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Editor-in-Chief

**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

Partners

**Summaries of the Issue**

### PHOTONICS AND OPTOINFORMATIСS

APPLICABILITY ANALYSIS OF THE PHASE CORRELATION ALGORITHM
FOR STABILIZATION OF VIDEO FRAMES SEQUENCES FOR CAPILLARY
BLOOD FLOW
Karimov Konstantin Astachovich, Volkov Mikhail Vladimirovich

365

Videocapillaroscopy is a convenient and non-invasive method of blood flow parameters recovery in the capillaries. Capillaries position can vary at recorded video sequences due to the registration features of capillary blood flow. Stabilization algorithm of video capillary blood flow based on phase correlation is proposed and researched. This algorithm is compared to the known algorithms of video frames stabilization with full-frame superposition and with key points. Programs, based on discussed algorithms, are compared under processing the experimentally recorded video sequences of human capillaries and under processing of computer-simulated sequences of video frames with the specified offset. The full-frame superposition algorithm provides high quality of stabilization; however, the program based on this algorithm requires significant computational resources. Software implementation of the algorithm based on the detection of the key points is characterized by good performance, but provides low quality of stabilization for video sequences capillary blood flow. Algorithm based on phase correlation method provides high quality of stabilization and program realization of this algorithm requires minimal computational resources. It is shown that the phase correlation algorithm is the most useful for stabilization of video sequences for capillaries blood flow. Obtained findings can be used in the software for biomedical diagnostics.

### OPTICAL ENGINEERING

POINT-BY-POINT INSCRIPTION OF FIBER BRAGG GRATINGS
INTO BIREFRINGENT OPTICAL FIBER THROUGH PROTECTIVE ACRYLATE COATING BY TI:SA FEMTOSECOND LASER
Arkhipov Sergey Vladimirovich, Grehn Moritz , Varzhel Sergey V., Vladimir E. Strigalev, Griga Nils , Eichler Hans Joachim

373

The paper deals withpoint-by-point inscriptionof fiber Bragg gratings by the 800 nm Ti:Sa femtosecond laser pulses into a unique birefringent fiber with elliptical stress cladding of home manufacture. The proposed inscriptionmethod has advantages over the conventional phase mask method. The possibility to create complex grating structures and relatively high transparency of acrylate coating to the Ti:Sa femtosecond laser radiation of 800 nm gives the possibility for inscriptionof phase shifting gratings, chirped grating and superstructures without stripping the fiber. Also, this method makes it possible to inscribethese diffractive structures with and without co-doping of GeO2 in the fiber core. Achieved reflectance was 10%. The microscopic image of the diffractive structure in the fiber core is presented. The grating of 1.07 µm is realized by pulling the fiber with constant speed while the laser pulses are applied with a repetition frequency of 1 kHz. The results are usable in the sphere of creation of different fiber optic sensitive elements based on Bragg gratings.

ELLIPSOMETRY METHOD APPLICATION IN OPTICS OF INHOMOGENEOUS MEDIA
Gorlyak Andrei Nikolaevich, Khramtsovsky Igor Anatolievich, Solonukha Vladimir Mikhailovich

378

Physico-mathematical methods of modeling and measurements of polarization optical characteristics of “inhomogeneous surface layer – inhomogeneous medium” reflective system have been improved based on generalization of the polarized light reflection theory in the Born approximation from inhomogeneous media interface. Theoretical and experimental justification for simultaneous application of multi-angular and scanning ellipsometry methods is given for gradient optics elements in inhomogeneous layer presence on the surface of the optical detail. The measurement of the main ellipsometric parameters – linear reduced polarization azimuth Ψand phase difference Δbetween mutually orthogonal p– and s– components of a reflected polarized light beam – was carried out on a dual-channel installation, in which the scheme of measurements of polarization parameters Ψand Δby balanced (null) ellipsometry method is used in the first channel; the photometric scheme of measurements of parameters Ψand Δby Fourier method of output detection is used in the second channel. Such separation of channels gives the possibility for measuring of polarization parameters of reflected light beam separately and, thereby, improving the accuracy of ellipsometric measurements in relation to observable physical quantity of measurements object. The values of refractive index n(r) and absorption index k(r) were calculated by axial section of selfoc on the basis of measurements of polarization parameters Ψand Δwith angle of incidence of the light beam φ=45о within the limits of scanning ellipsometry method and a model of geometrically flat interface of homogeneous media. Empirical data indicated the model incorrectness of the geometrically flat interface for polarization measurements of refractive index distributionn(r) and absorption index k(r) in gradient optical engineering elements. For the reflective system “inhomogeneous surface layer – inhomogeneous medium” the refractive index n(r) change by axial section of an element r is proportional to phase difference Δ(r) between mutually orthogonal components of a reflected light beam. At the same time the linear reduced polarization azimuth Ψ(r) in the section gradient optical element varies slightly. The main proportions for calculation of refractive index nсand thickness dсof superficial layer in each local point r of selfoc are adduced on the basis of the ellipsometry equation, obtained within the framework of the polarized light reflection Born theory. Empirical data of experimental researches make it possible to give quantitative assessment of surface processing quality for optical engineering elements. Elaborated ellipsometric techniques are recommended in technological production of optical base assemblies with gradient and fiber optics elements.

