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Abstract. The paper analyzes the applications of the theory of finite groups in the coding theory, in the theory of compact Riemann surfaces, in the theory of formal languages and in the studying of the solutions of the Yang – Baxter equation. The main results and open problems are given for each of these directions.

Keywords: finite group, class of groups, formation, group code, Hurwitz group, Riemann surface, formal language, Yang – Baxter equation.

For citation: Vasil'ev, A. F. Problems of the theory of classes of finite groups through the prism of applications. I / A. F. Vasil'ev, V. I. Murashka, V. G. Safonov // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 7–16. – DOI: https://doi.org/10.54341/20778708_2026_2_67_7 (in Russian). – EDN: QCYRRH

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Abstract. This paper examines the problem of forced vibrations of a five-layer rod symmetric in thickness under a local, uniformly distributed surface load. The three load-bearing layers (the central layer and the two outer layers) are assumed to be thin and high-strength. Bernoulli’s assumptions are adopted for them. In the two relatively thick lightweight fillers, Timoshenko’s assumption is applied, i. e., additional shear of the normal is taken into account. The system of differential equations of vibration is derived using variational methods. An analytical solution to the problem is obtained by expanding the sought displacements into a series based on a constructed system of eigenfunctions. A parametric analysis of the dependence of displacements on the length of the load patch, the materials of the load-bearing layers, and the fillers is performed.

Keywords: symmetrical five-layer rod, localized load, vibrations, parametric displacement analysis.

For citation: Budnikova, D. A. Vibrations of a five-layer rod under the action of a local load / D. A. Budnikova // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 17–22. – DOI: https://doi.org/10.54341/20778708_2026_2_67_17 (in Russian). – EDN: ESGYJF

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Abstract. The formulation of an initial-boundary value problem for forced vibrations of a five-layer circular plate with thickness asymmetry under the action of an instantaneously applied local load distributed over a circle is proposed. The central and outer load-bearing layers are assumed to be thin and obey the Kirchhoff hypotheses. The two relatively thick fillers are lightweight; the Timoshenko hypothesis is valid for them. The system of differential equations of motion is derived by the variational method. An analytical solution to the problem is constructed by expanding the sought-for displacements into a series in a system of orthonormal eigenfunctions. A numerical analysis of the obtained solution is performed.

Keywords: five-layer circular plate, thickness asymmetry, forced vibrations, local load, displacements.

For citation: Lachugina, E. A. Vibrations of a five-layered circular plate under a locally instantly applied load / E. A. Lachugina // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 23–28. – DOI: https://doi.org/ 10.54341/20778708_2026_2_67_23 (in Russian). – EDN: FDQMOW

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Abstract. This paper presents a study of the polycrystalline CVD diamond processing using pulsed nanosecond laser radiation and the development of an intelligent system for predicting the geometric parameters of the resulting microstructures based on fuzzy logic. Experimental investigations were carried out using an Nd:YAG laser with a wavelength of 532 nm. The variable parameters included the number of pulses, pulse energy, and laser beam diameter. The Mamdani fuzzy inference algorithm, implemented in Python, was used to construct the model. The experimental design matrix was based on a face-centered central composite design. It was established that within the investigated range of processing parameters, material removal occurs primarily due to thermomechanical fracture and graphitization, leading to nonlinear crater growth under multi-pulse exposure. A fuzzy model was developed to relate the processing conditions to the depth and width of the resultant cavities. The model validation revealed a reasonably high approximation accuracy, with a coefficient of determination of 0.7906 for the depth and 0.7940 for the width on the test set. The mean absolute percentage error (MAPE) on the test set did not exceed 12.5%. The proposed approach enables effective prediction of laser processing outcomes for superhard materials, hence reducing the necessity for expensive physical experimental tests.

Keywords: diamond, nanosecond pulsed lasers, laser processing, fuzzy modeling.

For citation: Investigation of polycrystalline CVD diamond processing by nanosecond laser pulses using fuzzy models / Yu. V. Nikityuk, D. G. Piliptsov, S. I. Sokolov, B. Zhou // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 29–34. – DOI: https://doi.org/10.54341/20778708_2026_2_67_29. – EDN: TXEXSI

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Abstract. In the paper we have analyzed the behavior of isotherms families of Reissner – Nordstrom (RN) and Born – Infeld (BI) black holes in anti-de Sitter space (AdS) using thermodynamic equations of state (EOS) of the form P=P(T,r₊), parameterized by the event horizon r₊. It is shown that unlike RN-AdS black holes, the isotherm family of BI-AdS black holes contains two critical isotherms: one with "a van der Waals" (vdW) origin and the other with "a non-van der Waals" (nvdW) origin.

Keywords: equation of state, isotherms family, critical isotherm, anti-de Sitter space, Reissner – Nordstrom black hole, Born – Infeld black hole.

