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Editor-in-Chief

**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

Partners

**Summaries of the Issue**

### REVIEW

VISUALIZATION METHODS OF VORTICAL FLOWS IN COMPUTATIONAL FLUID DYNAMICS AND THEIR APPLICATIONS
Volkov Konstantin N.

1

The paper deals with conceptions and methods for visual representation of research numerical results in the problems of fluid mechanics and gas. The three-dimensional nature of unsteady flow being simulated creates significant difficulties for the visual representation of results. It complicates control and understanding of numerical data, and exchange and processing of obtained information about the flow field. Approaches to vortical flows visualization with the usage of gradients of primary and secondary scalar and vector fields are discussed. An overview of visualization techniques for vortical flows using different definitions of the vortex and its identification criteria is given. Visualization examples for some solutions of gas dynamics problems related to calculations of jets and cavity flows are presented. Ideas of the vortical structure of the free non-isothermal jet and the formation of coherent vortex structures in the mixing layer are developed. Analysis of formation patterns for spatial flows inside large-scale vortical structures within the enclosed space of the cubic lid-driven cavity is performed. The singular points of the vortex flow in a cubic lid-driven cavity are found based on the results of numerical simulation; their type and location are identified depending on the Reynolds number. Calculations are performed with fine meshes and modern approaches to the simulation of vortical flows (direct numerical simulation and large-eddy simulation). Paradigm of graphical programming and COVISE virtual environment are used for the visual representation of computational results. Application that implements the visualization of the problem is represented as a network which links are modules and each of them is designed to solve a case-specific problem. Interaction between modules is carried out by the input and output ports (data receipt and data transfer) giving the possibility to use various input and output devices.

### PHOTONICS AND OPTOINFORMATICS

POINT SOURCE IN THE LAYERED MEDIUM WITH METAMATERIALS: METHOD OF RECURRENT RELATIONS
Konstantin V. Pravdin, Igor Yu. Popov

11

Multilayer systems with metamaterials are studied. A system comprising parallel alternated layers filled with metamaterial and vacuum is considered. The problem of obtaining expressions for electric part of the Green’s function is raised for the NIM situation. A NIM situation is a case when electric and magnetic permeabilities are equal –1 for metamaterial and +1 for vacuum. The Maxwell’s equations for a point source of electromagnetic field are considered. A differential equation for electric p-polarized scalar part of the Green’s function for every layer is obtained with standard boundary conditions. Solution is obtained with the fundamental system of solutions with unknown coefficients. For the unknown coefficients the recurrence relations method is chosen as evident in usage and easy in analysis of obtained solutions. The solutions of the recurrence relations are obtained in general form by the method of generating functions. As a result the formulae for required Green’s function are obtained for every layer in the condition of NIM situation. s-polarized part is obtained in a similar way. It is easy to obtain a vector form of the electric Green’s function with its scalar form and the standard alternations. Obtained results can be used by simulations of superlens systems and multilayer covers with metamaterials.

DYNAMIC PARAMETERS ESTIMATION OF INTERFEROMETRIC SIGNALS BASED ON SEQUENTIAL MONTE CARLO METHOD
Volynsky Maxim Alexandrovich, Gurov Igor P, Ermolaev Petr A, Skakov Pavel Sergeevich

18

The paper deals with sequential Monte Carlo method applied to problem of interferometric signals parameters estimation. The method is based on the statistical approximation of the posterior probability density distribution of parameters. Detailed description of the algorithm is given. The possibility of using the residual minimum between prediction and observation as a criterion for the selection of multitude elements generated at each algorithm step is shown. Analysis of input parameters influence on performance of the algorithm has been conducted. It was found that the standard deviation of the amplitude estimation error for typical signals is about 10% of the maximum amplitude value. The phase estimation error was shown to have a normal distribution. Analysis of the algorithm characteristics depending on input parameters is done. In particular, the influence analysis for a number of selected vectors of parameters on evaluation results is carried out. On the basis of simulation results for the considered class of signals, it is recommended to select 30% of the generated vectors number. The increase of the generated vectors number over 150 does not give significant improvement of the obtained estimates quality. The sequential Monte Carlo method is recommended for usage in dynamic processing of interferometric signals for the cases when high immunity is required to non-linear changes of signal parameters and influence of random noise.

