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Abstract. Amorphous carbon coatings were formed by the pulsed cathodearc evaporation method. The dependences of the deposition rate of the phase composition, RMS roughness , and mechanical properties of the coatings on the orientation of the substrate relative to the carbon plasma flow were determined. It was shown that the deposition parameters and coating properties change non-monotonically with increasing angle of incidence of the flow on the substrate. The ŕnalysis of the AFM data showed the dependence of the RMS roughness of the coatings on the angle of incidence of the flow. The highest content of the sp³-phase, hardness, and elastic modulus are achieved at an angle of incidence of 15°.

Keywords: carbon coatings, deposition, structure, morphology, mechanical properties.

For citation: Influence of deposition conditions on the structure and mechanical properties of a-C coatings / Jingjie Wang, D.G. Pilipstov, A.V. Rogachev, A.S. Rudenkov, K.A. Sakhovsky, S.Yu. Chepkasov // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 7-12. – DOI: https://doi.org/10.54341/20778708_2024_4_61_7 (in Russian). – EDN: ANRURM

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Abstract. The optimal conditions for synthesis are determined. The technology for obtaining composite protective sol-gel coatings that contain finely dispersed powders of titanium oxide (carbon) and nanosized graphene powder is described. The results of analyzing the thickness, adhesion, and surface morphology of the resulting coatings are presented. The influence of the composition and concentration of graphene on the hardness, impact resistance, abrasion resistance and hydrophobic properties is established. The moisture resistance, resistance to salt fog and resistance to temperature fluctuations of the resulting sol-gel coatings are investigated.

Keywords: sol-gel, film-forming solution, compositional coatings, thickness, adhesion, mechanical strength, resistance to thermal cycling.

For citation: Synthesis and properties of protective compositional sol-gel coatings containing graphene / V.V. Vaskevich, D.L. Kovalenko, Tuan Anh Nguyen, V.E. Gaishun, Thien Vuong Nguyen // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 13-18. – DOI: https://doi.org/10.54341/20778708_2024_4_61_13 (in Russian). – EDN: YFRDBX

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Abstract. The polarization and energy properties of vector light beams with simple astigmatism are investigated analytically. Graphical modelling of polarization ellipses, intensity and transverse energy fluxes of the investigated vector astigmatic light beams is carried out.

Keywords: astigmatic beams, Gaussian beams, polarization, transverse energy fluxes.

For citation: Girgel, S.S. Energy and polarisation properties of vector Gaussian light beams with simple astigmatism / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 19-24. – DOI: https://doi.org/ 10.54341/20778708_2024_4_61_19 (in Russian). – EDN: UUWZHB

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Abstract. The influence of the characteristics of the inner coating of double-layer pipes on the parameters of hydraulic shock (head (pressure) and flow rate (velocity) of a moving liquid) by the well-known method of characteristics is investigated [1], [2]. A technique has been proposed and a program has been created in the Delphi environment that allows determining the parameters of a water hammer when liquids move in two-layer pipes coated with a composite with a different arrangement of fibers in the matrix of a composite material, provided that the axes of anisotropy coincide with the direction of the fibers. The velocity of the liquid wave in the orthotropic tube was determined according to the developed method [3]–[5], it is shown that the results obtained are in good agreement with other experimental and theoretical data. The proposed technique can be used for a new technology for restoring the op-erability of pipelines by inserting a special “stocking” made of synthetic felt (composite).

Keywords: coated pipe, orthotropy, fibers, matrix, wave velocity, hydraulic shock, method of characteristics, pressure, fluid flow.

For citation: Mozharovsky, V.V. The effect of the composite lining of double-layer pipes used in the technology of polymer “stocking” sanitation on the parameters of a water hammer / V.V. Mozharovsky, S.V. Kirhintsava // Problems of Physics, Mathematics and Tech-nics. – 2024. – № 4 (61). – P. 25-29. – DOI: https://doi.org/10.54341/20778708_2024_4_61_25 (in Russian). – EDN: QYDGBF

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Abstract. The influence of the architecture and structure of the two-layer system based on ethyl cellulose and sulfuric acid, as well as the formation modes, on the morphology and phase composition of carbon coatings formed on their surface is determined. It is shown that, due to the epitaxial nature of growth, the carbon layers deposited on the surface of the two-layer system EC/H₂SO₄ with a higher Csp³/Csp² ratio are also characterized by a higher Csp³/Csp² ratio, compared to the carbon layers formed on the surface of H₂SO₄/EC.

