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Abstract. A laboratory thin-film capacitor was manufactured based on a multilayer sol-gel film of barium titanate using a titanium substrate. The results of measuring the capacitance and dielectric loss tangent of the formed capacitor in the frequency range 0.2 kHz – 200 kHz are presented. It has been established that when moving from the low-frequency range to the high-frequency one, the value of the dielectric loss tangent decreases by an order of magnitude and amounts to 0.032-0.039 for the frequency range from 50 kHz to 200 kHz. For the entire range under study, the capacitance value of the capacitor is 560-750 pF and the specific capacitance is 41-55 nF/cm². For the frequency range 1 kHz – 10 kHz, the dielectric constant of barium titanate is calculated to be from 108 to 127.

Keywords: BaTiO₃, sol-gel method, film capacitor capacitance, dielectric loss tangent.

For citation: Thin-film capacitor based on barium titanate formed by the sol-gel method on titanium / N.V. Gaponenko, R.T. Makhmutov, E.I. Lashkovskaya, E.V. Telesh, K.V. Shustsikava, V.A. Kovalev, Yu.V. Radyush, D.V. Zhigulin, V.A. Pilipenko, A.V. Semchenko // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 7-12. – DOI: https://doi.org/10.54341/20778708_2024_3_60_7 (in Russian). – EDN: XIDSWV

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Abstract. A number of components of the cavitation noise spectrum, used to assess cavitation activity, have been studied. It is shown that the nature of the dependences of the studied parameters on the ultrasound intensity differs for small and large distances from the emitter. It has been established that the relationship between the studied parameters is characterized by a high degree of correlation for close distances from the emitter under conditions of a developed cavitation region. In the cavitation region far from the emitter, these parameters are not clearly related to each other and are characterized by a low level of correlation. Based on the data obtained, an approach to choosing the optimal method for assessing cavitation activity is proposed.

Keywords: cavitation, ultrasound, cavitation noise, cavitation noise spectrum.

For citation: Study of the spectrum of cavitation noise in the field of a submersible ultrasonic embedier / V.S. Minchuk, V.S. Gavgiluk, T.A. Dezhkunov, A.Yu. Perkhunova, N.V. Dezhkunov // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 13-17. – DOI: https://doi.org/10.54341/20778708_2024_3_60_13 (in Russian). – EDN: YHJRPI

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Abstract. This paper describes the development of tools for modeling and searching for optimal parameters for the process of laser cutting of brittle non-metallic materials using laser chopping. Software tools are designed for finite element modeling, neural network modeling and searching for optimal parameters using a genetic algorithm and are implemented in Python. The use of the developed software is shown using the example of searching for optimal parameters for cutting a quartz plate.

Keywords: neural network modeling, finite element modeling, FEniCS laser cutting, genetic algorithm, parameter optimization.

For citation: Development of software tools for modeling and optimization of laser cutting parameters of brittle non-metallic materials / Yu.V. Nikitjuk, V.A. Prokhorenko, O.M. Demidenko, V.S. Smorodin, A.V. Voruev // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 18-22. – DOI: https://doi.org/10.54341/20778708_2024_3_60_18 (in Russian). – EDN: VFWQQP

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Abstract. A corrective modeling of the density function of Venus based on the PVM model, which assumes a five-layer internal structure of the planet, is carried out. The analytical and graphical forms of new density functions are obtained for three physically valid approximations, conditioned by permissible changes in the dimensions of the planet’s core and crust.

Keywords: internal structure, planet mass, planet radius, density function, spherical layer, PVM model.

For citation: Novikova, O.V. Density function for a model of earth-like Venus / O.V. Novikova, G.Yu. Tyumenkov // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 23–26. – DOI: https://doi.org/10.54341/ 20778708_2024_3_60_23 (in Russian). – EDN: RNRZHA

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Abstract. The bending of an elastic circular five-layer plate under the action of a local transverse load distributed in a circle was studied. The plate, symmetrical in thickness, has three thin load-bearing layers (two external and one internal), the deformation of which obeys Kirchhoff’s hypotheses. In two relatively thick fillers, the normal remains straight and does not change its length, but rotates through some additional angle. The system of differential equations for the equilibrium of the plate was obtained by the Lagrange variational method. The analytical solution of the problem is written in Bessel functions in final form. Numerical results of the study of deflections and relative shifts are presented depending on the radius of the force circle, the thickness of the internal load-bearing layer, and the materials of the external load-bearing layers.

Keywords: five-layer plate, circular load, analytical solution, numerical investigations.

For citation: five-layer plate, circular load, analytical solution, numerical investigations.

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Abstract. A metamaterial consisting of paired planar spirals has been simulated for phase manipulation of electromagnetic waves in the microwave range. The optimal geometric parameters of the metamaterial and the phase values at the resonators were obtained to control the radiation pattern. It was proposed to realize the phase change of the wave emitted by a planar spiral element by changing the capacitance of the varicap when the voltage on it changes.

Keywords: metamaterial, phase manipulator, paired planar spiral, microwave range.

