
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N2 (39) 2019
REVIEWS
Rudenkov A.S., Yarmolenko M.A. Carbon nanotubes: classification, features of synthesis,
research methods and applications
Modern classification of carbon nanotubes (CNT) is considered. A comparative analysis of the methods for their synthesis has been carried out; key technological parameters affecting the type and architecture of the formed CNTs have been identified. The most effective catalysts for the growth process of CNT have been established, the main methods of detection, the fields of application, and promising directions of introduction into production are given.
Keywords: carbon nanotubes, synthesis, catalyst, purification, application.
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
M.A. Yarmolenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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PHYSICS
Villa N., Golosov D.A., Nguyen T.D. Dielectric properties of tantalum oxide thin films deposited by reactive magnetron sputtering
The article presents the results of studies of the dielectric characteristics of tantalum oxide films deposited by reactive magnetron sputtering of a Ta target in an Ar/O_{2} gas mixture. Dependencies of dielectric constant, dielectric loss tangent, band gap, leakage current density on oxygen content in Ar/O_{2} gas mixture during film deposition were established. Films with a dielectric constant of 12–30 units, a dielectric loss tangent of 0.01, a leakage current density of less than 0.1 A/cm2 at an electric field strength of 2.0õ10^{6} V/cm, and band gap of 4.5–4.85 eV, were obtained.
Keywords: tantalum oxide, reactive magnetron sputtering, MOS structure, dielectric properties.
N. Villa – Belarusian State University of Informatics and Radioelectronics, Minsk
D.A. Golosov – Belarusian State University of Informatics and Radioelectronics, Minsk
T.D. Nguyen – Belarusian State University of Informatics and Radioelectronics, Minsk
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Yiming Liu, Rogachev A.V., Yarmolenko M.A., Rogachev A.A., Xiaohong Jiang, Rudenkov A.S. Molecular structure of singlelayer and bilayer coatings, which are perspective when used in osteosynthesis processes
The features of the formation of the molecular structure of the individual layers that make up the multilayer coatings, the processing of which leads to the formation of hydroxyapatite (HA). The efficiency of using polymethylsilsesquioxane (PMSQ) as a separate layer of a multilayer coating system is estimated. It is shown that the exchange processes between the multilayer system and the buffer solution are responsible for the destruction of the crosslinked organosilicon layer. Established the formation of calcium phosphates and zinc in the interaction of etidronate and phosphorus oxide (V) with the corresponding metals.
Keywords: hydroxyapatite, polymethylsilsesquioxane, etidronate, electronbeam dispersion.
Liu Yiming – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.V. Rogachev – Faculty of Physics and Information Technology, F. Skorina Gomel State University
M.A. Yarmolenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.A. Rogachev – Faculty of Physics and Information Technology, F. Skorina Gomel State University
Jiang Xiaohong – Nanjing University of Science and Technology
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Yiming Liu, Rogachev A.V., Yarmolenko M.A., Rogachev A.A., Xiaohong Jiang, Rudenkov A.S. Bioactive multilayer coatings that initiate bone growth: structure and properties
The composition of a multilayer coating on the basis of Mg + Ca + P_{2}O_{5} applied to the surface of the intramedullary implant in order to initiate bone tissue growth has been proposed and substantiated. It is shown that the Mg + Ca + Ethidronate + P_{2}O_{5} +
Zn + P_{2}O_{5} multilayer system, which was heattreated at 200^{0} C, has high resistance to abrasion. In SBF buffer solution the layer system is transformed into HA. Influence of heat treatment is manifested in increase of structural order of separate layers.
Keywords: hydroxyapatite, polymethylsilsesquioxane, etidronate, electronbeam dispersion.
Liu Yiming – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.V. Rogachev – Faculty of Physics and Information Technology, F. Skorina Gomel State University
M.A. Yarmolenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.A. Rogachev – Faculty of Physics and Information Technology, F. Skorina Gomel State University
Jiang Xiaohong – Nanjing University of Science and Technology
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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Polyakov A.V. Recirculation method for temperature measurement by the fiber optical sensor
A new principle of physical quantities measurement is described, based on recording changes in the frequency of single optical pulses recirculation at different wavelengths in a closed fiber optic loop with their periodic regeneration in amplitude, shape and duration. It was established that the relative longterm instability of the recirculation frequency does not exceed 2õ10^{6} for fibers longer than 200 m with a measurement time of 1 s and an observation time more than 1 hour. Using numerical simulations, it was shown that the resolution of the temperature sensor is 0.15–0.1^{0} C in the temperature range 0–500^{0} C using quartz fiber with a metallic coating.
Keywords: fiber optic sensor, recirculation frequency, relative longterm instability, temperature, resolution.
A.V. Polyakov – Belarusian State University, Minsk
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Serdyukova M.A., Serdyukov A.N. A massive gravitational field in flat spacetime. I. Gauge invariance and field equations
The canonical linear theory of a massive spinless field is adapted as specialrelativistic gaugeinvariant model of gravity with a quadratic selfaction.
Keywords: scalar gravity, massive graviton, scale invariance, gravitationally dependent mass.
