Main - Problems of physics, mathematics and technics

Andreev V.V., Haurysh V.Yu., Krutov A.F. Method of calculation of electroweak characte-ristics of mesons in the Poincare invariant quantum mechanics

On the basis of the point form of Poincare-invariant quantum mechanics, a method for calculating the formsfactors and the decay con-stants of mesons, as relativistic coupled quark systems, is presented. As an example of the developed technique, an integral representation of the radiative decay constant of a vector meson is obtained.

Keywords: quark, Poincare-invariant quantum mechanics, form factor, decay constant.

V.V. Andreev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.Yu. Haurysh – P.O. Sukhoi Gomel State Technical University

A.F. Krutov – Samara University

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Vakulina E.V., Maksimenko N.V. Amplitude of Computon scattering on hadrons of spin 1 with ac-count of spin polarizables

Within the framework of the Duffin � Kemmer � Petu formalism the Lagrangians of two-photon interactions with spin 1 hadrons are obtained in covariant form, taking into account the spin-new polarizabilities that are characteristic of spin 1/2 particles. On the basis of these Lagrangians, the covariant spin structures of the Compton scattering amplitude for spin 1 hadrons have been calculated. It is established that in the low-energy approximation the spin polarizabilities contribute to the Compton scattering amplitude in third order in the photon energy. The tensor-covariant structures of the forward scattering amplitude that contribute to the spin polarizabilities of spin 1 hadrons are determined.

Keywords: hadrons, polarizability, Lagrangian, Compton scattering.

E.V. Vakulina – I.G. Petrovsky Bryansk State University, Novozibkov

N.V. Maksimenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University

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Gaida L.S., Matuk E.V., Svistun A.Ch. Interaction of electromagnetic radiation with spheroidal metal nanoparticles in liquid

Results of theoretical researches of the effect of forces of light pressure upon spheroidal silver nanoparticles which are in liquid are given in work. Dependences of gradient force, forces of absorption and dispersion on the size and arrangement of spheroidal nanoparticles in the field of the focused laser beam of a Gaussian form are received.

Keywords: spheroidal metal nanoparticle, Gaussian beam, gradient force, forces of dispersion and absorption.

L.S. Gaida – Y. Kupala Grodno State University

E.V. Matuk – Y. Kupala Grodno State University

A.Ch. Svistun – Y. Kupala Grodno State University

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Kapshai V.N., Fialka S.I. Relativistic scattering cross sections of a two-particle system in the case of interaction potentials containing a �barrier�

Quasipotential equations for scattering states of a two-particle system with arbitrary angular momentum are investigated in the relativistic configuration representation. The case of spherically symmetric interaction potentials containing a �barrier� is considered. Scattering cross sections obtained from numerical calculations are presented, their resonant behavior is discussed in detail. Relativistic and non-relativistic results are compared.

Keywords: quasipotential approach, Logunov � Tavkhelidze equation, Gross equation, Kadyshevsky equation, relativistic configuration representation, resonant states.

V.N. Kapshai – Faculty of Physics and Information Technology, F. Skorina Gomel State University

S.I. Fialka – Faculty of Physics and Information Technology, F. Skorina Gomel State University

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Okojie J.E., Golosov D.A., Melnikov S.N., Zavadski S.M., Kolos V.V., Poplevka E.A., Zhukovich Yu.A. Ferroelectric properties of strontium-bismuth tantalate thin film deposited by RF magnetron sputtering method

Characteristics of ferroelectric thin films of strontium-bismuth tantalate (SBT), which were deposited by means of HF magnetron sput-tering on Pt/TiO_x/SiO₂/Si substrates, are investigated. The dependences of permittivity, residual polarization, and coercitivity of SBT films on the modes of subsequent annealing are established. Films with the residual polarization of 2Pr = 3.02 mC/cm² and coercitivity of 2E_c=140 kV/cm are obtained at the annealing temperature of 800� C. The dielectric constant and loss tangent at the frequency of 1.0 MHz were accordingly equal to and The Curie temperature of the films reached 310�315� C.

