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Abstract. The influence of the temperature and composition of the electrolyte, the number and value of the periods of photonic crystal (PC) structures of anodic oxide on aluminum and without aluminum on the spectral position of the stop zones (SZ) was studied. A hyp-sochromic shift of the SZ maximum by 76 nm was established with an increase in the electrolyte temperature from 7 to 12° C and by 103 nm with a change in the number of periods from 52 to 230, a bathochromic shift by 160 nm with an increase in the structure period by 1.5 times. PC structures with a transmittance of 0.1% and a reflectivity of 83% in the SZ region were obtained. The PC structures have a color, the colorimetric characteristics are determined, presented on the chromaticity dia-gram and are consistent with the SZ position.

Keywords: photonic crystal structure, anodic aluminum oxide, specular reflection spectrum, stop zone.

For citation: Gasenkova, I.V. Analysis of stop zones of photonic-crystalline structures of anodic aluminum oxide / I.V. Gasenkova, N.I. Mukhurov, I.M. Andrukhovich // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 7–13. – DOI: https://doi.org/10.54341/20778708_2025_1_62_7 (in Russian). – EDN: QGYDDM

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Abstract. The new solutions of the parabolic equation describing vectorial Cartesian paraxial TM Gaussian light beams with complex astigmatism are investigated. The admissible values of the free parameters at which Gaussian beams carry finite power are established. The explicit expressions describing energy and polarization properties of vector Gaussian light beams with complex astigmatism are proposed. The graphical modeling and corresponding analysis of polarization ellipses, intensity and transverse energy fluxes of vector Gaussian paraxial light beams with homogeneous and inhomogeneous (TM-modes) polarization are performed.

Keywords: polarization, vector beams, Gauss beams, complex astigmatism, TM-modes, transverse energy fluxes.

For citation: Girgel, S.S. Energy and polarization properties of vector Gaussian light beams with complex astigmatism / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 14–19. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_14 (in Russian). – EDN: VHVSNG

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Abstract. Bragg diffraction of circularly polarized needle light beams by a slow shear ultrasound wave in paratellurite crystals is studied. It is shown that by changing the cone angle of the Bessel light beam incident on the diaphragm, a high diffraction efficiency of ~90% is achieved for the needle beam formed and incident on the acousto-optic cell. It is found that with an increase in the length of the acousto-optic interaction, the diffraction efficiency of the needle light beams reaches a maximum value at lower ultrasound powers. It is shown that at small cone angles of the light beam, the diffraction efficiency of the needle light beam is comparable to the diffraction efficiency of the Gaussian one.

Keywords: needle light beam, Bragg diffraction of light, diffraction efficiency, uniaxial gyrotropic crystal, paratellurite crystal.

For citation: Diffraction of needle light beams by ultrasonic waves in paratellurite crystals / G.V. Kulak, V.I. Kazakov, T.V. Nikolaenko, P.I. Ropot // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 20–24. – DOI: https://doi.org/10.54341/20778708_2025_1_62_20 (in Russian). – EDN: VOFSNR

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Abstract. A mathematical model for the study of the natural vibrations of a five-layer circular plate asymmetric in thickness with pinched or hinged contours is developed. Transcendental equations depending on boundary conditions are written out to find the eigenvalues. The formula linking the eigennumbers and frequencies of oscillations is given. A numerical study of the influence of the thickness of the inner non-substantial layer and the elastic characteristics of the layer materials on the eigennumbers and frequencies is carried out. It is shown that an increase in the elastic moduli of the materials or in the thickness of the supporting layer leads to an increase in the natural frequencies.

Keywords: five-layer circular plate, thickness asymmetry, natural oscillations, frequencies.

For citation: Lachugina, E.A. Free vibrations of a five-layer circular plate at different fixations of the contour / E.A. Lachugina // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 25–30. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_25 (in Russian). – EDN: WGDTTR

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Abstract. The deformation of asymmetrical in thickness elastioplastic three-layer plates with compressible filler under the action of thermoradiation loads is investigated. Kinematic hypotheses are based on the hypothesis of a broken line: for the outer layers, Kirchhof’s hypotheses are accepted, in a rigid compressible filler the deformed normal remains rectilinear. At the contact boundaries, the conditions of continuity of displacements are used. A system of equilibrium equations and its analytical solution in displacements are obtained.

Keywords: plasticity, three-layer rectangular plate, thermal radiation load, compressible filler.

For citation: Melnikova, A.S. Deformation of elastoplastic rectangular three-layer plate with compressible filler in thermoradiation field / A.S. Melnikova // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 31–36. – DOI: https://doi.org/10.54341/20778708_2025_1_62_31 (in Russian). – EDN: RTQKOE

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Abstract. A methodology was developed for constructing theoretical and numerical dependencies and algorithms for determining contact and wear parameters, including for gears with coatings. The asymptotic dependences of calculating the parameters of contact interaction and wear of elastic bodies with composite coatings are proposed. A computer program has been created that makes it possible to build a profile of the teeth of gears, determine the contact zone of the interacting teeth of gears, calculate the thickness of the worn layer, and take into account the location of fibers in the matrix of the composite material for wear parameters. The proposed approaches can be used in production processes to select materials when creating structural elements of machine parts.

