Green’s functions of the quasipotential approach of quantum field theory are found in the relativistic configurational representation and are expressed in terms of elementary functions in case of scattering states characterized by orbital quantum number l = 1 (p-states). Asymptotic properties of the Green’s functions are determined at large values of the relativistic coordinate. It is shown that all the Green’s functions coincide in the nonrelativistic limit with the partial Green’s function of the Schrodinger equation. The equations for the corresponding partial wave functions of the scattering states are solved exactly in case of spherically symmetric potentials «δ-sphere» and their superpositions. Characteristic features of the behavior of partial scattering cross sections for such potentials are determined.

Keywords: Green’s functions, quasipotential approach, relativistic configurational representation, scattering states, p-states, delta-function potential.

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

A.A. Grishechkina – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

The polarization and energy characteristics of diffracted zero- and first-order waves under Bragg diffraction of light on holographic phase gratings in a “reoksan” medium with a significant amplitude of the refractive index of the recording medium are theoretically investigated. It is founded that the reflection and transmission coefficients of diffracted waves for the s- and p-polarization of incident light experience significant changes when the refractive index of the layer is modulated. It is shown that under the conditions of Fresnel reflection of light waves from the boundaries of the modulated layer and the increase in the amplitude of the perturbation of the refractive index of the medium, there is a significant rotation of the polarization plane of the diffracted wave for the transmitted and reflected diffraction orders.

Keywords: holographic phase grating, Bragg light diffraction, Fresnel reflection, reflection and transmission coefficients, light modulation, holographic “reoksan” medium.

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

V.N. Naunyka – I.P. Shamyakin Mozyr State Pedagogical University

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

The problem of computer implementation of calculating of the stress-strain state of laminated pipes made of composites and determining the wave velocity during water hammer is solved. Two variants of the problem are considered: a pipe with an inner coating consisting of a functionally gradient material, and a pipe with an inner coating of a composite, a fibrous composite consisting of a matrix and fibers, the elastic modulus of which is determined by the rule of mixtures.

Keywords: laminated pipe, functional-gradient material, composite, lined pipe, stress-strain state, wave velocity.

V.V. Mozharovsky – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

S.V. Kirhintsava – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

The displacements in a circular physically nonlinear three-layer plate under axisymmetric thermal force loading in its plane are investigated. For thin bearing layers, the relations of the theory of small elastic-plastic deformations are used. A relatively thick filler is physically non-linearly elastic. The distributed load depends on the radial coordinate and is applied in the median plane of the filler. Systems of differential equations of equilibrium in forces and in displacements are given. To solve the boundary value problem, an iteration method based on the Ilyushin elastic solution method is proposed. The numerical approbation of the obtained solution is carried out.

Keywords: round three-layer plate, displacements, axisymmetric tension-compression, plasticity.

A.V. Nestsiarovich – Belarusian State University of Transport, Gomel

Modeling of the process of laser splitting of quartz glasses obtained by the sol-gel method using artificial neural networks and the finite element method was carried out. To form a training data set and data for testing neural networks, calculations of temperature fields and fields of thermoelastic stresses were performed using the finite element method in the ANSYS program. Calculations were completed for 875 variants of input parameters, 800 of which were used for training neural networks. The influence of the architecture of the neural network, the size of the training data array, and the training time on the accuracy of determining thermoelastic stresses and temperatures in the zone of laser processing of quartz sol-gel glasses were investigated.

Keywords: neural network, laser splitting, quartz plate.

Y.V. Nikitjuk – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

A.N. Serdyukov – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

V.À. Prohorenko – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

I.Y. Aushev – University of Civil Protection of the Ministry for Emergency Situations of the Republic of Belarus, Minsk

The morphological features and phase composition of carbon coatings doped with silicon and titanium are considered. It is shown that silicon doping of carbon-titanium coatings leads to a decrease in the content of sp²-hybridized clusters, free graphite atoms due to the formation of Si-C bonds, an increase in roughness, and some improvement in the hydrophobic properties of the surface.

Keywords: carbon coatings, silicon, titanium, morphology, phase composition, surface energy.

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

A.V. Rogachev – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

D.G. Piliptsou – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

The cosmological application of the proposed early special-relativistic gauge-invariant theory of a massive gravitational field predicts the existence in the universe of a dynamical spatially uniform background gravitational field with a single non-zero time component, which dominates in Universe controlling its cyclic evolution through the balanced exchange of energy with gravitating matter. The previous and continuing increase in the rest energy of matter perfectly explains the cosmological redshift of atomic spectra without the hypothesis of a general recession of distant galaxies. The excellent numerical agreement of theory with the data from SNe Ia is achieved by fitting only two parameters: the age of the current cycle (24 Gyr) and the current value of the background scalar strength expressed through the Hubble constant (68 kms^–1 Mpc^–1). The predicted cosmological acceleration of the decay of unstable nuclei and particles is confirmed by (1 + z)-stretching of the light curves of SNe Ia, the observed afterglow of which occurs owing to the high-energy gamma-ray photons released in the chain of beta decays ⁵⁶Ni→⁵⁶Co→⁵⁶Fe.