### OPTICAL ENGINEERING

SECTIONING METHOD APPLICATION AT ELLIPSOMETRY OF INHOMOGENEOUS REFLECTION SYSTEMS
Gorlyak Andrei Nikolaevich, Solonukha Vladimir Mikhailovich, Khramtsovsky Igor Anatolievich

24

The paper deals with investigation of application peculiarities of ellipsometry methods and UF spectrophotometry at mechanical and chemical processing of optical engineering surface elements made of quartz glass. Ellipsometer LEF–3M–1, spectrophotometer SF–26 and interferometer MII–4 are used as experiment tools; they obtain widely known technical characteristics. Polarization characteristics of reflected light beam were measured by ellipsometry method; spectrophotometry method was used for measuring radiation transmission factor in UF spectrum area; by interference method surface layer thickness at quartz glass etching was measured.
A method for HF–sectioning of inhomogeneous surface layer of polished quartz glass is developed based on ellipsometry equation for reflection system «inhomogeneous layer – inhomogeneous padding». The method makes it possible to carry out the measuring and analysis of optical characteristics for inhomogeneous layers system on inhomogeneous padding and to reconstruct optical profile of surface layers at quartz glass chemical processing.
For definition of refractive index change along the layer depth, approximation of experimental values for polarization characteristics of homogeneous layers system is used. Inhomogeneous surface layer of polished quartz glass consists of an area (with thickness up to 20 nm) and layer refractive index less than refractive index for quartz glass and an area (with thickness up to 0,1 μm) and layer refractive index larger than refractive index for quartz glass. Ellipsometry and photometry methods are used for definition of technological conditions and optical characteristics of inhomogeneous layers at quartz glass chemical processing for optical elements with minimum radiation losses in UF spectrum area.

### AUTOMATIC CONTROL AND ROBOTICS

TRUST AND REPUTATION MODEL DESIGN FOR OBJECTS OF MULTI-AGENT ROBOTICS SYSTEMS WITH DECENTRALIZED CONTROL
Igor A. Zikratov, Zikratova Tatyana Viktorovna, Lebedev Ilya S, Andrei V. Gurtov

30

The problem of mechanisms design for protection of multi-agent robotics systems from attacks of robots-saboteurs is considered. Functioning analysis of these systems with decentralized control is carried out. The type of the so-called soft attacks using interception of messages, misinformation formation and transmission to group of robots which are also realizing other actions without identified signs of invasion of robots-saboteurs. Analysis of existing information security models of the system based on the trust level computation, calculated in the process of agents’ interaction is carried out. Information security model is offered in which robots-agents produce the trust levels to each other on the basis of situation analysis emerging on a certain step of iterative algorithm with usage of onboard sensor devices. On the basis of calculated trust levels, recognition of “saboteur” objects in the group of legitimate robots-agents is done. For measure of likeness (adjacency) increase for objects from the same category (“saboteur” or “legitimate agent”), calculation algorithm for agents reputation is offered as a measure of public opinion about qualities of this or that agent-subject. Implementation alternatives of the algorithms for detection of saboteurs on the example of the basic algorithm for distribution of purposes in the group of robots are considered.

INTERVAL OBSERVER FOR A BIOLOGICAL REACTOR MODEL
Kharkovskaia Tatiana A, Kremlev Artem Sergeevich, Dina M. Sabirova, Efimov Denis V., Tarek Raissi

39

The method of an interval observer design for nonlinear systems with parametric uncertainties is considered. The interval observer synthesis problem for systems with varying parameters consists in the following. If there is the uncertainty restraint for the state values of the system, limiting the initial conditions of the system and the set of admissible values for the vector of unknown parameters and inputs, the interval existence condition for the estimations of the system state variables, containing the actual state at a given time, needs to be held valid over the whole considered time segment as well. Conditions of the interval observers design for the considered class of systems are shown. They are: limitation of the input and state, the existence of a majorizing function defining the uncertainty vector for the system, Lipschitz continuity or finiteness of this function, the existence of an observer gain with the suitable Lyapunov matrix. The main condition for design of such a device is cooperativity of the interval estimation error dynamics. An individual observer gain matrix selection problem is considered. In order to ensure the property of cooperativity for interval estimation error dynamics, a static transformation of coordinates is proposed. The proposed algorithm is demonstrated by computer modeling of the biological reactor. Possible applications of these interval estimation systems are the spheres of robust control, where the presence of various types of uncertainties in the system dynamics is assumed, biotechnology and environmental systems and processes, mechatronics and robotics, etc.