Keywords: contact parameters, composite coatings, gears, asymptotic dependencies.

For citation: Mozharovsky, V.V. Asymptotic dependences of calculation of contact parameters and wear of teeth of gears with composite coating during contact interaction / V.V. Mozharovsky, D.S. Kuzmenkov, S.V. Kirhintsava // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 37–42. – DOI: https://doi.org/10.54341/20778708_2025_1_62_37 (in Russian). – EDN: SKXJLW

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Abstract. A method for forming composite copper-carbon coatings by deposition from combined flows of carbon plasma and electric arc evaporation of copper with increasing carbon content during layer growth is proposed. The studies of the structural-phase composi-tion performed by the method of Raman and X-ray photoelectron spectroscopy showed that an increase in the copper concentration stimulates graphitization of the carbon matrix: it leads to a decrease in the size of Csp² clusters and an increase in their concentration. The presence of copper in the coating in the form of individual particles 100...500 nm in size was established by the method of atomic force microscopy. The coatings are characterized by a decrease in hardness and elasticity with an increase in the indentation depth.

Keywords: nanocomposite copper-carbon coatings, chemical composition, hardness, pulsed cathodic arc evaporation.

For citation: Structure, mechanical properties of gradient nanocomposite copper-carbon coatings / A.S. Rudenkov, Wang Jingjie, A.V. Rogachev, Liu Jubo, D.G. Piliptsov, E.A. Kulesh, A.N. Kupo // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 43–50. – DOI: https://doi.org/10.54341/20778708_2025_1_62_43 (in Russian). – EDN: ADUQNG

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Abstract. The average active resistances and capacitances of nucleotides and hydrogen bonds in the DNA molecule were calculated based on the comparison of the theoretical model with known experimental data. A circuit similar to the structure of the DNA molecule in terms of electrical conductivity was designed to study the currents and voltages at different parts of the equivalent electrical circuit of the DNA molecule. It is shown that for DNA segments consisting of one hundred fifty or more pairs of nucleotides, the model of an in-finite electrical circuit with repeating links can be applied.

Keywords: DNA molecule, nucleotides, hydrogen bonds, electric circuit, electrical resistance, electrical capacity.

For citation: Modelling of DNA-like electrical circuit and calculation of the average active resistances and capacitances of nucleotides and hydrogen bonds / I.V. Semchenko, E.D. Piskunova, A.L. Samofalov, P.V. Somov // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 51–57. – DOI: https://doi.org/10.54341/20778708_2025_1_62_51 (in Russian). – EDN: CJVZWE

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Abstract. To predict the characteristics of the metamaterial-phase-manipulator, the optimization of the relevant parameters of such a device was carried out using an artificial neural network and a genetic algorithm. It is shown that the relative error in determining the values of the investigated parameters did not exceed 1% compared to the values calculated by the finite element method.

Keywords: metamaterial, phase manipulator, planar spiral, artificial neural networks, genetic algorithms.

For citation: Optimization of metamaterial phase manipulator parameters using neural network modeling and genetic algorithm / P.V. Somov, A.L. Samofalov, Yu.V. Nikityuk, S.A. Khakhomov, I.V. Semchenko, Dazhi Ding // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 58–63. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_58. – EDN: CMNQKR

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Abstract. The study on the polyadic analogues of normal subgroups in polyadic groups of special form is carried on.

Keywords: polyadic operation, semiinvariant l-ary subgroups, n-semiinvariant l-ary subgroups.

For citation: Gal’mak, A.M. Polyadic analogues of normal subgroups in polyadic groups of special form. III / A.M. Gal’mak // Prob-lems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 64–66. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_64 (in Russian). – EDN: CRZWMH

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Abstract. The equivalence of the iterated modulus of smoothness and the Petre K-functional is proved.

Keywords: iterated modulus of smoothness, K-functional.

For citation: Kazimirov, G.N. Equivalent structural characteristic of a function from a Lebesgue space / G.N. Kazimirov, V.V. Burakovskiy // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 67–69. – DOI: https://doi.org/ 10.54341/20778708_2025_1_62_67 (in Russian). – EDN: NEPSMJ

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Abstract. The object of the investigation in the article is a G-network consisting of unreliable quarantine, control and service queues in the systems (QS). After the destruction of one positive claim, negative claims can either leave the network or move between the QS of the network. It is assumed that in a certain proportion of cases, a virus can deceive antivirus software (ASW) and cause harm to a com-puter network. This is possible until the virus is detected by the ASW of a certain QS. Using the method of multidimensional generating functions (MDGF), the average characteristics of a given QS are found if all of its characteristics, except for the number of SLs, operate in saturation mode.

