PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (24) 2015
Beams of Kummer without the Gaussian apodization with transferable terminating power
The new solutions of the parabolic equation featuring paraxial light beams are offered. Such beams are featured by Kummer functions of complex argument with two free parameters without a Gaussian. Restrictions on these parameters, at which beams of Kummer transfer terminating power and are physically realized, are discovered.
Keywords: paraxial beams, beams of Kummer, square integrability.
S.S. Girgel – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (286 KB)
Propagation of singular beams in a cubic optically active photorefractive crystal
The features of the propagation of singular beams with various signs of the topological charge in a cubic optically active photorefractive crystal of
cut, to which an external electric field is applied, are investigated. The dependence of the angle of rotation of the sin-gular beam on value of external electric field applied to the crystal and sign of unit topological charge of the beam is analyzed. It is shown how the optical activity affects the distribution of singular beam in the crystal.
Keywords: singular beam, photorefractive crystal, optical activity.
Zh.V. Kolyadko – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
Download PDF (849 KB)
V.V. Shepelevich – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
V.V. Davydovskaya – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
The movement of the metal nanoparticles near the surface of the air bubble in the liquid by the radiation pressure force
The effect of laser radiation pressure on the metal nanoparticles located near an air bubble in water is experimentally investigated. The reasons of the observed movement of nanoparticles along a bubble surface are discussed.
Keywords: light pressure of laser radiation, metal nanoparticles.
E.V. Matuk – Y. Kupala Grodno State University, Grodno, Belarus
Download PDF (393 KB)
L.S. Gaida – Y. Kupala Grodno State University, Grodno, Belarus
D.V. Guzatov – Y. Kupala Grodno State University, Grodno, Belarus
Electromagnetic field in the Majorana – Oppenheimer formalism in the anti de Sitter Universe
Exact solutions with spherical symmetry of the Maxwell equations in the oscillating anti de Sitter Universe are constructed. 3-Dimensional complex formalism by Majorana – Oppenheimer, generalized to pseudo-Riemannian space-time models in accordance with the tetrad method, is applied. The established dependence of the constructed solutions on the time variable leads to independence of the Pointing vector on time. This means that the change in time of the anti de Sitter geometry cannot be seen by measuring the energy flow density.
Keywords: Maxwell's equations, tetrad formalism, anti de Sitter Universe, non-static coordinates, complex formalism of the Majorana – Oppenheime, exact solutionsr.
Å.Ì. Ovsiyuk – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
Download PDF (319 KB)
Influence of metal concentration on the phase composition, structure and properties of carbon-metal coating
The morphological features, phase composition, microhardness and tribological properties of composite carbon coatings formed by co-precipitation of carbon plasma streams of pulsed cathodic arc discharge and flows of atoms of the metal ions (Cr, Ti, Cu) generated by magnetron sputtering, and their dependence on the power source sputtering are determined. It is shown that such layers are characterized by high density and order of sp2-clusters and low roughness. The hardness increases and the wear rate of counterbody decreases with in-creasing the power of magnetron.
Keywords: carbon coatings, sp2-clusters, alloying, magnetron, phase composition, morphology, roughness, hardness, friction, wear.
A.S. Rudenkov – F. Skorina Gomel State University, Gomel, Belarus
Download PDF (956 KB)
Analytical solution of the inverse problem of a spectrophotometer absorbing layer on an absorbing substrate with a dielectric layer
On the example of a two-layer structure of a semiconductor – insulator – semiconductor the possibility of an analytical determination of the optical parameters and thickness of the upper layer on the reflection spectrum envelope at normal incidence of light is considered. It is very difficult to calculate these functions even in the case of absence of the transition zones between the layers. Mismatching enve-lopes calculated and measured reflection coefficients in certain areas of the spectra indicates the presence of inhomogeneous surface and transition zones in real structures pSi – SiO2 – cSi.
Keywords: bilayer structure, optical spectra, envelopes extrema, transition layers, pSi – SiO2 – cSi.
N.I. Staskov – À.A. Kuleshov Mogilev State University, Mogilev, Belarus
Download PDF (782 KB)
S.O. Parashkov – À.A. Kuleshov Mogilev State University, Mogilev, Belarus
A.V. Shylov – À.A. Kuleshov Mogilev State University, Mogilev, Belarus
N.A. Krekoten – JSC “INTEGRAL”, Minsk, Belarus
Modulation of optical radiation in case of thin film reflection of dense resonant medium
The possibility of temporal modulation of quasi-continuous radiation in the reflection of thin film of dense resonant medium is theoretically defined for the relative weakness of the relaxation processes. Resonant conversion of the light field in the reflection mode coherent interaction can be used to form the optical signals in ultrafast interaction processes of light radiation with thin layers.
Keywords: resonant reflection, thin optical films, dense resonant medium, dipole-dipolar interaction.