For citation: Novikava, V. U. On the specifics of the isotherms family of Born – Infeld AdS black holes / V. U. Novikava, G. Yu. Tyumenkov // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 35–39. – DOI: https://doi.org/10.54341/20778708_2026_2_67_35 (in Russian). – EDN: UXVKOL

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Abstract. The results of the design and numerical full-wave simulation of a spatiotemporally modulated metasurface intended for simulating the Doppler effect are presented. The elemental base of the metasurface includes planar single-turn spirals fabricated on an Arlon AD255C dielectric substrate and varactors embedded into the spiral arms for dynamic control of the electromagnetic response. It is shown that a variation of the varactor capacitance in the range of 0.03–0.24 pF provides a shift in the resonant frequency and a linear change in the phase of the reflected wave, which is equivalent to the Doppler frequency shift under physical motion of the object.

Keywords: metasurface, spatiotemporal modulation, Doppler effect, planar spiral, varactor, dynamic control.

For citation: Design of a spatiotemporal modulated metasurface based on planar spirals and varactors / I. V. Semchenko, I. A. Fanyaev, A. L. Samofalov, M. Yu. Yeusiyevich, S. A. Khakhomov, A. A. Kavaliou, P. V. Somov, Jihong Gu, Dazhi Ding // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 40–45. – DOI: https://doi.org/10.54341/ 20778708_2026_2_67_40 (in Russian). – EDN: VNGTHH

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Abstract. The theoretical foundations of simulating the Doppler effect by creating a temporal boundary for a metamaterial are presented. Cases of simulating both an approaching and receding object emitting waves are considered. Options for parallel or sequential connection of varactors to the metamaterial microresonators for wave conversion at the temporal boundary are proposed.

Keywords: Doppler effect, temporal boundary, metamaterial, varactor, dynamic control.

For citation: Theoretical foundations of simulating the Doppler effect by creating a temporal boundary of a metamaterial / I. V. Semchenko, I. A. Fanyaev, A. L. Samofalov, P. V. Somov, M. Yu. Yeusiyevich, S. A. Khakhomov, Jihong Gu, Dazhi Ding // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 46–51. – DOI: https://doi.org/ 10.54341/20778708_2026_2_67_46 (in Russian). – EDN: VOGRKZ

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Abstract. The temperature dependences of the surface conductivity σ_□(T) of CVD graphene with and without electrochemically deposited Co – CoO particles were studied. For the initial CVD graphene, the σ_□(T) dependence is described by a model incorporating two-dimensional quantum corrections to the Drude conductivity theory under weak localization conditions, as well as an activated carrier transport mechanism due to the large-scale potential relief (LSPR). After deposition of Co – CoO nanoparticles, a decrease of the LSPR contribution was observed. However, overall, no significant effect of Co – CoO nanoparticles on the nature of the charge carrier transport mechanisms characteristic of the initial graphene samples was observed.

Keywords: CVD graphene, electrical conductivity, electrical transport, quantum corrections, large-scale potential relief.

For citation: Effect of Co – CoO particle deposition on charge carrier transport mechanisms in CVD-graphene / A. A. Kharchanka, A. K. Fedotov, N. A. Kazimirov, J. A. Fedotova, A. O. Konakov, M. V. Chichkov, M. D. Malinkovich // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 52–58. – DOI: https://doi.org/10.54341/20778708_ 2026_2_67_52 (in Russian). – EDN: XSSUKR

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Abstract. The article studies homomorphisms of polyadic groupoids of a special form, that is polyadic groupoids with l-ary operation η_s,σ,k, that is called polyadic operation of a special form and defined on Cartesian power of A^k n-ary groupids <A,η> by substitution σ∈S_k and n-ary operation η.

Keywords: polyadic groupoid, n-ary groupoid, homomorphism, semiinvariant l-ary subgroups, quotient group.

For citation: Gal'mak, A. M. Homomorphisms of polyadic groupoids of a special form / A. M. Gal'mak // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 59–63. – DOI: https://doi.org/10.54341/20778708_2026_2_67_59 (in Russian). – EDN: YHRUBL

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Abstract. In this paper all groups are finite, G always denotes a finite group. A σ_ℑ-pair is any pair σ, ℑ, where σ={σ_i|i∈I={0}∪I} some partition of the set of all primes and ℑ is a complete (in the sence of Wielandt) class of σ₀-groups which contains all soluble σ₀-groups. A group G is said to be: (i) σ_ℑ-primary provided G is a σ_i-group for some i∈I and G∈ℑ if i=0; (ii) σ_ℑ-nilpotent if every chief factor H/K of G is σ_ℑ-central in G, that is, the semidirect (H/K)×(G/C_G(H/K)) is σ_ℑ-primary; (iii) σ_ℑ-soluble if every chief factor of G is σ_ℑ-primary. A σ_ℑ-property of a group we mean any of its properties, that depends on σ_ℑ and which does not imply any restrictions on σ_ℑ. In this paper, we develop a new aspect of the theory of σ_ℑ-properties related to applications of σ_ℑ-pairs. In particular, on the set of all σ_ℑ-pairs we define a partial order ≤ and we prove that if Σ={σ^j_ℑj|j∈J} is the set of all σ_ℑ-pairs such that every group in is σ^j_ℑj-nilpotent (respectively, σ^j_ℑj-soluble) for all i>j, then with respect to ≤ there exists the least element in Σ.