Keywords: non-volatile memory, FeRAM, ferroelectric, strontium-bismuth tantalate, SBT, HF magnetron sputtering.

J.E. Okojie – Belarusian State University of Informatics and Radioelectronics, Minsk

D.A. Golosov – Belarusian State University of Informatics and Radioelectronics, Minsk

S.N. Melnikov – Belarusian State University of Informatics and Radioelectronics, Minsk

S.M. Zavadski – Belarusian State University of Informatics and Radioelectronics, Minsk

V.V. Kolos – JSC �Integral�, Minsk

E.A. Poplevka – Belarusian State University of Informatics and Radioelectronics, Minsk

Yu.A. Zhukovich – JSC �Integral�, Minsk

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Semchenko A.V., Sidsky V.V., Tyulenkova O.I. The investigation of the sorption properties of silica gels synthesized by sol-gel method

The sorption properties of silica gels synthesized by sol-gel method were studied. Silica gel with magnetic properties possesses high sorption capacity in relation to Sn²⁺ ions and small sorption capacity to Sr²⁺ and Cu²⁺ ions and provides deep extraction of Sn²⁺ ions from liquid phases. With increasing of the concentration of iron carbonate the sorption properties of the synthesized samples are reduced, which is associated with the appearance of desorption.

Keywords: sol-gel method, sorption capacity, strontium ions, copper ions, plumbum ions, liquid phases, deep extraction.

A.V. Semchenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.V. Sidsky – Faculty of Physics and Information Technology, F. Skorina Gomel State University

O.I. Tyulenkova – Faculty of Physics and Information Technology, F. Skorina Gomel State University

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Adarchenko N.M., Bliznets I.V., Rizhik V.N. On finite semi-p-decomposable groups

A finite group G is called p-decomposable if We say that a finite group G is semi-p-decomposable if the normalizer of every non-normal p-decomposable subgroup of G is p-decomposable. We prove the following Theorem. Suppose that a finite group G is semi-p-decomposable. If a Sylow p-subgroup P of G is not normal in G, then the following conditions hold: (i) G is p-soluble and G has a normal Hall -subgroup H. (ii) is p-decomposable. (iii) is a maximal p-decomposable subgroup of G, and is abelian.

Keywords: finite group, p-soluble group, p-decomposable group, Sylow subgroup, Hall subgroup.

N.M. Adarchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

I.V. Bliznets – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

V.N. Rizhik – Bryansk State Agrarian University

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Belokon L.M. Intersections of maximal -subgroups containing formation radicals

Intersections of all maximal -subgroups of a finite group G, containing for nonempty radical formations and the abnormally full subgroup -functor are studied.

Keywords: radical formations of finite groups, -radicals, subgroup m-functor, intersections of maximal -subgroups.

L.M. Belokon – Mogilev State University of Food Technologies

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Vasilyeva T.I., Balychev S.V. On the influence of k-primary Hall subgroups on the structure of finite soluble groups

Let t be a natural number. In the class of finite soluble groups the properties of the class of all groups whose any k-primary Hall subgroups for belong to the saturated formation are found.

Keywords: soluble group, Hall subgroup, hereditary formation, saturated formation.

T.I. Vasil'eva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

S.V. Balychev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

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Kamornikov S.F., Shemetkova O.L. On -subnormal subgroups of a finite factorised group

The properties of -subnormal and -subnormal subgroups of a finite factorised group are studied.

Keywords: finite factorised group, -subnormal subgroup, -subnormal subgroup, formation, residual.