METHOD OF SOFTWARE-BASED COMPENSATION OF TECHNOLOGICAL
VARIATION IN CHROMATICITY COORDINATES OF LCD PANELS
Zharinov Igor Olegovich, Zharinov Oleg O

387

Subject of research. The problem of software-based compensation of technological variation in chromaticity coordinates of liquid crystal panels is considered. A method of software-based compensation of technological variation in chromaticity coordinates is proposed. The method provides the color reproduction characteristics of the series-produced samples on-board indication equipment corresponding to the sample equipment, which is taken as the standard. Method. Mathematical calculation of the profile is performed for the given model of the liquid crystal panel. The coefficients that correspond to the typical values of the chromaticity coordinates for the vertices of the triangle color coverage constitute a reference mathematical model of the plate LCD panel from a specific manufacturer. At the stage of incoming inspection the sample of the liquid crystal panel, that is to be implemented within indication equipment, is mounted on the lighting test unit, where Nokia-Test control is provided by the formation of the RGB codes for display the image of a homogeneous field in the red, green, blue and white. The measurement of the (x,y)-chromaticity coordinates in red, green, blue and white colors is performed using a colorimeter with the known value of absolute error. Instead of using lighting equipment, such measurements may be carried out immediately on the sample indication equipment during customizing procedure. The measured values are used to calculate individual LCD-panel profile coefficients through the use of Grassman's transformation, establishing mutual relations between the XYZ-color coordinates and RGB codes to be used for displaying the image on the liquid crystal panel. The obtained coefficients are to be set into the memory of the graphics controller together with the functional software and then used for image displaying. Main results. The efficiency of the proposed method of software-based compensation for technological variation of chromaticity coordinates of liquid crystal panel was estimated by the ratio criterion of the areas of cross sections of the histograms p(x,y) at a given probability confidence level, calculated before and after compensation procedure. The sections of histograms, representing distributions of chromaticity coordinates were obtained by mathematical simulation in MathCad 15.0. The simulation software of the method of software-based compensation gives the possibility to obtain the mutual arrangement between the figures formed by sections of the histograms of (x,y)-chromaticity coordinates, and it may be observed as significant reduction of the area after compensation procedure is performed, and changes in the geometry of the cross section shape as well. Sets of dependency curves were obtained, depicting the efficiency criterion value versus resolution of the colorimeter that is used for measuring the chromaticity coordinates. Practical relevance. Research results are usable for engineers who are designing modern indication equipment based on LCD-panels and by manufacturers for colorimetric calculations and for estimation of technological tolerance of chromaticity coordinates among display units in mass production as well.

HIGH-PRECISION DETERMINATION OF THE ANGULAR POSITION FOR POINT
LIGHT SOURCE WITH CCD-ARRAYS
Lebedko Yevgeny Georgievich, Zvereva Elena N, Nguen Vu Tung

398

Subject of study. A method of angular position measuring for point light source in the system with CCD arrays is proposed by converting of angle – time – code in low light conditions and at high signal / noise ratio. Assessment of the method potential accuracy is given. It is determined by instrumental irremovable random errors of measurement in terms of optimal processing of incoming information with a single reading it with CCD – arrays. Method. This work introduces an optoelectronic system circuit with CCD arrays with stretched sensing elements and a point of reference for angular position measuring. In this case the arrays have images projections of both the reference point source and the target point source, which angular position is measured with high precision. From the CCD array output the signals arrive at an optimal (or apt) linear filter, and then to the signal peak position detection circuit. The scheme provides minimum error due to the influence of noise. Pulse edges, corresponding to the signals maximum, make a time interval filled with high-frequency counting pulses. The number of pulses in this interval will correspond to the measured angular position of the target point source. Main results. Analysis of random errors has been carried out in terms of statistical decision theory. Analysis takes into account the spectral function of the signals defined by transfer functions of the optical system and a CCD array as an image analyzer. Research of measurement accuracy is carried out depending on the clock frequency of reading information from CCD arrays for different values of signal-to-noise ratio. It has been shown that even with a single readout with CCD array by the proposed opto-electronic circuit measuring error does not exceed 0.01 of the sensing element size. Practical significance. The results are usable in high-precision measuring opto-electronic systems of star sensors for determining the angular position of the low-power point light sources.

