For citation: Molecular structure and anti-fungicidal properties of coatings based on clotrimazole and polymers formed from the active gas phase / M.A. Yarmolenko, Jiang Xiao Homg, A.A. Rogachev, A.V. Rogachev, A.S. Rudenkov, V.A. Yarmolenko, S.A. Frolov // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 50-56. – DOI: https://doi.org/10.54341/20778708_2024_1_58_50 (in Russian). – EDN: SILLPY

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Abstract. The sequence of phase transformations during the crystallization of Sr_1,5La_0,5FeMoO_6-δ was investigated by the solid-phase reactions method. It has been established that in order to effectively minimize the influence of intermediate reaction products, it is advisable to use precursors and combined heating modes. As a result, it was possible to obtain the single-phase Sr_1,5La_0,5FeMoO_6-δ powder with the Curie temperature of 450 K and a magnetization value of 40,9 A•m²•kg^-1 at T=77 K in the magnetic field of 0.86 T.

Keywords: lanthanum-strontium ferromolybdate solid solution, thermogravimetric analysis, X-ray phase analysis, crystallization rate, sequence and degree of phase transformations, magnetization.

For citation: Degree of phase transformations under conditions of polythermal synthesis of strontium-substituted ferromolybdate / M.V. Yarmolich, N.A. Kalanda, A.V. Petrov, S.K. Lazarouk A.V. Semchenko, D. Sangaa, S. Munkhtsetseg // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 57-62. – DOI: https://doi.org/10.54341/ 20778708_2024_1_58_57 (in Russian). – EDN: QHXPQQ

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Abstract. The structure of a finite group G is investigated, in which all subgroups of order 2 and 3 as well as all cyclic subgroups of order 4 are hereditarily G-permutable in G.

Keywords: finite group, hereditarily G-permutable subgroup, soluble group.

For citation: Bychkov, P.V. Finite groups with hereditarily G-permutable subgroups of small order / P.V. Bychkov, S.F. Kamornikov, V.N. Tyutyanov // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 63-67. – DOI: https://doi.org/10.54341/20778708_2024_1_58_63 (in Russian). – EDN: NMFTFX

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Abstract. À new scheme for approximating Laurent series with rational functions is investigated. The concept of a generalized polynomial is introduced, and building upon this, a corresponding Pade problem for the Laurent series is formulated and solved. A constructive solution to this problem enables the determination of rational functions, which are then considered as Pade approximations of the Laurent series. It has been established that in the simplest case, these specific Pade approximations of the Laurent series behave similarly to the classical Pade approximations of power series: they localize the singular points of the function that is the sum of the Laurent series.

Keywords: Pade polynomials, power series, Laurent series, Pade – Laurent problem, Fabry’s theorem.

For citation: Starovoitov, A.P. Rational approximations of Laurent series / A.P. Starovoitov, N.V. Ryabchenko // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 68-73. – DOI: https://doi.org/10.54341/20778708_2024_1_58_68 (in Russian). – EDN: MQPGHY

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Abstract. The electrostatic field calculation in toroidal screens of high-voltage power line overvoltage limiter is considered. The calculation is implemented by addition theorems method. The algebraic equations for calculations of coefficients of screen potential expansion in terms of toroidal functions are obtained. The way of storm-cloud charge influence on electrostatic field near the limiter accounting is described. The field of obtained results application is analyzed too.

Keywords: overvoltage limiter, toroidal screen, electrostatic field, addition theorems, electrostatic potential, harmonic toroidal functions, storm-cloud.

For citation: Komnatny, D.V. Electrostatic field of overvoltage limiter calculation by addition theorems method / D.V. Komnatny // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 74-78. – DOI: https://doi.org/ 10.54341/20778708_2024_1_58_74 (in Russian). – EDN: LTQHPX

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Abstract. An important task in the design of sensor devices, including thermography, is the development of systems that provide accurate processing of input data, as well as their conversion into a digital signal. The results of application of the generalized electrical (compact) model of the thermal uncooled detector bolometric type (microbolometer) implemented in the Verilog-A hardware description language, which takes into account the peculiarities of the design and materials used for its fabrication, in the design of circuit and topological solutions of the integrated circuit for reading data from a matrix of detectors located in the focal plane, using the TSMC 0.18 μm design library, are presented.

Keywords: uncooled thermal detector of bolometric type, microbolometer, infrared detector, vanadium oxide, matrix in the focal plane, readout integral circuit, modeling.

For citation: Readout integrated circuit of thermal uncooled bolometric type detectors / Tran Van Trieu, Dao Dinh Ha, P.E. Novikov, K.V. Korsak, I.Yu. Lovshenko, V.R. Stempitsky // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 79-85. – DOI: https://doi.org/10.54341/20778708_2024_1_58_79 (in Russian). – EDN: FUIQSP

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Abstract. The production process of fulfilling orders with parameters that require readjustment of equipment has been studied. The problem of determining the optimal strategy for readjustment of production equipment is an optimization problem, which is formulated as a traveling salesman problem. When solving this problem, the nodes of the graph are orders, the arcs are changeovers with known cost when moving from one order to another. The optimization criterion is the minimum total cost of equipment changeovers. Based on the matrix of the cost of equipment changeovers during the execution of orders with known parameters, the research of the problem solution with the help of a genetic algorithm was carried out. The examples are given for estimating the total cost of changeovers for orders with several parameters with different levels. The implementation steps of the genetic algorithm for solving the problem are presented, and the results of the experiments are shown.

Keywords: industrial enterprise, orders with parameters, equipment changeover, optimization, traveling salesman problem, fully connected graph, genetic algorithm.

For citation: Solving the problem of order fulfillment management of an industrial enterprise / O.M. Demidenko, A.I. Yakimov, E.M. Borchik, E.A. Yakimov, D.A. Denisevich // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 86-92. – DOI: https://doi.org/10.54341/20778708_2024_1_58_86 (in Russian). – EDN: CAFDUQ

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Abstract. A method for control adaptation is proposed based on multi-level coupling of neuroregulators and simulation models of technological operations for adaptive control of the technological cycle with control feedback. A new-generation intellectual system based on open semantic technologies for intelligent systems (OSTIS) is described alongside with the principles of its creation, implemented algorithms and construction procedure.

Keywords: OSTIS integrated environment, event processing unit, knowledge base, control system, models of neuroregulators, feedback synthesis, computer adaptation system.

For citation: Smorodin, V.S. Intellectual adaptive control system with feedback connections / V.S. Smorodin, V.A. Prokhorenko // Problems of Physics, Mathematics and Technics. – 2024. – №1 (58). – P. 93-98. – DOI: https://doi.org/ 10.54341/20778708_2024_1_58_93 (in Russian). – EDN: CSOCYZ

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