A numerical method for bound state equations with the Cornell potential in momentum space is represented. A new quadrature formula was obtained. The formula can be used for solving integral equations and for numerical integral computations as well. Some effects for two particle quantum systems with the Cornell potential were observed. For the case of non-relativistic Schrodinger equation with the Cornell potential the exploration of wave functions’ behavior near the critical value of the Coulomb potential parameter was provided. A curve that characterizes the critical value dependence from the linear part parameter of potential was plotted.

Keywords: bound states, momentum space, quadrature formula, Cornell potential, collapse, wave function, Schodinger equation.

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

Babich K.S. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

In the paper the authors consider the possibility of protective SiO2 coatings based on sol-gel method by hydrolysis of organometallic compounds of silicon in water-alcohol mixture. We study the rheology of film-forming solutions prepared according to the time and storage conditions of the solution. We describe the optimal parameters of application and heat treatment to obtain homogeneous coatings. The mechanical resistance to abrasion as the main type of coatings tested for strength and adhesion to the substrate surface is investigated. The authors give analysis of the properties of water repellency of coatings obtained depending on the composition and treatment temperature.

Keywords: sol-gel technology, rheology, heat treatment, protective coatings, hydrophobic properties.

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

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

Kovalenko D.L. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

The pecularities of the optical-acoustical excitation of the acoustical pulse of longitudinal and shear ultrasonic waves for the near Fresnel zone and acoustical diffraction on the rectangular opening are investigated. Some enhancement of the acoustical pulse amplitude and reduction of the duration under transition from the nearest Fresnel zone to the far Fraunhofer zone are stated. It has been shown that under displacement from the center of the opening in the Fresnel zone the amplitude of acoustical pulse is reduced and duration is enhanced. The pulse amplitude is reduced significantly under transition to the geometrical shadow.

Keywords: laser excitation, ultrasonic waves, duration and amplitude of pulse, diffraction zone, solid state body.

Gudelev V.G. – B.I. Stepanov Institute of Physics NASB, Minsk, Belarus

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

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

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

The analysis of voltage-current and voltage-farad characteristic of SiO2/ZnO/Si-structures are described. SiO₂/ZnO/Si-structures are synthesized by sol-gel metrod with using of zinc nitrate, chloride and acetate as initials. The defects density on the ZnO/Si boundary by Mott-Shottky relationship Ñ₂(U) is calculated. The main conductivity mechanism (space-charge limited current) is determined. It is shown that sol-gel films synthesized from zinc acetate have good photosensitivity.

Keywords: sol-gel, ZnO, voltage-current and voltage-farad characteristic.

Malyutina-Bronskaya V.V. – B.I. Stepanov Institute of Physics NASB, Minsk, Belarus

Polikanin A.M. – B.I. Stepanov Institute of Physics NASB, Minsk, Belarus

Zalesskiy V.B. – B.I. Stepanov Institute of Physics NASB, Minsk, Belarus

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

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

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

The simulation of chiral properties of a sample of the artificial medium consisting of copper helices in the microwave range has been carried out. Comparison of calculated values of the angle of rotation of the polarization plane of the wave transmitted through artificial structure with the experimental results led to the conclusion that the proposed model qualitatively describes the properties of the artificial structure with a high chirality in the microwave range.

Keywords: composite media, chirality, helical element, the plane of polarization.

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

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

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

It is shown that the kinetic characteristics of electron-beam dispersion of organosilicone compounds and molecular structure of the layers, deposited from the gas phase, which was formed under dispersion, are conditioned by the processes of chemical interaction, occurring in the area of electron stream towards the target. Under dispersion in plasma activation of gas phase environment the layers with lower density of hydrocarbon fragments and higher density of unsaturated bonds are formed. The possibility of the formation of highly dispersed composite coatings based on organosilicone compounds is found. The molecular structure of the organosilicone compounds has notable differences from the structure of the original components.

Keywords: organosilicone compound, electron-beam dispersion, morphology, molecular structure, composition coating.

Yarmolenko M.A. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

Rogachev A.V. – Rector of F. Skorina Gomel State University, Gomel, Belarus

Gorbachyov D.L. – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A description of a finite group with the property that every its maximal chain of length 3 contains a proper S-quasinormal subgroup, and a description of a finite group with the property that every its 3-maximal subgroup is subnormal (S-quasinormal) are obtained.

Keywords: Sylow subgroup, Schmidt group, n-maximal subgroup, nilpotent group, maximal chain of length n, soluble group, S-quasinormal subgroup, subnormal subgroup.

Andreeva D.P. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Skiba A.N. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Stochastic integral with respect to continuous martingale is considered in the algebra of generalized stochastic processes. The sufficient conditions when the above generalized stochastic process associates an ordinary stochastic process are formulated. The explicit form of the ordinary stochastic process is described.

Keywords: algebra of generalized stochastic processes, martingale, stochastic integral.

