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Abstract. An analysis of the main technological methods for controlling the structure and properties of composite carbon coatings has been carried out. The experimental data on the influence of discharge voltage, as well as the shape, duration, and frequency of discharge pulses during carbon plasma generation on the phase composition and properties of carbon coatings, have been summarized. The main features of the formation, phase composition, and properties of carbon coatings doped with carbide-forming and chemically inert elements and compounds with respect to carbon, as well as their changes during heat treatment, have been analyzed.

Keywords: carbon coatings, composite coatings, structure, mechanical properties.

For citation: Technological methods for controlling the structure and improving the mechanical properties of composite carbon coatings / D.G. Piliptsou, Jiang Xiaohong, A.V. Rogachev, A.S. Rudenkov, K.A. Sakhovskij // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 7–13. – DOI: https://doi.org/10.54341/20778708_2025_4_65_7 (in Russian). – EDN: XHSDAV

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Abstract. The analytical expressions in closed form are proposed and investigated for various types of decentered circular Kummer – Gauss light beams. Various options are analyzed, including both new types of beams and special cases involving well-known Laguerre – Gauss beams. The constraints on free parameters are formulated so that such decentered Kummer – Gauss beams carry finite power. The influence of various free parameters on the intensity patterns of such beams is investigated graphically.

Keywords: paraxial beams, circular beams, Kummer – Gauss beams, decentered beams.

For citation: Girgel, S.S. Decentered circular Kummer – Gauss beams of various types / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 14–19. – DOI: https://doi.org/10.54341/20778708_2025_4_65_14 (in Russian). – EDN: ZOXOSH

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Abstract. The results of the study of the influence of changes in the permittivity coefficient of dielectric inclusions in complexly structured medium on their scattering properties in the optical and microwave ranges are presented. The dependences of the transmission and reflection coefficients of the electromagnetic field on the dielectric constant of the material, the geometric dimensions of the elements and the frequency of the optical and microwave fields are given. An analysis of the identified dependencies was carried out and requirements for the dielectric and geometric parameters of the constituent structures were determined to ensure changes in the transmission and reflection coefficients by frequency and value.

Keywords: microwave radiation, periodic structure, polymers, permittivity coefficient, transmission and reflection coefficients.

For citation: Kalosha, L.A. Modeling of systems based on materials with variable dielectric parameters for reconstructing the scattering characteristics of optical and microwave fields / L.A. Kalosha, L.S. Gaida, D.V. Zaerko // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 20–28. – DOI: https://doi.org/10.54341/20778708_2025_4_65_20 (in Russian). – EDN: ZRJSZY

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Abstract. The study focuses on developing a metamodel for the laser cleaving process of crystalline quartz, encompassing modeling and optimization. Using a finite element model implemented in the APDL programming language, temperature fields and thermoelastic stress fields were determined. These fields arise in a monocrystalline quartz plate due to sequential laser heating and coolant exposure, analyzed for three distinct variants: I – analysis of the ZY-plane cross-section with laser beam movement along the X-axis; II – analysis of the YX-plane cross-section with laser beam movement along the X-axis; III – analysis of the XY-plane cross-section with laser beam movement along the Z-axis. A central composite design was employed to conduct a numerical experiment, where the factors included processing speed, geometric parameters of the elliptical laser beam, CO₂ laser power, and quartz plate thickness. According to the experimental design, calculations were performed for 27 factor combinations, determining the maximum temperature values (T₁, T₂, T₃) for three processing variants of a square quartz plate, along with three corresponding values of maximum tensile stress (S₁, S₂, S₃) acting perpendicular to the laser-induced crack fronts. The optimal artificial neural network architectures were identified for predicting maximum temperatures and thermoelastic stresses in the laser processing zone of crystalline quartz using TensorFlow. Neuro-fuzzy models were developed in the ANFIS framework, followed by a comparative analysis of neural network and neuro-fuzzy approaches. Furthermore, the most effective input parameters for laser cleaving of crystalline quartz were determined through optimization using the MOGA.

Keywords: laser cutting, Artificial Neural Networks, adaptive network-based fuzzy inference system, MOGA optimization genetic algorithm, ANSYS program.

For citation: Nikityuk, Yu.V. Study and optimization of laser cleaving of crystalline quartz using genetic algorithm, neural network and neuro-fuzzy models / Yu.V. Nikityuk, L.N. Marchenko, A.N. Serdyukov // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 29–34. – DOI: https://doi.org/10.54341/20778708_2025_4_65_29. – EDN: ZXSJJW

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Abstract. In the paper we study the Joule – Thomson expansion of Kerr and charged black holes in AdS-space, as well as two-parameter fluids. Based on the equations of state, analytical expressions for inversion temperatures are obtained, inversion curves in the TP-plane are constructed, and the regions of positive and negative effects are determined. Similarities and differences in the behavior of black holes and two-parameter fluids in the considered process are found.