REQUIREMENTS FOR IMAGE QUALITY OF EMERGENCY SPACECRAFTS
Alexander I. Altuchov, Korshunov Denis S., Shabakov Evgeniy I

405

The paper deals with the method for formation of quality requirements to the images of emergency spacecrafts. The images are obtained by means of remote sensing of near-earth space orbital deployment in the visible range.
of electromagnetic radiation. The method is based on a joint taking into account conditions of space survey, characteristics of surveillance equipment, main design features of the observed spacecrafts and orbital inspection tasks. Method. Quality score is the predicted linear resolution image that gives the possibility to create a complete view of pictorial properties of the space image obtained by electro-optical system from the observing satellite. Formulation of requirements to the numerical value of this indicator is proposed to perform based on the properties of remote sensing system, forming images in the conditions of outer space, and the properties of the observed emergency spacecraft: dimensions, platform construction of the satellite, on-board equipment placement. For method implementation the authors have developed a predictive model of requirements to a linear resolution for images of emergency spacecrafts, making it possible to select the intervals of space shooting and get the satellite images required for quality interpretation. Main results. To verify the proposed model functionality we have carried out calculations of the numerical values for the linear resolution of the image, ensuring the successful task of determining the gross structural damage of the spacecrafts and identifying changes in their spatial orientation. As input data were used with dimensions and geometric primitives corresponding to the shape of deemed inspected spacecrafts: Resurs-P", "Canopus-B", "Electro-L". Numerical values of the linear resolution images have been obtained, ensuring the successful task solution for determining the gross structural damage of spacecrafts.

CALCULATION AND RESEARCH OF CONTACT OPHTHALMIC DUAL
APPLICATION LENSES
Cherkasova Dina Nikolaevna, Кузьмина Е. С., Kuzmin Dmitriy Alexandrovich

411

Subject of research. Algorithm for calculation of contact ophthalmic lenses for dual application has been suggested based on unified approach for their calculation. The algorithm has been tested on the composition of Goldmann ophthalmic lenses and Panfundoscope lens optical systems. Method. The condition of mutual unambiguous orientation of patient’s eye and instruments is performed at the initial calculation step by face mounting and movement of coordinate table with optical head. Then such type of patient's eye optical system model is selected that the lens would be combined with the front surface of eye cornea optical system. Pupil of patient eye is under anesthesia. At the final calculation step we determine the functions of optical lens image quality and their values based on medical and technical requirements for the components of the complex system. Main results. The algorithm for ophthalmic lenses calculation has been suggested and its correctness has been proved practically on the example of two basic models in the group of such type lenses being applied in practice as a part of complex system with ophthalmic laser coagulators. Optical calculation of Goldmann ophthalmic contact lenses and Panfundoscope is presented. The method of neutralization is optimal for Goldmann lenses. The first component in Panfundoscope operates the position of object planes whereas the second component operates the position of complex system with ophthalmocoagulator's pupils. Computer modeling of complex system "Computer model of eye-ophthalmic lens" in ZEMAX confirmed the correctness of calculation algorithm in which the criteria of diffraction image quality has been used. Application possibility of simplified computer eye model called "Reduced eye" by Verbitskiy has been demonstrated. Practical relevance. The general scientific approach to the problem of synthesis, calculation and research of complex system with contact ophthalmic lenses for diagnostics and laser intervention on the eyeground has been found and confirmed. The results obtained have practical significance for the further development of optical calculation method and optical ophthalmologic instruments such as the fundus camera, wavefront analysers, opthalmoscopes and systems of vision optical correction.

### AUTOMATIC CONTROL AND ROBOTICS

APPROACHES FOR STABILIZING OF BIPED ROBOTS IN A STANDING
POSITION ON MOVABLE SUPPORT
Bazylev Dmitry N, Pyrkin Anton Alexandrovich, Margun Alexei A., Zimenko Konstantin A., Kremlev Artem Sergeevich, Ibraev Denis D., Čech Martin

418

Subject of research. The problem of stabilization for biped walking robots on the surface is considered. The angle and angular velocity of the movable surface varies randomly in a limited range. Methods. Two approaches of stabilization of biped robots are proposed. The first approach requires the construction of kinematic and dynamic models of the robot. Dynamic equations were obtained using the Euler-Lagrange method. The control algorithm is based on the method of inverse dynamics, in which the original nonlinear dynamic model is linearized by a feedback. The second stabilization algorithm uses only the kinematic model of the robot. A hybrid controller is developed for this approach. In the case of low angular velocities of the movable support the robot stabilization is performed by PD controller on the basis of the angle error of deflection of the servo shaft. In the case of relatively high angular velocities of the support the controller also uses the gyroscope readings mounted in the robot torso. Maintenance of the robot’s gravity center over the center of bearing area for providing a stable position was chosen as a goal of control in both approaches. Main results. Efficiency and effectiveness of the proposed approaches for stabilization of biped robots on the moving surface are demonstrated by the numerical simulation. Both methods provide stability of the balancing robots on changing the angle of inclination and angular velocity of the moving surface in the ranges (50; 50) and (40 / sec; 40 / sec) , respectively. Comparative analysis of these approaches under identical requirements for quality indicators of transients is also provided: transient time 0.2 sec п t and overshoot 0%. The conditions under which each of the control methods will be more effective in practice are identified.

