The results of theoretical and experimental studies of influence of forces of light pressure upon the movement of the silver nanoparticles which are in liquid environments with various value of viscosity are given. The expression of the main equation of dynamics taking into account the gradient force, forces of absorption and dispersion operating on a metal spherical nanoparticle in the field of the focused laser beam of a Gaussian form are received. The speeds of the movement of silver nanoparticles and their movement in environments with various coefficients of viscosity are experimentally determined.

Keywords: metal nanoparticle, Gaussian beam, gradient force, forces of dispersion and absorption, speed of nanoparticles, liquid viscosity.

A.A. Afanas’ev – B.I. Stepanov Institute of Physics of NAS Belarus

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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The developed method allows to increase the accuracy of measurement of luminous flux using single photon avalanche photodetectors by taking into account dark pulses and afterpulses. The device for implementing this method was proposed. The defined for the applicability of the developed method were conditions.

Keywords: single photon avalanche photodetector, single photon pulses, dark pulses, afterpulses, luminous flux.

Î.Y. Gorbadey – Belarusian State Academy of Telecommunications

À.Î. Zenevich – Belarusian State Academy of Telecommunications

Å.V. Novikov – Belarusian State Academy of Telecommunications

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The theory of formation photodeflection signal in the layer of chiral carbon nanotube by irradiation of polarized modes of Bessel light beams was developed. For the first time the solution for the heat equation is obtained using integral transforms Fourier – Bessel and Laplace for a three-layer medium, which is irradiated with light polarization modes of Bessel beams with an intensity distribution in space.

Keywords: photodeflection spectroscopy, chiral carbon nanotubes, Bessel light beam, energy dissipation, Bessel function, heat equation, angles photodeflection.

G.S. Mityurich – Department of Physics, F. Skorina Gomel State University

E.V. Lebedeva – Department of Physics, F. Skorina Gomel State University

A.N. Serdyukov – Department of Physics, F. Skorina Gomel State University

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In the framework of the general three-body problem of celestial mechanics dynamic equations for non-relativistic three-body system with Newtonian potential are solved and new periodic orbits are simulated. Principle of least action, Fourier analysis and Mathematica’s possibilities of computer simulation were used.

Keywords: three-body system, gravitational interaction, action functional, periodic orbit, Fourier series, computer simulation.

G.Yu. Tyumenkov – Department of Physics, F. Skorina Gomel State University

A.Yu. Pesenko – Belarusian State University of Informatics and Radioelectronics

D.A. Bogdanovich – Gomel City Lyceum ¹1

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The generation of the second harmonic of Bessel light beams in quadratic-nonlinear crystals with radial-periodically domain structure was proposed and investigated. The type of interaction when the incident Bessel beam radially or azimuthally polarized is considered. A system of truncated equations for the field amplitudes of the fundamental and second harmonic fields is achiered. Numerically investigated The overlap integrals describing the efficiency of second harmonic generation were numerically investigated.

Keywords: Bessel beam, system of reduced equations, overlap integral, second-harmonic generation, quadratic nonlinear crystal.

P.A. Khilo – P.O. Sukhoi Gomel State Technical University

N.A. Khilo – B.I. Stepanov Institute of Physics of NAS Belarus

O.I. Pronevich – P.O. Sukhoi Gomel State Technical University

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Regularities of substrate temperature influence and density of a volatile dispersion products flow, following heat treatment of the formed layers on molecular structure and properties of polymer-based coatings deposited from an active gas phase are considered. Features of nucleation and growth of polymer particles on the activated surface are determined.

Keywords: electron beam dispersion, polymer coatings, molecular structure, morphology, heat treatment.

M.A. Yarmolenko – Department of Physics, F. Skorina Gomel State University

A.A. Rogachev – Department of Physics, F. Skorina Gomel State University

A.V. Rogachev – Director of the Research Institute of Physical Chemistry of F. Skorina Gomel State University

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The properties of intersection of maximal subgroups in groups with the operators are studied.

Keywords: finite group, subnormal subgroup, local formation.

R.V. Borodich – Department of Mathematics, F. Skorina Gomel State University

E.N. Borodich – Department of Mathematics, F. Skorina Gomel State University

M.V. Selkin – Department of Mathematics, F. Skorina Gomel State University

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A new series of separated lattices of saturated formations was found.

Keywords: formation, complete lattice of formations, lattice of saturated formations, -separated lattice of saturated formations.

N.N. Vorob’ev – P.M. Masherov Vitebsk State University

A.R. Kuznetsova – P.M. Masherov Vitebsk State University

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Let G be a finite group. A chain of subgroups of G such that is a maximal subgroup of for every is called a maximal chain of length n. A subgroup H of G is said to be an n-maximal subgroup of G if H is the latest member of some maximal chain of G of length n. In this review, we give the analisis of the most famous papers in which finite groups with generalized normal n-maximal subgroups are developed.

Keywords: finite group, maximal subgroup, maximal chain, n-maximal subgroup, normal subgroup, subnormal subgroup, K--subnormal subgroup, permutable subgroup.

