The dependences of the intensity of the output pulse flux on the voltage of the reverse bias of the noise diodes and the current flowing through their p-n junction are determined. The main processes influencing the intensity of the output pulse flux of silicon noise diodes operating in the microplasma breakdown mode are established. It is obtained that shock processes, thermal generation and tunneling of carriers of electric charge can be classified as such processes.

Keywords: noise diode, microplasma breakdown, autocorrelation function.

Î.Y. Gorbadey – Belarusian State Academy of Telecommunications, Minsk

À.Î. Zenevich – Belarusian State Academy of Telecommunications, Minsk

We investigate the effects of annealing and presence of the Pd buffer sublayer on the modifications of interfaces and crystal structure of multilayered Co/Pd thin films deposited by the thermal evaporation method and with the thicknesses of Co 0.2–0.4 nm and Pd 0.6–1.0 nm at which one can expect the maximum magnetic anisotropy.

Keywords: Co/Pd thin films, perpendicular magnetic anisotropy, interfaces of multilayered thin films, crystal structure of thin films, X-ray reflectivity, thin films analysis by X-ray diffraction, X-ray diffraction of thin films with inclination of diffraction vector with respect to the surface normal.

A.A. Maximenko – Institute for Nuclear Problems of Belarusian State University, Minsk

The system of 10 radial equations for a spin 1 particle in the external Coulomb field, is studied. With the use of the space reflection op-erator, the system is split to subsystems, consisted of 4 and 6 equations respectively. The system of 4 equations is solved in terms of hy-pergeometric functions, which gives the known energy spectrum. Combining the 6-equation system, we derive several equations of the 2-nd order for some separate functions. On of them may be recognized as a confluent Heun equation. A series of bound states is con-structed in terms of the so called transcendental confluent Heun functions, which provides us with solutions for the second class of bound states, with corresponding formula for energy levels. The subsystem of 6 is equations reduced to the system of the 1-st order equations for 4 functions f_i, i=1, 2, 3, 4. We derive explicit form of a corresponding of the 4-th order equation for each function. From four independent solutions of each 4-th order equation, only two solutions may be referred to series of bound states.

Keywords: vector particle, Coulomb field, Lorentz condition, bound states, transcendental Heun functions, exact solutions, differential equations of second and fourth order.

E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University

O.V. Veko – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk

Ya.A. Voynova – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk

A.D. Koral'kov – I.P. Shamyakin Mosyr State Pedagogical University

V.V. Kisel – Belarusian State University of Informatics and Radioelectronics, Minsk

V.M. Red'kov – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk

The influence of sublayers of various nature on the phase composition and morphology of one-component and composite carbon coatings is determined by the methods of Raman spectroscopy and atomic force microscopy. It is shown that when depositing titanium-doped carbon coating on a titanium sublayer, more dispersed Csp² clusters are formed. At the same time, doped carbon coatings are characterized by lower roughness and grain size.

Keywords: carbon coatings, alloying, titanium, cluster, phase composition, morphology.

D.G. Piliptsov – F. Scorina Gomel State University

A.À. Rogachev – F. Scorina Gomel State University

S.A. Chizik – A.V. Lykov Heat and Mass Transfer Institute of the NAS of Belarus, Minsk

A.S. Rudenkov – F. Scorina Gomel State University

E.À. Kulesh – F. Scorina Gomel State University

N.N. Fedosenko – F. Scorina Gomel State University

The effects of annealing and the presence of the Pd buffer sublayer on the variation of magnetic properties (coercive force, squareness of magnetization curves, effective magnetic anisotropy constant) as well as remagnetization mechanisms and magnetic domain structure in multilayered Co/Pd thin films with perpendicular magnetic anisotropy observed for the thicknesses of Co 0.2–0.4 nm and Pd 0.6–1.0 nm have been investigated.

Keywords: Co/Pd thin films, perpendicular magnetic anisotropy, magnetization reversal mechanisms, structure of magnetic domains.

J.F. Fedotova – Institute for Nuclear Problems of Belarusian State University, Minsk

A.A. Maximenko – Institute for Nuclear Problems of Belarusian State University, Minsk

J.V. Kasiuk – Institute for Nuclear Problems of Belarusian State University, Minsk

Let p be a prime, and H is a p-prefrattini subgroup of a finite soluble group G. In the paper it is proved that there exist elements such that the equality holds.

Keywords: finite soluble group, p-prefrattini subgroup, core of subgroup, generalized Frattini subgroup.