S.F. Kamornikov – F. Skorina Gomel State University

O.L. Shemetkova – Plekhanov Russian University of Economics, Moscow

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Malinkovsky Yu.V., Borodin N.N. Queueing networks with finite number of flows of negative customers and with limited sojourn time

The exponential queueing network with the usual positive and so called negative customers is considered. The sojourn time of customers in the network nodes is limited by the random variable which conditional distribution is exponential when customer quality in node is fixed. The customers serviced in nodes and customers leaving the nodes when sojourn time is completed can stay positive, become negative or leave the network in accordance with different routing matrixes.

Keywords: network, negative customer, limited sojourn time.

Yu.V. Malinkovsky – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

N.N. Borodin – P.O. Sukhoi Gomel State Technical University

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Monakhov V.S. On the supersoluble residual of mutually permutable products

We prove that if a group G=AB is the mutually permutable product of the supersoluble subgroups A and B, then the supersoluble residual of G coincides with the nilpotent residual of the derived subgroup G'.

Keywords: finite group, supersoluble subgroup, mutually permutable product, residual.

V.S. Monakhov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

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Sidortsov M.V., Drapeza A.A., Starovoitov A.P. Speed of convergence of quadratic Hermite � Pade approximations confluent hypergeometric functions

The speed of convergence (including non-diagonal) of quadratic Hermite � Pade approximations of the system of the second kind

is found. It consists of two degenerate hypergeometric functions when

are arbitrary distinct complex numbers, and

These proved theorems supplement and generalize the results obtained earlier by other authors.

Keywords: Hermite integrals, Hermite � Pade polynomials, Taylor series, Hermite � Pade approximations, asymptotic equality.

M.V. Sidortsov – Department of Mathematics, F. S�orina Gomel State University

N.A. Starovoitova – F. S�orina Gomel State University

A.P. Starovoitov – Department of Mathematics, F. S�orina Gomel State University

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Skiba A.N. On one generalization of the local formations

Throughout this paper, all groups are finite. Let be some partition of the set of all primes The natural numbers n and m are called -coprime if for every such that we have Let be a natural number and let be a class of groups. Then we say that is: (i) -closed (respectively weakly -closed) provided contains each finite group G which satisfies the following conditions: (1) G has subgroups such that for all (2) The indices (respectively the indices are pairwise -coprime); (ii) -closed (respectively weakly -closed) provided contains each finite group G which satisfies the following conditions: (1) G has modular subgroups such that for all (2) The indices (respectively the indices ) are pairwise -coprime. In this paper, we study properties and applications of (weakly) -closed and (weakly) -closed classes of finite groups.

Keywords: finite group, formation -function, -local formation, (weakly) -closed class of groups, (weakly) -closed class of groups.

A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

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Bykhovtsev V.E., Smorodin V.S., Bondareva Yu.D. System analysis of the mathematical model of ground basis at the optimization of parameters of building RIT-pile

Based on the development of a mathematical model of a complex system, as a multiparameter image of an object of investigation, the conditions of constructing a RIT-pile of optimal material capacity for a given load were obtained by the method of system analysis.

Keywords: multiparametric image, finite set of mathematical models, soil bases, RIT-piles, optimization of material consumption.

V.E. Bykhovtsev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

V.S. Smorodin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Yu.D. Bondareva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

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Varuyeu A.V., Demidenko O.M., Liauchuk V.D., Chechat P.L. Encapsulation of backbone traffic of data processing center

The process of creating a virtual backbone line based on protocols of an overlay communication is considered. The traffic transference is limited to public data channels.

Keywords: topology, media content, backbone traffic, VXLAN, VTEP, EVE-NG, channel of data transference.