OPTIMAL CONTROL SYSTEM FOR PRECISION ELECTRIC DRIVE WITH GUARANTEED DEGREE OF STABILITY
Abdullin Artur A, Drozdov Valentine Nilovich, Andrei A. Plotitsyn

46

Improved design method of optimal control system for the linear object with elastic coupling is considered. Standard optimal control system design implies the selection of state and input penalty matrix for the quadratic functional. Moreover the system performance quality depends greatly on the specific penalty matrix. Instead of the state and input penalty matrix selection procedure the selection of desired stability degree is proposed. The proposed method of optimal control system design is based on the idea of new state matrix utilization. The new state matrix has its eigenvalues at the specified distance to the right from the eigenvalues of the original state matrix. Thereupon we can assign the closed loop state feedback system matrix eigenvalues at that specified distance to the left from imaginary axis of the complex plane, in the other words, we can achieve the desired stability degree of the system. The proposed method of control algorithm design is demonstrated for a control system of an electric drive with two-mass mechanism (object). Object characteristic was evaluated by amplitudefrequency response obtained during identification experiment. Unavailable or immeasurable variables of the control object state were estimated by reduced-order observer while optimal control system design.

### MATERIAL SCIENCE AND NANOTECHNOLOGIES

NONLINEAR OPTICAL MOLECULAR CRYSTAL BASED ON 2,6-DIAMINOPYRIDINE: SYNTHESIS AND CHARACTERIZATION
Ilia M. Pavlovetc, Fokina Maria I, Sergiu I. Draguta, Timofeeva Tatiana V, Denisyuk Igor Yu.

52

The paper deals with investigation of a new nonlinear optical material based on nonlinear optical chromophore (4-Nitrophenol) and aminopyridine (2,6-Diaminopyridine). Calculation results are presented for molecular packing in the crystalline compound, based on the given components. According to these results the finite material must have a noncentrosymmetric lattice, which determines the presence of the second order nonlinear optical response. Investigations carried out in this work confirm these calculations. Results of experiments are given describing the co-crystallization of these components and the following re-crystallization of the obtained material. In order to get a monocrystal form, the optimal conditions for the synthesis of molecular crystals based on these components are determined. Sufficiently large homogeneous crystals are obtained, that gave the possibility to record their spectra in the visible and near infrared parts of the spectrum, to determine their nonlinear optical properties and the level of homogeneity. Their optical (optical transmission and optical laser damage threshold) and nonlinear optical properties are presented. For observation and measurement of the nonlinear optical properties an installation was built which implements the comparative method for measurements of nonlinear optical properties. A potassium titanyl oxide phosphate crystal was used as a sample for comparison. Results are given for the conversion efficiency of the primary laser radiation in the second optical harmonic relative to the signal obtained on the potassium titanyl oxide phosphate crystal. Obtained results show that the molecular co-crystal based on 2,6-Diaminopyridine is a promising nonlinear optical material for generating the second optical harmonic on the Nd: YAG laser (532 nm).

THERMOELECTRIC PROPERTIES OF HOT-PRESSED p-TYPE Mg2Si0.3Sn0.7 SOLID SOLUTION
Grigory N. Isachenko, Leonid V. Bochkov, Alexander Yu. Samunin, Mikhail I. Fedorov, Lev P. Bulat, Elena A. Gurieva, Alexander Shik