Keywords: carbon, sulfuric acid, ethyl cellulose, morphology, phase composition.

For citation: Morphology and phase composition of carbon coatings formed on the surface of two-layer system based on ethyl cellulose and sulfuric acid / A.S. Rudenkov, A.V. Rogachev, M.A. Yarmolenko, D.G. Piliptsou, Y.V. Nikityuk // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 30-39. – DOI: https://doi.org/10.54341/20778708_2024_4_61_30 (in Russian). – EDN: RIERVT

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Abstract. A linear homogeneous system of p first order differential equations in R^d is called biharmonic if each component of its arbitrary continuously differentiable solution satisfies the equation Δ²u=0, where Δ is the Laplace operator in R^d. In this article we give an example of a biharmonic system in R⁴, which is neither a four-dimensional analogue of the Cauchy – Riemann system nor an elliptic pseudo-symmetric system. For this system we consider the Dirichlet problem in an arbitrary bounded region with a sufficiently smooth boundary. It is proved that at some point of the boundary the rank of the Lopatinski matrix of the Dirichlet problem is not maximal. It is also shown that at this point the limit problem for the considered Dirichlet problem is not uniquely solvable.

Keywords: elliptic system, Dirichlet problem, regularizable boundary value problem, Lopatinski condition.

For citation: Basik, A.I. Irregularizability of the Dirichlet problem for one biharmonic system in / A.I. Basik, E.V. Gricuk, D.V. Haluts // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 40-44. – DOI: https://doi.org/ 10.54341/20778708_2024_4_61_40 (in Russian). – EDN: UESTUB

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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. II / A.M. Gal’mak // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 45-47. – DOI: https://doi.org/10.54341/ 20778708_2024_4_61_45 (in Russian). – EDN: QDMGXA

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Abstract. A finite non-nilpotent group is called a B-group if every proper subgroup of its quotient group by Frattini subgroup is primary. The p-length l_p(G) of a finite p-soluble group, which is the product of two B-subgroups, is studied. It has been proved that l_p(G)≤1 if p does not divide the index of one of the B-subgroups.

Keywords: finite group, B-group, p-soluble group, p-length, product of subgroups.

For citation: Kniahina, V.N. On the p-length of a product of two B-groups / V.N. Kniahina // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 48-52. – DOI: https://doi.org/10.54341/20778708_2024_4_61_48 (in Russian). – EDN: DBDFPO

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Abstract. One-line exponential queueing network, in which the waiting time by customers in the nodes is random variable whose conditional distribution (on fixed customers qualities) is exponential, was considered. The customers served in the nodes and the non-served customers move in the network according to a different routing matrices. A network modification with exponential bounded waiting times and product form stationary distribution is presented. To achieve this goal additional compensative flows of moving in the network control signals are introduced.

Keywords: qoueueing network, stationary distribution, product form, waiting time, sojourn time, exponential restricts, compensative flows, modificatory network.

For citation: Malinkovskii, Yu.V. Open one-line Jackson networks with exponential constrains on waiting times modification by product form of the stationary distribution / Yu.V. Malinkovskii // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 53-56. – DOI: https://doi.org/10.54341/20778708_2024_4_61_53 (in Russian). – EDN: PVNWEO

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Abstract. Throughout the paper, all groups are finite and G always denotes a finite group; P is the set of all primes and σ={σ_i|i∈I} is an arbitrary partition of P. By a σ-property of a group we mean any property of it that depends on σ and that does not imply any restrictions on σ. In this paper, further applications of the theory of σ-properties of a group in the study of generalized T-groups and other classes of finite groups are analyzed.

Keywords: finite group, σ-property of a group, σ-subnormal subgroup, σ-permutable subgroup, PσT-group.

