The main methods of forming coatings based on boron and carbon are considered. The main phase States formed during the synthesis of such coatings are described. Attention is paid to the analysis of the relationship between the structure and mechanical properties. A method and device for deposition of boron-carbon coatings from combined flows of carbon plasma formed by electrospark evaporation of graphite cathode by pulsed arc and boron ions generated by evaporation of the target by pulsed laser radiation is proposed.

Keywords: carbon coatings, doped, boron, microhardness, wear, coefficient of friction.

B. Zhou – Nanjing University of Science and Technology

D.G. Piliptsov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

X. Jiang – Nanjing University of Science and Technology

E.A. Kulesh – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Download PDF (427 KB)

---

It is shown that, for Bessel light beam, it is possible to separately observe isotropic and anisotropic Bragg diffraction of circularly polarized waves on Lamb modes in gyrotropic cubic crystals. In this case, the effective acousto-optical interaction in the transmitted and reflected diffraction orders is realized in a narrow range of layer thickness near the mode cut-off thickness. Of greatest for acousto-optic diagnostics of Lamb modes is the zero mode of a Bessel light beam under the condition of isotropic diffraction of circularly polarized waves with accurate transverse phase synchronism of the diffracted beams.

Keywords: plan-parallel slab, Lamb's waves, acousto-optical diffraction, gyrotropic cubic crystal, reflection coefficients and transmission coefficients.

G.V. Kulak – I.P. Shamyakin Mozyr State Pedagogical University

G.V. Krokh – I.P. Shamyakin Mozyr State Pedagogical University

Ò.V. Nikolaenko – I.P. Shamyakin Mozyr State Pedagogical University

Download PDF (459 KB)

---

Previously, the nonrelativistic problems of a vector particle in the Coulomb field on the background of Lobachevsky and Riemann space models were studied, when a s modified Duffin - Kemmer equation was applied with additional spin-orbital interaction, which permitted to get three independent second order differential equations in nonrelativistic Pauli-like approximation and obtain three series of energies levels. However, the states with minimal value for quantum number of total angular momentum j=0 were not considered, in the present paper these states are investigated. Conventional and modified Duffin - Kemmer equations provide us with solutions in hypergeometric and transcendental general Heun functions, even without transition to the nonrelativistic limit. These equations lead to slightly different energy spectra. Because the difference between two energy spectra at j=0 turn out to be insignificant, we may expect similar property for states with larger values of j, even though solutions for conventional equation in Pauli approximation are not known.

Keywords: particle with spin 1, Duffin - Kemmer equation, Coulomb potential, minimal values of total angular momentum, Heun equation, exact solution, energy spectrum.

E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University

A.D. Koral'kov – I.P. Shamyakin Mosyr State Pedagogical University

Download PDF (285 KB)

---

The paper aims to identify the interaction patterns of the microwaves with the metamaterials, consisting of rectangular omega elements, as well as to develop a one-sided and double-sided “ideal” microwave absorber based on such structures.

Keywords: omega-element, metamaterial, absorber, microwave range, reflection, absorption.

I.V. Semchenko – F. Skorina Gomel State University

S.A. Khakhomov – F. Skorina Gomel State University

A.L. Samofalov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

I.A. Faniayeu – Faculty of Physics and Information Technology, F. Skorina Gomel State University

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

Y. Song – Nanjing University of Science and Technology

S. Fan – Nanjing University of Science and Technology

J. Wang – Jiangnan University, Wuxi

Download PDF (4,42 MB)

---

For a linear massive spinless field adapted as a gauge-invariant model of gravity in the framework of the special theory of relativity, a canonical energy-momentum tensor is constructed and the laws of conservation of energy and momentum are formulated. It is shown that the general requirement of a positive definiteness of the energy density of any physical reality in the case of an attractive field de-termines its scalar nature and far-reaching gravitational variability of the inertial mass of matter particles.

Keywords: spinless massive gravity, gravitational energy, variable 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

Download PDF (315 KB)

---

It is shown that a change in the inertial mass of unstable particles (and atomic nuclei) in a scalar gravitational field that occurs as a result of the transfer of part of the rest energy of particles to the field, or, conversely, when their rest energy increases due to accretion of field energy, is accompanied by a change in the rate of radioactive decay. The application of the scalar theory of gravity to the homogeneous universe predicts the secular acceleration of the rate of decay of unstable nuclei and particles in the current era. On a cosmological time scale, this process is confirmed by the observed (1+z)-stretching of the light curves of supernovae type Ia afterglow caused by the hard gamma-radiation from the decaying unstable 56Ni and 56Co nuclides created by the explosion of accreting white dwarfs.