57

It is shown that thermoelectric energy conversion which gives the possibility for utilizing a low potential heat is one of the ways for adoption of energy-saving technologies; and semiconductor materials with p-type and n-type conductivities having high thermoelectric figure of merit are necessary for operation of thermoelectric generators. The paper deals with possibility of usage of the p-Mg2Si0.3Sn0.7 solid solution (with a nanostructured modification) as a couple for the well studied thermoelectric material based on n-Mg2Si-Mg2Sn. A technological scheme for fabrication of heavily doped Mg2Si0.3Sn0.7 solid solution of p-type by hot pressing from nanopowder is developed. The given technology has made it possible to reduce duration of a homogeneous material fabrication and has improved its physical and chemical properties. The samples were made by three ways: direct fusion for polycrystals fabrication; hot pressing from microparticles; nanostructuring, i.e. hot pressing from nanoparticles. By X-ray diffraction it is shown that sizes of structural elements in the fabricated samples are about 40 nm. The probe technique is used for measurement of electric conductivity and Seebeck coefficient. The stationary absolute method is used for measurement of thermal conductivity. Thermoelectric figure of merit is defined by measured values of kinetic coefficients in the temperatures range of 77 – 800 K. It was demonstrated, that electric conductivity, Seebeck coefficient and the power factor do not depend practically on a way of solid solution preparation. Thermal conductivity of samples pressed from nanoparticles has appeared to be higher, than of samples, obtained by direct fusion; i.e. in this case nanostructuring has not led to increase of thermoelectric figure of merit. The conclusion is drawn, that polycrystalline semiconductor Mg2Si0.3Sn0.7 can be used as a p-branch for a thermoelectric generator though nanostructuring has not led to the figure of merit growth. The assumption is made, that thermoelectric figure of merit improvement can be expected at the further reduction of the nanograins size.

POSSIBILITY RESEARCH FOR SILICON CARBIDE BULK CRYSTALS GROWTH OF 3C POLYTYPE FOR POWER DEVICES
Bulat Pavel V, Lebedev Alexander A, Yuri N. Makarov

64

The paper deals with creation of heteropolytypes instrument structures on silicon carbide for power devices not subjected to degradation of electrical properties. The phenomenon of polytypism is considered. Characteristics of different SiC polytypes are given. Information is cited about the causes and effects for degradation of p-n -structures of power devices based on SiC at large density direct current passing. It is shown that hetero-transitions between SiC polytypes may have more structural perfection than hetero-transitions between semiconductors with different chemical nature. Conclusion is made about application prospects for heterostructures based on 3C-SiC polytype in devices of modern power electronics. A brief overview of the possible methods for 3C-SiC single crystals growth is done. A basic scheme for creation of heteropolytype 3C-SiC structures based on substrates of 6H-SiC polytype is suggested.

MODIFICATION OF SURFACE LAYERS FOR SILICATE GLASSES BY ELECTRON IRRADIATION
Brunov Vyacheslav S, Oleg A. Podsvirov, Sidorov Alexander Ivanvich, Denis V. Churaev

70

Experimental research results of silicate glass surface layers modification by the influence of electron beams with 5-50 keV energies and 20-50 mC/cm2 doses are presented. It is shown that during the glasses exposure to an electron beam with 20-50 keV electron energies, a gradient optical waveguide with increased refractive index on waveguide axis Δn = 0.01-0.04 is formed in the surface layer. Сhemical etching rate is increased in the exposed area by up to two times which is related to glass grid destruction. Depending on irradiation dose thin film or silver nanoparticles with the size less than 20nm are formed on the surface of the silver containing glasses for electron energies less than 10 keV. Silver films drawn on the surface of the glass are dissolved into the glass bulk for electron energies 20-50 keV and 20-50 mC/cm2 dose. Basic mechanisms causing these effects are: chemical bonds breaking of spatial glass grid by high energy electrons, formation of negative volume charge inside the glass and field migration of positive metal ions into the volume charge region. Achieved results can be used in photonics, integral optics and nanoplasmonics device fabrication.

LUMINESCENT PROPERTIES OF SILICATE GLASSES WITH CERIUM IONS AND ANTIMONY
Alina M. Klykova, Sidorov Alexander Ivanvich, Shakhverdov Teimur Azimoich

