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Abstract. In this article, using computer-aided design programs, additive manufacturing means, such as numerically controlled equipment, the samples of metasurfaces for screening metal or metallized objects of a complex shape and reducing the reflection of radiation from them have been produced and experimentally studied.

Keywords: unit cell, metasurface element, ring resonator, electrical conductivity, transformation of radiation polarization, anechoic chamber, radiation absorption coefficient.

For citation: Balmakou, A.P. Modeling, creating and experimental study of metasurfaces covering objects of complex shape / A.P. Balmakou, S.A. Khakhomov, I.V. Semchenko, J. Li, J. Wang, W. Song // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 7–13. – DOI: https://doi.org/10.54341/20778708_2022_1_50_7 (in Russian)

Information about the authors:

A.P. Balmakou – Francisk Skorina Gomel State University

S.A. Khakhomov – Francisk Skorina Gomel State University

I.V. Semchenko – Francisk Skorina Gomel State University

J. Li – Jiangnan University, Wuxi

J. Wang – Jiangnan University, Wuxi

W. Song – Beijing Institute of Technology

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Abstract. The new solutions of the Helmholtz equation describing nondiffracting nonparaxial shifted Bessel wave fields with various azimuthal dependences are offered. They are characterised by five free parametres. Pictorial modelling of such beams is fulfilled. The dependences of the patterns of intensity of Bessel fields on the free parametres are analysed.

Keywords: beams, Bessel beams, azimuthal dependence, shifted fields, Bessel fields.

For citation: Girgel, S.S. Shifted Bessel fields with various azimuthal dependences / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 14–18. – DOI: https://doi.org/10.54341/20778708_2022_1_50_14 (in Russian)

Information about the authors:

S.S. Girgel – Faculty of Physics and Information Technology, F. Skorina Gomel State University

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Abstract. The system of equations for the vector-bispinor describing a spin 3/2 massless particle, is solved in cylindric coordinates of the Minkowski space. The covariant tetrad formalism is applied. Three operators, i∂_t, J₃, i∂_z are diagonalized on the constructed solutions. After separating the variables, the system of 16 functions in the variable r is derived. It is shown that the gauge solutions with cylindric symmetry, which are specified according to the Pauli – Fierz theory, satisfy these 16 equations identically. There are constructed 6 linearly independent solutions. Four of them coincide with the gauge ones, and two remain solutions do not contain the gauge degrees of freedom. These two solutions are expressed in terms of Bessel functions.

Keywords: spin 3/2, cylindric symmetry, massless field, exact solutions, gauge degrees of freedom.

For citation: Ivashkevich, A.V. Spin 3/2 massless field, solutions with cylindrical symmetry, eliminating the gauge degrees of freedom / A.V. Ivashkevich // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 19–27. – DOI: https://doi.org/10.54341/20778708_2022_1_50_19

Information about the authors:

A.V. Ivashkevich – B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus

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Abstract. Using artificial neural networks, the properties of semiconductor sol-gel layers of Zn_õMg_yO were predicted. To form a training data set and a data set for testing neural networks by the sol-gel method, layers were formed based on ZnO : Mg films. The measurement of the photoelectric characteristics of the sol-gel coatings was carried out on an automated basic laser testing complex in accordance with National Standart-17772-88. The experiments were performed for 150 input parameters, 135 of which were used to train neural networks. In this work, we studied the influence of the architecture of neural networks on the accuracy of predicting the properties of Zn_õMg_yO semiconductor sol-gel layers.

Keywords: neural network, sol-gel method, thin films.

For citation: Prediction of the properties of semiconductor Zn_õMg_yO sol-gel layers using artificial neural networks / Y.V. Nikitjuk, A.V. Semchenko, V.V. Sidsky, K.D. Danilchenko, V.À. Prohorenko // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 28–32. – DOI: https://doi.org/10.54341/20778708_2022_1_50_28 (in Russian)

Information about the authors:

Y.V. Nikitjuk – Francisk Skorina Gomel State University

A.V. Semchenko – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

V.V. Sidsky – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

K.D. Danilchenko – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

V.À. Prohorenko – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

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Abstract. The research results of surface electromyograms (EMG) characteristics of human skeletal muscles, recorded during typical movements are introduced. The most dominant frequencies in the EMG spectrum, during the influence on a muscle, as well as the patterns of change in the EMG spectrum with an increase in the force developed by a muscle, are discovered. It was suggested to synthesize electrostimulation signals into a system with biotechnical feedback, using the discovered patterns.