Keywords: spinless massive gravity, variable mass, radioactive decay.

M.A. Serdyukova – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Download PDF (227 KB)

---

The analytical evaluation of the hysteresis reflection properties of a thin layer on the basis of a dense resonant medium on the power scale and the linear frequency detuning of the external signal is carried out. The role of such a resonant reflector as a Q-factor (compact modulator) of the resonator in the laser circuit is determined.

Keywords: resonant reflection, thin optical films, dense resonant medium, dipole-dipolar interaction, quasi-resonance polarization.

E.V. Timoschenko – Mogilev State A. Kuleshov University

Yu.V. Yurevich – Mogilev State University of Food Technologies

Download PDF (466 KB)

---

Based on the design experience of traditional helical antenna and multi-layer PCB structure, a multi-layer PCB bifilar helical antenna that works in C band is proposed in this paper. The antenna is composed of several symmetrical metal arcs, which are distributed on different layers and connected by plated via-holes. Meanwhile, the design and the simulation results are given in the paper. The results show that the antenna has low profile, circularly polarized radiation and better impedance matching, providing a novel solution for the design of multi-layer structure antenna.

Keywords: low profile, bifilar helical antenna, multi-layer PCB, circular polarization.

J. Zhao – Nanjing University of Science and Technology

Y. Song – Nanjing University of Science and Technology

L. Wang – Nanjing University of Science and Technology

I.V. Semchenko – F. Skorina Gomel State University

A.L. Samofalov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Download PDF (458 KB)

---

The method of embedding of the space of distributions on the circle into the algebra of mnemofunctions was considered in this paper. The subalgebra of mnemofunctions, generated by rational mnemofunctions, was detached. A complete description of this subalgebra was given. Its generators were singled out, the multiplication rule of distributions in this subalgebra was formulated explicitly.

Keywords: mnemofunction, analytical representation of distribution, algebra of rational mnemofunctions.

A.B. Antonevich – Belarusian State University

T.R. Shahava – Belarusian State University

Download PDF (325 KB)

---

The following is proved: A finite group G is p-supersoluble if and only if it has a normal subgroup N with p-supersoluble quotient G/N such that either N is p'-group or p divides |N| and |G:N_G(L)| equals to a power of p for any cyclic p-subgroup L of N of order p or order 4 (if p=2 and a Sylow 2-subgroup of N is non-abelian).

Keywords: finite group, p-nilpotent group, p-supersoluble group.

I.M. Dergacheva – Belarusian State University of Transport

E.A. Zadorozhnyuk – Belarusian State University of Transport

I.P. Shabalina – Belarusian State University of Transport

Download PDF (257 KB)

---

Single-frequency oscillations in a van der Pol self-oscillating system with delays in the feedback circuit and from the reflected load under simultaneous additive and multiplicative random influences are investigated.

Keywords: stochastic differential equations, single-frequency oscillations, delay, van der Pol oscillator, additive random effects, multiplicative random effects.

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

A.I. Kulyba – F. Skorina Gomel State University

Download PDF (227 KB)

---

Let be some partition of the set of all primes. In this paper the problem of permutability of -subnormal subgroups of finite group is established.

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

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

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

Download PDF (264 KB)

---

The problem of the given motions realization of dynamic systems in the bounded control class is considered. The regulator operation algorithm is constructing with optimal control methods. According to this algorithm, in real-time, the current values of limited feedbacks are calculated (generates), with the help of which the closed-loop system stably carries out a given movement. To solve the problem the feedback optimal control realization of linear-quadratic problem with restrictions is suggested. The results are illustrated on the problem of dynamic systems synthesis, realizing limited cycles.

Keywords: dynamic system, given motions realization problem, bounded stabilizing feedback, auxiliary optimal control problem, regulator.