For citation: Safonov, V.G. Ńharacterization of some classes of finite groups / V.G. Safonov, A.N. Skiba // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 57-64. – DOI: https://doi.org/10.54341/20778708_2024_4_61_57 (in Russian). – EDN: FSGNTY

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Abstract. The structural features of deposits of nickel, copper, tin and silver formed during electrolysis using activating laser radiation have been studied. It has been shown that the introduction of laser radiation into electrolysis processes makes it possible to obtain electro-plated coatings with improved performance characteristics, in particular electrical conductivity, at a rate of formation of a given submicron microgeometry of up to 5.69 μm/s.

Keywords: submicron topology, atomic force microscopy, local electrochemical deposition.

For citation: Formation of the surface topology of metal coatings by the thermochemical method under laser activation conditions / A.N. Kupo, N.N. Fedosenko, E.B. Shershnev, Y.V. Nikitiuk, N.A. Alyashkevich // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 65-69. – DOI: https://doi.org/10.54341/20778708_2024_4_61_65 (in Russian). – EDN: FSLULQ

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Abstract. The analysis of biomedical images of proteinograms obtained as a result of gel electrophoresis is a research area of current interest. As a result of the study of various methods and means of analyzing electrophoregrams, the authors proposed a resource-efficient and fast model of convolutional neural network, which allows the classification of human blood serum proteinograms with high accuracy at low requirements to computing resources of the computer.

Keywords: neural networks, computer vision, image recognition, proteinograms, electrophoresis.

For citation: Kurochka, K.S. Neural network model and classifier training algorithm for processing human serum gel electrophoresis data / K.S. Kurochka, K.A. Panarin, K.S. Makeeva // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 70-77. – DOI: https://doi.org/10.54341/20778708_2024_4_61_70 (in Russian). – EDN: INSQVT

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Abstract. This paper presents a computer system for adaptive control of the technological operation of laser cutting of fragile non-metallic products. The procedures for synthesizing the structure of the neural regulator of the parameters of the technological operation of cutting and the automated selection of the optimal architecture of the neural network based on the specified criteria for the quality of control adaptation are described. Stabilization of the parameters of the technological operation of laser cutting by the method of thermal splitting is given on the example of processing silicate glasses with elliptical laser beams.

Keywords: control adaptation system, neural network modeling, synthesis of the structure of the neuroregulator, stabilization of the parameters of a technological operation.

For citation: Prokhorenko, V.A. Adaptive control system for technological operation of laser processing of brittle non-metallic materials / V.A. Prokhorenko, Yu.V. Nikitjuk, V.S. Smorodin // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 78-81. – DOI: https://doi.org/10.54341/20778708_2024_4_61_78 (in Russian). – EDN: KIVJIH

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Abstract. An approach to the study of the mutual influence of various causes of mortality is outlined. The concepts of observed and effective mortality are introduced. A method is proposed to restore the current mortality values that are not distorted by the influence of other causes of mortality. The approach is demonstrated by the example of restoring the current mortality values while excluding mortality from external causes.

Keywords: biology of life expectancy, age dynamics of total mortality, observed and current mortality, health strategy, calculations of changes in life expectancy, mortality values, process of extinction, compensatory effect, assessment of the contribution of individual causes of mortality.

For citation: Sukach, E.I. Probabilistic-algebraic method of analysis of medical statistics / E.I. Sukach, A.P. Konchits // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 82-88. – DOI: https://doi.org/10.54341/ 20778708_2024_4_61_82 (in Russian). – EDN: BBUQIH

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Abstract. Let σ be a partition of the set of all prime numbers. In the paper the results of different years and different authors concerning the Kegel-Wielandt σ-problem are discussed, and the approaches to its solution are analised.

Keywords: finite group, Hall subgroup, finite simple group, subnormal subgroup, Kegel – Wielandt problem, partition of the set of all prime numbers, σ-subnormal subgroup, σ-complete group, Kegel – Wielandt σ-problem, subgroup lattice.

For citation: Kamornikov, S.F. The Kegel – Wielandt σ-problem: review of results / S.F. Kamornikov, V.N. Tyutyanov // Problems of Physics, Mathematics and Technics. – 2024. – № 4 (61). – P. 89-97. – DOI: https://doi.org/10.54341/ 20778708_2024_4_61_89 (in Russian). – EDN: BHOFNX

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