The way to improve the accuracy of the measurement of the statistical distribution of single-photon impulses by eliminating the errors introduced by dark impulses is proposed.

Keywords: single photon pulses, photon counter, statistical distribution of single photon pulses.

A.O. Zenevich – Higher State College of Communications, Minsk, Belarus

The complex resonance energy (rapidity) spectra of relativistic two particle systems are found on the basis of exact solutions of the covariant two-particle equations with -function potential and a superposition of two -function potentials. It is established that the exact partial two particle relativistic amplitudes have resonance behavior precisely at those energy (rapidity) values, which correspond to the real part of the complex resonance energies.

Keywords: relativistic two-particle equations, relativistic configuration representation, -function potential, resonance state, scattering amplitude, scattering cross section.

V.N. Kapshai – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

M.S. Danilchenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Yu.A. Grishechkin – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The participants of the optical-acoustical diagnosing of wedge-form defects in solid state body is investigated. It is shown that due to interferential effects scattering efficiency varies nonlinearly with an increase of defect size, reaching a maximum at a certain amount of it. It has been established that the study of the pulse energy characteristics of ultrasonic scattering radiation on the wedge-form defects, at the approximation different from Rayleigh allows determining the size of the defect, angle at the vertex of the wedge, angle of the in-clination and location.

Keywords: optical-acoustical diagnosing, wedge-form defect, ultrasonic wave, ultrasonic scattering, relative intensity.

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

A.G. Matveeva – I.P. Shamyakin Mosyr State Pedagogical University, Mozyr, Belarus

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

The theory of optical skin effect at the excitation of a metallic film by an obliquely incident TE polarized plane wave is developed. Analytical expressions for the electric field in the film and for the film reflectance that contain separated contributions of the normal and anomalous skin effects are obtained with the use of the perturbation method. Angular reflectance spectra for Ag, Au and Ti films are investigated numerically. It is shown, that the accuracy of the normal skin effect approximation is reduced with decreasing of the film thickness. The use of this approximation in solving of the inverse problem of optical reflectometry of Ag and Au films of few nanometers in thickness led to significant errors for the reconstructed parameters of the films.

Keywords: anomalous skin effect, metallic film, reflectance of light, inverse optical problem.

A.B. Sotsky – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

S.O. Parashkov – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

A.N. Vasilenko – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

The computing estimation of a dielectric susceptibility dispersive dependence of a thin layer of the dense resonant medium taking into account absorption saturation is carried out. The possibility of bistability in Lorentz complex function and hysteresis jumps in film resonant reflection are specified.

Keywords: thin optical films, resonant reflection, dipole-dipolar interaction.

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

Yu.V. Yurevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus

The realization of uniaxial polarization rotator of electromagnetic waves formed by array of smooth one-turn helices is presented. Helices have a simple form that makes them more preferred for a practical point than compared to other chiral elements. The calculation of the electric field obtained theoretically and by computer simulation is shown. Experimental researches in the S-band are studied.

Keywords: polarization rotator, one-turn helix, polarizability, co- and cross-polarizations.

I.A. Faniayeu – F. Skorina Gomel State University, Gomel, Belarus

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

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

A.L. Samofalov – F. Skorina Gomel State University, Gomel, Belarus

Calculation of the thermoelastic fields formed in crystals of diamond upon exposure of laser radiation along the axes of symmetry of the second (L₂), the third (L₃) and the fourth (L₄) order is executed. The received results can be used for optimisation of the process of laser processing of diamond crystals.

Keywords: laser treatment, diamond, graphite, finite element method.

E.B. Shershnev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

Yu.V. Nikitjuk – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.E. Shershnev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

S.I. Sokolov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The analytical solution of the boundary problem, describing the scattering of the electric dipole field, located inside perfectly conducting thin unclosed spherical shell and on a permeable ball. For some parameters of the problem directivity pattern of the electric field is constructed.

Keywords: electric dipole, dual series equations, infinite system of linear algebraic equations of the second kind with a completely continuous operator, directional diagram of the electric field.