S.F. Kamornikov – F. Scorina Gomel State University

The mathematical model of calculation of the changing pressure at contact of a rigid cylindrical indenter with a viscoelastic isotropic strip rigidly fastened to an orthotropic basis is offered. The solution of the contact problem is reduced to integral equation. The realization of the numerical solution of the integral equation is presented.

Keywords: mathematical model, viscoelastic strip, orthotropic base, cylindrical indenter, contact problem.

V.V. Mozharovsky – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

N.A. Maryina – Belarusian State University of Transport, Gomel

D.S. Kuzmenkov – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

The solvability of a finite group G with two non-conjugate maximal subgroups A and B has been proved. It satisfies the following requirements: subgroups A and B have primary indices in G; all proper subgroups of A and B are supersoluble.

Keywords: finite group, solvable group, maximal subgroup, supersoluble subgroup, non-conjugate subgroups, primary index.

V.S. Monakhov – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

D.A. Khadanovich – F. Scorina Gomel State University

Let where are prime numbers, for Let and let is the set of some Sylow subgroups of the group G, that are taken one at a time for every It is proved that if every subgroup from the set normalises some non-identity s-subgroup from G, then G has solvable normal subgroup R and s divide |R|.

Keywords: finite group, Sylow subgroup, s-solvable group.

E.Ì. Palchik – Polotsk State University, Novopolotsk

S.Yu. Bashun – Polotsk State University, Novopolotsk

Necessary conditions for the system in the title to be Painleve type system were given.

Keywords: system of the ordinary differential equations, Painleve's property, movable critical singularities, method of small parameter.

V.M. Petsevich – Y. Kupala Grodno State University

V.A. Pronko – Y. Kupala Grodno State University

The new criteria of associativity of the operation are found for some specific substitutions.

Keywords: polyadic operation, groupoid, semigroup, group, associativity.

A.D. Rusakou – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

M.V. Selkin – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

Some properties of -subnormal subgroups and the groups that are products of two -subnormal subgroups are obtained.

Keywords: finite group, simple non-abelian group, factorized group, -subnormal subgroup.

V.N. Tyutyanov – International University «MITSO», Gomel

T.V. Tihonenko – P.O. Sukhoi Gomel State Technical University

P.V. Bychkov – F. Scorina Gomel State University

Some properties and examples of n-multiply -local formations are described. One application of such formations in the theory of finite factorisable groups are cosidered.

Keywords: finite group, formation -function, n-multiply -local formation, -nilpotent group, -closed class of groups.

Z. Chi – University of Science and Technology of China, Hefei

V.G. Safonov – Belarusian State University, Minsk

A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

The article is devoted to creation of system of transfer and information processing, using infrared radiation. The system capable to completely imitate real behavioural factors of conducting firing from the fire weapon, such as rate of fire, accuracy, chance of a misfire etc., and also the giving opportunity to identify hits on "opponent" with the subsequent processing of this hit and information transfer for further processing on the server is realized. The system can be used for carrying out military and tactical games without use of the real weapon.

Keywords: information, infrared radiation, firing, weapon, microcontroller, finite-state machine, programming.

A.À. Petushkov – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

M.I. Zhadan – Faculty of Mathematics and Programming Technologies, F. Scorina Gomel State University

The method of multiservice NGN simulation models building automation based on usage of domain specific language which allows to effectively combine predefined and user defined simulation models of multiservice NGN components is presented. This method is tailored mostly for simulation of multiservice NGNs based on MPLS TE that implement convergence of circuit switching packet switching networks and broadcast networks.

Keywords: simulation, IPTV, VoIP, AoIP, NGN, MPLS TE, DSL.

A.I. Khobnia – F. Scorina Gomel State University

O.M. Demidenko – F. Scorina Gomel State University

A simple implementation of a hardware random number generator that uses the avalanche breakdown effect of the bipolar transistor transition is offered. According to the results of statistical experiments, a conclusion is made about the possibility of using this device in various hardware-software systems.

Keywords: hardware random numbers generator, noise generator, avalanche breakdown of a transistor, statistical criterion.

P.L. Chechet – Faculty of Physics and Information Technology, F. Scorina Gomel State University

V.D. Liauchuk – Faculty of Physics and Information Technology, F. Scorina Gomel State University

A.V. Varuyeu – Faculty of Physics and Information Technology, F. Scorina Gomel State University

A.A. Liauchuk – Faculty of Physics and Information Technology, F. Scorina Gomel State University