### MATERIAL SCIENCE AND NANOTECHNOLOGIES

LASER ABLATION OF MONOCRYSTALLINE SILICON
UNDER PULSED-FREQUENCY FIBER LASER
Veiko Vadim Pavlovich, Skvortsov Albert Matveevich, Huynh Cong Tu , Petrov Andrei Anatolievich

426

Subject of research. The paper deals with research of the surface ablation for single-crystal silicon wafers and properties of materials obtained in response to silicon ablation while scanning beam radiation of pulse fiber ytterbium laser with a
wavelenght λ = 1062 nm in view of variation of radiation power and scanning modes. Method. Wafers of commercial p-type conductivity silicon doped with boron (111), n-type conductivity silicon doped with phosphorus (100) have been under research with a layer of intrinsical silicon oxide having the thickness equal to several 10 s of nanometers and SiO2 layer thickness from 120 to 300 nm grown by thermal oxidation method. The learning system comprises pulse fiber ytterbium laser with a wavelenght λ = 1062 nm. The laser rated-power output is equal to 20 W, pulse length is 100 ns. Pulses frequency is in the range from 20 kHz to 100 kHz. Rated energy in the pulse is equal to 1.0 mJ. Scanning has been carried out by means of two axial scanning device driven by VM2500+ and controlled by personal computer with «SinMarkТМ» software package. Scanning velocity is in the range from 10 mm/s to 4000 mm/s, the covering varies from 100 lines per mm to 3000 lines per mm. Control of samples has been carried out by means of Axio Imager A1m optical microscope Carl Zeiss production with a high definition digital video camera. All experiments have been carried out in the mode of focused laser beam with a radiation spot diameter at the substrate equal to 50 μm. The change of temperature and its distribution along the surface have been evaluated by FLIR IR imager of SC7000 series. Main results. It is shown that ablation occurs without silicon melting and with plasma torch origination. The particles of ejected silicon take part in formation of silicon ions plasma and atmosphere gases supporting the plasmo-chemical growth of SiO2. The range of beam scanning modes is determined where the growth of SiO2 layer is observed. Beginning with scanning velocity equal to 2000 mm/s, the torch existence is not fixed visually; silicon oxide origination is stopped, and silicon particles with nanometer sizes are formed as a result of silicon destruction. The process of silicon destruction is followed by sounds of different frequency depending on scanning velocity. Practical significance. The surface ablation for single-crystal silicon has been shown for the first time ever to be influenced significally by such features of laser radiation as laser beam scanning velocity and the covering of scanning lines. Laser beam scanning modes of pulse fiber ytterbium laser with a wavelenght λ = 1062 nm have been found out providing the synthesis of nanostructured silicon dioxide particles or silicon nanoparticles.

SYNTHESIS OF MULTI-LAYER SUBSTRATE FOR OBSERVING
OF HYDROXYBENZOIC ACIDS MOLECULES BY SERS
Yasenko Egor Andreevich, Chelibanov Vladimir Petrovich

435

Subject of study. The paper deals with the results of the multilayer substrate synthesis having an effect of SERS from hydroxybenzoic acid molecules which are adsorbed on its surface. Methods. To produce SERS substrate we have applied colloid chemistry methods: washing of colloids using a laboratory centrifuge OPn-8, carrying out serial chemical reactions for modifying the surface of semiconductor particles of SiO2 in the solution, determining the maximum of the absorption spectrum of the substrate obtained (in the range from 400 to 1000 nm). To observe hydroxybenzoic acids molecules the method of Raman scattering on OPTEC-785 Video-M spectrometer has been used. Main results. A new method of the substrate chemical synthesis is proposed, which has the effect of SERS by radiationexcitation wavelength of 785 nm, based on micron silica particles with immobilized surface of gold and silver. Raman spectra of hydroxybenzoic acids (Gallic and p-hydroxybenzoic) in free and adsorbed state have been experimentally obtained and interpreted. It was shown that both acids in a crystalline state are in the form of dimers. Also, the presence of a certain group of characteristic bands indicates that the hydroxybenzoic acid is chemically bonded to the substrate surface through an oxygen bridge of deprotonated hydroxyl groups. However, unlike Gallic acid, p-hydroxybenzoic acid passes into the monomer form. Practical significance. This technique for enhancing substrate preparation is usable in the laboratory without sophisticated technical equipment. Experimental data on the method of securing the hydroxybenzoic acids and form of their existence on the surface of the substrate will be useful in the design of sensor systems based on them. Characteristic bands of undistorted aromatic ring of hydroxybenzoic acids may also be used in developing

EUROPIUM ION INFLUENCE ON THE FORMATION OF Ag-NANOPARTICLES
IN FLUORINE PHOSPHATE GLASSES
Pysh'ev Rostislav O, Kolobkova Elena V

443

The paper deals with research of formation characteristics of silver nanoparticles in fluorophosphate glasses 0.25 Na2O - 0.5 P2O5 - 0.10 Ga2O3 - 0.075 AlF3 - 0.025 NaF - 0.05 ZnF2 doped with EuF3 (0.8 and 4 wt.%) and without them. The synthesis was carried out in closed glassy carbon crucibles in argon atmosphere. Nanoparticles were formed after a low temperature process of Ag+ → Na+ ion-exchange (320 °C) and subsequent heat treatment. It was shown that in the initial glasses doped with EuF3, rare earth ions exist in two valence forms (Eu2+ and Eu3+) in dynamic equilibrium and the concentration of Eu2+ increases proportionally to the total concentration of fluoride. It was shown that sizes of molecular clusters or metal nanoparticles depend on the concentration of europium fluoride and duration of ion exchange. The metallic Ag-nanoparticles sizes were defined for different times of heat treatment and ion exchange. The possibility of the stimulating growth of nanoparticles through the introduction of additional EuF3 in the glass was proved. The possibility of obtaining nanoparticles without the heat treatment in glasses with a high concentration of EuF3 was shown. Chemical mechanism for the formation of Ag-nanoparticles during the ion exchange was suggested.

