A technique for calculating matrix elements of elementary particles interaction reactions using the “building” blocks (basic elements of Feynman diagrams) method is presented. In this approach, the matrix element is reduced to basic matrix elements involving basis spinors. Such blocks are calculated in advance using the Method of Basis Spinors (MBS) and then used for further calculations.

Keywords: basis spinor, Feynman diagram, Dirac matrix, fermion.

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

Numerical solutions of quantum field theory equations describing scattering s-states of two scalar particles are found in cases of a one-boson exchange potential and the Yukawa potential. Scattering amplitudes, scattering lengths and phase shifts are calculated on the basis of the solutions obtained. It is shown that the scattering amplitudes found satisfy a unitarity condition. The comparison of the results ob-tained in this simple model with experimental data for neutron-proton systems is carried out.

Keywords: two-particle equations, relativistic configurational representation, one-boson exchange potential, scattering amplitude, scattering length, phase shift, composite Gaussian quadrature, deuteron.

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

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

Dislocation model was developed for the calculation of the stress-strain state in a double lenticular. The model is suitable for use in the case of complex shape of the twin boundaries. Displacement fields and internal stresses caused by double lenticular in Ni₂MnGa were calculated on the based of the model in the approximation of a continuous distribution of twinning dislocations at the twin boundaries. It was found that stress is localized at the twin boundaries, and can be observed within the twin compensation voltages.

Keywords: twinning, dislocations, stress fields.

E.V. Shmatok – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

O.M. Ostrikov – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

The analytical solution of a boundary problem, describing the process of penetration of the sound field of a spherical radiator, located in-side a thin unclosed spherical shell, through the elastic spherical shell is developed. Influence of some parameters of a problem on the value of the attenuation coefficient (screening) of a sound field inside the spherical shell is numerically investigated.

Keywords: dual series equations for Legendre polynomials, infinite system of linear algebraic equations of the second kind with a completely continuous operator, attenuation coefficient of a sound field.

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

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

N.N. Kiseleva – Y. Kupala Grodno State University, Grodno, Belarus

In the paper the properties of intersection of maximal subgroups in groups with the operators are studied.

Keywords: maximal subgroup, formation, -residual, group of operators.

R.V. Borodich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

E.N. Borodich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

M.V. Selkin – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

A series of -soluble normalizer subgroup functors is given in this work. New examples of -Schunk classes of finite -soluble groups are constructed.

Keywords: finite group, -soluble group, -Schunk class, normalizer subgroup functor.

T.I. Vasil'eva – Belarusian State University of Transport, Gomel, Belarus

À.I. Prokopenko – Belarusian State University of Transport, Gomel, Belarus

The characterization of supersolvable groups with generalized subnormal subgroups is given.

Keywords: formation, Sylow subgroup, soluble group, critical subgroup, Frattini subgroup, generelized subnormal subgroup.

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

The authors define and study m-semicyclic n-ary groups for any divisor m–1 of natural number n–1. The class of all m-semicyclic n-ary groups is included in the class of all m-semiabelian n-ary groups identified by E. Post. Moreover, the class of all m-semicyclic n-ary groups includes the class of all cyclic n-ary groups and belongs to the class of all semicyclic n-ary groups. New criteria of cyclicity for n-ary group and for m-semicyclicity of n-ary group formulated by one of the subgroups of the universal covering group of Post are determined.

Keywords: n-ary group, cyclic group, semicyclic group, m-semicyclic group.

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

N.A. Shchuchkin – Volgograd State Socio-Pedagogical University, Volgograd, Russia

The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the derived -length of the -solvable groups in which the Sylow p-subgroups are either bicyclic or of order p³ for any is at most 7 and if then the derived -length is at most 4.

Keywords: finite group, -solvable group, bicyclic group, Sylow subgroup, derived -length.

D.V. Gritsuk – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

A full classification of finite groups with all n-maximal (n=2,3) subgroups -subnormal is given.

Keywords: -subnormal subgroup, -subnormal subgroup, supersoluble group, minimal nonsupersoluble group, SDH-group.

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

Xiaolan Yi – Zhejiang Sci-Tech University, Hangzhou, China

Let be a class of groups. A finite group G is called a -group if its every abelian chief factor of G is -central and every nonabelian chief factor of G is a simple group. It is established that the class of -groups forms a composite formation. The properties of the products of normal -subgroups of finite groups are investigated.

Keywords: finite group, -group, composition formation, radical formation, semiradical formation.

E.N. Myslovets – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The application of probabilistic-algebraic simulation is proposed to use in the control of the electro-power systems. The technique estimates the probabilistic characteristics of the reliability of the power grid structures including many elements with probabilistic reliability parameters.

Keywords: structurally-difficult system, network reliability, power systems.

O.Ì. Demidenko – F. Skorina Gomel State University, Gomel, Belarus

E.I. Sukach – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

D.V. Ratobylskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Y.V. Zherdetsky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The idea of creating software and statistical tools, with which you can simulate, analyze and take decisions to reduce the impact vibrations, voltage unbalance, frequency deviations in the electrical network and higher reliability of electric facilities and systems is considered.

Keywords: mathematical simulation, reliability, power consumption, electrics, electrical schema.

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

V.N. Halushko – Belarusian State University of Transport, Gomel, Belarus

S.V. Bakhur – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

The analysis of commonly used traffic detectors and advantages and disadvantages of optical traffic detectors (IP-cameras) is given. The model of the traffic flow data collection and analysis automation system and the method of modification of the Multi-Layer Background Subtraction algorithm using parallel computing based on the graphic processors are suggested. The experimental investigations show that the modified method can help to decrease video frame processing speed in 1.9 times.

Keywords: traffic flow, traffic detector, traffic density, traffic flow intensity, Multi-Layer Background Subtraction algorithm.

I.A. Melnikau – Belarusian-Russian University, Mogilev, Belarus

K.A. Demedenkov – Belarusian-Russian University, Mogilev, Belarus

I.A. Yeuseyenka – Belarusian-Russian University, Mogilev, Belarus

The existing approaches to software testing of pseudorandom sequences, their advantages and disadvantages are reviewed. The methods for testing multiple generators in order to select one of them for use in a certain subject area is offered. Some results of testing famous generators for the numerical integration by Monte Carlo method are shown.

Keywords: random number generator, pseudorandom number sequences, Monte Carlo method, testing of pseudorandom sequences.

D.N. Shevchenko – Belarusian State University of Transport, Gomel, Belarus

S.V. Krivenkov – Belarusian State University of Transport, Gomel, Belarus

Transmittance and reflectance spectra of electromagnetic radiation by double-layer interference structures made of lithium niobate plate and naporous alumina membrane with evaporated thin nichrome film were studied. In the quarter-wave range the effect of nichrome film thickness on reflective characteristics of the proposed double-layer interference structures was also established in the frequency range of 8–12 HGz.

Keywords: electromagnetic radiation, resonant absorption, reflection coefficient, multi-layer interference structure, nanoporous alumina.

Ahmed A. Al-Dilami – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

I.A. Vrublevsky – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

K.V. Chernyakova – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

G.A. Pykhir – Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus