## Comparative analysis of models for estimation of hollow structures scattering characteristics

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Abstract. The possibility of using a model of a hollow structure with a simple shape to estimate the scattering characteristics of a hollow structure with a complex shape was investigated. The examples are given in which the scattering characteristics are calculated if a plane electromagnetic wave is incident.

Keywords: integral equation method, radio wave scattering, modeling.

For citation: Avetisyan, T.V. Comparative analysis of models for estimation of hollow structures scattering characteristics / T.V. Avetisyan, J.E. Lvovich, A.P. Preobrazhensky // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 7-10. – DOI: https://doi.org/10.54341/20778708_2023_2_55_7 (in Russian). – EDN: CQTDWZ

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## To the determination of the unit of electric current in SI system

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Abstract. In the international system of units "SI", one of the main ones is the ampere. During its existence, the unit of electric current strength, the ampere, was redefined several times. According to the definition of 1948, the ampere was determined through the interaction force of two parallel straight conductors of infinite length and a negligibly small circular cross-sectional area. Since 2019, changes in the SI have come into force, which redefined the ampere based on fixing the numerical value of the elementary electric charge, adopted in Resolution 26 of the CGPM in 2018. The consequence of this was, in particular, that the coefficients for converting between SI units and units of the CGS system were no longer accurate. In this paper, we consider the possibility of modifying the 1948 definition by changing the configuration of interacting currents. In this case, infinite conductors are replaced by circular currents of finite length.

Keywords: system of units "SI", ampere, electric current, interaction of currents.

For citation: Akhramenko, N.A. To the determination of the unit of electric current in SI system / N.A. Akhramenko // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 11-14. – DOI: https://doi.org/10.54341/ 20778708_2023_2_55_11. – EDN: FEEKTQ

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## Polarizing properties and crossflows of energy of vector Bessel – Gauss TM light beams

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Abstract. The analytical expressions in the closed form for vector light Bessel – Gauss beams with nonhomogeneous polarization (TM-modes) are offered and are investigated. At restrictions on free parameter such Bessel – Gauss beams transfer terminating power. The pictures of polarization, intensity and crossflows of energy of such beams are calculated and are graphically investigated.

Keywords: paraxial beams, vector beams, Bessel – Gauss beams, nonhomogeneous polarization, TM-modes.

For citation: Girgel, S.S. Polarizing properties and crossflows of energy of vector Bessel – Gauss TM light beams / S.S. Girgel // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 15-19. – DOI: https://doi.org/10.54341/ 20778708_2023_2_55_15 (in Russian). – EDN: FOAIZW

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## Electret state in nanocomposites based on polylactide

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Abstract. The electret properties of composites based on polylactide (PLA) filled with montmorillonite (MML) have been studied. With an increase of filler content, the stability of the electret state increases, as well as the charge and amplitudes of the TSD currents. The current spectra are analyzed based on the concept of a superposition of discrete elementary Debye maxima described by first-order kinetics. The coincidence of experimental and calculated values of the current density is shown, the charge and activation energy are calculated. Low temperature maxima can be caused either by the release of charge carriers from traps localized at the interface between PLA and MML (Maxwell – Wagner polarization), or charge relaxation from traps caused by unfreezing of PLA segmental mobility.

Keywords: polylactide, montmorillonite, biodegradable, electret, thermal depolarization currents, activation energy.

For citation: Electret state in nanocomposites based on polylactide / M.A. Kovalenko, S.V. Zotov, V.A. Goldade, A.A. Pavlov, A.M. Kamalov, M.E. Borisova // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 20-24. – DOI: https://doi.org/10.54341/20778708_2023_2_55_20 (in Russian). – EDN: GETVXH

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## Optimization of the parameters of the process of controlled thermal cracking of silicate glasses under the action of a hot airflow

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Abstract. The optimization of the parameters of sharpening silicate glass with a hot airflow was carried out using the MOGA genetic al-gorithm in the DesignXplorer module of the Ansys program. Using the APDL programming language, the calculations of the temperature and thermoelastic stresses, which are typical for thermal cracking of silicate glasses were made. With the help of the central compositional plan of the numerical experiment, regression models were built in which the sharpness speed, hot air nozzle diameter and hot air temperature at the center of the heat spot were used as variable factors, and the maximum temperatures and thermoelastic stresses in the treatment zone were used as responses. The impact of variable factors on responses was assessed. Optimization of controlled thermal splitting under the consumption of air heat according to the criterion of maximum thermoelastic losses and maximum processing speed made it possible to determine the technological parameters that improve the reliability and productivity of the process of sharpening silicate glasses.

Keywords: laser cutting, hot airflow, coolant, MOGA, ANSYS.