Bedziuk N.V. – Department of Mechanics and Mathematics, Belarusian State University, Minsk

The Nehari theorem for classical Hankel operators is generalized to compact abelian groups with linearly ordered duals.

Keywords: compact abelian group, linearly ordered group, Hankel operator, Hardy space.

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

In this paper elements of the height 3 of the lattice of all -closed n-multiply -composition formations are described. It is proved that if is an element of the height 3 of the lattice then the lattice of -closed n-multiply -composition subformations of is distributive.

Keywords: finite group, formation, -composition satellite, -closed n-multiply -composition formation, height of formation.

Zhiznevsky P.A. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

The effect of delay on dynamical regimes of the abridged equation of the non-autonomous van der Pol-Duffing oscillator with an external harmonic influence was investigated. The abridged equation was derived and the maps of dynamical regimes for different values of the parameter characterizing the delay were presented.

Keywords: van der Pol-Duffing oscillator, stationary states, influence of delay, abridged equation, external periodic effect, Routh-Hurwitz stability criterion, bifurcation.

Korzhik R.I. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

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

The article deals with the cross-system of two differential equations of the second degree and third-degree derivative of the variables. The necessary and sufficient conditions having the Painleve property for solutions of this system are obtained.

Keywords: cross system of differential equations, property of Painleve, singular solution, test of Painleve, resonances.

Martynov I.P. – Y. Kupala Grodno State University, Grodno, Belarus

Parmanchuk O.N. – Y. Kupala Grodno State University, Grodno, Belarus

Pecevich V.M. – Y. Kupala Grodno State University, Grodno, Belarus

We consider a single-server queueing system with batch arrivals and batch service. Besides, the flow of the disaster enters the queueing system. The disaster completely clears the queue of the system if it is not empty, and renders no influence if the queue of the system is empty. Stationary distribution of the states of the process describing the queueing system behavior is found.

Keywords: queueing system, batch arrivals, batch service, disaster.

Starovoitov A.N. – Belarusian State University of Transport, Gomel, Belarus

It is proved that the representation image of the free group in is an unipotent subgroup, when for all primitive elements p and for some associated primitive elements and of the group

Keywords: unipotent subgroup, primitive element, representation of group.

Tavgen O.I. – Belarusian State University, Minsk, Belarus

Du Junhua – College of Sciences of Qiqihar University, Qiqihar, China

Liu Chunyan – Harbin University of Science and Technology, Harbin, China

Let and be an infinite set of primes. It is proved that the lattice of all -closed n-multiply -composition formations is not distributive.

Keywords: finite group, formation of groups, -composition satellite of formation, non-distributive lattice.

Tsarev A.A. – P.M. Masherov Vitebsk State University, Vitebsk, Belarus

The paper considers the mathematical model of the warranty service process of «Gomselmash» agricultural techniques provided by regional dealer centers. The service process of åach center is described by a queueing network. The stationary distribution of conditions probabilities of the network and ergodicity conditions are found. Formulas for definition of numerical characteristics of network stationary functioning are received.

Keywords: queueing network, stationary distribution, ergodicity conditions, numerical characteristics.

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

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

Letunovich Y.E. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Voroshilov D.E. – Production Association «Gomselmash», Gomel, Belarus

The paper is devoted to the application of the method of probability-algebraic simulation for research of probability characteristics of complex systems. It contains the description of the idea of the method and methodology of probability-algebraic simulation. In the paper the example of the description of the transport network model and estimation of the organization of communications is presented by method means.

Keywords: probability-algebraic simulation, modeling, graph, transport network, message network.

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

In the paper the description of approaches to reduce the dimension of structurally complex systems on assessing their reliability is given. The use of probability-algebraic simulation for the parts of the system with a parallel-series connection of components is proposed. Calculation of reliability of structurally complex systems with many states is achieved by using methods of information system models with multi-state settlement to the binary model.

Keywords: reliability of a multicomponent system, structurally complex system, multi-state system, the probability-algebraic simulation, probabilistic reliability.

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

The facilities of primary diagnostics of the heart and vascular system based on hydrodynamic model of the blood flow and realized in software BIODIS V2.2 have been demonstrated.

Keywords: cardiovascular system, hemodynamics, pressure, adaptivity, primary diagnosis, computer modeling, software.

Shilko S.V. – V.A. Belyi Metal-Polymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus

Kuzminsky Yu.G. – V.A. Belyi Metal-Polymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus

Borisenko M.V. – Belarusian State University of Transport, Gomel, Belarus

The technique and results of research of sequences of data with uniform, normal and exponential noise by transformation a Singular Spectrum Analysis method are presented. The pecularities of restoration of noise component in sequences of data are shown, the algorithm of updating restored noise component in view of a standard deviation is offered.

Keywords: SSA-method, time sequence data, uniform, normal, exponential distribution; correction.

Yakimau E.A. – Belarusian-Russian University, Mogilev, Belarus

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

Albkeirat D.M. – Belarusian-Russian University, Mogilev, Belarus