**BLOCKS-BASED ALGORITHMS COMBINATION FOR OPTICAL FLOW CALCULATION FOR MOVING OBJECTS DETECTION AND TRACKING IN VIDEO SEQUENCES**

**R. BOGUSH, V. LYSENKO, G. SAMOSCHENKOV**

The combined algorithm moving objects detection and tracking in video sequences with use of blocks-based approach for motion estimation is considered. For time acceleration we use multilevel successive elimination algorithm and diamond search for an interim maps of motion vector construction. We use multiplicative minimax similarity function for accuracy improvement of object localization at motion vector analysis. Since interim map not necessarily leads to optimal motion vectors, we use an additional post processing for motion field based on candidate vectors. We apply minimax similarity function for updating algorithm of moving object tracking. In paper results of experiments are presented according to time expenses of the moving object detection and tracking.

**COMBINED ALGORITHM FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS GASDYNAMIC PROBLEM FOR GAS TRANSPORTATION NETWORKS**

**D. HLUKHAU, A. OSKIN, S. AVILKIN**

This paper presents an algorithm for solving systems of nonlinear equations, taking into account the features of such systems in models of networks of gas transportation. We analyze results of the comparative tests of the algorithm with classical algorithms such as the method of coordinate relaxation, block relaxation, conjugate gradient method, and, also, features of the selected class of nonlinear systems. We concluded about high sensitivity of algorithms for solving this class of systems from the initial approximation and the parameters of the iterative process. We proposed method for self-optimization for solving the problem for specific networks of gas transmission.

**MULTILEVEL SYSTEM PHYSICOCHEMICAL, MULTIFRACTAL AND WAVELET ANALYSIS OF THE NANOSTRUCTURES AND THEIR PROPERTIES IMAGES **

**P. VITIAZ, M. KHEIFETZ, V. SENUT, A. KOLMAKOV, V. ANTIPOV, L. VINOGRADOV**

The state diagrams elements analysis of the physicochemical system states according to the suggested topological model enabled to define the self-organization principles at pattern and phase formation. The topological model elements have been studied on the ground of the undissociated compound stages being isolated from the dissociated ones with a singular point formed on the state diagram. The rational stage sequence of structures, phases and layers interfacing has been viewed from the structure and energy positions: fractal surface structure growth; an increased number of fractal base elements; fractal meander complication; layer percolation in the interfacial area; fractal degeneration. A multifractal approach to the different structures quantification has been recommended which was realized through the measure of set approximating the structure un-der study. Wavelet analysis has been suggested to describe the nanostructures of the materials with the features and parameters of the wavelet analysis influencing the material description being defined.

**THE GRAPH PARTITION MATRIX ALGORITHM MODIFICATION FOR THE DECOMPOSITION PROBLEMS SOLUTION**

**O. SHESTOPALOVA, P. KIZIN**

The graph partition matrix algorithm modification for the decomposition problems solution assuming no constrained partition components dimensions is introduced. The modification ensures the graph partition with components definition having the maximum links density and the maximum connectivity on the defining length path. The length path optimal value definition for maximum connectivity components selection is determined under the fit of the minimal length path distribution bar chart maximum. The inspection showed that the selection ensures the best conditions for the matrix algorithm last step formalization – the graph partition selection with using of block-diagonal strong connectivity matrix.

**SIMULATION OF ULTRASOUND INFLUENCE ON BLOOD COAGULATION PROCESSES**

**E. LASHKEVICH, V. BONDARIK**

Research of ultrasound influence on parameters of coagulation system in the course of a fibrinous clot formation is conducted. Research was spent by computer simulation of coagulation in the time of influence on blood test by ultrasonic fluctuations of various frequency and amplitude. As mathematical model of a fibrillation, the system from sixteen differential equations in which diffusion coefficients for each coagulation factor were considered as depending on frequency and amplitude of fluctuations was used. Threshold values of ultra-sonic fluctuations parameters have been defined and have been shown that influence on blood test by ultrasonic fluctuations with the parameters which values are below the established thresholds, does not influence essential on a coagulation process that makes it possible to use ultrasound for the diagnostic and therapeutic purposes. Regularities of influence of ultrasonic fluctuations with overthreshold values of parameters on fibrillation processes that allows to describe better biochemistry of at clot formation processes are revealed, and can be used for creation of new methods of diagnostics.