PROPERTIES AND OPTICAL APPLICATION OF POLYCRYSTALLINE
ZINC SELENIDE OBTAINED BY PHYSICAL VAPOR DEPOSITION
Dunaev Anatoliy Alexeevich, Egorova Irina Lvovna

449

Findings on production technology, mechanical and optical properties of polycrystalline zinc selenide are presented. The combination of its physicochemical properties provides wide application of ZnSe in IR optics. Production technology is based on the method of physical vapor deposition on a heated substrate (Physical Vapor Deposition - PVD). The structural features and heterogeneity of elemental composition for the growth surfaces of ZnSe polycrystalline blanks were investigated using CAMEBAX X-ray micro-analyzer. Characteristic pyramid-shaped crystallites were recorded for all growth surfaces. The measurements of the ratio for major elements concentrations show their compliance with the stoichiometry of the ZnSe compounds. Birefringence, optical homogeneity, thermal conductivity, mechanical and optical properties were measured. It is established that regardless of polycrystalline condensate columnar and texturing, the optical material is photomechanically isotropic and homogeneous. The actual performance of parts made of polycrystalline optical zinc selenide in the thermal spectral ranges from 3 to 5 μm and from 8 to 14 μm and in the CO2 laser processing plants with a power density of 500 W/cm2 is shown. The developed technology gives the possibility to produce polycrystalline optical material on an industrial scale.

COMPARISON OF TWO TEMPERATURE MEASUREMENT METHODS
BY UPCONVERSION FLUORESCENCE SPECTRA OF ERBIUM-DOPED
LEAD-FLUORIDE NANO-GLASS-CERAMICS
Vladimir A. Aseev, Varaksa Yury Anatolievich, Kolobkova Elena V, Sinitsin Georgy Vladimirovich, Khodasevich Mikhail Alexandrovich, Anatoly S. Yasyukevich

457

The study and compare of two temperature measurement methods is performed for the case of a lead-fluoride nano-glassceramics in the range from 317 to 423 K with a view to their application to temperature sensors. A method of temperature
measurement by means of violet, green and red upconversion fluorescence spectra regression on latent structures and a method of temperature measurement by two fluorescence bands intensity ratio in green range are considered. It is shown that a four-dimensional space of latent structures is an optimum one in terms of temperature measurement accuracy. It made possible temperature determining with a relative error not larger than 0.15% at temperatures higher than 340 K by making use of fluorescence spectra training set with the step of 10 K. The method using two green bands fluorescence intensity ratio is inferior by the accuracy. Independence of pump power fluctuations is a significant advantage of the second method. To take advantage of the first method a stabilization of the pump power is necessary. The results of the work can be taken into account while developing optical temperature sensors with a better performance (in relation to accuracy and measurement
range) compared to existing ones which utilize temperature redistribution of fluorescence intensities in two closely-spaced bands or temperature dependence of fluorescence lifetime.

### COMPUTER SCIENCE

CENTRALIZED MAC PROTOCOL FOR HIERARCHICAL CACHING
PROCESSORS
Antonov Alexander A, Klyuchev Arkadiy O, Komar Maria S., Kustarev Pavel V , Koucheryavy Yevgeni A., Moltchanov Dmitri A., Petrov Vitaly I., Platunov Alexey E

463

The subject of research is the architecture of modern processors with hierarchical organization of cache subsystem. Analysis of implementation possibility of wireless connectivity between cores and Level 3 cache has been carried out. In order tospecify the requirements to wireless communication channel, communication in modern general-purpose processors has been explored by an example of Intel Core i7 (Haswell). Interaction model of cache subsystem components has been developed, and on its basis interaction characteristics between them are being evaluated. Analysis of the model shows that the latency of cache line transmission via the proposed channel is about 0.26 nanoseconds, which correlates well with the latency of L1 cache (about 2 nanoseconds). Also, wireless channel satisfies the distance requirements, giving the possibility for data transmission upto 3 centimeters, as well as power requirements with consumption of 1 uW. The result of research is the developed medium access protocol for wireless connectivity between computational cores and Level 3 cache. To account for required simplicity of implementation and efficiency of operation, it is proposed to use the single frequency range for all radio interfaces and time division multiple access scheme with prescribed fields for addressing and data. The paper deals with protocol data unit structure, which is used for communication between units. Possibility of shared time counter creationis used for synchronization between units. Time division duplex with possibly dynamic non-equal time shares is used to organize uplink and downlink communications. Time division mechanism gives the possibility for the system to adapt to load irregularities between the cores through allocation of various amounts of time slots for each core.