For citation: Optimization of the parameters of the process of controlled thermal cracking of silicate glasses under the action of a hot airflow / Y.V. Nikitjuk, A.F. Ivanov, I.P. Sitdikova, Z.F. Zaripova, K.L. Gorshkova, I.Y. Aushev // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 25-30. – DOI: https://doi.org/10.54341/20778708_2023_2_55_25 (in Russian). – EDN: JHWYWX

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## Application of PWM signals to generate low-temperature atmospheric plasma

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Abstract. The use of pulse-width modulated signals for generating low-temperature atmospheric plasma in an inert gas environment is studied. The results of studies of the energy consumption of a low-temperature plasma generation system depending on the fill factor, as well as the pulse repetition rate, are presented. The system operating modes are identified, in which the minimum energy consumption is achieved, and possible ways to control the low-temperature plasma generation system to obtain the necessary plasma properties are determined.

Keywords: low-temperature atmospheric pressure plasma, parameters of control signals for plasma generation, energy consumption of devices for generating low-temperature atmospheric pressure plasma.

For citation: Application of PWM signals to generate low-temperature atmospheric plasma / A.N. Osipov, Y.N. Kalenkovich, V.A. Rokach, T. Ma // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 31-38. – DOI: https://doi.org/ 10.54341/20778708_2023_2_55_31 (in Russian). – EDN: KBEWMH

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## Exponential queueing networks with countable set of flows of negative customers and limited sojourn time

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Abstract. An exponential queuing network with one-line nodes is considered. The network receives a Poisson flow of requests with a parameter Λ and a countable number of Poisson flows of negative customers with parameters
λ_{l}, (*l*=1,∞), respectively. The incoming request with probability *p _{i}* and the negative customer of the

*l*-th flow with probability

*q*are sent to the

_{il}*i*-th node Negative customers are not served. The customer of the

*l*-th flow arriving at the

*i*-th node, immediately deletes exactly

*l*requests (if there are any), and deletes all the requests if their number is less than

*l*,

*i*=1,

*N*,

*l*=1,∞. The sojourn time of requests in network nodes is a random variable with exponential conditional distribution for a fixed number of requests. The requests served at nodes and the requests leaving nodes for the sojourn time is over can remain requests, become customers of the

*i*-th flow, or leave the network.

Keywords: network, negative customer, limited sojourn time, stationary distribution.

For citation: Borodin, N.N. Exponential queueing networks with countable set of flows of negative customers and limited sojourn time / N.N. Borodin, Yu.V. Malinkovskii // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 39-43. – DOI: https://doi.org/10.54341/20778708_2023_2_55_39 (in Russian). – EDN: LHIIYJ

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## Symmetrical token ring lan with messages of different types and gated service

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Abstract. We study a symmetrical ring topology local network with a token access protocol with number *N* of stations, each of them has *n* buffers of capacity 1 for each type of incoming messages. After the token arrives at any station, all the messages in the buffers are serviced in accordance with the gated service discipline. Incoming messages of *n* types are Poisson, independent intensity flows λ_{i}, 1≤*i*≤*n*, for an arbitrary station. A system of vector-matrix equations is presented, which makes it possible to calculate the probabilities of stationary states, as well as the main characteristics of the studied ring network.

Keywords: token, local network (LAN), station, messages of n types, single buffer, gated discipline, state probabilities.

For citation: Burakovski, V.V. Symmetrical token ring lan with different types messages and gated service / V.V. Burakovski // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 44-46. – DOI: https://doi.org/10.54341/ 20778708_2023_2_55_44 (in Russian). – EDN: OBVDGQ

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##
*l*-ary groups of a special form. I

Powers in ## QR code

Abstract. The article deals with powers in polyadic groups of a special form, that is in polyadic groups with *l*-ary operation η_{s,σ,k}, that is called polyadic operation of a special form and is defined on Cartesian power of *A ^{k}*

*n*-ary group <

*A*,η> by substitution σ

^{l}=σ and

*n*-ary operation η.

Keywords: polyadic operation, *n*-ary group, power.

For citation: Gal’mak, A.M. Powers in *l*-ary groups of a special form. I / A.M. Gal’mak // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 47-51. – DOI: https://doi.org/10.54341/20778708_2023_2_55_47 (in Russian). – EDN: OEPOEU

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##
_{J}-nilpotent finite groups

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Abstract. Throughout the article all groups are finite and *G* always denotes finite group; P is the set of all prime numbers and J is some class of groups, closed under extensions, homomorphic images and subgroups. In this paper, σ_{J}=σ_{0}∪{σ_{i}|*i*∈*I*} is a partition of the set P i.e. and σ_{i}∩σ_{j}=∅ for all indices *i*≠*j* from {0}∪*I*, for which J is a class of σ_{0}-groups with π(J)=σ_{0}. The group *G* is called: σ_{J}-primary if *G* is either an J-group or a σ_{i}-group for some *i*≠0;
σ_{J}-nilpotent if *G* is the direct product of some σ_{J}-primary groups. Finite σ_{J}-nilpotent groups are characterized.