A.V. Varuyeu – Faculty of Physics and Information Technology, F. Skorina Gomel State University

O.M. Demidenko – F. Skorina Gomel State University

V.D. Liauchuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University

P.L. Chechet – Faculty of Physics and Information Technology, F. Skorina Gomel State University

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	PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (34) 2018 PHYSICS Andreev V.V., Haurysh V.Yu., Krutov A.F. Method of calculation of electroweak characte-ristics of mesons in the Poincare invariant quantum mechanics On the basis of the point form of Poincare-invariant quantum mechanics, a method for calculating the formsfactors and the decay con-stants of mesons, as relativistic coupled quark systems, is presented. As an example of the developed technique, an integral representation of the radiative decay constant of a vector meson is obtained. Keywords: quark, Poincare-invariant quantum mechanics, form factor, decay constant. V.V. Andreev – Faculty of Physics and Information Technology, F. Skorina Gomel State University V.Yu. Haurysh – P.O. Sukhoi Gomel State Technical University A.F. Krutov – Samara University Download PDF (376 KB) Vakulina E.V., Maksimenko N.V. Amplitude of Computon scattering on hadrons of spin 1 with ac-count of spin polarizables Within the framework of the Duffin � Kemmer � Petu formalism the Lagrangians of two-photon interactions with spin 1 hadrons are obtained in covariant form, taking into account the spin-new polarizabilities that are characteristic of spin 1/2 particles. On the basis of these Lagrangians, the covariant spin structures of the Compton scattering amplitude for spin 1 hadrons have been calculated. It is established that in the low-energy approximation the spin polarizabilities contribute to the Compton scattering amplitude in third order in the photon energy. The tensor-covariant structures of the forward scattering amplitude that contribute to the spin polarizabilities of spin 1 hadrons are determined. Keywords: hadrons, polarizability, Lagrangian, Compton scattering. E.V. Vakulina – I.G. Petrovsky Bryansk State University, Novozibkov N.V. Maksimenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University Download PDF (252 KB) Gaida L.S., Matuk E.V., Svistun A.Ch. Interaction of electromagnetic radiation with spheroidal metal nanoparticles in liquid Results of theoretical researches of the effect of forces of light pressure upon spheroidal silver nanoparticles which are in liquid are given in work. Dependences of gradient force, forces of absorption and dispersion on the size and arrangement of spheroidal nanoparticles in the field of the focused laser beam of a Gaussian form are received. Keywords: spheroidal metal nanoparticle, Gaussian beam, gradient force, forces of dispersion and absorption. L.S. Gaida – Y. Kupala Grodno State University E.V. Matuk – Y. Kupala Grodno State University A.Ch. Svistun – Y. Kupala Grodno State University Download PDF (300 KB) Kapshai V.N., Fialka S.I. Relativistic scattering cross sections of a two-particle system in the case of interaction potentials containing a �barrier� Quasipotential equations for scattering states of a two-particle system with arbitrary angular momentum are investigated in the relativistic configuration representation. The case of spherically symmetric interaction potentials containing a �barrier� is considered. Scattering cross sections obtained from numerical calculations are presented, their resonant behavior is discussed in detail. Relativistic and non-relativistic results are compared. Keywords: quasipotential approach, Logunov � Tavkhelidze equation, Gross equation, Kadyshevsky equation, relativistic configuration representation, resonant states. V.N. Kapshai – Faculty of Physics and Information Technology, F. Skorina Gomel State University S.I. Fialka – Faculty of Physics and Information Technology, F. Skorina Gomel State University Download PDF (970 KB) Okojie J.E., Golosov D.A., Melnikov S.N., Zavadski S.M., Kolos V.V., Poplevka E.A., Zhukovich Yu.A. Ferroelectric properties of strontium-bismuth tantalate thin film deposited by RF magnetron sputtering method Characteristics of ferroelectric thin films of strontium-bismuth tantalate (SBT), which were deposited by means of HF magnetron sput-tering on Pt/TiO_x/SiO₂/Si substrates, are investigated. The dependences of permittivity, residual polarization, and coercitivity of SBT films on the modes of subsequent annealing are established. Films with