ANALYSIS AND ESTIMATION OF THE TRIE MINIMUM LEVEL IN NON-HASH
DEDUPLICATION SYSTEM
Zhukov Maxim A., Afanasiev Dmitry B.

470

Subject of research. The paper deals with a method of restriction for the trie minimum level in non-hash data deduplication system. Method. The subject matter of the method lies in forcibly completing the trie to a specific minimum level. The proposed method makes it possible to increase performance of the process by reducing the number of collisions at the lower levels ofthe trie. The maximum theoretical performance growth corresponds to the share of collisions in the total number of data read operations from the storage medium. Proposed method application increases the metadata size to the amount of new structures containing one element. Main results. The results of the work have been proved by the data of computational experiment with non-has deduplication on 528 GB data set. The process analysis has shown that 99% of the execution time is taken to head positioning of hard-drives. The reason is a random distribution of the blocks on the storage medium. Application of the method of minimum level restriction for the trie in non-hash data deduplication system on the experimental data set gives the possibility to increase performance maximum by 16% and the increase of metadata size is 49%. The total amount of metadata is 34% less than with hash-based deduplication using the MD5 algorithm, and is 17% less than using Tiger192 algorithm. These results confirm the effectiveness of the proposed method. Practical relevance. The proposed method increases the performance of deduplication process by reducing the number of collisions in the trie construction. The results are of practical importance for professionals involved in the development of non-hash data deduplication methods.

CREATION OF PARTIAL ORDERS OF VARIANTS FOR SELECTION
OF OPTIMAL ALTERNATIVES IN HOMOGENEOUS SETS
Kandyrin Yuri V, Shkurina Galina L

476

Subject of consideration. The paper deals with the method for structure creation of the initial set of homogeneous variants in the database adapted to selection task solution according to their target (functional) assignment. This task is actual for the electronic quick reference guides: on materials, components, parts, medicines, etc. which special-purpose designation in homogeneous group is more time-proof, than requirements on admissibility in each new selection task. Method. The offered approach is based on data structure creation representing the partial order of alternatives, designed by unconditional Pareto criterion, from a set of linear or partial orders of variants with smaller dimension. The dimension of quality measures taken into account specifies the partial order dimension, and its structure is predetermined by a special-purpose designation of variants in homogeneous set through taken into account quality measures. The final elements in the partial order graph represent Pareto optimal variants, which need to be tested only on admissibility in each new selection task. The resulting partial order is formed by means of factor sets. Main results. We have worked out the method of data adaptive adjustment on selection task which gives the possibility to start solution at once with Pareto optimal variants only by their admissibility check. The offered approach is much more effective than the traditional one, when in the beginning selection of valid variants is done, and then of the optimal ones, owing to reduction the number of multiple combinatorial criteria comparison in each new selection task. The method efficiency is confirmed by the fact that the power of Pareto optimal variants is always less or equal to the power of initial variants, that is theoretically proved in [1]. It means, that the search of valid variants under the same requirements on smaller power set is always less labour-intensive, than the search of valid variants on the greater power set, owing to the less number of operations of binary comparisons of variants. Practical significance. The results of work are usable at creation of the electronic quick reference guides for standard and generic items, both as part of automated design engineering systems, and at creation of the Helps for managers and suppliers of components and materials. In the first case they are satellite systems, in the second case the off-line ones.

ABSTRACT MODELS FOR SYSTEM VIRTUALIZATION
Koveshnikov Michael G, Shcheglov Konstantin A, Shcheglov Andrey Yu

483

The paper is dedicated to issues of system objects securing (system files and user system or application configuration files) against unauthorized access including denial of service attacks. We have suggested the method and developed abstract system virtualization models, which are used toresearch attack scenarios for different virtualization modes. Estimation for system tools virtualization technology effectiveness is given. Suggested technology is based on redirection of access requests to system objects shared among access subjects. Whole and partial system virtualization modes have been modeled. The difference between them is the following: in the whole virtualization mode all copies of access system objects are created whereon subjects’ requests are redirected including corresponding application objects;in the partial virtualization mode corresponding copies are created only for part of a system, for example, only system objects for applications. Alternative solutions effectiveness is valued relating to different attack scenarios. We consider proprietary and approved technical solution which implements system virtualization method for Microsoft Windows OS family. Administrative simplicity and capabilities of correspondingly designed system objects security tools are illustrated on this example. Practical significance of the suggested security method has been confirmed.

### MODELING AND SIMULATION

SELF-CONSISTENT FIELD MODEL OF BRUSHES
FORMED BY ROOT-TETHERED DENDRONS
Zhulina Ekaterina B, Leermakers Franciscus Andrianus Maria , Oleg V. Borisov

493

We present an analytical self-consistent field (scf) theory that describes planar brushes formed by regularly branched root-tethered dendrons of the second and third generations. The developed approach gives the possibility for calculation of the scf molecular potential acting at monomers of the tethered chains. In the linear elasticity regime for stretched polymers, the molecular potential has a parabolic shape with the parameter k depending on architectural parameters of tethered macromolecules: polymerization degrees of spacers, branching functionalities, and number of generations. For dendrons of the second generation, we formulate a general equation for parameter k and analyze how variations in the architectural parameters of these dendrons affect the molecular potential. For dendrons of the third generation, an analytical expression for parameter k is available only for symmetric macromolecules with equal lengths of all spacers and equal branching functionalities in all generations. We analyze how the thickness of dendron brush in a good solvent is affected by variations in the chain architecture. Results of the developed scf theory are compared with predictions of boxlike scaling model. We demonstrate that in the limit of high branching functionalities, the results of both approaches become consistent if the value of exponent bin boxlike model is put to unity.In conclusion, we briefly discuss the systems to which the developed scf theory is applicable. These are: planar and concave spherical and cylindrical brushes under various solvent conditions (including solvent-free melted brushes) and brush-like layers of ionic (polyelectrolyte) dendrons.