A.V. Lubochkin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Download PDF (310 KB)

---

The identification of a linear source for the third-order single equation that describes the propagation of longitudinal waves in a dispersive medium with an integral condition of the first kind is investigated. At first, the original problem reduces to an equivalent problem in a certain sense. Using the Fourier method, the equivalent problem is reduced to solving a system of integral equations. With the help of the method of compressed mappings, the existence and uniqueness of the solution of a system of integral equations, which is also the only solution to an equivalent problem, are proved. Using equivalence, it is possible to prove the existence and uniqueness of the classical solution of the original problem.

Keywords: inverse problem, third-order equations, Fourier method, classical solution.

Ya.T. Mehraliev – Baku State University

U.S. Alizade – Baku State University

Download PDF (315 KB)

---

A subgroup A of a group G is called seminormal in G, if there exists a subgroup B such that G=AB and AB₁ is a proper subgroup of G for every proper subgroup B₁ of B. We introduce the new concept that unites subnormality and seminormality. A subgroup A of a group G is called semisubnormal in G, if either A is subnormal in G, or is seminormal in G. In this paper we proved the supersolubility of a group G under the condition that all Sylow subgroups of two non-conjugate maximal subgroups of G are semisubnormal in G. Also we obtained the nilpotency of the second derived subgroup (G')' of a group G under the condition that all maximal subgroups of two non-conjugate maximal subgroups are semisubnormal in G.

Keywords: supersoluble groups, semisubnormal subgroup, derived subgroup, Sylow subgroup, maximal subgroup.

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

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

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

Download PDF (285 KB)

---

In this paper one construction of composition formations was introduced. This construction contains formations of quasi--groups, ñ-supersoluble groups and groups defined by ranks of chief factors. The structure of groups from introduced formations was described. As corollaries some results of different authors were obtained. A question of L.A. Shemetkov about the intersection of -maximal subgroups and the -hypercenter was investigated for these formations.

Keywords: finite group, ñ-supersoluble group, quasinilpotent group, quasi--group, hereditary local formation, composition formation, -maximal subgroup, -hypercenter.

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

Download PDF (319 KB)

---

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 I Hermite – Pade polynomials for an arbitrary system of power series were obtained. The results obtained complement and generalize the well-known result in the theory of Hermite – Pade approximations.

Keywords: Hermite-Pade 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

A.À. Drapeza – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Download PDF (252 KB)

---

V.I. Zenkov put in the Kourovskaya notebook the following problem 19.109: is it true that in a non-abelian finite simple group G all maximal subgroups are Hall subgroups if and only if every second maximal subgroup is pronormal in G? This paper shows that this problem is solved negatively.

Keywords: finite group, second maximal subgroup, pronormal subgroup.

V.N. Tyutyanov – International University MITSO, Gomel

Download PDF (248 KB)

---

A group is called primary if it is a finite p-group for some prime p. If is some partition of that is, and for all then we say that a finite group G is: -primary if it is a -group for some i; -nilpotent if for some -primary groups If for some primary non-identity subgroup A of G, then we say that is a local section of G. In this paper, we study a finite group G under hypothesis that all proper local sections of G belong to a saturated hereditary formation and we determine the normal structure of G in the case when all local sections of G are -nilpotent.

Keywords: finite group, hereditary saturated formation, -hypercentre, local section, -nilpotent group.

B. Hu – Jiangsu Normal University, Xuzhou

J. Huang – Jiangsu Normal University, Xuzhou

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

Download PDF (269 KB)

---

The automated design and calculation of various types of the bases of a small depth are presented. The change under loading of physicomechanical characteristics of soil of the bases is considered. The created application allows making calculations, according to the norms and rules of Construction Norms and Regulations. For writing of web service the framework of Spring and architectural style of programming of REST are used. Interaction of the user with web service is realized through the client application on the basis of the JavaFX technology.

Keywords: base, soil, layers, levels, buildings and constructions, loadings, diagnostics, report, design.

A.V. Glubokov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

M.I. Zhadan – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

E.M. Berezovskaya – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Download PDF (676 KB)

---

The problems of development, tool filling, and usages of the integrated program complex of the composer of digital geological models are considered. Possibilities of interactive graphics visualization and comparison of results are marked. The results of application of artificial neural networks in the analysis and interpretation of geospatial data are presented and discussed.

Keywords: digital geological model, Computer Algebra System Mathematica, interactive graphics visualization, artificial neural network.

V.B. Taranchuk – Belarusian State University, Minsk

Download PDF (1,15 MB)

---