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Abstract. In various problems in physics, some quantities that are infinite are often used. There are cases when several quantities simultaneously tend to infinity. Sometimes there are situations that require a more careful approach to solving. In this paper, using the example of a problem from the section “Electrostatics”, some features of the solution when using infinite quantities are considered.

Keywords: electric field, intensity, half-plane, surface charge density.

For citation: Akhramenko, N.A. Some features of solving physical problems with infinite quantities / N.A. Akhramenko, M.V. Bui // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 7–10. – DOI: https://doi.org/10.54341/20778708_2025_2_63_7. – EDN: SLSGBO

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Abstract. The problem of natural vibrations of a five-layer symmetrical in thickness rod with two fillers is considered. The bearing layers are assumed to be thin, high-strength. The Bernoulli hypotheses on cross-sections of flat and perpendicular to the deformed axial line, after load application, are accepted for them. In relatively thick lightweight aggregates, the Timoshenko hypothesis is fulfilled, according to which the cross-section remains flat and incompressible, but is rotated by some additional angle. The differential equations of the vibrations are obtained with the variational method, taking into account transverse forces of inertia. A transcendental equation for the eigenvalues of a rod with rigidly sealed ends is is derived, and its numerical solutions are obtained. The dependence of the natural frequencies of vibrations on the thickness of external bearing layers for different materials of the rod layers is investigated.

Keywords: symmetric five-layer rod, two fillers, eigenvalues, vibration frequencies, numerical results.

For citation: Budnikova, D.A. Natural frequencies of vibration of a five-layer rod / D.A. Budnikova // Problems of Physics, Mathemat-ics and Technics. – 2025. – № 2 (63). – P. 11–15. – DOI: https://doi.org/10.54341/20778708_2025_2_63_11 (in Russian). – EDN: AXVKJG

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Abstract. The paper presents an algorithm for calculating the meson form factors of the γγ^*→P(qq) process in a model based on the composite quark model and the point form of Poincare-invariant quantum mechanics. It is shown that the use of structure functions of constituent quarks for the light sector leads to a behavior of the q²F_P⁰(q²) value of the γγ^*→π⁰, γγ^*→η and γγ^*→η' processes at large momentum transfers consistent with experimental data. A self-consistent model satisfactorily describing electroweak decays of pseudoscalar mesons of the light sector is proposed.

Keywords: constituent quark model, anomalous magnetic moment, root-mean-square radius, form factor, asymptotic behavior.

For citation: Haurysh, V.Yu. Pseudoscalar P₀(qq)-mesons form-factor in composite relativistic quark model / V.Yu. Haurysh, V.V. Andreev // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 16–21. – DOI: https://doi.org/ 10.54341/20778708_2025_2_63_16 (in Russian). – EDN: YCVASK

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Abstract. The solutions of the parabolic equation describing Arnaud’s scalar paraxial light Gaussian beams with complex astigmatism are investigated. The admissible values of free parameters at which such beams carry finite power and are physically realizable have been specified. The explicit expressions describing the properties of an elliptical light spot, its deformation and rotation as it propagates are proposed. The graphical modeling and the corresponding analysis of intensity ellipses are performed.

Keywords: vector beams, Gaussian beams, complex astigmatism, quadratic integrability, rotating beams.

For citation: Girgel, S.S. Arnaud's rotating scalar Gaussian beams with complex astigmatism / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 22–26. – DOI: https://doi.org/10.54341/20778708_ 2025_2_63_22 (in Russian). – EDN: YHUDZG

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Abstract. Exact solutions of the three-dimensional modified Kadyshevsky equation in the momentum representation, describing the bound s-states of a system of two scalar particles in the case of the Coulomb potential in the limit of zero energy, are found. The solution of the problem is obtained by transforming it to an analogue of the Schrodinger equation with the Coulomb potential in the momentum representation, supplemented by boundary conditions of the special type. The wave functions and quantization conditions imposed on the coupling constant are obtained.

Keywords: modified Kadyshevsky equation, Coulomb potential, momentum representation, Schrodinger equation.

For citation: Grishechkin, Yu.A. Exact solution of the quasipotential equation with the Coulomb potential in the momentum representation for coupled s-states with energy equal to zero / Yu.A. Grishechkin, V.N. Kapshai // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 27–29. – DOI: https://doi.org/10.54341/20778708_2025_2_63_27 (in Russian). – EDN: VANBVZ

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Abstract. In the paper we consider the Joule – Thomson expansion of the Redlich – Kwong fluid and a charged AdS black hole. Based on the equations of state, the analytical expressions for inversion temperatures are obtained, the inversion curves in the TP-plane are constructed, and the cooling and heating regions are determined. Similarities and differences in the behavior of a charged AdS black hole and the Redlich – Kwong fluid in this process are analyzed.

Keywords: Redlich – Kwong fluid, charged AdS black hole, Joule – Thomson expansion, isenthalpic process, inversion curve, cooling and heating regions.