Keywords: synthesis of electrostimulation signals, time-frequency analysis of electromyograms.

For citation: Synthesis of electrostimulation signals based on time-frequency analyses of electromyograms / A.N. Osipov, I.O. Khazanovsky, D.A. Kotov, P.I. Baltrukovich // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 33–36. – DOI: https://doi.org/10.54341/20778708_2022_1_50_33 (in Russian)

Information about the authors:

A.N. Osipov – Belarusian State University of Informatics and Radioelectronics, Minsk

I.O. Khazanovsky – Belarusian State University of Informatics and Radioelectronics, Minsk

D.A. Kotov – Belarusian State University of Informatics and Radioelectronics, Minsk

P.I. Baltrukovich – Belarusian State University of Informatics and Radioelectronics, Minsk

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Abstract. Kinetic features of deposition and electrophysical properties of two-layer coatings based on zinc oxide and polyaniline (PANI) are determined. The coatings were formed in vacuum by consistent influence of low-energy electrons stream on zinc acetate powder and a mechanical mixture of PANI and phosphorus (V) oxide powders. The application of phosphorus oxide leads to the appearance of linear conductive sections in the PANI structure with a high density of polaron, delocalized structures. For the ZnO – PANI + P₂O₅ coatings up to 200 nm thick in the temperature range from 20 to 100^o C the values of specific conductivity, activation energy of charge carriers were determined.

Keywords: hybrid coatings, polyaniline, zinc oxide, electrophysical properties, electron beam deposition.

For citation: Features of electron-beam synthesis and electrophysical properties of hybrid coatings based on polyaniline and zinc oxide / A.A. Rogachev, A.M. Mikhalko, Ì.À. Yarmolenko, Jin Xuhui, Hongliang Zhang, Hongtao Cao, A.V. Rogachev // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 37–43. – DOI: https://doi.org/ 10.54341/20778708_2022_1_50_37 (in Russian)

Information about the authors:

A.A. Rogachev – Institute of Chemistry of New Materials of the National Academy of Sciences of Belarus, Minsk

A.M. Mikhalko – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

M.A. Yarmolenko – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

Jin Xuhui – Beijing Institute of Technology

Hongliang Zhang – Beijing Institute of Technology

Hongtao Cao – Institute of Materials Technology & Engineering Chinese Academy of Sciences, Ningbo

A.V. Rogachev – Francisk Skorina Gomel State University

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Abstract. Regularities for the influence of the pulsed laser radiation intensity with λ = 1064 nm on the dispersion parameters of polytetrafluoroethylene (PTFE), the growth rate of polymer coatings, and their chemical composition have been established. Increased intensity of laser radiation increases the rate of the coating deposition without a noticeable effect on the reactivity of volatile dispersion products. The increased intensity of laser exposure leads to an increase in the content of oxygen groups, fluorine-containing graphite-like clusters in the molecular structure of the deposited coating, and the decrease of the contact angle of water wetting. Based on the analysis of changes in the chemical composition of the coatings, a conclusion was made about a two-stage dispersion process: at the initial stage, the composition of volatile products is independent of the laser radiation intensity; at a later stage, it is determined by the degree of defluorination of the target material, which depends on the intensity of radiation.

Keywords: laser dispersion, polymer coating, polytetrafluoroethylene, deposition kinetic, chemical composition.

For citation: Yarmolenko, M.A. Kinetic features of deposition and chemical composition of coatings, formed from volatile products of laser dispersion of polytetrafluoroethylene / M.A. Yarmolenko // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 44–48. – DOI: https://doi.org/10.54341/20778708_2022_1_50_44 (in Russian)

Information about the authors:

M.A. Yarmolenko – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

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Abstract. The features of macromolecular compounds (organosilicon resin, polytetrafluoroethylene) of their mixtures with copper formate degradation under the influence of laser radiation with different wavelengths are determined. The reactivity of the generated volatile degradation products was evaluated. The molecular structure and morphology of deposited coatings were studied. At the same intensity, the influence of shorter-wavelength laser radiation (λ = 266 nm) on an organosilicon polymer leads to the formation of coatings with a lower concentration of Si – O – C groups relative to the content of Si – C₆H₅ groups compared to radiation with a wavelength of 535 and 355 nm. The value of the laser radiation length has no noticeable effect on the molecular structure of coatings based on PTFE and PTFE + copper. This may indicate a predominantly photothermal mechanism of the initial targets degradation.