For citation: Designing a phase manipulator using metamaterials based on paired planar spirals / A.L. Samofalov, I.A. Faniayeu, P.V. Somov, I.V. Semchenko, A.A. Kovalev, Hui Chu // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 32–37. – DOI: https://doi.org/10.54341/20778708_2024_3_60_32 (in Russian). – EDN: AZMISC

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Abstract. The theoretical calculation, modelling and experimental study of the metasurface based on single-turn planar spirals for obtaining maximum absorption in the absence of electromagnetic wave reflection in the microwave range have been carried out. The calculation of the structural parameters of the absorbing metamaterial was carried out for two glass-textolites – Arlon AD255C and Taconic TLY. The results of the studies confirmed the possibility of using the proposed structure as a non-reflective absorber of electromagnetic waves.

Keywords: metasurface, absorption, planar spiral, microwave range.

For citation: Metasurface based on single-turn planar spirals with non-reflective absorber property in the microwave range / I.A. Faniayeu, A.L. Samofalov, I.V. Semchenko, S.A. Khakhomov, A.Y. Kravchenko, Mengmeng Li // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 38–43. – DOI: https://doi.org/10.54341/20778708_2024_3_60_38 (in Russian). – EDN: DDYWPW

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Abstract. The process of acousto-optical (AO) diffraction of a TE-type Bessel beam and a Bessel acoustic beam in acoustically trans-versely isotropic crystals has been studied. AO diffraction by a vertically polarized (SV-) acoustic wave is considered, which makes it possible to use diagonal components of the dielectric constant tensor in the AO process. It has been established that due to the indicated diagonal components, isotropic diffraction of a Bessel light beam can be realized with a high interaction efficiency. The proposed AO diffraction scheme is of interest for modulating Bessel light beams with the possibility of dynamically adjusting their parameters.

Keywords: Bessel light beams, Bessel acoustic beams, acousto-optic diffraction.

For citation: Khilo, P.A. Isotropic diffraction of a Bessel light beam during acousto-optic interaction / P.A. Khilo, M.A. Revenok // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 44–47. – DOI: https://doi.org/ 10.54341/20778708_2024_3_60_44 (in Russian). – EDN: MXGOED

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Abstract. The effect of thermal expansion of the matrix material on the effective thermal conductivity coefficient of a closed-cell material is examined using direct numerical simulation. Computational experiments have been performed. An increase in the thermal conductivity coefficient of the composite material was established depending on the heat treatment time.

Keywords: effective thermal conductivity coefficient, thermal expansion coefficient, mathematical model, grid methods, computational experiment.

For citation: Aulas, A.N. Simulation of the influence of thermal expansion on the thermal conductivity coefficient of a closed-pore material / A.N. Aulas // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 48–53. – DOI: https://doi.org/10.54341/20778708_2024_3_60_48 (in Russian). – EDN: QWEGKN

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Abstract. The article studies the normal subgroups in polyadic groups of special form, that is in polyadic groups with l-ary operation η_{s, σ, k}, that is called polyadic operation of special form and is defined on Cartesian power of A^k n-ary group <A, η> by substitution σ∈S_k which order divides l–1 and n-ary operation η.

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. I / A.M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 54–58. – DOI: https://doi.org/10.54341/ 20778708_2024_3_60_54 (in Russian). – EDN: QXHKOX

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Abstract. The approximations of the conjugate function on the segment [-1, 1] by Vallee Poussin sums of conjugate rational integral Fourier - Chebyshev operators with restrictions on the number of geometrically different poles are investigated. An integral representation of the corresponding approximations is established. An integral representation of approximations, the estimation of pointwise approximations and uniform approximations with a certain majorant are obtained for a conjugate function with density (1-x)^γ, γ∈(0,1). Its asymptotic expression for n→∞ depending on the parameters of the approximating function, is established. The optimal values of the parameters at which the highest rate of decreasing majorant is provided are found. As a consequence, the estimates of approximations of conjugate function on the segment [-1, 1] by Vallee Poussin sums of conjugate polynomial Fourier - Chebyshev series are found.

Keywords: conjugate function, Fourier - Chebyshev series, Vallee Poussin sums, function with power singularity, pointwise and uniform approximations, best approximations, asymptotic estimates.

For citation: Patseika, P.G. On rational approximations of conjugate function on an interval by conjugate Vallee Poussin sums / P.G. Patseika // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 59–70. – DOI: https://doi.org/ 10.54341/20778708_2024_3_60_59 (in Russian). – EDN: RCLUXH

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Abstract. In this work, based on the well-known results on classical Pade approximants of power series, the conditions are found under which trigonometric Pade - Jacobi approximants exist for a given Fourier series. This made it possible to describe the class of Fourier series in Chebyshev polynomials of the first and second kind, for which there are nonlinear Pade - Chebyshev approximants. In particular, another proof of the well-known theorem of S.P. Suetin is given.

Keywords: Pade approximants, Pade - Chebyshev approximations, power series, Fourier series, series in Chebyshev polynomials.

