
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (8) 2011
PHYSICS
Andreev V.V., Babich K.S. Quantum and relativistic effects for two particle systems with the cornell potential
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 nonrelativistic 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
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Vaskevich V.V., Gaishun V.E., Kovalenko D.L., Sidsky V.V. Protective solgel coating with hydrophobic properties
In the paper the authors consider the possibility of protective SiO2 coatings based on solgel method by hydrolysis of organometallic compounds of silicon in wateralcohol mixture. We study the rheology of filmforming 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: solgel 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
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Gudelev V.G., Kulak G.V., Matveeva A.G., Nikolaenko T.V. Laser excitation of longitudinal and shear ultrasound waves pulses in solid state bodies in a near zone
The pecularities of the opticalacoustical 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
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MalyutinaBronskaya V.V., Polikanin A.M., Zalesskiy V.B., Semchenko A.V., Sidsky V.V., Gayshun V.E. Synthesis of heterostructures SIO_{2}/ZnO/Si BY solgel method
The analysis of voltagecurrent and voltagefarad characteristic of SiO2/ZnO/Sistructures are described. SiO_{2}/ZnO/Sistructures are synthesized by solgel metrod with using of zinc nitrate, chloride and acetate as initials. The defects density on the ZnO/Si boundary by MottShottky relationship Ñ_{2}(U) is calculated. The main conductivity mechanism (spacecharge limited current) is determined. It is shown that solgel films synthesized from zinc acetate have good photosensitivity.
Keywords: solgel, ZnO, voltagecurrent and voltagefarad characteristic.
MalyutinaBronskaya 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
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Samofalov A.L., Semchenko I.V., Khakhomov S.A. Simulation and investigation of artificial anisotropic structures with high chirality in the microwave range
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
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Yarmolenko M.A., Rogachev A.A., Rogachou A.V., Gorbochev D.L. Kinetic characteristics of dispersion of organosilicon compounds in vacuum and molecular structure of the coatings, deposited from volatile products of dispersion
It is shown that the kinetic characteristics of electronbeam 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, electronbeam 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
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MATHEMATICS
Andreeva D.P., Skiba A.N. Finite groups with given maximal chains of length
A description of a finite group with the property that every its maximal chain of length 3 contains a proper
Squasinormal subgroup, and a description of a finite group with the property that every its 3maximal subgroup is subnormal
(Squasinormal) are obtained.
Keywords: Sylow subgroup, Schmidt group, nmaximal subgroup, nilpotent group, maximal chain of length
n, soluble group,
Squasinormal 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
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Bedziuk N.V. Generalized stochastic integral with respect to continuous martingale
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
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Dyba R.V. The Nehari theorem for compact abelian groups with linearly orded duals
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
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Zhiznevsky P.A. Elements of the height 3 of the lattice of all
closed
nmultiply
composition formations
Korzhik R.I., Zhogal S.P. Influence of delay on stationary states of the nonautonomous
Van der PolDuffing oscillator
The effect of delay on dynamical regimes of the abridged equation of the nonautonomous van der PolDuffing 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 PolDuffing oscillator, stationary states, influence of delay, abridged equation, external periodic effect, RouthHurwitz 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
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Martynov I.P., Parmanchuk O.N., Pecevich V.M. On a cross system of two differential equations with the Painleve property
The article deals with the crosssystem of two differential equations of the second degree and thirddegree 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
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Starovoitov A.N. Queueing system with batch arrivals, batch service and disasters
We consider a singleserver 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
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Tavgen O.I., Du Junhua, Liu Chunyan. The representation image unipotency of the group
F_{2} by mapping of primitive elements into unipotent matrices with small Jordan blocks
Tsarev A.A. On nondistributivity of the lattice of all nmultiply
composition formations
Yakubovich O.V., Boyarovich Y.S., Letunovich Y.E., Voroshilov D.E. Application of
Jackson’s network to modelling of the warranty service of agricultural techniques
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
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INFORMATION SCIENCE
Ratobylskaya D.V. Choice of the rational variant of the organization of the transport network communicatoins on the basis of probabilityalgebraic simulation
The paper is devoted to the application of the method of probabilityalgebraic simulation for research of probability characteristics of complex systems. It contains the description of the idea of the method and methodology of probabilityalgebraic 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: probabilityalgebraic simulation, modeling, graph, transport network, message network.
Ratobylskaya D.V. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Sukach E.I. Approaches to reducing the dimension of multicomponent of structurally complex multistate systems in the assessment of reliability
In the paper the description of approaches to reduce the dimension of structurally complex systems on assessing their reliability is given. The use of probabilityalgebraic simulation for the parts of the system with a parallelseries 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 multistate settlement to the binary model.
Keywords: reliability of a multicomponent system, structurally complex system, multistate system, the probabilityalgebraic simulation, probabilistic reliability.
Sukach E.I. – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
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Shilko S.V., Kuzminsky Yu.G., Borisenko M.V. Mathematical model and software for monitoring of cardiovascular system
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 MetalPolymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus
Kuzminsky Yu.G. – V.A. Belyi MetalPolymer Research Institute National Academy of Sciences of Belarus, Gomel, Belarus
Borisenko M.V. – Belarusian State University of Transport, Gomel, Belarus
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Yakimau E.A., Demidenko O.Ì., Albkeirat D.M. On restoration of noise component in data sequences by a singular spectrum analysis method
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: SSAmethod, time sequence data, uniform, normal, exponential distribution; correction.
Yakimau E.A. – BelarusianRussian University, Mogilev, Belarus
Demidenko O.M. – Prorector of F. Skorina Gomel State University, Gomel, Belarus
Albkeirat D.M. – BelarusianRussian University, Mogilev, Belarus
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