## To finding the maximums in Young’s experience

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Abstract. In the physics literature devoted to the section “Optics”, various schemes for observing interference are considered, among which Young’s experiment occupies a significant place. The interference maxima in this experiment are described with a fairly simple formula. The distances between adjacent interference fringes, following from this formula, are the same for any order of maximum. In this paper, we consider a possible refinement of finding interference maxima and how this will affect the distance between adjacent interference fringes.

Keywords: interference, ray path, maxima conditions, coherence.

For citation: Akhramenko, N.A. To finding the maximums in Young’s experience / N.A. Akhramenko, I.O. Delikatnaya, E.I. Dotsenko // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 7–9. – DOI: https://doi.org/ 10.54341/20778708_2022_4_53_7. – EDN: CDBYZP

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## Light-absorbing sol-gel coatings for applications in optical technology

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Abstract. A technique for obtaining composite sol-gel coatings containing finely dispersed forms of carbon powders is presented. Optimal compositions have been developed and modes of deposition and heat treatment of formed coatings on aluminum substrates have been selected. The results of the study of thickness, adhesion to the substrate, hardness and resistance to cyclic effects of temperature changes (from minus 20° C to plus 150° C) are presented. The influence of the concentration of introduced carbon powders on the reflection coefficient of the formed sol-gel coatings has been established.

Keywords: film-forming solution, sol-gel, heat treatment, coating thickness, adhesion, hardness, reflection coefficient.

For citation: Light-absorbing sol-gel coatings for applications in optical technology / V.V. Vaskevich, V.E. Gaishun, D.L. Kovalenko, V.V. Sidsky, A.V. Semchenko, Y.A. Kosenok, N.V. Nasonova // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 10–15. – DOI: https://doi.org/10.54341/20778708_2022_4_53_10 (in Russian). – EDN: CMVFFF

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## Energy properties of the vector circular Kummer beams with terminating power. I. The homogeneous polarization

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Abstract. Analytical expressions in the closed shape for the vector circular 3D light Kummer beams with the homogeneous polarisation are offered and explored. These expressions do not contain a Gaussian. At certain restrictions on the free parametres such Kummer beams transfer terminating power. The transverse (spin and orbital) energy fluxes of such beams are calculated and graphically studied. It has been established, that the azimuthal function essentially influences the properties of transverse beam energy fluxes.

Keywords: paraxial beams, vector circular beams, Kummer beams.

For citation: Girgel, S.S. Energy properties of the vector circular kummer beams with terminating power. I. The homogeneous polarization / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 16–20. – DOI: https://doi.org/10.54341/20778708_2022_4_53_16 (in Russian). – EDN: ETJLTY

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## Study of the physical properties of composite antistatic coatings synthetized by sol-gel method

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Abstract. The compositions have been developed and the methods for the formation of composite antistatic coatings of various compositions with high optical, adhesive and mechanical characteristics for the modification of structural materials used in instrumentation by sol-gel method have been determined. The studies of the mechanical, optical and electrophysical properties of the ob-tained coatings have been carried out. All obtained coatings have transmittance of 75–85% in the visible and near-infrared ranges (400–800 nm), high mechanical hardness up to 5 N. The samples of the FTO composition are characterized by the best electrical conductivity.

Keywords: composite antistatic coatings, sol-gel method, heat treatment, hardness, optical properties, electrophysical properties.

For citation: Study of the physical properties of composite antistatic coatings synthetized by sol-gel method / K.D. Danilchenko, A.A. Maevsky, A.V. Semchenko, V.V. Sidski, V.V. Vaskevich, V.E. Gaishun, D.L. Kovalenko, O.I. Tyulenkova, N.V. Nasonova // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 21–24. – DOI: https://doi.org/ 10.54341/20778708_2022_4_53_21 (in Russian). – EDN: GGGCSZ

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## On the reduced form of thermodynamic coefficients of real gases

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Abstract. A form of writing the relationships that determine the physical parameters (thermodynamic coefficients) based on the equations of state of real gases is proposed. For each ratio, the main dimensionless part, expressed in terms of the given thermodynamic variables, is singled out. An explicit form of the reduced relations for the van der Waals, Redlich – Kwong and Soave – Redlich – Kwong equations of state is obtained. The graphs of coefficients in the given variables are constructed.

Keywords: thermodynamic coefficient, reduced variables, equation of real gas state, van der Waals equation, Soave – Redlich – Kwong equation, Redlich – Kwong equation.