For citation: Novikava, V.U. Joule – Thomson expansion: Redlich – kwong fluid and charged AdS black hole / V.U. Novikava, G.Yu. Tyumenkov // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 30–34. – DOI: https://doi.org/ 10.54341/20778708_2025_2_63_30 (in Russian). – EDN: VYPBIO

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Abstract. The influence of the method for forming the ethyl cellulose layer, the architecture of the two-layer systems based on ethyl cellulose and sulfuric acid on the morphology and phase composition of the carbon coatings formed on their surface is determined. It is established that in the case of laser deposition of ethyl cellulose, the carbon layers deposited on the H₂SO₄ / EC surface are characterized by a higher Csp³ / Csp² ratio, compared to the coatings formed on the EC / H₂SO₄ surface. At the same time, in the case of electron beam deposition of ethyl cellulose, the opposite effect is observed: in the carbon layer deposited on the H₂SO₄ / EC surface, a lower Csp³ / Csp² ratio is recorded, compared to the layers on the EC / H₂SO₄ surface, which is due to the presence of a droplet phase during laser dispersion of ethyl cellulose and, as a consequence, various processes of EC layer structure formation and its catalytic effect on the carbon coating.

Keywords: carbon, sulfuric acid, ethylcellulose, morphology, phase composition.

For citation: Influence of conditions and mode of formation of a sublayer based on ethyl cellulose and sulfuric acid on the structure of carbon coatings / A.S. Rudenkov, A.V. Rogachev, M.A. Yarmolenko, D.G. Piliptsou // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 35–43. – DOI: https://doi.org/10.54341/20778708_2025_2_63_35 (in Russian). – EDN: WCOOVW

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Abstract. The article studies polyadic groups in which cosets of a semi-invariant n-ary subgroup can be n-ary subgroups.

Keywords: l-ary group, semi-invariant l-ary subgroup, coset, congruence.

For citation: Gal'mak, A.M. Cosets that are poplyadic subgroups / A.M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 44–50. – DOI: https://doi.org/10.54341/20778708_2025_2_63_44 (in Russian). – EDN: PHKJNB

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Abstract. Throughout the paper, all groups are finite and G always denotes a finite group; G is called a Schmidt group if G is not nilpotent, but every proper subgroup of G is nilpotent. A subgroup A of G is called Up-normal in G if every principal pd-factor of G between A_G and A^G is cyclic. We say that a subgroup A of G is partially p-subnormal in G if A=<L,T> for some subnormal subgroup L and Up-normal subgroup T of G. In this paper, we prove the following theorem. Theorem. If every Schmidt subgroup of a group G is partially p-subnormal in G, then the derived subgroup G' of G is p-nilpotent.

Keywords: finite group, Schmidt group, p-nilpotent group, Up-normal subgroup, partially p-subnormal subgroup.

For citation: Dergacheva, I.M. Finite groups with partially p-subnormal Schmidt subgroups / I.M. Dergacheva, E.A. Zadorozhnyuk, I.P. Shabalina // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 51–55. – DOI: https://doi.org/10.54341/20778708_2025_2_63_51 (in Russian). – EDN: PXPTVX

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Abstract. The paper describes the asymptotic behavior of trigonometric Hermite – Jacobi approximations and nonlinear Hermite – Chebyshev approximations for the systems of special functions associated with Mittag – Leffler functions. The exact ordinal estimates of uniform deviations of the indicated approximations from the corresponding special functions are found. In some cases, the obtained ordinal estimates are asymptotically exact.

Keywords: Mittag – Leffler functions, Hermite – Pade approximations, Pade – Chebyshev approximations, trigonometric Hermite – Jacobi approximations, nonlinear Hermite – Chebyshev approximations.

For citation: Starovoitov, A.P. On the asymptotics of convergence of trigonometric Hermite – Jacobi approximations and nonlinear Hermite – Chebyshev approximations / A.P. Starovoitov, M.A. Kukhlich, N.V. Ryabchenko // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 56–61. – DOI: https://doi.org/10.54341/20778708_2025_2_63_56 (in Russian). – EDN: MPCXET

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Abstract. This study employs a combined approach of artificial neural networks (ANN) and an analytical moving heat source model to simulate the laser processing of diamonds. The training and testing datasets for the neural networks were generated using Mathcad, with calculations performed for 1,152 input parameter combinations, including 50 dedicated to ANN validation. Optimal ANN configurations were identified to achieve high-precision predictions of laser-induced temperature distributions in diamonds. The results provide a basis for optimizing technological parameters in diamond laser processing for electronic applications.

Keywords: laser cutting, diamond, artificial neural network.

For citation: Neural network modeling of laser processing parameters for diamonds in electronics technologies / A.N. Kupo, Yu.V. Nikityuk, E.B. Shershnev, V.A. Emelyanov // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 62–66. – DOI: https://doi.org/10.54341/20778708_2025_2_63_62. – EDN: ONFMXU

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Abstract. A design of a two-cathode magnetoelectric filter has been proposed to reduce the heterophase of the plasma flow during the formation of multicomponent coatings. The effect of the configuration of the magnetic fields of the separator on the spatial distribution of the concentration of elements in a multicomponent plasma flow in a vacuum chamber was experimentally studied. It is shown that when using a separating system with a Y-shaped plasma guide, the control of the ratio of elements in deposited coatings is possible as a result of changing the arrangement of the parts in the vacuum chamber and due to the asymmetry of arc discharge currents on the evaporators.