Yu.V. Yurevich – A.A. Kuleshov Mogilev State University, Mogilev, Belarus
Download PDF (1,17 MB)
V.A. Yurevich – Mogilev State University of Food Technologies, Mogilev, Belarus
-subgroups of finite groups
On the problem of intersections of the maximal
Erugin’s problem on the existence of irregular solutions in one case of the linear system with nonzero mean of periodic coefficient
The necessary and sufficient conditions under which linear periodic differential system has strongly irregular periodic solutions were obtained.
Keywords: strongly irregular periodic solution, linear differential system, periodic coefficient.
M.S. Belokursky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (313 KB)
On operator generalization of Frattini subgroup
The behavior of normal subgroups in generalized Frattini extension is studied.
Keywords: formation, normal subgroups, Sylow p-subgroup, group of operators.
R.V. Borodich – F. Skorina Gomel State University, Gomel, Belarus
Download PDF (328 KB)
S.N. Bykov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
The problem of characterization of all hereditary regular transitive subgroup functors is solved. It is proved that any natural transitive subgroup functor is
-subnormal for some primitive class
Keywords: finite solvable group, primitive group, subgroup functor, natural transitive subgroup functor (NT-functor), formation.
S.F. Kamornikov – Gomel Branch of International University «MITSO», Gomel, Belarus
Download PDF (330 KB)
On periodic solutions of differential equation with linear-fractional right-hand part
The conditions of existence of periodic solutions of differential equation with linear-fractional right-hand side are given.
Keywords: differential equation, reflecting function, Poincare mapping, linear-fractional function, periodic solution.
V.V. Mironenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (283 KB)
On the results of the study of simplified systems in the problem of motion of four bodies in a plane
The system describing the motion of four bodies in a plane is considered. The method of the small parameter of a simplified system consisting of nonlinear differential equations, each of which has a second order is determined. For these systems, a set of interparticle interaction constants in which all its solutions of the system are meromorphic functions is specified.
Keywords: motion of four bodies in a plane, interaction constant, simple system, meromorphic function.
A.T. Sazonava – Y. Kupala Grodno State University, Grodno, Belarus
Download PDF (297 KB)
-properties of finite groups II
Let G be a finite group, some partition of the set of all primes and Ï a subset of the set
. A set of subgroups of G is said to be a complete Hall Ï-set of G if contains exact one Hall -subgroup of G for every such that We say also that G is: Ï-full if G possess a complete Hall Ï-set; a Ï-full group of Sylow type if for each
every subgroup E of G is a
-group, that is, E has a Hall
-subgroup H and every
-subgroup of E is contained in some conjugate of
In this paper we study properties of finite Ï-full groups. The work continues the research of the paper .
Keywords: finite group, Ï-full group,
Skiba A.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (473 KB)
On localization of the zeroes Hermite – Pade approximants to the exponential functions
The upper estimates are determined for modules of the zeros of Hermite polynomials (Hermite – Pade approximation type I) of the exponential system
are arbitrary complex numbers. The proven statements complement and generalize known results about the behavior of the zeros of Hermite polynomials for exponential system by E. Saff and R. Varga, H. Stahl, F. Wielonsky.
Keywords: exponential system, Hermite polynomials, Hermite – Pad’e approximation, zeros of Pad’e approximation.
A.P. Starovoitov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (369 KB)
E.P. Kechko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Curganova L.A. Calculation of piles-CIT on the first limiting condition
The limiting bearing ability of a pile-cit in the nonlinear-deformed soil basis, taking into account ground consolidation in zone running-impulse processing is considered.
Keywords: pile-cit, mathematical model, limiting bearing ability.
V.E. Bykhautsau – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (313 KB)
D.V. Prokopenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
L.A. Curganova – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Algorithm of construction of optimal according to criterion of zero correlation non-binary
This paper considers the construction of cryptographic S-boxes of the length
which are optimal from the point of view of the ab-sence of correlation between the output and input vectors. Constructed sets of S-boxes can be recommended for upgrading of the existing block symmetric ciphers, as well as for the synthesis of new high-speed encryption algorithms based on the principles of multi-valued logic.
Keywords: S-box, matrix of correlation coefficients, Kim scheme.
O.N. Zhdanov – M.F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia
Download PDF (338 KB)
A.V. Sokolov – Odessa National Polytechnic University, Odessa, Ukraine
Web-application electrical calculations
The idea of creating software is considered. With this software, one can automate the calculations for determining the rational schemes and designs of electrical networks, determine the electrical load, loss of power and loss of supply, reactive power compensation, maintain the required voltage quality, quantity and variety of power transformers.
Keywords: software tools, web-application, power supply, power consumption, circuitry.
S.F. Maslovich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (1,53 MB)
A.B. Gorbach – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
V.N. Halushko – Belarusian State University of Transport, Gomel, Belarus
A.V. Drobov – Gomel State Technical College, Gomel, Belarus