Keywords: background gravitational field, secular drift of atomic spectra, cosmological redshift, optical radiation of type Ia supernovae.

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

A.N. Serdyukov – Faculty of Physics and Information Technology, Francisk Skorina Gomel State University

The bending of a circular three-layer plate with an asymmetric thickness under neutron irradiation conditions is considered. The axi-symmetric continuous load is perpendicular to the plate plane. The kinematics of the package is described using the polyline hypothesis. For load-bearing layers, the Kirchhoff hypotheses are accepted. The relatively thick filler obeys Timoshenko's hypothesis about the straightness and incompressibility of the deformed normal. The work of tangential stresses in the filler is taken into account. Differential equilibrium equations are obtained by the Lagrange variational method. The contour of the plate is pivotally supported. The statement of the boundary value problem for finding the three desired functions: deflection, shear and radial displacement of the median plane of the filler is given. The solution for a uniformly distributed load is obtained in the final form. Its numerical parametric analysis is carried out.

Keywords: three-layer circular plate, bending, distributed axisymmetric load, elasticity, neutron irradiation.

E.I. Starovoitov – Belarusian State University of Transport, Gomel

The article goes on with the studies on the described earlier relationship between sets of generators in group A and sets of generators in polyadic group < A^k, [ ]_{l, σ, k} > with l-ary operation [ ]_{l, σ, k} that is defined on Cartesian power A^k of group A for arbitrary integer l ≥ 2 and arbitrary substitution σ from the set S_k of all substitutions of the set {1, 2, …, k}.

Keywords: group, l-ary group, set of generators.

A.M. Gal'mak – Belarusian State University of Food and Chemical Technologies, Mogilev

A finite non-nilpotent group G is called B-group if every proper subgroup of the quotient group G / Ô(G) is nilpotent. In this paper, it is established that the metanilpotency of a finite group for which the derived subgroup of each B-subgroup is subnormal.

Keywords: finite group, B-group, subnormal subgroup, derived subgroup.

V.N. Kniahina – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

Throughout the article, all groups are finite and G always denotes a finite group. Moreover, σ is some partition of the set of all primes , i. e. where and for all A σ-property of a group is any of its properties that do not depend on the choice of the partition σ of the set . This work is devoted to further the study of the σ-properties of a group. A lot of known results are generalized.

Keywords: finite group, σ-nilpotent group, σ-soluble group, σ-subnormal subgroup, Schmidt group.

I.N. Safonova – Belarusian State University, Minsk; Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University

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

The paper considers one of the original solutions of the photovoltaic thermoelectric battery, which was implemented in the COMSOL Multiphysics software environment. Furthermore, the diurnal and seasonal variations of the ambient temperature and the effects of the concentrated solar radiation were taken into account. The temperature patterns in the different sections of the battery as well as the tem-perature gradient patterns inside the thermoelectric converters are calculated. It is shown that the increasing of the output voltage up to maximum values of 0,635 and 0,78 V in January and July, respectively, was achieved due to the temperature stabilization of the back side of the external electrodes.

Keywords: numerical simulation, COMSOL Multiphysics, photo- and thermoelectric converters, concentrated solar radiation, temperature gradient, output voltage.

A.K. Esman – Belarusian National Technical University, Minsk

G.L. Zykov – Belarusian National Technical University, Minsk

V.A. Potachits – Belarusian National Technical University, Minsk

The results of the review and analysis of ways to represent the input characteristics of radio engineering systems are considered. The results of the work of the method for finding adequate mathematical models of radio engineering devices in an analytical form are pre-sented.

Keywords: approximation, frequency characteristics, mathematical models of radio engineering systems, broadband matching, radio engineering.

V.O. Isaev – Military Academy of the Republic of Belarus, Minsk

P.V. Boykachev – Military Academy of the Republic of Belarus, Minsk

The principles of construction of an adaptive control system are described for technological cycle of production with external control ac-tions. Adaptive control feedback connections are created based on data processing for the neuroregulator model and the simulation model included in the technical means of coupling with the control system and the database for the simulation model of a technological cycle of production. Formalization of an adaptive control process that uses neural network based modeling for decision making proc-esses is given. Neuroregulator models, their training and testing procedures are described.

Keywords: adaptive control, technological production process, neural network, neuroregulator, phase plane of states, optimal trajectory.

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

V.À. Prohorenko – Faculty of Mathematics and Programming Technologies, Francisk Skorina Gomel State University