the residual polarization of 2Pr = 3.02 mC/cm² and coercitivity of 2E_c=140 kV/cm are obtained at the annealing temperature of 800� C. The dielectric constant and loss tangent at the frequency of 1.0 MHz were accordingly equal to and The Curie temperature of the films reached 310�315� C. Keywords: non-volatile memory, FeRAM, ferroelectric, strontium-bismuth tantalate, SBT, HF magnetron sputtering. J.E. Okojie – Belarusian State University of Informatics and Radioelectronics, Minsk D.A. Golosov – Belarusian State University of Informatics and Radioelectronics, Minsk S.N. Melnikov – Belarusian State University of Informatics and Radioelectronics, Minsk S.M. Zavadski – Belarusian State University of Informatics and Radioelectronics, Minsk V.V. Kolos – JSC �Integral�, Minsk E.A. Poplevka – Belarusian State University of Informatics and Radioelectronics, Minsk Yu.A. Zhukovich – JSC �Integral�, Minsk Download PDF (1,21 MB) Semchenko A.V., Sidsky V.V., Tyulenkova O.I. The investigation of the sorption properties of silica gels synthesized by sol-gel method The sorption properties of silica gels synthesized by sol-gel method were studied. Silica gel with magnetic properties possesses high sorption capacity in relation to Sn²⁺ ions and small sorption capacity to Sr²⁺ and Cu²⁺ ions and provides deep extraction of Sn²⁺ ions from liquid phases. With increasing of the concentration of iron carbonate the sorption properties of the synthesized samples are reduced, which is associated with the appearance of desorption. Keywords: sol-gel method, sorption capacity, strontium ions, copper ions, plumbum ions, liquid phases, deep extraction. A.V. Semchenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University V.V. Sidsky – Faculty of Physics and Information Technology, F. Skorina Gomel State University O.I. Tyulenkova – Faculty of Physics and Information Technology, F. Skorina Gomel State University Download PDF (671 KB) MATHEMATICS Adarchenko N.M., Bliznets I.V., Rizhik V.N. On finite semi-p-decomposable groups A finite group G is called p-decomposable if We say that a finite group G is semi-p-decomposable if the normalizer of every non-normal p-decomposable subgroup of G is p-decomposable. We prove the following Theorem. Suppose that a finite group G is semi-p-decomposable. If a Sylow p-subgroup P of G is not normal in G, then the following conditions hold: (i) G is p-soluble and G has a normal Hall -subgroup H. (ii) is p-decomposable. (iii) is a maximal p-decomposable subgroup of G, and is abelian. Keywords: finite group, p-soluble group, p-decomposable group, Sylow subgroup, Hall subgroup. N.M. Adarchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University I.V. Bliznets – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University V.N. Rizhik – Bryansk State Agrarian University Download PDF (261 KB) Belokon L.M. Intersections of maximal -subgroups containing formation radicals Intersections of all maximal -subgroups of a finite group G, containing for nonempty radical formations and the abnormally full subgroup -functor are studied. Keywords: radical formations of finite groups, -radicals, subgroup m-functor, intersections of maximal -subgroups. L.M. Belokon – Mogilev State University of Food Technologies Download PDF (389 KB) Vasilyeva T.I., Balychev S.V. On the influence of k-primary Hall subgroups on the structure of finite soluble groups Let t be a natural number. In the class of finite soluble groups the properties of the class of all groups whose any k-primary Hall subgroups for belong to the saturated formation are found. Keywords: soluble group, Hall subgroup, hereditary formation, saturated formation. T.I. Vasil'eva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University S.V. Balychev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University Download PDF (296 KB) Kamornikov S.F., Shemetkova O.L. On -subnormal subgroups of a finite factorised group The properties of -subnormal and -subnormal subgroups of a finite factorised group are studied. Keywords: finite factorised group, -subnormal subgroup, -subnormal subgroup, formation, residual. S.F. Kamornikov – F. Skorina Gomel State University O.L. Shemetkova – Plekhanov Russian University of Economics, Moscow Download PDF (247 KB) Malinkovsky Yu.V., Borodin N.N. Queueing networks with finite number of flows of negative customers and with limited sojourn time The exponential queueing network with the usual positive and so called negative customers is considered. The sojourn time of customers in the network nodes is