Keywords: finite group, σ_{J}-subnormal subgroup, σ_{J}-soluble group, σ_{J}-nilpotent group, Hall subgroup.

For citation: On σ_{J}-nilpotent finite groups / I.M. Dergacheva, I.P. Shabalina, E.A. Zadorozhnyuk, I.A. Sobol // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 52-55. – DOI: https://doi.org/10.54341/20778708_2023_2_55_52 (in Russian). – EDN: SDSTAN

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## On rational conjugate Fejer sums on an interval and approximations of the conjugate function

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Abstract. The approximations of the conjugate function on the segment [-1,1] by Fejer sums of conjugate rational integral Fourier – Chebyshev operators with restrictions on the number of geometrically different poles are investigated. An integral representation of the corresponding approximations is established. An integral representation of approximations, estimation of pointwise approximations and uniform approximations with a certain majorant are obtained for a conjugate function with
density (1-*x*)^{γ}, γ∈(1/2,1). Its asymptotic expression for
*n*→∞, depending on the parameters of the approximating function is established. In the final part, the optimal values of parameters at which the highest rate of decreasing majorant is provided are found. As a corollary, the estimates of approximations of conjugate function on the segment [-1,1] by Fejer sums conjugate polynomial Fourier – Chebyshev series are found.

Keywords: conjugate function, Fourier – Chebyshev series, Fejer sums, function with power singularity, pointwise and uniform approximations, best approximations, asymptotic estimates.

For citation: Patseika, P.G. On rational conjugate Fejer sums on an interval and approximations of the conjugate function / P.G. Patseika // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 56-67. – DOI: https://doi.org/ 10.54341/20778708_2023_2_55_56 (in Russian). – EDN: VGNTRP

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## Existence and uniqueness of consistent Hermite – Fourier approximations

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Abstract. The trigonometric analogues of algebraic Hermite – Pade approximations were defined, these are Hermite – Fourier approximations. In particular, the theorem of existence of Hermite – Fourier approximations was proved, the sufficient
condition of their uniqueness was obtained, and the criterion of the existence and uniqueness of Hermite – Fourier polynomials, which are the numerator and denominator of Hermite – Fourier approximations associated with an arbitrary set of trigonometric series *k*. When the conditions of the criterion were met, the explicit type of the specified polynomials was established.

Keywords: trigonometric series, Fourier sums, trigonometric Pade approximants, Hermite – Pade polynomials, Hermite – Pade approximations.

For citation: Starovoitov, A.P. Existence and uniqueness of consistent Hermite – Fourier approximations / A.P. Starovoitov, E.P. Kechko, T.M. Osnach // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 68-73. – DOI: https:// doi.org/10.54341/20778708_2023_2_55_68 (in Russian). – EDN: VYPYFH

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## Influence of aluminum doping degree on the properties of titanium-aluminum oxide films

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Abstract. The characteristics of titanium-aluminum oxide films deposited by reactive magnetron sputtering of Ti-Al compound targets have been studied. The dependences of the permittivity, dielectric loss tangent, band gap, leakage current density, and breakdown field strength on the degree of film doping with aluminum *C*_{Al} and the oxygen concentration in the Ar/O_{2} gas
mixture during the deposition of *Ã*_{O2} are obtained. It has been established that an increase in *C*_{Al} leads to a decrease in dielectric losses and leakage current, an increase in the band gap and the strength of the breakdown field of the films. However, in this case, the dielectric constant of the films decreases to values less than 10.

Keywords: reactive magnetron sputtering, composite target, thin films, titanium-aluminum oxide, elemental composition, dielectric permittivity, dielectric loss tangent, leakage current, band gap.

For citation: Influence of aluminum doping degree on the properties of titanium-aluminum oxide films / H.T. Doan, D.A. Golosov, J. Zhang, N.A. Kananovich, S.M. Zavadski, S.N. Melnikov // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 74-82. – DOI: https://doi.org/10.54341/20778708_2023_2_55_74 (in Russian). – EDN: XACNAE

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## Stabilization of technological cycle parameters when constructing feedback control

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Abstract. An approach for solving problem of stabilization of technological cycle operation parameters is proposed. The approach is based on applying the methods of neural network modeling of controlled parameters of technological operations. Modern approaches for solving such problems are considered; the procedure of hybrid intellectual adaptive control system creation is demonstrated. The proposed approach allows automating processes of development and operation of hybrid intellectual computer systems when implementing innovative solutions in the field of traffic flows control, automation in the most advanced branches of industry and agriculture.

Keywords: neural network methods, parameters stabilization, adaptive control, neuroregulator models.

For citation: Smorodin, V.S. Stabilization of technological cycle parameters when constructing feedback control / V.S. Smorodin, V.A. Prokhorenko // Problems of Physics, Mathematics and Technics. – 2023. – N 2 (55). – P. 83-88. – DOI: https://doi.org/10.54341/20778708_2023_2_55_83 (in Russian). – EDN: ZEKWIK

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