For citation: Dey, E.A. On the reduced form of thermodynamic coefficients of real gases / E.A. Dey, G.Yu. Tyumenkov // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 25–29. – DOI: https://doi.org/10.54341/ 20778708_2022_4_53_25 (in Russian). – EDN: HETCXZ

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## Optimization of laser processing of diamonds

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Abstract. Using the genetic algorithm MOGA of the ANSYS Workbench program, the parameters of laser cutting of diamonds were optimized. The finite element calculation of temperatures and thermoelastic stresses was performed using the APDL programming language. Using a face-centered version of the central compositional plan of the experiment, a regression model of laser cutting of diamonds was constructed. Cutting speed, laser beam radius, and laser power density were used as variable factors. The maximum temperatures and thermoelastic stresses in the laser treatment zone were used as responses. An assessment of the influence of processing parameters on the maximum temperatures and voltages generated by laser radiation showed that the main factor is the power density of laser radiation. Optimization of laser cutting of diamonds was carried out for two options for setting the problem: according to the criterion of minimum thermoelastic stresses and according to the criteria of minimum thermoelastic stresses and maximum processing speed. The parameters obtained as a result of optimization and the parameters obtained as a result of finite element modeling are compared. The maximum relative error of the results obtained using the MOGA algorithm did not exceed 9% when determining temperatures and 15% when determining thermoelastic stresses. As a result of the simulation, the processing parameters were determined, the use of which will increase the productivity and reliability of laser cutting of diamonds.

Keywords: laser cutting, diamond, MOGA, ANSYS.

For citation: Optimization of laser processing of diamonds / V.A. Emelyanov, E.B. Shershnev, Y.V. Nikitjuk, S.I. Sokolov, I.Y. Aushev // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 30–36. – DOI: https://doi.org/ 10.54341/20778708_2022_4_53_30 (in Russian). – EDN: KYDPZC

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## Implementation of a mathematical model for calculating natural vibrations of a pipeline (vessel) made of composite

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Abstract. The paper considers a computer implementation of a method for calculating the natural oscillations of a pipeline (vessel) made of composite, based on the solution of a boundary value problem for a 4th-order differential equation describing transverse oscillations of an extended rectilinear section of the pipeline with different boundary conditions. The intrinsic transverse vibrations of a pipeline made of composite and a functionally gradient material containing a uniformly moving fluid with a constant velocity are investigated.

Keywords: natural oscillations, pipeline, composite, functionally gradient material, mathematical model.

For citation: Mozharovsky, V.V. Implementation of a mathematical model for calculating natural vibrations of a pipeline (vessel) made of composite / V.V. Mozharovsky, S.V. Kirhintsava // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 37–42. – DOI: https://doi.org/10.54341/20778708_2022_4_53_37 (in Russian). – EDN: LQYCCM

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## Exact solutions of the two-dimensional Logunov – Tavkhelidze equation with some analogues of the harmonic oscillator potential in the momentum representation

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Abstract. The exact solutions of the two-dimensional Logunov-Tavkhelidze equation which describes the bound states of systems of two scalar particles of the equivalent mass for some variants of the relativistic generalization of the harmonic oscillator potential are obtained in the momentum representation.

Keywords: two-dimensional Logunov – Tavkhelidze equation, partial wave function, bound states, harmonic oscillator, two-dimensional momentum representation.

For citation: Paulenko, A.V. Exact solutions of the two-dimensional Logunov – Tavkhelidze equation with some analogues of the harmonic oscillator potential in the momentum representation / A.V. Paulenko, Yu.A. Grishechkin // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 43–45. – DOI: https://doi.org/10.54341/20778708_2022_4_53_43 (in Russian). – EDN: LRXSGO

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## Morphology and structure of nanocomposite polymer coatings containing lead formate

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Abstract. The features of the influence of the polymer matrix nature on the morphology and structure of nanocomposite coatings formed by laser dispersion of a mixture of polymers and lead formate are determined. The influence of polymer polarity, heat treatment on the distribution of individual structural formations of coatings, the band gap of a metal-containing filler has been established. The nature of the polymeric material does not significantly affect the process of electron-beam decomposition of lead formate.

Keywords: polymer coatings, lead, formate, polytetrafluoroethylene, polycaprolactan, fluoroplast-30, morphology, structure.