76

The paper deals with the results of an experimental study of luminescence excitation spectra and luminescence of silicate glasses containing cerium ions and antimony. The aim of this work was to study the features of the luminescence and the effect of UV irradiation and heat treatment on luminescence and the state of cerium ions and antimony in glass. We investigated glass system Na2O-ZnO-Al2O3-SiO2-NaF-NaBr with additives CeO2 and Sb2O3. Synthesis was carried out in platinum crucibles in the air at 14500C. The samples were polished glass plates with a thickness of 0.5-1 mm. UV irradiation was carried out with a mercury lamp having a wide range of radiation in the spectral range 240-390 nm. It was conducted in a Nabertherm muffle furnaces. Luminescence spectra and excitation spectra were measured using a spectrofluorimeter MPF-44A (PerkinElmer) at the room temperature. Measured luminescence spectra were corrected in view of the spectral sensitivity of the photodetector for spectrofluorimeter. Adjustment of the excitation spectra for the spectral dependence of the intensity of the excitation source was not carried out. During the experiments it was found that in silicate glasses Sb3+ ions can exist in two energy states, which corresponds to a different environment with oxygen ions. Heat treatment of these glasses in an oxidizing atmosphere leads to an increase in ion concentration of Sb3+ ions with a greater amount of oxygen in the environment. In glasses containing antimony and cerium ions, ultraviolet irradiation causes a change in the valence of cerium ions and antimony, which is accompanied by luminescence quenching. Subsequent heat treatment of glass leads to the inverse processes and restore luminescence excitation spectra. The study of fluorescent properties of silicate glasses with cerium and antimony ions led to the conclusion of the practical significance of this work. Promising multifunctional materials can be created on the basis of these glasses that meet all the needs of modern photonics.

THERMAL INSULATION PROPERTIES RESEARCH OF THE COMPOSITE MATERIAL WATER GLASS–GRAPHITE MICROPARTICLES
Valeriy A. Gostev, Pitukhin E.A., Ustinov Anton S. , Darya A. Yakovleva

81

Research results for the composite material (CM) water glass–graphite microparticles with high thermal stability and thermal insulation properties are given. A composition consisting of graphite (42 % by weight), water glass Na2O(SiO2)n (50% by weight) and the hardener - sodium silicofluoric Na2SiF6 (8% by weight). Technology of such composition receipt is suggested. Experimental samples of the CM with filler particles (graphite) and a few microns in size were obtained. This is confirmed by a study of samples by X-ray diffraction and electron microscopy. The qualitative and quantitative phase analysis of the CM structure is done. Load limit values leading to the destruction of CM are identified. The character of the rupture surface is detected. Numerical values of specific heat and thermal conductivity are defined. Dependence of the specific heat capacity and thermal conductivity on temperature at monotonic heating is obtained experimentally. Studies have confirmed the increased thermal insulation properties of the proposed composition. CM with such characteristics can be recommended as a coating designed to reduce heat losses and resistant to high temperatures. Due to accessibility and low cost of its components the proposed material can be produced on an industrial scale.

### COMPUTER SCIENCE

СREATING OF BARCODES FOR FACIAL IMAGES BASED ON INTENSITY GRADIENTS
Kukharev Georgy A, Matveev Yuri Nikolaevich, Nadezhda L. Shchegoleva

88

The paper provides analysis of existing approaches to the generating of barcodes and description of the system structure for generating of barcodes from facial images. The method for generating of standard type linear barcodes from facial images is proposed. This method is based on the difference of intensity gradients, which represent images in the form of initial features. Further averaging of these features into a limited number of intervals is performed; the quantization of results into decimal digits from 0 to 9 and table conversion into the standard barcode is done. Testing was conducted on the Face94 database and database of composite faces of different ages. It showed that the proposed method ensures the stability of generated barcodes according to changes of scale, pose and mirroring of facial images, as well as changes of facial expressions and shadows on faces from local lighting. The proposed solutions are computationally low-cost and do not require the use of any specialized image processing software for generating of facial barcodes in real-time systems.

PARAMETRIC OPTIMIZATION OF THE MULTIMODAL DECISION-LEVEL FUSION SCHEME IN AUTOMATIC BIOMETRIC PERSON’S IDENTIFICATION
Andrey V. Timofeev

96

This paper deals with an original method of structure parametric optimization for multimodal decision-level fusion scheme which combines the results of the partial solution for the classification task obtained from assembly of the monomodal classifiers. As a result, a multimodal fusion classifier which has the minimum value of the total error rate has been obtained. Properties of the proposed approach are proved rigorously. Suggested method has an urgent practical application in the automatic multimodal biometric person’s identification systems and in the systems for remote monitoring of extended objects. The proposed solution is easy for practical implementation into real operating systems. The paper presents a simulation study of the effectiveness of this optimized multimodal fusion classifier carried out on special bimodal biometrical database. Simulation results showed high practical effectiveness of the suggested method.