Keywords: AdS-space, Kerr black hole, charged black hole, two-parameter fluids, Joule – Thomson expansion, inversion curve, cooling and heating regions.

For citation: Novikava, V.U. Similarities and differences of Joule – Thomson expansion of Kerr and charged black holes in AdS-space and two-parametric fluids / V.U. Novikava, G.Yu. Tyumenkov // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 35–41. – DOI: https://doi.org/10.54341/20778708_2025_4_65_35 (in Russian). – EDN: AITAVS

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Abstract. The paper proposes a formulation of the boundary value problem for the bending of a thickness-symmetric elastoplastic circular five-layer plate with two fillers. The deformation of the inner and outer load-bearing layers is governed by Kirchhoff's hypotheses. In the relatively thick fillers, Timoshenko’s hypothesis is assumed. The physical state equations correspond to the theory of small elastoplastic deformations. The system of nonlinear differential equations of plate equilibrium is obtained with the variational method of Lagrange, taking into account the work of tangential stresses in the fillers. An iterative method based on the Ilyushin method of elastic solutions is proposed to solve this problem. The sought functions are the deflection of the plate and the relative shear in the fillers.

Keywords: circular five-layer plate, thickness symmetry, elastic-plastic deformation, equations of equilibrium.

For citation: Salicki, V.S. Equations of equilibrium of an elastic-plastic pentalayer symmetric in thickness plate / V.S. Salicki // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 42–46. – DOI: https://doi.org/10.54341/ 20778708_2025_4_65_42 (in Russian). – EDN: VWYSNY

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Abstract. A generalization of Foster’s theorem to the case of an antenna radiating into free space is considered. It is demonstrated that the frequency derivative of the phase of the antenna input reflection coefficient is a positive quantity and is proportional to the time delay of the radiated radio pulse. By employing the Lorentz reciprocity lemma and analyzing the energy balance within a volume surrounding the antenna, a relationship is derived that links this time delay to the stored reactive energy in the antenna’s near field. The obtained relation enables experimental determination of the time delay from measured reflection coefficient parameters and permits the use of this quantity as a diagnostic and comparative metric for antennas. The theorem holds practical significance for antenna design and for understanding fundamental physical limitations.

Keywords: Foster’s theorem, antenna, Poynting vector, reflection coefficient phase, delay time, radio pulse.

For citation: Solovtsov, S.L. Foster’s theorem for a free-space antenna / S.L. Solovtsov, I.A. Fanyaev, V.P. Kudzin // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 47–50. – DOI: https://doi.org/10.54341/20778708_2025_4_ 65_47 (in Russian). – EDN: WJVEXT

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Abstract. The formulation of the boundary value problem of bending a five-layer symmetrical thickness rod is given. The central and outer layers are assumed to be load-bearing, thin, of increased rigidity, and absorb the bulk of the mechanical load. In them, the deformation obeys the Bernoulli hypothesis. Two relatively thick rigid fillers provide a redistribution of forces between the load-bearing layers. Tymoshenko's hypotheses are valid for them. The principle of possible displacements is applied to derive a system of differential equations for the equilibrium of the rod. An analytical solution of the boundary value problem and calculation formulas for displacements under uniformly distributed load are obtained. Numerical approbation of the obtained solution is carried out.

Keywords: five-layer symmetrical rod, elasticity, bending.

For citation: Starovoitov, E.I. Bending of a five-layer symmetrical thickness rod / E.I. Starovoitov, K.V. Suslov // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 51–55. – DOI: https://doi.org/10.54341/20778708_2025_4_65_51 (in Russian). – EDN: ULZAYM

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Abstract. The molecular structure, morphology, and electrical conductivity of polypyrrole coatings deposited on an iron chloride sublayer were determined. The changes in the molecular structure and electrical conductivity during heat treatment of the synthesized polypyrrole layers were established. To effectively mitigate the degradation of polypyrrole coatings during heating, the formation of a sulfate or phosphate passivation layer on their surface was proposed. The decrease in conductivity during heat treatment and the increase in the threshold voltage, above which a conductivity increase is observed, during storage are attributed to the chemical interaction between the copper electrode and iron chloride.