Keywords: finite group, σ_ℑ-property of a group, σ_ℑ-pair, σ_ℑ-primary group, the lattice of σ_ℑ-pairs.

For citation: Skiba, A. N. On σ_ℑ-properties of finite groups I / A. N. Skiba // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 64–71. – DOI: https://doi.org/10.54341/20778708_2026_2_67_64. – EDN: NTXFHQ

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Abstract. Let be a τ-closed σ-local formation of finite groups, where σ is some partition of the set of all prime numbers, τ is a subgroup functor in the sense of A.N. Skiba. A formation is called a minimal τ-closed σ-local non--formation or a -critical formation if , but all proper τ-closed σ-local subformations of are contained in the class of groups . In the case when is the formation of all meta-σ-nilpotent groups, the formation is called a minimal τ-closed σ-local non-meta-σ-nilpotent formation. In this paper, we obtain a description of minimal τ-closed σ-local non-meta-σ-nilpotent formations of finite groups.

Keywords: finite group, meta-σ-nilpotent group, formation σ-function, σ-local formation, subgroup functor, critical σ-local formation.

For citation: Skrundz, V. V. Minimal τ-closed σ-local non-meta-σ-nilpotent formations / V. V. Skrundz // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 72–78. – DOI: https://doi.org/10.54341/20778708_2026_2_67_72 (in Russian). – EDN: OWIQJS

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Abstract. This paper proposes a method for measuring the specific heat capacity of a liquid using a noise diode. It has been established that the accuracy of the method depends significantly on the parameters of the diode used. To improve measurement accuracy, it is recommended to use noise diodes with a wide overvoltage range, in which the dependence of the noise pulse repetition rate on the overvoltage is close to linear. Of the diodes used in the study, the ND103L noise diode manufactured in the Republic of Belarus is recommended, allowing for liquid specific heat capacity measurements with an error of no more than 5%. An additional advantage of using noise diodes as sensing elements in the development of specific heat capacity measuring devices is that the frequency and time interval determination are implemented using standardized circuit units – counters – which simplifies the measuring devices.

Keywords: noise diode, liquid specific heat capacity, noise pulse repetition rate, temperature.

For citation: Using noise diodes to measure the specific heat capacity of liquids / A. O. Zenevich, O. V. Kochergina, E. V. Novikov, I. L. Terekh // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 79–84. – DOI: https://doi.org/10.54341/20778708_2026_2_67_79 (in Russian). – EDN: EKLFBI

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Abstract. A relationship has been put forward that describes how the failure rate of power cables depends on their operating time. A high degree of agreement is demonstrated between experimental statistical data on the normalized failure rate of polymer-insulated cables and the calculated time dependency trends of the failure rate indicator, which are consistent with the proposed relationship. An analysis of failure rates was conducted, and a quantitative assessment of the reliability indicators was provided for power cables in the distribution networks of 6–10 kV in Gomel, Belarus. The results obtained can be used to model "life curves" and calculate the functional reliability of electrical cables with paper and polyethylene insulation.

Keywords: reliability, probability distribution, failure rate parameter, power cables, polymer insulation.

For citation: Kiselevich, V. V. Evaluation of reliability indicators for power cables with paper and polyethylene insulation / V. V. Kiselevich // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 85–92.– DOI: https://doi.org/10.54341/20778708_2026_2_67_85 (in Russian). – EDN: MBJRAV

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Abstract. This paper considers the problem of formalizing adaptive control for the laser polishing process of quartz glass, performed on a CNC laser machine. An approach is proposed in which the process operation is represented as a stochastic serial-parallel graph structure reflecting possible process states, diagnostic procedures, control actions, and probabilistic transitions between them. The basic control loop defines the standard trajectory of the operation for fixed parameters of processing speed and laser radiation power, while the adaptive loop generates corrective control ΔU based on current monitoring results. Control adaptation is achieved by activating additional microprocessing operations at each discrete-time step, forming sequential sets of corrective actions for changing the processing speed and laser radiation power. A neural network controller trained using reinforcement learning methods on simulation model data is used to synthesize the correct control adaptation policy. The simulation model is constructed using finite element calculations of the temperature-stress state of the laser processing zone. The control quality criterion is developed taking into account the need to maintain the maximum temperature within an acceptable range of values. The proposed method enables the construction of an optimal process development trajectory in real time through closed-loop monitoring and adaptive correction of process operation control variables. The obtained results can be used in the development of intelligent control systems for laser material processing operations.

Keywords: ŕdaptive control, laser polishing, quartz glass, stochastic graph model, discrete-event modeling, microtechnological operations, neural network controller, reinforcement learning, technological process.

For citation: Method and means of neural network modeling of the problem of controlling the technological operation of laser polishing / V. A. Prokhorenko, Yu. V. Nikitjuk, V. S. Smorodin, S. I. Sokolov, A. A. Sereda // Problems of Physics, Mathematics and Technics. – 2026. – № 2 (67). – P. 93–98. – DOI: https://doi.org/10.54341/20778708_2026_2_67_93 (in Russian). – EDN: NDCHVJ

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