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD
Nikolai A. Balonin, Balonin Yury N, Sergeev Mikhail B

103

Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets.); calculation methods for the quasi-orthogonal local maximum determinant Mersenne matrices are not studied enough sufficiently. The goal of this paper is to develop the theory of Mersenne and Hadamard matrices on the base of generalized Scarpis method research.
Methods. Extreme solutions are found in general by minimization of maximum for absolute values of the elements of studied matrices followed by their subsequent classification according to the quantity of levels and their values depending on orders. Less universal but more effective methods are based on structural invariants of quasi-orthogonal matrices (Silvester, Paley, Scarpis methods, ets.).
Results. Generalizations of Hadamard and Belevitch matrices as a family of quasi-orthogonal matrices of odd orders are observed; they include, in particular, two-level Mersenne matrices. Definitions of section and layer on the set of generalized matrices are proposed. Calculation algorithms for matrices of adjacent layers and sections by matrices of lower orders are described. Approximation examples of the Belevitch matrix structures up to 22-nd critical order by Mersenne matrix of the third order are given. New formulation of the modified Scarpis method to approximate Hadamard matrices of high orders by lower order Mersenne matrices is proposed. Williamson method is described by example of one modular level matrices approximation by matrices with a small number of levels.
Practical relevance. The efficiency of developing direction for the band-pass filters creation is justified. Algorithms for Mersenne matrices design by Scarpis method are used in developing software of the research program complex. Mersenne filters are based on the suboptimal by determinant matrices and are used for image masking and compression.

### ENGINEERING AND TECHNOLOGIES

STRESS STATE STUDY FOR PARTS OF ALUMINIUM-MAGNESIUM AND ALUMINIUM WROUGHT ALLOYS AT ROTARY SPINNING
Leonov Dimilyan B, Vasilkov Sergey D., Ivanov Andrey Yu

112

The paper deals with the problems of rotary spinning of pipe or sheet workpieces made of aluminium-magnesium and aluminium wrought alloys. The need to control depth distribution of internal stresses in the workpiece surface layer in the rotary spinning process is determined. An Al-Mg5 aluminum alloy part is researched, which is obtained after 3 - stage rotary spinning. By the use of non-destructive resistance electric contact method, measurements and analysis of the stressed state for the workpieces after each stage of rotary spinning are made. According to the experiment planning theory, research of the influence of processing and thermal treatment modes on the levels of residual stresses σ in the workpieces material is conducted. The value of the residual stresses is assumed as an optimization parameter, and the technological modes of spinning and the modes of the thermal treatment applied between the rotary spinning stages - as factors of the process. Statistical estimation is made, which makes it possible to obtain an adequate mathematical model (estimated by the Fisher’s criterion) describing the relation between the optimization parameter and the optimization factors. Technological processing modes with the lowest level of residual stresses in the surface layer of the researched samples and the optimal depth distribution of residual stresses in the workpiece surface layer are obtained. Developed method is applicable in all operating conditions for parts manufacturing of different geometry and different materials.

HIGH-RISE TEMPERATURE DEPENDENCES FOR ISOTHERMAL SPACE OBJECT OF THE SPHERICAL FORM
Dzitoev Azamat M., Lapovok Yevgeniy V., Khankov S.I.

117

Thermal balance of spherical space object in a near-earth space is investigated. Analytical description of stationary average temperature of such object in view of the existence of internal sources of thermal emissions and sunlight absorbed by its surface is received. Mathematical model, describing thermal balance of space object, is presented by the uniform equation combining two private models. One model considers heat irradiation from the object into space and radiation towards the Earth as well. The second one considers a shielding of a radiation stream into space by the Earth only. The choice of a model is defined by the direction of resultant radiation stream between object and the Earth. Functions describing high-rise dependences of temperature for space object of the spherical form are received. In the Earth shadow the choice of a model and the formulas, describing temperature for space object, is defined by the value of specific power of thermal emissions and its temperature level. On a solar site of a trajectory the choice of high-rise function type depends also on the ratio between coefficient of sunlight absorption and the degree of blackness for object surface. Criteria are offered making it possible to choose the function type, describing the relative change of object temperature with the height growth, prior to the beginning of calculations. Results of calculations carried out with the usage of high-rise functions, following from two models, are presented, and the limits of applicability for these functions are specified. Deduced analytical formulas give the possibility to calculate the temperature of spherical space object. Received conclusions are correct for convex form objects of standard configurations.