G.Ch. Shushkevich – Y. Kupala Grodno State University, Grodno, Belarus

S.V. Shushkevich – Y. Kupala Grodno State University, Grodno, Belarus

A.I. Kuts – Y. Kupala Grodno State University, Grodno, Belarus

A lower estimation for the norm of a resolvent operator, the spectrum of which is a unite circle is considered. It is shown that for arbitrary function that is analytic on a unit circle, there exist an operator such that its resolvent norm is greater than

Keywords: resolvent, discrete weighted shift operator.

A.B. Antonevich – Belarusian State University, Minsk, Belarus

Ali A. Shukur – Belarusian State University, Minsk, Belarus

Asymptotic properties of diagonal Hermite – Pade approximants of type I for exponential system with arbitrary real are studied. The obtained theorems complement the results of P. Borwein and F. Wielonsky.

Keywords: Hermite – Pade approximants of type I, asymptotic equality, saddle-point method.

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

Sufficient conditions for equivalence in sense of Mironenko of the quasi-periodic and periodic differential systems were obtained.

Keywords: reflecting function, equivalence, differential system, quasi-periodic system.

M.S. Belokursky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The structure of a finite soluble group with two maximal subgroups belonging to the local subformation of the formation of all metanilpotent groups, one of which is selfnormalizable and the other is normalizable is studied.

Keywords: finite group, soluble group, maximal subgroup, metanilpotent groups, local formation.

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

A subgroup M of a group G is a modular subgroup in G if the following conditions are true: (1) for all with and (2) for all with Conditions for -embedding of hypercentral subgroups of finite groups with given modular primary subgroups are found.

Keywords: finite group, modular subgroup, Sylow p-subgroup, -hypercentre.

V.A. Vasil’ev – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The l-ary subgroups of general linear l-ary group are studied.

Keywords: general linear group, l-ary group, vector-matrice, determinant, vector-determinant.

A.M. Gal'mak – Mogilev State University of Food Technologies, Mogilev, Belarus

The properties of the lattice of all regular transitive subgroup functors are investigated. The notion of -subnormal subgroup functor is introduced. It is proved that the set of all -subnormal subgroup functors is a sublattice and ideal of the lattice . The connection of lattices and is investigated. The existence of a congruence defined on such that the lattices and are isomorphic, in particular, is proved.

Keywords: finite solvable group, subgroup functor, regular transitive subgroup functor, lattice, congruence, isomorphism of lattices.

S.F. Kamornikov – Gomel Branch of International University «MITSO», Gomel, Belarus

All saturated soluble formations whose all s-critical groups are soluble were described. With every local formation such that for all and otherwise, was associated directed graph without loops whose vertices are prime numbers from and is an edge of if and only if . With the help of such kind’s graphs all hereditary soluble formations with the Shemetkov property were described.

Keywords: minimal simple group, s-critical group, hereditary local formation, formation with the Shemetkov property, graph associated with formation.

V.I. Murashka – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The solvability of the finite group in which any Schmidt subgroup is -subnormal, was proved.

Keywords: finite group, Schmidt subgroup, -subnormal subgroup.

V.N. Tyutyanov – Gomel Branch of International University, Gomel, Belarus

The mathematical methods for determining the reliability of the information and technical systems are described.

Keywords: reliability, information system, technical system.

O.M. Demidenko – Prorector of F. Skorina Gomel State University, Gomel, Belarus

A.I. Kucherov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

The typical automatic tracking correlation system of optical observable objects is described. Influence of background components of the reference image on the efficiency of tracking algorithm is considered. The method of lowering of probability of tracking failure caused by the influence of background components is offered and justified. Results of the experiments confirming efficiency of the offered decision are presented.

Keywords: tracking algorithms, correlation functions of images, tracking failure, reference images.

S.S. Zaplatnikov – Military Academy of the Republic of Belarus, Minsk, Belarus

A.V. Khizhniak – Military Academy of the Republic of Belarus, Minsk, Belarus

A.V. Sheviakou – Military Academy of the Republic of Belarus, Minsk, Belarus