INTERFERENCE OF UNIDIRECTIONAL SHOCK WAVES
Bulat Pavel V, Denissenko Petr V.

500

Subject of study.We consider interference of unidirectional shock waves or, as they are called, catching up shock waves. The scope of work is to give a classification of the shock-wave structures that arise in this type of interaction of shock waves, and the area of their existence. Intersection of unidirectional shock waves results in arising of a shock-wave structure at the intersection point, which contains the main shock wave, tangential discontinuity and one more reflected gas-dynamic discontinuity of unknown beforehand type. The problem of determining the type of reflected discontinuity is the main problem that one has to solve in the study of catching shock waves interference. Main results.The paper presents the pictures of shock-wave structures arising at the interaction of catching up shock waves. The areas with a regular and irregular unidirectional interaction of shocks are described. Characteristic shock-wave structures are of greatest interest, where reflected gas-dynamic discontinuity degenerates into discontinuous characteristics. Such structures have a number of extreme properties. We have found the areas of existence for such shock-wave structures. There are also areas in which the steady-state solution is not available. The latter has determined revival of interest for the theoretical study of the problem, because the facts of sudden shock-wave structure destruction inside the air intake of supersonic aircrafts at high Mach numbers have been discovered. Practical significance.The theory of interference for unidirectional shock waves and design procedure are usable in the design of supersonic air intakes. It is also relevant for application possibility investigation of catching up oblique shock waves to create overcompressed detonation in perspective detonation air-jet and rocket engines.

APPLICABILITY OF VARIOUS DIFFERENTIAL TURBULENCE MODELS
IN THE CALCULATION OF SUPERSONIC GAS JETS
Ilina Ekaterina E., Il'ina Tamara E., Denissenko Petr V.

509

Subject of study. The paper presents research results of the applicability of the most common turbulence models to the calculation of turbulent supersonic jets containing shock waves. The aim of the study is to develop an efficient method for calculating non-isobaric turbulent supersonic gas jets containing shock waves. In the axisymmetric case such jets are characterized by irregular reflection of shock waves from the axis of symmetry, that is followed by the formation of normal shock waves (Mach disks), which are compatible with the peaks of pressure and temperature on the jet axis. The flow behind the Mach disk is subsonic. The appearance of subsonic flow region and the abrupt change of flow parameters on the direct shock wave leads to some methodological difficulties in the application of the standard two-parameter differential models of turbulence. It is known that various turbulence models lead to significantly different parameters distribution along the axis of the jet. In particular, the degree of blurring for shock wave structure of the jet for some turbulence models is significantly different from the observed one by experiment. Main results. Comparison of widely represented in modern commercial computing packages turbulence models was completed: k-ωturbulence model, Realizable k-ε model, RNG k-ε model, SAS-model, Standard SST k-ω model, transition SST- model. Testing has shown that Realizable k-ε and transition SST turbulence models provide the best results in the calculation of supersonic flows, typical for advanced jet engines. The first model provides reliable data about the distribution of pressure along the jet axis, bottom pressure, the pressure distribution on the walls of the nozzle and ejector at low differential pressure at the nozzle exit and the environment, which are typical for the normal operation of air-jet engines. Good accuracy can be obtained at a fairly coarse grid without the use of any special techniques and tricks. Transition SST turbulence model provides a better match with the experimental results in the case of a large pressure difference between the nozzle exit and the environment. It is more particular about the difference grid quality, boundary and initial conditions, characterized by essentially increasing calculation time. At the same time, it guarantees qualitative accurate picture of shock-wave structure with acceptable accuracy of the pressure distribution determination along the jet axis. Practical significance. Practical application of recommendations listed in the paper will give the possibility for researchers to avoid gross inaccuracies in the calculation of supersonic gas jets.

ON PRICE CHOICE AT SELLING OF INFORMATION RESOURCES
Ivanova Olga S., Amelkin Sergei A., Tsirlin Anatoly M.