### MODELING AND SIMULATION

METAGRAPH VISUALIZATION METHOD
Olena S. Shtogrina, Oleksandra S. Kryvenko

124

development for metagraph visualizing is made. The paper deals with issues that arise when solving the problem of metagraph visualization, such as: the placement of nodes that belong to metavertices and do not belong to them, figures intersection of metavertices. These problems are exemplified. Criteria are proposed for the final image to be considered coherent, understandable for users and corresponding to a predetermined metagraph. The problem of metagraph visualization is posed. The method based on the principles of force algorithms is proposed for the problem solving. The rules for forces between metagraph nodes are defined in the framework of the method. These forces depend on nodes type between which they are performed and the presence of edges between them. This method does not involve human intervention during the formation of the image, thus saving time at frequent changes that require rebuilding of the image. The resulting image gives the possibility to portray clearly the entities of the subject area and the links between them. Graphical analysis methods can be applied to the image. Areas for the future researches are identified. They are: minimization of the number of edges intersections and the area occupied by the resulting image. Results of the modified visualization method can improve the visual metagraph representation.

ANALYTICAL AND MODEL STUDY OF ACTIVE SEMICONDUCTOR CONVERTER IN ELECTRICAL DRIVE SYSTEMS
Sergei G. German-Galkin, Zenon C. Zwierzewicz, Polyakov Nikolay A

131

Mathematical description of the active semiconductor converter based on the main (smooth) component method and method of resulting vector is proposed. Equations are obtained which describe steady state modes of operation for the active semiconductor converter. According to these equations of steady state modes of operation, control and electromagnetic characteristics of the active semiconductor converter are estimated and provided. It is shown that the active semiconductor converter is a strongly non-linear system. To investigate its dynamics only modern simulation software should be used. Structural model of the active semiconductor converter is developed with the usage of Simulink software package, and investigation of its dynamics is performed. Modeling showed that dynamic processes during switching of the active semiconductor converter operation mode from active voltage converter mode to grid-commutated inverter mode are strongly non-linear. At some combinations converter operation failure may ensue. Closed-loop non-linear structure of control system is suggested for the active semiconductor converter. Regulators are synthesized which provide specified static and dynamic features to the whole system. Structural model of closed-loop control system is developed. Its investigation is performed and its dynamic characteristics are obtained. Research results confirmed the features of the active semiconductor converter built into during its synthesis.

COMPUTATIONAL MODELING IN THE STUDY OF GLOW DISCHARGE PHYSICAL PROCESSES IN THE AIR AT LOW PRESSURES
Tchernycheva Maria V, Veronica P. Marek, Chirtsov Alexander S, Danila A. Shvager

140

Simple numerical models of low-pressure air gas discharge have been developed based on modern concepts of nonlocal plasma methods of the computational simulation of multi-component discharge environments. Voltage drop at the discharge gap has been calculated as a sum of incidences in the cathode sheath and on the positive column of a glow discharge as part of the semi-empirical approach. Electron impact ionization of the ground state, the recombination of charged particles on the walls of the discharge tube, ion-electron emission from the cathode, and the energy loss of electrons in collisions with ground state molecules have been taken into account in the models. The calculated voltage drop, depending on the pressure, has been compared with the results of another numerical discharge model based on the solutions of hydrodynamic equations for the particle densities in a two-dimensional case. Within these approximations, both models give satisfactory agreement between their results, which are strongly underestimated against the experiment corresponding to the normal highpressure glow discharge. The resulting discrepancy can be explained by an incompleteness of elementary processes taken into account in the simulation. For example, an unaccounted presence of gases from triatomic molecules as an impurity can lead to an increase in the collision energy losses of electrons, which in turn should lead to an increased electric field in the positive column, as compared with the values obtained in the models.