limited by the random variable which conditional distribution is exponential when customer quality in node is fixed. The customers serviced in nodes and customers leaving the nodes when sojourn time is completed can stay positive, become negative or leave the network in accordance with different routing matrixes. Keywords: network, negative customer, limited sojourn time. Yu.V. Malinkovsky – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University N.N. Borodin – P.O. Sukhoi Gomel State Technical University Download PDF (259 KB) Monakhov V.S. On the supersoluble residual of mutually permutable products We prove that if a group G=AB is the mutually permutable product of the supersoluble subgroups A and B, then the supersoluble residual of G coincides with the nilpotent residual of the derived subgroup G'. Keywords: finite group, supersoluble subgroup, mutually permutable product, residual. V.S. Monakhov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University Download PDF (217 KB) Sidortsov M.V., Drapeza A.A., Starovoitov A.P. Speed of convergence of quadratic Hermite � Pade approximations confluent hypergeometric functions The speed of convergence (including non-diagonal) of quadratic Hermite � Pade approximations of the system of the second kind is found. It consists of two degenerate hypergeometric functions when are arbitrary distinct complex numbers, and These proved theorems supplement and generalize the results obtained earlier by other authors. Keywords: Hermite integrals, Hermite � Pade polynomials, Taylor series, Hermite � Pade approximations, asymptotic equality. M.V. Sidortsov – Department of Mathematics, F. S�orina Gomel State University N.A. Starovoitova – F. S�orina Gomel State University A.P. Starovoitov – Department of Mathematics, F. S�orina Gomel State University Download PDF (317 KB) Skiba A.N. On one generalization of the local formations Throughout this paper, all groups are finite. Let be some partition of the set of all primes The natural numbers n and m are called -coprime if for every such that we have Let be a natural number and let be a class of groups. Then we say that is: (i) -closed (respectively weakly -closed) provided contains each finite group G which satisfies the following conditions: (1) G has subgroups such that for all (2) The indices (respectively the indices are pairwise -coprime); (ii) -closed (respectively weakly -closed) provided contains each finite group G which satisfies the following conditions: (1) G has modular subgroups such that for all (2) The indices (respectively the indices ) are pairwise -coprime. In this paper, we study properties and applications of (weakly) -closed and (weakly) -closed classes of finite groups. Keywords: finite group, formation -function, -local formation, (weakly) -closed class of groups, (weakly) -closed class of groups. A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University Download PDF (252 KB) INFORMATION SCIENCE Bykhovtsev V.E., Smorodin V.S., Bondareva Yu.D. System analysis of the mathematical model of ground basis at the optimization of parameters of building RIT-pile Based on the development of a mathematical model of a complex system, as a multiparameter image of an object of investigation, the conditions of constructing a RIT-pile of optimal material capacity for a given load were obtained by the method of system analysis. Keywords: multiparametric image, finite set of mathematical models, soil bases, RIT-piles, optimization of material consumption. V.E. Bykhovtsev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University V.S. Smorodin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University Yu.D. Bondareva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University Download PDF (316 KB) Varuyeu A.V., Demidenko O.M., Liauchuk V.D., Chechat P.L. Encapsulation of backbone traffic of data processing center The process of creating a virtual backbone line based on protocols of an overlay communication is considered. The traffic transference is limited to public data channels. Keywords: topology, media content, backbone traffic, VXLAN, VTEP, EVE-NG, channel of data transference. A.V. Varuyeu – Faculty of Physics and Information Technology, F. Skorina Gomel State University O.M. Demidenko – F. Skorina Gomel State University V.D. Liauchuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University P.L. Chechet – Faculty of Physics and Information Technology, F. Skorina Gomel State University Download PDF (654 KB)

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