Grodno State University

Hrodna, Belarus

Grodno State University

Hrodna, Belarus
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Grin A.,Grodno State University | Schneider K.R.,Weierstrass Institute for Applied Analysis And Stochastics
International Journal of Bifurcation and Chaos | Year: 2012

We study a polynomial Liénard system depending on three parameters a, b, c and exhibiting the following properties: (i) The origin is the unique equilibrium for all parameters. (ii) If a crosses zero, then the origin changes its stability, and Andronov-Hopf bifurcation arises. We consider a as control parameter and investigate the dependence of Andronov-Hopf bifurcation on the unfolding parameters b and c. We establish and describe analytically the existence of surfaces and curves located near the origin in the parameter space connected with the existence of small-amplitude limit cycles of multiplicity two and three (existence of degenerate Andronov-Hopf bifurcation). © 2012 World Scientific Publishing Company.


Matalytski M.,Grodno State University
Probability in the Engineering and Informational Sciences | Year: 2017

This paper is devoted to the research of an open Markov queueing network with positive customers and signals, and positive customers batch removal. A way of finding in a non-stationary regime time-dependent state probabilities has been proposed. The Kolmogorov system of difference-differential equations for state probabilities of such network was derived. The technique of its building, based on the use of the modified method of successive approximations combined with a series method, has been proposed. It is proved that the successive approximations converge over time to the stationary state probabilities, and the sequence of approximations converges to the unique solution of the Kolmogorov equations. Any successive approximation can be represented as a convergent power series with infinite radius of convergence, the coefficients of which satisfy the recurrence relations; that is useful for estimations. Model example illustrating the finding of time-dependent state probabilities of the network has been provided. Copyright © Cambridge University Press 2017


Lyalikov A.M.,Grodno State University
Technical Physics Letters | Year: 2010

A simple method of imaging optical fiber-to-fiber pitch deviations in multifiber lightguides is proposed, which is based on the filtration of spatial frequencies in the pattern formed by a coherent light reflected from the sample edge. A device that implements this method is described and the results of monitoring the quality of fiber optic plates are presented. © Pleiades Publishing, Ltd., 2010.


Lyalikov A.M.,Grodno State University
Technical Physics Letters | Year: 2010

A new method for measuring the residual wedge angle on transparent plates is described and theoretically justified. The proposed method is based on the sequential processing of two interference images of the plate with a number of interference fringes doubled as compared to that used in the traditional interferometric techniques. © 2010 Pleiades Publishing, Ltd.


But' A.I.,Grodno State University | Lyalikov A.M.,Grodno State University
Technical Physics Letters | Year: 2011

It is shown how to increase the sensitivity of wedge angle measurements by means of the formation of holographic interferograms. The sensitivity can be improved by increasing the number of interference fringes in the interference patterns formed during the optical processing of a pair of holograms of a wedgeshaped plate. The proposed method has been experimentally verified. © 2011 Pleiades Publishing, Ltd.


Ivanov A.Y.,Grodno State University | Vasil'Ev S.V.,Grodno State University
Journal of Physics: Conference Series | Year: 2016

It is shown that by varying the external electric field with different polarity from 0 to 106 V/m-1 in the course of laser processing with the mean radiation flux density ∼106 W/cm-2 the change in the evolution features of the plasma torch at the surface of some metals (Cu, Al, Sn, Pb) at early stages is quantitative rather than qualitative. At the same time the characteristic size of the target material droplets, carried out from the irradiated zone, becomes essentially (by several times) smaller as the amplitude of the external electric field strength grows, independently of its polarity.


Ivanov A.Y.,Grodno State University | Kapytski A.V.,Grodno State Medical University | Zharkiy N.V.,Grodno State University | Yerema N.A.,Grodno State University
Journal of Physics: Conference Series | Year: 2016

Acoustic emission of a zone of the destruction formed during influence of pulse laser radiation on a surface of metal is considered. Dependence of the time form of acoustic fluctuations on parameters of an irradiated material and the law of increase in depth of a crater was estimated. It is revealed, that at action on a surface of the copper sample of a laser impulse duration ∼ 20 μs time of growth of a zone of destruction makes approximately 40 μs. It is shown also that having detected a diffraction picture appearing on incidence of SHF-radiation on the surface of solid and having achieved during the experiment the best coincidence of the experimental and calculated using the computer model data one can define the character of the zone of destruction on the surface of structure being under treatment relief.


Ivanov A.Yu.,Grodno State University | Vasiliev S.V.,Grodno State University
Proceedings of the International Conference on Advanced Optoelectronics and Lasers, CAOL | Year: 2013

It is shown that by varying the external electric field with different polarity from 0 to 106 V m-1 in the course of laser processing with the mean radiation flux density ∼106 W cm-2 the change in the evolution features of the plasma torch at the surface of some metals at early stages is quantitative rather than qualitative. At the same time the characteristic size of the target material droplets, carried out from the irradiated zone, becomes essentially (by several times) smaller as the amplitude of the external electric field strength grows, independently of its polarity. © 2013 IEEE.


Matalytski M.A.,Grodno State University
Automation and Remote Control | Year: 2015

We consider methods for finding expected incomes in systems of Markov queueing networks with incomes and bounded waiting time for claims in the queues. This work deals with the case when incomes from transitions between network states are either deterministic functions of states and time or stochastic values with given moments of orders one and two. © 2015, Pleiades Publishing, Ltd.


Ereminaa A.R.,Grodno State University | Malinkovskiib Y.V.,Gomel State University
Automatic Control and Computer Sciences | Year: 2012

Open and closed queuing networks with multimode strategies and several types of requests are studied. Single-line nodes can operate in several modes. The time spent in each mode has an expo- nential distribution. The queuing discipline of the server is the discriminatory processor sharing (DPS). The number of requests is a random variable with an arbitrary distribution function. The invariance is established of the stationary distribution of the probabilities of the network states with respect to the functional form of the distributions of the work required to service the requests. © Allerton Press, Inc., 2012.

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