**OBJECT-ASSOCIATIVE APPROACH TO THE CONSTRUCTION OF AN ALGORITHM CALCULATION AND VISUALIZATION OF CYLINDRICAL SLIP SURFACE IN CALCULATIONS OF SLOPE STABILITY **

**D. HLUKHAU, A. KREMNEV, T. HLUKHAVA**

Object-associative approach to organization of complex data, developed in Polotsk State University, allows to implement efficient algorithms for calculation and visualization of complex geometrical problems. In this paper, we construct an object-associative system for data organizing which allows to manipulate and visualize data of calculating stability of slopes. We shows the advantages of this system compared with other systems of complex data organization based on a comparison of software features for calculating stability of slopes with a program developed based on object-associative approach.

**CONSTRUCTING MATHEMATICAL MODEL OF THE EXCITATION PROCESS OF DYNAMIC COMPONENTS OF RADIAL FORCES IN THE CENTRIFUGAL PUMP’S IMPELLER**

**V. PITOLIN**

Centrifugal superchargers (pumps, fans and compressors) have found wide industrial application (from spacecrafts up to usual apartment houses). Therefore struggle against noise and vibration of these mechanisms is directed not only at maintenance of their reliability and profitability, but also is the major component of ensuring normal living conditions. The mechanism of noise occurrence in the centrifugal pump is not so obvious, as it seems at first sight. There is a line of the phenomenon’s features which should be realized in calculated model. For example, presence of a minimum of vibration on frequency that is multiple to number of blades at some operating modes of a supercharger and changing an oscillation phase. To explain these phenomena, existing models are analyzed and the improved mathematical model for evaluation of the dynamic components of the radial forces exerted by the flow of fluid in the impeller blower, which are the main cause of excitation of vibrations and sound at frequencies multiples of the number of blades at the impeller, is offered.

**CONSTRUCTION OF VIRTUAL MUSEUM COMPOSITIONS BASED ON MIND CARD AND ONTOLOGY**

**A. OSKIN**

Describe a new algorithm for constructing the virtual museum tracks. A distinctive feature of the algorithm is the use of applied ontology created for the museum's composition as a basis for building a virtual museum of the composition. At the same time as an intermediate format for ontologies used mind map. The proposed algorithm offers great opportunities for the creation, use and reuse of information and educational environments. The use of ontologies increases versatility designed environments, and use Mind Manager allows you to increase the didactic value of the produced training materials and significantly reduce the time to develop them. In accordance with the methodology, built a virtual museum track “Painter J A Maciejewski”.

**SOLUTION OF A MULTIDIMENSIONAL HYPERGEOMETRIC ABEL-TYPE INTEGRAL EQUATIONS**

**O. SKOROMNIK**

Multidimensional integral equations of the first kind with the Gauss hypergeometric function in the kernels over special bounded pyramidal domains in Euclidean space are considered. The interest in such equations is caused by their applications to problems on reflection of waves on a rectilinear boundary and on a supersonic flow around spatial corners. Solutions of these equations in closed form are established, and necessary and sufficient conditions for their solvability in the space of summable functions are given. The results generalize those for multidimensional Abel type integral equation and for the corresponding one-dimensional hypergeometric equations.

**MICROINDENTION OF PHOTOPOLYMERIC-SILICON STRUCTURES**

**N. VABISHCHEVICH, S. VABISHCHEVICH, D. BRINKEVICH, V. VOLOBUYEV, M. LUKASHEVICH, V. ODZHAEV, V. PROSOLOVICH**

Physicomechanical properties of the polymer - silicon structures implanted by ions Sb with energy 60 kэV in the fluence range 1?10^{15}…5?10^{16} cm^{–2} was investigated by the microindention method. It was revealed, that processes of radiating defect formation at low energy Sb+ ion implantation of photopolymer – silicon structures proceed beyond the projected range of Sb ions. The effect of radiating hardening of polymer was observed on all thickness of a film, and behind beyond the projected range of Sb ions the specified effect was expressed more strongly. Most likely, it was caused by processes of radiating sewing together. It was shown, that ion implantation leads to deterioration of adhesive interaction of a photopolymeric film with silicon.

