
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N1 (22) 2015
PHYSICS
Zenevich A.O. A method of measuring the distribution of singlephoton pulses
The way to improve the accuracy of the measurement of the statistical distribution of singlephoton 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
Download PDF (303 KB)
Kapshai V.N., Danilchenko M.S., Grishechkin Y.A. Covariant equations and resonance states of twoparticle systems with
function potentials
The complex resonance energy (rapidity) spectra of relativistic two particle systems are found on the basis of exact solutions of the covariant twoparticle 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 twoparticle 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
Download PDF (329 KB)
Kulak G.V., Matveeva A.G., Nikolaenko T.V. Features of opticalacoustical diagnostics of wedgeshaped defects of solids
The participants of the opticalacoustical diagnosing of wedgeform 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 wedgeform defects, at the approximation different from Rayleigh allows determining the size of the defect, angle at the vertex of the wedge, angle of the inclination and location.
Keywords: opticalacoustical diagnosing, wedgeform 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
Download PDF (422 KB)
Sotsky A.B., Parashkov S.O., Vasilenko A.N. Reflection of the TE polarized light from a metallic film at the anomalous skin effect
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
Download PDF (404 KB)
Timoschenko E.V., Yurevich Yu.V. Nonlinear susceptibility of the thin film of dense resonant medium
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, dipoledipolar interaction.
E.V. Timoschenko – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
Yu.V. Yurevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
Download PDF (417 KB)
Faniayeu I.A., Semchenko I.V., Khakhomov S.A., Samofalov A.L. Uniaxial electrically thin rotator of polarization of electromagnetic waves
The realization of uniaxial polarization rotator of electromagnetic waves formed by array of smooth oneturn 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 Sband are studied.
Keywords: polarization rotator, oneturn helix, polarizability, co and crosspolarizations.
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
Download PDF (564 KB)
Shershnev E.B., Nikitjuk Yu.V., Shershnev A.E., Sokolov S.I. Features of formation of thermoelastic fields at laser processing of diamond crystals
Calculation of the thermoelastic fields formed in crystals of diamond upon exposure of laser radiation along the axes of symmetry of the second (L_{2}), the third (L_{3}) and the fourth (L_{4}) 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
Download PDF (389 KB)
Shushkevich G.Ch., Shushkevich S.V., Kuts A.I. Scattering of the electric dipole field on the thin unclosed spherical shell and ball
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
Download PDF (552 KB)
MATHEMATICS
Antonevich A.B., Shukur Ali A. Estimation of resolvents for discrete weighted shift operators
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
Download PDF (338 KB)
Astafyeva A.V. Asymptotics of diagonal Hermite – Pade approximants for a system of four exponentials
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, saddlepoint method.
A.V. Astafyeva – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (355 KB)
Belokursky M.S. On coincidence of reflecting functions of the quasiperiodic and periodic differential systems
Sufficient conditions for equivalence in sense of Mironenko of the quasiperiodic and periodic differential systems were obtained.
Keywords: reflecting function, equivalence, differential system, quasiperiodic system.
M.S. Belokursky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (320 KB)
Buzlanov A.V. Finite soluble groups with metanilpotent maximal subgroups
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
Download PDF (323 KB)
Vasilyev V.A. On
hypercentrally embedded subgroups of finite groups
Gal'mak A.M. lAry subgroups of general linear
lary group
The lary subgroups of general linear lary group are studied.
Keywords: general linear group, lary group, vectormatrice, determinant, vectordeterminant.
A.M. Gal'mak – Mogilev State University of Food Technologies, Mogilev, Belarus
Download PDF (344 KB)
Kamornikov S.F. On the lattice of all solvable regular transitive subgroup functors
Murashka V.I. Soluble formations with the Shemetkov property
Tyutyanov V.N. Finite groups with
subnormal Schmidt subgroups
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
Download PDF (330 KB)
INFORMATION SCIENCE
Demidenko O.M., Kucherov A.I. Comparative analysis of mathematical methods to improve the reliability of the information and technical systems
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
Download PDF (350 KB)
TECHNICS
Zaplatnikov S.S., Khizhniak A.V., Sheviakou A.V. Lowering of failure probability in correlation tracking systems of optically observable objects
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
Download PDF (567 KB)