For citation: Starovoitov, A.P. On the existence of trigonometric Pade approximations / A.P. Starovoitov, T.M. Osnach, N.V. Ryabchenko // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 71-76. – DOI: https://doi.org/ 10.54341/20778708_2024_3_60_71 (in Russian). – EDN: JIITRH

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Abstract. A new linear hypersingular integro-differential equation of the first order has been explicitly solved. The equation is given on a closed curve located on the complex plane. The coefficients of the equation are expressed as sums of some summands. A finite number of the same functions are included in all summands of sums in a certain way. Classical and generalized Sokhotsky formulas, the theory of the Riemann boundary value problem, formulas for solving linear differential equations, properties of analytical functions are used. The solution is illustrated with an example.

Keywords: integro-differential equation, Sokhotsky formulas, Riemann boundary problem, linear differential equation.

For citation: For citation: Shilin, A.P. Linear integro-differential equation with coefficients in the form of special sums / A.P. Shilin // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 77–80. – DOI: https://doi.org/10.54341/ 20778708_2024_3_60_77 (in Russian). – EDN: JLQBBW

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Abstract. The methods and modes of technological operations for attaching solder preforms to the base of the housing for mounting the crystal and sealing electronic modules of infrared receivers, which ensure their reliable fixation on metalized surfaces, are described. The dependences of the fastening strength of the preforms on the modes of operations are determined.

Keywords: infrared radiation receivers, crystal assembly, sealing, preform, welding, soldering.

For citation: Vidritskiy, A.E. Assembly of electronic modules of infrared radiation receivers with the use of solder preforms / A.E Vidritskiy, V.L. Lanin // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 81–85. – DOI: https://doi.org/10.54341/20778708_2024_3_60_81 (in Russian). – EDN: JVEVVM

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Abstract. The use of smoothing filters for pre-processing images of architectural plans is considered. A comparative analysis of Gaussian and Roudin - Osher - Fatemi (ROF) filters based on the Chambolle model is carried out. The software modules are implemented in the Python programming language using OpenCV. The results showed that for pre-processing not very noisy images it is better to use a Gaussian filter, and for images with a high noise level it is better to use the ROF filter, which prevents the loss of special corner points.

Keywords: preprocessing, filtering, noise, Gaussian blur, Gaussian filter, Rudin – Osher – Fatemi filter, Chambolle model, Python, OpenCV.

For citation: Aksionova, N.A. Comparative analysis of filtration algorithms for images of architectural plans / N.A. Aksionova // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. 86–91. – DOI: https://doi.org/10.54341/ 20778708_2024_3_60_86 (in Russian). – EDN: HTGWNV

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Abstract. A new method and software tool for identifying anomalies in the operation of solar panels have been developed based on an artificial neural network of the autoencoder type, trained using solar power plant telemetry data. The method is based on statistical studies of deviations measured from the values of current and voltage of all solar panels of the power plant restored by the neural network. A criterion for assessing the presence of a malfunction in the operation of a solar panel based on statistical studies is introduced. Using the developed methodology and software for searching for anomalies in telemetry data over six months of observations, 14 to 45 anomalies were detected in 33 solar panels under different evaluation criteria. All the cases were analyzed for the causes of anomalies in the operation of solar panels. It has been established that the use of four standard deviations for average daily measured values of current ΔI and voltage ΔU as anomaly detection criterion in the analysis of the results of the artificial neural network operation makes it possible to detect faulty solar panels. And the use of three and two standard deviations as anomaly detection criterion can help to detect a decrease in the efficiency of solar panels associated with degradation, excessive shading and other factors.

Keywords: solar panel, normalized power value, anomaly detection, maximum power point, solar power plant, telemetry.

For citation: Methods and software for anomalies searching in the telemetry data of a solar power plant based on the artificial neuron network - autoencoder / K.S. Dzick, N.I. Mukhurov, I. Kruse, R.M. Asimov, V.S. Asipovich // Problems of Physics, Mathemat-ics and Technics. – 2024. – № 3 (60). – P. 92–100. – DOI: https://doi.org/10.54341/20778708_2024_3_60_92 (in Russian). – EDN: HUPWAR

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Abstract. The article presents the scientific biography of the Honored Scientist of the Republic of Belarus, Corresponding Member of the National Academy of Sciences of Belarus, Doctor of Chemical Sciences, Professor Alexander Vladimirovich Rogachev, a well-known Belarusian scientist in the field of physical chemistry of composite, multilayer thin-film systems based on polymer and inorganic (metallic, carbon, carbides and nitrides of metals) materials, synthesis of complex chemical compounds from the active gas phase, materials science, physics of condensed matter, theory of interphase processes, which is an actively developing scientific direction in the field of physical chemistry of heterogeneous systems, friction and wear.

Keywords: plasma chemistry, gas phase, functional properties, vacuum technologies, polymer and inorganic materials, relaxation-diffusion theory, nanoscale structures, phase composition, coatings.

For citation: Alexander Vladimirovich Rogachev (to the 75th Anniversary) // Problems of Physics, Mathematics and Technics. – 2024. – № 3 (60). – P. – DOI: https://doi.org/10.54341/20778708_2024_3_60_101 (in Russian). – EDN: ISLOKR