Keywords: polypyrrole coatings, molecular structure, electrical conductivity, morphology, heat treatment.

For citation: Yarmolenko, M.A. Gas-phase synthesis, molecular structure of multilayer coatings based on polypyrrole / M.A. Yarmolenko, A.V. Rogachev, A.A. Rogachev // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 56–61. – DOI: https://doi.org/10.54341/20778708_2025_4_65_56 (in Russian). – EDN: DFVRRQ

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Abstract. The study on the l-ary quotient groups of polyadic groups of a special form is carried on.

Keywords: polyadic operation, semiinvariant l-ary subgroup, n-semiinvariant l-ary subgroup, quotient group, congruence, coset.

For citation: Gal'mak, A.M. Polyadic quotient groups of polyadic groups of a special form. II / A.M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 62–66. – DOI: https://doi.org/10.54341/20778708_2025_4_65_62 (in Russian). – EDN: RJSZOU

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Abstract. A finite non-nilpotent group is called a B-group if all proper subgroups of its quotient group by the Frattini subgroup are primary. A finite group whose Sylow subgroups are all cyclic is called a z-group. We study a finite group G that can be represented as a product of its B-subgroup and z-subgroup of coprime orders. For a solvable groups G, we prove that the second derived subgroup is nilpotent, the derivative length of the quotient group by the Frattini subgroup does not exceed three, and the p-length is at most two. If G is a simple group, then G is isomorphic to PSL₂(p^m), and all possible values of p^m are determined.

Keywords: finite group, B-group, z-group, p-length, derivative length, factorizable group.

For citation: Kniahina, V.N. On a finite group factorized by a B-group and a z-group / V.N. Kniahina // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 67–71. – DOI: https://doi.org/10.54341/20778708_2025_4_65_67 (in Russian). – EDN: TKJHKY

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Abstract. In this paper: G is a finite group; σ={σ_i|i∈I} is some partition of the set of all primes P; Π⊆σ σ(n)={σ_i|σ_i∩π(n)≠∅} (n is an integer) and σ(G)=σ(|G|). A group G is said to be: (i) σ-primary provided G is a σ_i-group for some i∈I; (ii) σ-nilpotent if G is the direct product of σ-primary groups; a Π-group if σ(G)⊆Π. A subgroup A of a finte group G is said to be: (i) σ-subnormal in G if there is a subgroup chain A=A₀≤A₁≤...≤A_t=G such that either A_i-1A_i or A_i/(A_i-1)_Ai is σ-primary for all i=1,...,t; (ii) a Hall Π-subgroup of G if A is a Π-group and σ(|G:A|)∩Π=∅. We say that a subgroup H of G is strongly σ-subnormal if H^G/H_G is σ-nilpotent. In this paper, we prove that the set of all strongly σ-subnormal subgroups which permute with a Hall Π-subgroup of a finite group G forms a sublattice of the lattice of all subgroups L(G) of G.

Keywords: finite group, lattice of subgroups, operator group, sublattice of a lattice, Hall Π-subgroup.

For citation: Kosenok, N.S. On a class of sublattices of the subgroup lattice of a finite group / N.S. Kosenok, I.V. Blisnets // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 72–74. – DOI: https://doi.org/10.54341/ 20778708_2025_4_65_72. – EDN: KEQNCF

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Abstract. We consider one two-stage (step) optimal control problem, described in two-time intervals by various Volterra-type integro-differential equations. Under the assumption that the control domain is open, the first and second variations of the Boltz-type quality functional are calculated. An analogue of the Euler equation (first order necessary optimality condition) has been received. Using the condition of non-negativity of the second variation of the quality functional along the optimal control, a number of constructively verifiable necessary conditions for second-order optimality are proved. The case of classically singular controls is studied.

Keywords: stepwise optimal control problem, integro-differential equation of Volterra type, variation of the functional, analogue of the Euler equation, optimal control, singular control in the classical sense.

For citation: Mansimov, K.B. An analogue of the Euler equation and necessary conditions for second-order optimality in one two-stage control problem for integro-differential equations of Volterra type / K.B. Mansimov, A.F. Mansimzade // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 75–84. – DOI: https://doi.org/10.54341/20778708_2025_4_65_75 (in Russian). – EDN: OBWYCA

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Abstract. The magnetron sputtering process of a vanadium target in an argon and oxygen atmosphere has been investigated. Hysteresis dependencies of the cathode current change on the oxygen content and sputtering power were obtained. The temperature coefficient of resistance of the obtained vanadium oxide thin films, with a resistivity up to 0,1 Ohm⋅m, reaches 2,6%/°C. The most suitable vanadium oxide films for infrared photodetectors have an amorphous structure with crystalline phases.