Keywords: vacuum arc plasma, heterophase of plasma flow, multi-component coatings, separation systems.

For citation: Application of separating devices for forming multi-component coatings from plasma flow of vacuum arc discharge / S.D. Latushkina, I.M. Romanov, O.I. Posylkina, I.A. Sechko, V.M. Komarovskaya // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 67–73. – DOI: https://doi.org/10.54341/20778708_2025_2_63_67 (in Russian). – EDN: LRECBR

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Abstract. The paper presents the results of a study of electrical stimulation of the neuromuscular system using a multi-element electrode in comparison with a standard electrode. The dependences of the threshold current of electrical stimulation on the time parameters of the pulse for standard and multi-element electrodes are studied. The efficiency of using electrode matrices, in which the electrical stimulation signal is delayed for a specified time for each channel, is determined.

Keywords: multi-element electrode, multi-channel electrical stimulation, partial electrode, pulse duration, stimulation current.

For citation: Osipov, A.N. Electrostimulation of the neuromuscular apparatus by a multi-element electrode / A.N. Osipov, I.O. Khazanovsky, A.V. Patseev // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 74–78. – DOI: https://doi.org/10.54341/20778708_2025_2_63_74 (in Russian). – EDN: HDUNGI

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Abstract. The study is devoted to the development of a metal-dielectric antenna. The work uses various methods for calculations, including rigorous electrodynamic approaches to describe the antenna characteristics, numerical analysis for structural and parametric synthesis, the integral equation method for determining currents along metal components, the collocation method for solving the integral equation, and the finite difference method for numerical calculations. As a result of the study, an algorithm was developed that allows designing metal-dielectric antennas taking into account various radio wave lengths and determining the operating frequency for the antenna.

Keywords: method of integral equations, radio wave scattering, modeling, metal-dielectric antenna.

For citation: Preobrazhensky, A.P. Design of a metal-dielectric antenna / A.P. Preobrazhensky, T.V. Avetisyan, Yu.P. Preobrazhensky // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 79–83. – DOI: https://doi.org/10.54341/20778708_2025_2_63_79 (in Russian). – EDN: HPOQHO

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Abstract. The paper proposes a calculation method and determines the optimal parameters for processing hard non-metallic materials, which have found their application in electronic engineering. It is shown that the proposed method makes it possible to optimize the processing of such materials as silicon, germanium, gallium arsenide, quartz glass, natural and synthetic diamond. When calculating the optimal processing parameters, the values of the physical and mechanical properties of these materials are used. The results obtained can be used to determine the technological parameters of hard brittle non-metallic materials processing in electronics.

Keywords: process optimization, hard brittle materials, electronic products and components.

For citation: Shershnev, E.B. Optimization of brittle non-metallic materials processing in the production of electronic products / E.B. Shershnev, A.N. Kupo // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 84–90. – DOI: https://doi.org/10.54341/20778708_2025_2_63_84 (in Russian). – EDN: KTINLJ

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Abstract. The paper presents a control adaptation technology based on the synthesis of neuroregulators using neural network algorithms. The technology includes a procedure for synthesizing a neuroregulator, which uses algorithms for optimizing the neural network architecture. The proposed approach to development provides for the possibility of setting numerical criteria for assessing the quality of adaptation and using a simulation model of the process control system. In the presence of a prototype regulator, the dynamics of its functioning are simulated to improve the adaptive characteristics of the system.

Keywords: neural network, adaptive control, neuroregulators, evolutionary algorithms, technological operation, adaptive control technology.

For citation: Prokhorenko, V.A. Technology of adaptive control of automated production systems based on neural networks / V.A. Prokhorenko, V.S. Smorodin // Problems of Physics, Mathematics and Technics. – 2025. – № 2 (63). – P. 91–96. – DOI: https://doi.org/10.54341/20778708_2025_2_63_91 (in Russian). – EDN: FUQEQA

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Abstract. The paper addresses the factorization of natural numbers into prime factors task in the context of discrete optimization and machine learning. The approach with decomposition into summands and the associated function for using with genetic algorithms (as fitness function) and neural networks (as error function) is proposed. The statistical analysis of changes in the discrete transformation function of the optimal divisor is performed in order to approximate the scope of optimal discrete transformations for a trial divisor.

Keywords: large numbers factoring, discrete optimization, machine learning, neural networks, genetic algorithms.

For citation: Chagochkin, A.A. Discrete optimization for the factorization problem / A.A. Chagochkin // Problems of Physics, Mathe-matics and Technics. – 2025. – № 2 (63). – P. 97–100. – DOI: https://doi.org/10.54341/20778708_2025_2_63_97 (in Russian). – EDN: FGHDOK

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