Keywords: G-network, unreliable service lines, systems with control and quarantine queues, method of multidimensional generating functions, non-stationary state probability, average characteristics.

For citation: Kopats, D.Y. G-network with unreliable systems with control and quarantine queues and the option of moving negative or-ders between systems / D.Y. Kopats // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 70–77. – DOI: https://doi.org/10.54341/20778708_2025_1_62_70 (in Russian). – EDN: NWEPAT

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Abstract. The inverse boundary value problem with an unknown time-dependent coefficient for a third-order pseudo-hyperbolic equation with periodic and integral conditions is studied. When solving the original inverse boundary value problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out. The existence and uniqueness of the solution to an auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is made again, as a result, the conclusion is made on the solvability of the original inverse problem.

Keywords: inverse problem, pseudo-hyperbolic equation, Fourier method, classical solution.

For citation: Mehraliyev, Y.T. Inverse problem of simultaneous determination of the right-hand side and the coefficient in a third-order pseudo-hyperbolic equation with periodic and integral conditions / Y.T. Mehraliyev, R.S. Sadikhzada // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 78–86. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_78 (in Russian). – EDN: NZDPLC

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Abstract. Let F and H be some σ-local formations of finite groups. Then F/_σH∩F denote the lattice of all σ-local formations X such that H∩F⊆X⊆F. The length of the lattice F/_σH∩F is called a H_σ-defect of the σ-local formation F. In particular, if H is the formation of all identity groups, then the H_σ-defect of a σ-local formation F is called a l_σ-length of the formation F. The general properties of H_σ-defect of σ-local formations are studied, the description of minimal σ-local non-H-formations for an arbitrary σ-nilpotent σ-local formation H is obtained, the description of the lattice structure of σ-local formations of H_σ-defect 1 is given. The descriptions of the lattice structure of reducible σ-local formations of finite H_σ-defect, as well as the lattice structure of reducible σ-local formations of finite l_σ-length are obtained.

Keywords: finite group, σ-local formation, critical σ-local formation, H_σ-defect of a σ-local formation, l_σ-length of a σ-local formation.

For citation: Safonova, I.N. On σ-local formations of finite groups with bounded H_σ-defect / I.N. Safonova, V.V. Skrundz // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 87–101. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_87 (in Russian). – EDN: OQGGJH

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Abstract. Relying on the known results on joint Hermite – Pade approximations of a system of trigonometric series, sufficient conditions are found under which linear Hermite – Chebyshev approximations exist and are determined uniquely. When the found conditions are met, the formulas are obtained that describe the explicit form of the numerators and denominator of linear Hermite – Pade approximations for a system of functions that are sums of Fourier series in Chebyshev polynomials of the first and second kind.

Keywords: Fourier series, series in Chebyshev polynomials, Hermite – Pade approximations, Pade – Chebyshev approximations, linear Hermite – Chebyshev approximations.

For citation: Starovoitov, A.P. Uniqueness and explicit form of Hermite – Chebyshev linear approximations / A.P. Starovoitov, I.V. Kruglikov // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 102–107. – DOI: https://doi.org/ 10.54341/20778708_2025_1_62_102 (in Russian). – EDN: HUFLRZ

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Abstract. The development of a machine vision system that allows you to determine the special points of angles on static images of architectural plans are described. The main objective of this development is to create a library in the Python programming language containing the Harris, Shi – Tomasi and FAST angle detectors. The developed software modules are an addition to Blender and allow you to speed up the process of three-dimensional modeling based on recognized corner points.

Keywords: angle detectors, singular points, computer vision.

For citation: Aksionova, N.A. Implementation of a computer vision system for angle detectors / N.A. Aksionova // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 108–112. – DOI: https://doi.org/10.54341/ 20778708_2025_1_62_108 (in Russian). – EDN: IRYMTE

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Abstract. The article presents a software implementation of a web application for studying the influence of hyperparameters on the ef-fectiveness of machine learning algorithms when solving problems of classification of biomedical data and predicting the presence of diseases as a continuation of previous studies on optimizing hyperparameters of machine learning algorithms for problems of classifica-tion of biomedical data. The web application is designed to facilitate the process of setting up models, providing a convenient tool for conducting experiments, making it possible to load a set of biomedical data, select a classification algorithm and set values for the corre-sponding hyperparameters. It can also be used as a medical decision support tool, providing more accurate diagnosis based on the analysis of the patient clinical data.

Keywords: hyperparameters, machine learning model, classification algorithms, performance assessment, early diagnosis of diseases, predictive analytics, web application.

For citation: Timoschenko, E.V. Web application for research of the influence of hyperparameters on the performance of machine learn-ing algorithms in early diagnosis of diseases / E.V. Timoschenko, A.F. Razhkov // Problems of Physics, Mathematics and Technics. – 2025. – № 1 (62). – P. 113–119. – DOI: https://doi.org/10.54341/20778708_2025_1_62_113 (in Russian). – EDN: JTWROE

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