**THE ANALYSIS OF PARAMETRICAL STABILITY OF CYLINDRICAL AXISYMMETRIC ANISOTROPIC SHELLS FROM FIBREGLASS TAKING INTO ACCOUNT DAMPING**

**WANG ZHIWEI, S. BOSIAKOV**

This paper is devoted to research of parametrical vibrations of cylindrical physically anisotropic shell from fiberglass. On a shell the longitudinal pulsing forces are operated. Boundary conditions are conditions of Nave. Fiberglass is considered as a homogeneous monolithic anisotropic material. Elastic properties of fiber-glass depend on a angle of winding of fiber glass. Forces of nonelastic strength are considered by means of additional members which contain the first derivatives on time from longitudinal, circular and radial displacements of a median surface of a shell. Logarithmic decrements are depending on an orientation angle of fiber-glass. The equation of Mathieu into account damping is obtained. With application of a method of small parameter the expressions describing critical frequencies are found. Frequencies the first and second areas of instability are limited. On an example of a shell from fabric fiberglass it is shown that the damping account leads to reduction of the first area of instability.

**RESONANCE AND HYSTERESIS EFFECT AT IMPULSE-PERIODICAL AGITATION OF OSCILLATIONS IN A LOCALLY NONEQUILIBRIUM MEDIUM**

**I. KONTSEVOY**

Forced thermal oscillations in a system “locally nonequilibrium medium – surface energy source” are studied theoretically. Resonance and hysteresis properties of this system are studied in details. Essential factors of the resonance curve behaviour are the duration of a pause between radiation impulses and the sample thickness. It’s shown that the area of the frequency hysteresis loop on the plane “frequency – goodness” strongly depends on sample thickness, deviation of the frequency from its stationary value, and duration of the frequency jump. Besides the hysteresis is displayed as stronger as the duration of the mentioned jump is.

**REGIMES OF COMBUSTION WAVE PROPAGATION IN TWO-LAYER SHS-MEDIUM**

**I. KOTIN**

The model of the two-layer sample used for deriving FGM by SHS has been offered. Combined equations have been solved in approximation of an infinitely narrow reaction zone. The system of the transcendental equa-tions on velocity of a burning wave, combustion temperatures in layers and on shift between front parts have been obtained. Analytical examination and numerical solution of the indicated system have been allowed to conclude that within the framework of viewed model the burning wave can propagate, at least, in two modes: «sepa-ration» mode and mode such as «merging». The «separation» mode takes place in the case of a small thermal interlaminar link: the burning rate is controlled by reaction in a more exothermic layer and by quantity of a heat loss from this layer in the second one. Moreover the part of front in the layer with major reaction heat effect leads. The critical conditions of the existence of this mode have been determined. The mode such as «merging» takes place 1) when a great thermal interlaminar link occurs; 2) when reaction heat effects of layers mixtures are close. The obtained results are in qualitative agreement with experimental data about burning of three-layer samples which have melting inert material in two layers.

**SIMULATION OF PHYSICAL PROCESSES FORMATION OF MICRO-AND NANOSTRUCTURES EXPEDITE THE FLOW OF IONS OF INERT AND REACTIVE GASES**

**I. SPRESOV**

In this article the physical processes of micro- and nanostructures formation with accelerated ion beams of inert and reactive gases are described. A new model was proposed: a process of application of thin membranes on the base with micron relief. The efficiency of ion streams application is justified in the formation of thin membranes, as well as in various areas of science and technology. Based on the mathematical model, the various forms of the base relative to the ion flow were explored. As the distance between the base and the source grows, the thickness of the membrane decreases; the velocity of coating is maximal when the angle of the base and the source is minimal. With the increasing of coating time, the membrane thickness increases proportionally with time, while increasing the angle of the base to the horizontal surface makes the membrane thickness decrease.