M.A. Serdyukova – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.N. Serdyukov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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MATHEMATICS
BeniashKryvets V.V., Yushkevich Y.A. On the Tits alternative for generalized tetraedron groups of type (2,2,N,2,2,2)
Generalized tetraedron groups have a presentation of the form
There exists a Rosenberger’s conjecture that the Tits alternative holds for generalized tetrahedron groups. This conjecture is open for groups of the form
In this paper, a number of sufficient conditions are found for fulfillment the Tits alternative for groups
Keywords: generalized tetraedron group, Tits alternative, free group, almost solvavle group.
V.V. BeniashKryvets – Belarusian State University, Minsk
Y.A. Yushkevich – M. Tank Belarusian State Pedagogical University, Minsk
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Vasilyeva T.I. On the intersections of generalized projectors with the products of normal subgroups of finite groups
Zhogal S.P., Zhogal S.I. On continuous in the mean square dependence on the initial data of solutions of one complex stochastic differential system with delay
The problems of the continuous in the mean square dependence on the initial data of the solutions of systems of differential equations containing a stochastic differential equation in partial derivatives of a hyperbolic type and ordinary stochastic differential equations with delay, which are connected by delay connections, are investigated.
Keywords: stochastic differential equations, delay, stochastic partial differential equations, units with lumped parameters, units with distributed parameters.
S.P. Zhogal – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
S.I. Zhogal – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Karaulova T.B. Injectors and Fischer subgroups of finite
soluble groups
Kniahina V.N., Chirik I.K. Finite factored groups with soluble
subnormal factors
We establish new criteria of partial solubility of a finite factored group with restrictions on indices in chains of subgroups from factors to the group. In particular, it is proved that if A and B are soluble subgroups of a group G such that there exist chains from A and B to G in which indices of neighboring nonnormal subgroups are either odd or equal to 2 or 4 and G = AB, then G is soluble.
Keywords: finite group, soluble group, factored group, generalized subnormal subgroup.
V.N. Kniahina – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
I.K. Chirik – University of Civil Protection of the Ministry for Emergency Situations of the Republic of Belarus, Minsk
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Kozlov A.A., Kalita K.D. The invariance of property of principal leading minors’ of the square matrix positivity in the similarity transformation
The set of square matrices with positive principal leading minors and the similarity transformation of them using lower triangular matrices with positive diagonal elements are discussed. The criterion of the preservation of the principal corner minors' of a matrix positivity in the similarity transformation using the abovestated transformation is established. Moreover a sufficient condition of the preservation of the positive separation property for square above mentioned matrices in the similarity transformation is obtained. The received results are planned to be further used in the theory of controllability of asymptotic invariants of linear systems of ordinary differential equations.
Keywords: invariance, similarity transformation, principal leading (corner) minors of a matrix, positive separation, lawobedience of two matrices.
A.A. Kozlov – Polotsk State University
K.D. Kalita – Polotsk State University
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Kosenok N.S., Selkin V.M., Mitsik V.N., Rizhik V.N. On finite
semispecial groups
Starovoitov A.P., Ryabchenko N.V., Volkov D.A. On the existence and uniqueness of type II Hermite – Pade polynomials
New concepts are introduced in the work. They are quite normal index and a quite perfect system of functions. Using these concepts, a uniqueness criterion was formulated and proved, explicit determinant representations of type II Hermite – Pade polynomials for an arbitrary system of power series were obtained. The results obtained complement and generalize the wellknown result in the theory of Hermite – Pade approximations.
Keywords: Hermite – Pad’e polynomials, normal index, perfect system, Hadamard determinant, Hankel determinant.
A.P. Starovoitov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
N.V. Ryabchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
D.A. Volkov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Tsekhan V.B. Complete controllability conditions for linear timeindependent system with delay in output
Strict justification and extension to the linear stationary system with delay in the equation of state and in the output of one approach to reception of complete observability conditions for systems with delay is executed. The approach is based on the reduction of the problem of complete observability of the system with delay to the problem of uniqueness of the solution of a special homogeneous boundary value problem for a system of differential equations without delay in the extended state space. The necessary and sufficient conditions for complete observability, complete identifiability are proved. Complete observability, identifiability in the sense of unambiguous reconstruction of an unobservable piece of the trajectory on the time period of the delay length by the known output function are proved. The conditions are of rank type and are expressed in terms of matrices of the original observation system.
Keywords: complete observability, complete identifiability, time delay, output, criterion.
V.B. Tsekhan – Yanka Kupala State University of Grodno
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INFORMATION SCIENCE
Dravitsa V.I., Reshetniak A.V., Yakushkin Å.À. Bases of digital monitoring of objects marked with RFID tags
A model of physical events to provide digital monitoring. RFIDobjects is described in accordance with the requirements of international standards ISO/IEC 19987: 2017 Information technology  EPC Information Services (EPCIS) Standard and ISO/IEC 19988: 2017 Information technology  Core Business Vocabulary Standard. Both of these standards are designed to be used together. Using standardized vocabulary provided CBV standard, is critical to ensure unambiguous identification of RFIDobjects using EPCIS services.
Keywords: EPC Information Services, Core Business Vocabulary, GS1, traceability in supply chains.
V.I. Dravitsa – Centre for Identification Systems, Minsk
A.V. Reshetniak – Centre for Identification Systems, Minsk
Å.À. Yakushkin – Centre for Identification Systems, Minsk
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