V.A. Kovaleva – Department of Mathematics, F. Skorina Gomel State University

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Stationary distribution of conditions probabilities of the open queueing network is investigated. Devices of the nodes can operate in several modes. There are two types of customers in the nodes: ordinary (active) customers and temporarily non-active customers. There are input flows of signals that allow customers to change the state: from non-active state pass into the state when they can receive service and backwards. Stationary distribution insensitivity with respect to functional form of distribution of work quantity for customer service is established.

Keywords: queueing network, non-active customers, multimode service, stationary distribution insensitivity.

J.S. Kruk – Belarusian National Technical University

Y.E. Dudovskaya – Department of Mathematics, F. Skorina Gomel State University

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Some topics in the perturbation theory related to the functional calculus of closed operators in Banach space which belongs to the authors are considered. Moment inequality for the above mentioned functional calculus is also proved.

Keywords: perturbation theory of linear operators, operator Lipschitz functions, operator differentiable functions, Gateaux derivative, moment inequality.

A.R. Mirotin – Department of Mathematics, F. Skorina Gomel State University

A.A. Atvinovskii – Department of Mathematics, F. Skorina Gomel State University

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In [1] J-construction of composition formations was introduced. Some properties of them were found and applications to the study of products of normal and mutually permutable subgroups were obtained. In this paper we continue investigation in this area.

Keywords: finite group, J-quasinilpotent group, Jc-supersoluble group, Jca-soluble group, Jca-supersoluble group, product of normal subgroups, mutually permutable product, composition formation.

E.N. Myslovets – Department of Mathematics, F. Skorina Gomel State University

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The implementation of contact for indenter with the orthotropic coating on the elastic isotropic substrate is shown. Methods of determining the exposure parameters are built on the basis of the theory developed for calculating composite coatings. To investigate the influence of material properties and thickness of the coating on the contact parameters the program, on which the calculation was performed for different coating thickness, was written. Depending on the ratio of module of elasticity of the coating and base diagrams are constructed to determine the parameters of contact (contact area, pressure and values of the indentation). The convergence of numerical solutions depending on the thickness of the coatings and the relationship of material properties is studied.

Keywords: contact parameters, indenter, orthotropic coating, composite.

V.V. Mozharovsky – Department of Mathematics, F. Skorina Gomel State University

D.S. Kuzmenkov – Department of Mathematics, F. Skorina Gomel State University

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Multi-component generators of pseudorandom multi-dimensional and two-dimensional signals based on the selection of the set of non-linear functions, the type of the relationship between the non-linear functions, the order of using the initial key parameters and the type of processing of the generated pseudorandom signal and allowing to improve the statistical and cryptographic properties of ones are developed. The results of the simulation of multi-component ring and parallel random generators, two-component generator with random permutations, the two-dimensional generator of the vertical-horizontal permutations matrix and multi-component moire mask generator are presented.

Keywords: one- and multi-component pseudorandom generators, chaotic function, moire mask, initial key parameters, stream encryption, entropy.

A.A. Boriskevich – Belarusian State University of Informatics and Radioelectronics

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The algorithmic and software toolkit of the pilot project expert-analytical optimization of partitioning the set of people into groups with different specialization is described. The proposed algorithm takes into account criteria such as the psychological type of personality, individual preferences of the targets, disposition or aversion to other participants, as well as the diversity of interests of the members formed groups and their complementarity. As a basic typology of participants the author's synthesis of a number of conventional approaches was used. Preliminary testing of the proposed algorithm and the program was carried out on the example of the distribution of students into specialization at mathematical faculty F. Skorina GSU.

Keywords: expert-analytical decision-making, multi-criterion optimization, typology of personality, splitting the set of people into groups.

A.N. Osipenko – P.O. Sukhoi Gomel State Technical University

N.B. Osipenko – Department of Mathematics, F. Skorina Gomel State University

E.V. Neudashenko – Department of Mathematics, F. Skorina Gomel State University

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The synthesis method for constructing full class of bent-functions of six variables based on the sign coding matrices, structural, synchronous and asynchronous permutations applied to the theory of Agievich bent-squares is proposed. The resulting full class of bent-functions can be used to solve many problems in the theory of information transmission, error-correcting coding, cryptography and cryptanalysis.

Keywords: bent-function, Agievich bent-square, sign coding matrix, structure permutation, synchronous and asynchronous permutation, Walsh-Hadamard transform.

A.V. Sokolov – Odessa National Polytechnic University

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The requirements for schools scheduling in the Republic of Belarus are described. The algorithm for automatic scheduling, must take into account the nuances of these requirements, in order that the resulting schedule can be considered acceptable for the Belarusian schools.

Keywords: scheduling, overview, sanitary norms, school schedule, combinatorial optimization.

A.S. Filipenka – Belarusian-Russian University, Mogilev

K.V. Ausiannikau – Belarusian-Russian University, Mogilev

S.V. Bolotov – Belarusian-Russian University, Mogilev

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