Keywords: magnetron sputtering, cathode current, electrical resistivity, temperature coefficient of resistance, thermistor.

For citation: Zanka, A.I. Influence of magnetron sputtering process parameters on the properties of vanadium oxide thin films / A.I. Zanka, A.E. Zhamoits, A.H. Shydlouski // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 85–90. – DOI: https://doi.org/10.54341/20778708_2025_4_65_85 (in Russian). – EDN: PBERFZ

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Abstract. The anomalous dependence of the Bloch coefficient (B) on the magnetic field in double perovskite Sr₂FeMoO_6-δ thin films was determined, which contradicts the classical model predicting the decrease of B. It has been found that the value of B increases monotonically with the increase of the magnetic field (in the range of 0.01–0.16 T). It was shown that this effect is not due to the dominance of the magnon contribution but is caused by the competition of demagnetization mechanisms associated with structural defects. The investigation results demonstrate that an external magnetic field alters the balance between magnon and defect contributions to thermal demagnetization.

Keywords: double perovskite, Sr₂FeMoO₆, Bloch's law, Bloch coefficient, thermal demagnetization, magnons, cation disorder, anti-phase boundaries.

For citation: Magnetic properties of Sr₂Fe_1-õMo_1+xO_6-δ films deposited by ion-plasma sputtering / D.A. Kiselev, S.S. Starukhina, A.S. Bykov, A.V. Petrov, A.G. Yudenkov, A.V. Semchenko, N.A. Kalanda // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 91–97. – DOI: https://doi.org/10.54341/20778708_2025_4_65_91 (in Russian). – EDN: PXYFEU

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Abstract. The study presents calculations of temperature fields in controlled laser thermal cleaving of brittle non-metallic materials using two laser beams with a coolant. An estimation of the upper limit of thermal micro-stress was conducted based on the temperature distribution data across the surface and within the volume of the materials. This information is essential for the substantiated selection of laser processing parameters for the specified materials, particularly quartz and silicate glasses, in microelectronics manufacturing processes.

Keywords: laser radiation, temperature field, micromechanical thermoelastic stresses, mathematical modeling.

For citation: Modeling the temperature field in dual-beam laser thermal cleaving processes for electronic materials / A.N. Kupo, Yu.V. Nikityuk, V.A. Yemelyanov, A.N. Serdyukov // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 98–102. – DOI: https://doi.org/10.54341/20778708_2025_4_65_98. – EDN: FDSCIN

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Abstract. A design of an active microresonator intended for the implementation of a reconfigurable metasurface applicable to B5G/6G wireless communication systems is proposed. The developed structure enables phase control of the transmitted electromagnetic wave and allows dynamic modification of the transmitted wavefront. The numerical simulations carried out in the Ka-band of microwave waves have confirmed the capability of wide-range phase tuning through the variation of varicap capacitance. The obtained results demonstrate the potential of employing the proposed metasurface in a new generation of wireless communications B5G/6G antennas for adaptive beam steering.

Keywords: Huygens principle, active metasurface, varicap, B5G applications, transmitted wave phase.

For citation: Active transmitting bianisotropic metasurface with phase control function for B5G/6G applications of wireless communications / I.A. Fanyaev, A.A. Timoshenko, A.L. Samofalov, S.A. Khakhomov, I.V. Semchenko, Jihong Gu, Dazhi Ding // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 103–107. – DOI: https://doi.org/10.54341/20778708_2025_4_65_103 (in Russian). – EDN: EBZCMH

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Abstract. The diagnosis of lumbar osteochondrosis based on measurement of intervertebral distances on lumbar x-rays is reviewed. For more accurate diagnosis and automation, a set of methods of mathematical data analysis is proposed, allowing to separate healthy patients, diseased patients and borderline cases of the disease in a set of patient images and corresponding measurements of intervertebral distances.

Keywords: lumbar spine, diagnosis of osteochondrosis, multivariate data, cluster analysis, ascending neuron, experimental data processing.

For citation: Application of a set of mathematical methods for the diagnosis of degenerative-dystrophic changes in the lumbar spine / K.M. Borchyk, D.A. Yakimov, A.Yu. Vladova, O.M. Demidenko, M.V. Alekseikov // Problems of Physics, Mathematics and Technics. – 2025. – № 4 (65). – P. 108–114. – DOI: https://doi.org/10.54341/20778708_2025_4_65_108 (in Russian). – EDN: CIFUJF

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