Keywords: laser dispersion, active gas phase, polymer, organosilicon, coating, metal, molecular structure.

For citation: Features of polymer materials degradation under influence of short-wave laser radiation / M.A. Yarmolenko, A.A. Rogachev, Yiming Liu, A.V. Rogachev, Lihong Gao, Zhuang Ma // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 49–54. – DOI: https://doi.org/10.54341/20778708_2022_1_50_49 (in Russian)

Information about the authors:

M.A. Yarmolenko – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

A.A. Rogachev – Institute of Chemistry of New Materials of the National Academy of Sciences of Belarus, Minsk

Yiming Liu – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

A.V. Rogachev – Francisk Skorina Gomel State University

Lihong Gao – Beijing Institute of Technology

Zhuang Ma – Beijing Institute of Technology

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Abstract. The article goes on with the studies on the described earlier relationship between sets of generators in group A and sets of generators in polyadic group < A^k, [ ]_{l, σ, k} > with l-ary operation [ ]_{l, σ, k}, that is defined on Cartesian power A^k of group A for arbitrary integer l≥2 and arbitrary substitution σ from the set S_k of all substitutions of the set {1, 2, …, k}.

Keywords: group, l-ary group, set of generators.

For citation: For citation: Gal'mak, A.M. On sets of generators of l-ary group < A^k, [ ]_{l, σ, k} >. IV / A.M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 55–61. – DOI: https://doi.org/10.54341/20778708_2022_1_50_55 (in Russian)

Information about the authors:

A.M. Gal'mak – Belarusian State University of Food and Chemical Technologies, Mogilev

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Abstract. The global theorem to Hadamard correctness to the first mixed problem for inhomogeneous general telegraph equation with all variable coefficients in a half-strip of the plane is proved by a novel method of auxiliary mixed problems. Without explicit continuations of the mixed problem data outside set of mixed task assignments the recurrent Riemann-type formulas of a unique and stable classical solution for the first mixed problem on a segment are derived. This half-strip of the plane is divided by the curvilinear characteristics of a telegraph equation into rectangles of the same height, and each rectangle into three triangles. The correctness criterion consists of smoothness requirements and matching conditions on the right-hand side of the equation, initial and boundary conditions of the mixed problem. The smoothness requirements are necessary and sufficient for twice continuous differentiability of the solution in these triangles. The matching conditions together with these smoothness requirements are necessary and sufficient for twice continuous differentiability of solution on the implicit characteristics in these rectangles.

Keywords: general telegraph equation, implicit characteristics of equation, correctness criterion, smoothness requirement, matching condition.

For citation: Lomovtsev, F.E. Global correctness theorem to the first mixed problem for the general telegraph equation with variable coefficients on a segment / F.E. Lomovtsev // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 62–73. – DOI: https://doi.org/10.54341/20778708_2022_1_50_62

Information about the authors:

F.E. Lomovtsev – Belarusian State University, Minsk

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Abstract. We study a finite group in which the normalizer of each Sylow subgroup has a Hall supplement with cyclic Sylow subgroups. In particular, it is established that such groups are supersoluble.

Keywords: finite group, Sylow subgroup, normalizer, cyclic subgroup, supplement.

For citation: Monakhov, V.S. On supersolvability of a finite group with Z-supplements to the Sylow normalizers / V.S. Mona-khov, I.K. Chirik // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 74–77. – DOI: https://doi.org/ 10.54341/20778708_2022_1_50_74 (in Russian)

Information about the authors:

V.S. Monakhov – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

I.K. Chirik – University of Civil Protection of the Ministry for Emergency Situations of the Republic of Belarus, Minsk

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Abstract. All considered groups are finite. Let G be a group, σ some partition of the set of all primes i. e. σ = {σ_i | i∈I}, where and σ_i∩σ_j=∅ for all i≠j, σ(G)={σ_i | σ_i∩π(|G|)≠∅}. A group G is called σ-primary if G is a σ_i-group for some i=i(G). We say that G is a σ-tower group if either G=1, or G has a normal series 1=G₀ < G₁ < ... < G_n-1=G such that G_k/G_k-1 is a σ_i-group, σ_i∈σ(G), while G/G_k and G_k-1 are σ_i'-groups for all k=1,...n. A subgroup A of G is said to be σ-subnormal in G if there is a subgroup chain A=A₀≤A₁ ≤ ... ≤ A_t=G such that either or A_i/(A_i-1)_Ai is σ-primary for all i=1,...,t. In this article, we prove that a non-identity soluble group G is a σ-tower group if for each σ_i∈σ(G), where |σ(G)|=n, a Hall σ_i-subgroup of G is supersoluble and every (n+1)-maximal subgroups of G is σ-subnormal in G. Thus, we give a positive answer to Question 4.8 in [1] in the class of all soluble groups with supersoluble σ-Hall subgroups.