For citation: Rudenkov, A.S. Morphology and structure of nanocomposite polymer coatings containing lead formate / A.S. Rudenkov, M.A. Yarmolenko // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 46–52. – DOI: https://doi.org/10.54341/20778708_2022_4_53_46 (in Russian). – EDN: OQAGKV

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## Analysis of energy characteristics of the second-harmonic generation in long cylindrical dielectric particles

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Abstract. The explicit forms of the power density, the total radiation power of the second-harmonic generation in a long thin cylindrical layer of a small radius, and the conditions for their maximum are found. The spatial distribution of the generated radiation is examined for special cases of the nonlinear dielectric susceptibility tensor. A numerical maximization of the intensity of the second-harmonic is carried out for the range of the particle base radius from nanometers to micrometers. The distribution of the generated radiation from a linear structure of cylindrical particles is determined. The conditions at which the generated radiation is maximal and the conditions at which there occurs no generation are found.

Keywords: second harmonic generation, cylindrical dielectric particle, second-order nonlinear dielectric susceptibility tensor, optimization, radiation power, directivity pattern, linear structure.

For citation: Talkachov, A.I. Analysis of energy characteristics of the second-harmonic generation in long cylindrical dielectric particles / A.I. Talkachov, A.A. Shamyna, V.N. Kapshai // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 53–63. – DOI: https://doi.org/10.54341/20778708_2022_4_53_53 (in Russian). – EDN: PMWHFF

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## Influence of laser assistance on the processes of volatile products dispersion generation of composite targets based on polyethylene and their reactivity

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Abstract. The regularities of the laser UV radiation influence on the generation processes and the reactivity of volatile products of electron-beam dispersion of polyethylene, when zinc oxide and copper nanoparticles are introduced into the target, are determined. Under laser assisting action, the coating growth rate and the pressure in the vacuum chamber decrease, while the reactive activity of the generated volatile fragments increases. The coatings are characterized by a lower content of trans-vinylene bonds, the morphology – by less dispersion of structural formations. The coatings based on polyethylene of ultra-high molecular weight are characterized by higher defectiveness.

Keywords: electron beam dispersion, laser assistance, polyethylene, molecular structure, zinc oxide, copper.

For citation: Influence of laser assistance on the processes of volatile products dispersion generation of composite targets based on polyethylene and their reactivity / Ì.À. Yarmolenko, À.V. Rogachev, À.S. Rudenkov, V.A. Emelyanov, S.A. Frolov, À.Ì. Mikhalko // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 64–72. – DOI: https://doi.org/ 10.54341/20778708_2022_4_53_64 (in Russian). – EDN: QVDUKL

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## On the center of a graph defined by Schmidt subgroups of a finite group

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Abstract. A Schmidt group is a non-nilpotent group whose proper subgroups are nilpotent. Schmidt graph of a finite group *G* is the prime graph with the vertex set π(*G*) in which (*p*,*q*) is an edge if and only if *G* has a Schmidt subgroup whose order is divisible by *pq*. In the paper the relationship of Schmidt graph properties with group properties is studied.

Keywords: finite group, prime graph, Schmidt group, Schmidt graph, soluble graph, centre of graph.

For citation: Bychkov, P.V. On the center of a graph defined by Schmidt subgroups of a finite group / P.V. Bychkov, S.F. Kamornikov, V.N. Tyutyanov // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 73–79. – DOI: https://doi.org/10.54341/20778708_2022_4_53_73 (in Russian). – EDN: VICESH

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## Quasireversibility of queuing systems with nonstandard batch customer motion

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Abstract. A useful condition for the quasireversibility of queuing systems is established.

Keywords: Markov chain, queuing system, quasireversibility, batch arrival and batch service, generating functions.

For citation: Malinkovskii, Yu.V. Quasireversibility of queuing systems with nonstandard batch customer motion / Yu.V. Malinkovskii // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 80–83. – DOI: https://doi.org/ 10.54341/20778708_2022_4_53_80 (in Russian). – EDN: VRLSRJ

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## Features and tools of the Nevod library in solving problems of extracting temporal markers in the text

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Abstract. Theoretical and methodological issues of semantic text analysis in terms of extracting facts are considered. Using the example of solving the problem of extracting temporal markers, the text search method, and its implementation in the Nevod library are presented. The functional completeness of the developed library is analyzed by comparing its capabilities with the tools of one of the leaders in the field of entity recognition – Microsoft.Recognizers.Text.

Keywords: semantic text analysis, automatic text processing, test data sets, pattern-based text search, pattern package, entity recognition, temporal markers, Nevod library, Mathematica computer algebra system.

For citation: Savionok, V.A. Features and tools of the Nevod library in solving problems of extracting temporal markers in the text / V.A. Savionok, V.B. Taranchuk // Problems of Physics, Mathematics and Technics. – 2022. – N 4 (53). – P. 84–92. – DOI: https://doi.org/10.54341/20778708_2022_4_53_84 (in Russian). – EDN: XJBRGC

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