STATISTICAL CHARACTERISTICS INVESTIGATION OF PREDICTION ERRORS FOR INTERFEROMETRIC SIGNAL IN THE ALGORITHM OF NONLINEAR KALMAN FILTERING
Ekaterina L. Dmitrieva, Gurov Igor P

149

Basic peculiarities of nonlinear Kalman filtering algorithm applied to processing of interferometric signals are considered. Analytical estimates determining statistical characteristics of signal values prediction errors were obtained and analysis of errors histograms taking into account variations of different parameters of interferometric signal was carried out. Modeling of the signal prediction procedure with known fixed parameters and variable parameters of signal in the algorithm of nonlinear Kalman filtering was performed. Numerical estimates of prediction errors for interferometric signal values were obtained by formation and analysis of the errors histograms under the influence of additive noise and random variations of amplitude and frequency of interferometric signal. Nonlinear Kalman filter is shown to provide processing of signals with randomly variable parameters, however, it does not take into account directly the linearization error of harmonic function representing interferometric signal that is a filtering error source. The main drawback of the linear prediction consists in non-Gaussian statistics of prediction errors including cases of random deviations of signal amplitude and/or frequency. When implementing stochastic filtering of interferometric signals, it is reasonable to use prediction procedures based on local statistics of a signal and its parameters taken into account.

VISUALIZATION SOFTWARE DEVELOPMENT FOR PROCEDURE OF MULTI-DIMENSIONAL OPTIMIZATION OF TECHNOLOGICAL PROCESS FUNCTIONAL PARAMETERS
Zubkova Tatiana M, Elena N. Ishakova, Marina A. Tokareva

156

A method for multi-criteria optimization of the design parameters for technological object is described. The existing optimization methods are overviewed, and works in the field of basic research and applied problems are analyzed. The problem is formulated, based on the process requirements, making it possible to choose the geometrical dimensions of machine tips and the flow rate of the process, so that the resulting technical and economical parameters were optimal. In the problem formulation application of the performance method adapted to a particular domain is described. Task implementation is shown; the method of characteristics creation for the studied object in view of some restrictions for parameters in both analytical and graphical representation. On the basis of theoretical research the software system is developed that gives the possibility to automate the discovery of optimal solutions for specific problems. Using available information sources, that characterize the object of study, it is possible to establish identifiers, add restrictions from the one side, and in the interval as well. Obtained result is a visual depiction of dependence of the main study parameters on the others, which may have an impact on both the flow of the process, and the quality of products. The resulting optimal area shows the use of different design options for technological object in an acceptable kinematic range that makes it possible for the researcher to choose the best design solution.

### INFORMATION TECHNOLOGIES IN EDUCATION

META-SITUATIONAL MODELING IN DESCRIPTION OF SOCIAL AND ECONOMIC PROCESSES IN EDUCATION
Konstantin A. Konev, Gulnara R. Shakirova

163

The paper deals with the development of meta-situational modeling concept in the field of formalized description of nondeterministic socio-economic processes in relation to education. The goal of the paper is to increase the efficiency and optimization of decision-making procedure, in general, and informational support for formalized processes, in particular. To achieve this goal, it is proposed to introduce the concept and methodology of modeling as meta-situational integration situation (event) and ontological (semantic) approaches. It is assumed that the two-level description of the situation (at declarative and descriptive levels) will give the possibility for varying levels of abstraction in relation to process and get access to data and knowledge about it at that stage, when it is objectively necessary. Another obvious advantage of the proposed approach is simplicity of implementation due to a widespread situation and ontological approaches and, consequently, their formalization methods (mathematical apparatus) and instrumental software implementation (programming languages, display formats, etc.). To verify the efficiency of the proposed meta-situational approach, a typical example of weakly formalized situations is considered - one of the options assessment tools traditionally used in education. Both components of the process are described in detail: situational one, specifying stepwise development procedures and ontological, characterizing taxonomic aspect of the process. The order of a formalized description for meta-situational model structure based on data representation formats similar to XML (category "Semantic Web") is determined.

### BRIEF PAPERS

COMPONENT ARCHITECTURE OF WEB SERVICES ACCESS MANAGEMENT SYSTEM
Andrey M. Dergachev, Dergachev Alexander A

172

The component architecture of Web services access management system is presented. The executive kernel of the system is designed –processor of requests to web services. The prototype of design pattern is implemented – the infrastructure of Web services management system for Internet-based information systems. The work is aimed at developing research in the field of formation of Web services requests submission plan, which is named as Web services execution plan. The main results of the work are: component architecture of Web services access management system; prototype of the design pattern –processor of requests to Web services.