Keywords: finite group, soluble group, σ-subnormal subgroup, Sylow tower group, σ-tower group.

For citation: Safonova, I.N. On one question of A.N. Skiba in the theory of σ-properties of finite groups / I.N. Safonova // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 78–83. – DOI: https://doi.org/10.54341/20778708_2022_1_50_78 (in Russian)

Information about the authors:

I.N. Safonova – Belarusian State University, Minsk; Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

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Abstract. Throughout the article, all groups are finite and G always denotes a finite group. A subgroup H of the group G is called -normal in G (p is a prime) if every chief factor of the group G between H^G and H_G is either cyclic or a p'-group. In this article, we prove that if each Schmidt subgroup of the group G is either subnormal or -normal in G, then the derived subgroup G' of G is p-nilpotent. Some well-known results are generalized.

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

For citation: Sel'kin, V.M. Finite groups with given Schmidt subgroups / V.M. Sel'kin, V.S. Zakrevskaya, N.S. Kosenok // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 84–88. – DOI: https://doi.org/10.54341/20778708_2022_1_50_84 (in Russian)

Information about the authors:

V.M. Sel'kin – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

N.S. Kosenok – Belarusian Trade and Economic University of Consumer Cooperatives

V.S. Zakrevskaya – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

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Abstract. This article introduces multiple analogs of determinants and Gram matrices, studies the possibility of constructing polyorthogonal systems of functions using the process of polyorthogonalization of an arbitrary finite subsystem of a linearly independent system of functions φ={φ₀(x), φ₁(x),...,φ_n(x),...} in Pre-Hilbert function spaces generated by measures μ₁,...,μ_k. The proven statements are a generalization of the Gram – Schmidt orthogonalization theorem.

Keywords: Pade approximations, polyorthogonal polynomials, normal index, perfect system, Gram determinant.

For citation: Starovoitov, A.P. Polyorthogonal systems of functions / A.P. Starovoitov // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 89–93. – DOI: https://doi.org/10.54341/20778708_2022_1_50_89 (in Russian)

Information about the authors:

A.P. Starovoitov – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

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Abstract. We study finite groups that have three or four pairwise non-conjugate maximal subgroups belonging to a given saturated formation. New criteria for the belonging of a finite group to saturated formations of a supersoluble type are obtained.

Keywords: finite group, maximal subgroup, non-normal subgroup, supersoluble group, w-supersoluble group, saturated formation.

For citation: Furs, A.K. Finite groups with a given system of formation maximal subgroups / A.K. Furs // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 94–100. – DOI: https://doi.org/10.54341/20778708_2022_1_50_94 (in Russian)

Information about the authors:

A.K. Furs – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

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Abstract. The paper considers a new pattern, revealed during the biomechanical analysis of the purposeful movement of an athlete, linking the control moment of the muscular system with the speed of its change. It is shown that in different phases of a sports exercise, these dynamic characteristics reach extreme values. At the same time, the observed extremes of moments and their dynamic velocities always go in pairs, usually having a time interval between them in fractions of a second, rarely more. The analysis of the nature of changes in the values of control moments and their dynamic speeds at the experimental and theoretical levels showed: firstly, the presence of such a pattern in different sports, and in different exercises, for example, in gymnastics and weightlifting; secondly, the analysis presented the complex nature of the influence of various power factors on the displacement of the peaks of the values of the control moment and the speed of its change, as the sum of such influences on the overall result.

Keywords: biomechanical analysis, dynamics, dynamic velocity, locomotion, control moment.

For citation: Pokatilov, A.E. The study of the dynamic characteristics of an athlete’s muscular system / A.E. Pokatilov // Problems of Physics, Mathematics and Technics. – 2022. – N 1 (50). – P. 101–110. – DOI: https://doi.org/10.54341/20778708_2022_1_50_101 (in Russian)

Information about the authors:

A.E. Pokatilov – Belarusian State University of Food and Chemical Technologies, Mogilev