517

The paper considers the problem of the pricing policy determination in the company, selling information resource at the market. The problem of the optimal price determination for an information resource is solved depending on the time for the case when the seller-company has no competitors in the market, the market is saturated, and buyers are not able to further spread of the resource. Conditions for the optimal choice of information resource price have been obtained; the maximum possible income of the company has been calculated for linear demand function, and conditions, determining the duration and volume of sales, providing the maximum of average income of the company, have been obtained as well. The problem of optimal price choice is solved by macrosystem approach that has made it possible to reduce it to the isoperimetric kind. It is shown that the optimal price dependence on time for a linear demand function should provide a linearly increasing rate of sales. Conditions have been derived under which the sales proceedings for an information resource are positive, relationship is determined between volume of sales and timeline at which the average income during the sales reaches its maximum. The results are given in dimensionless form, thereby reducing the number of independent parameters. These results are usable for the pricing analysis of software and other information products.

GENETIC ALGORITHM APPLICATION FOR MULTI-CRITERIA SCHEDULING PROBLEM
Arkhipov Ivan V.

525

The paper describes mathematical model and method of task solution for defining an enterprise work performance schedule. Two-stage feedstock processing is supposed to exist at the enterprise. At the first stage the sawing process into semimanufactured products is done. The second stage (finished products manufacturing stage) includes durable processing of obtained semimanufactured products at one of the interchangeable work centers. The sawing process into semimanufactured products is carried out according to a plan, developed in advance and in compliance with technological charts. Scheduling consists of separate cutting calculation and planning of all feedstock cutting with the aim of the most effective specification task performance based on available reserves. Following the cutting plan, an enterprise work performance schedule is created. This schedule consists of the cutting sequence with volume, start and end time, and plan for loading of after-treatment. The solution to this problem becomes more involved due to the necessity of taking into account all features, limitations and parameters of process equipment, as well as of raw material and production orders. Special method based on genetic algorithm has been proposed for handling the problem. The algorithm has been tested on several different realproduction plans. Its efficiency estimation is given. The software systemimplemented on the proposed algorithm has been tested on real operating data of several sawmills. Reduction of machine idle time and incomplete production decrease has been confirmed by the enterprise specialists.

INFLUENCE OF DFT-FUNCTIONAL AND BASIS SET OF FUNCTIONS ON CALCULATION RESULTS OF THE STRUCTURAL AND ENERGY PROPERTIES OF Ag

_{2}MOLECULAR CLUSTER Stolyarchuk Maxim V., Sidorov Alexander Ivanvich532

The paper deals with the impactassessmentforthe exchange-correlation functionalsand Slater-type basis sets on the properties of molecular cluster Ag2carried outwithin the framework of the density functional theory. For comparative analysis of these properties equilibrium bond length and the total binding energy of the molecular cluster were used. The effect of the change of all-electron basis sets dimension within four exchange-correlation functionals of different categories was analyzed. We also discuss the results obtained for the basis sets with different levels of frozen-core approximation. Results obtained with the gradient corrected exchange-correlation functionals and all-electron QZ4P basis set show the best agreement with the experimentally determined values. Small size frozen-core approximation reduces the computation time,and the deviation of the calculated values of the binding energy takes a smaller value compared to all-electron basis sets. The results are of methodological interest for the correct calculation of the characteristics of molecular clusters with the expected accuracy.

MATHEMATICAL MODEL FOR CALCULATION OF INFORMATION RISKS
FOR INFORMATION AND LOGISTICS SYSTEM
Korobeynikov Anatoliy Grigorievich, Grishentsev Alexey Yu., Komarova Irina , Ashevsky Dmitry Yu., Aleksanin Sergey A, Markina Galina L

538

Subject of research. The paper deals with mathematical model for assessment calculation of information risks arising during transporting and distribution of material resources in the conditions of uncertainty. Meanwhile information risks imply the danger of origin of losses or damage as a result of application of information technologies by the company. Method. The solution is based on ideology of the transport task solution in stochastic statement with mobilization of mathematical modeling theory methods, the theory of graphs, probability theory, Markov chains. Creation of mathematical model is performed through the several stages. At the initial stage, capacity on different sites depending on time is calculated, on the basis of information received from information and logistic system, the weight matrix is formed and the digraph is under construction. Then there is a search of the minimum route which covers all specified vertexes by means of Dejkstra algorithm. At the second stage, systems of differential Kolmogorov equations are formed using information about the calculated route. The received decisions show probabilities of resources location in concrete vertex depending on time. At the third stage, general probability of the whole route passing depending on time is calculated on the basis of multiplication theorem of probabilities. Information risk, as time function, is defined by multiplication of the greatest possible damage by the general probability of the whole route passing. In this case information risk is measured in units of damage which corresponds to that monetary unit which the information and logistic system operates with. Main results. Operability of the presented mathematical model is shown on a concrete example of transportation of material resources where places of shipment and delivery, routes and their capacity, the greatest possible damage and admissible risk are specified. The calculations presented on a diagram showed that risk value under the specified conditions becomes lower than permissible if the demanded time of material resources transportation determined by the customer is more than 50 minutes. This calculation provides additional information for the person making the decision about the offer acceptance or refusal on transportation of material resources to the specified points. Practical significance. Results of work are usable in the fully functional information and logistic systems for calculation of the information risks arising during the transporting or distribution of material resources. It will increase competitiveness of the logistic companies operating in the conditions of the modern market relations.

### BRIEF PAPERS

DETERMINATION OF VICKERS MICROHARDNESS IN β-Ga

_{2}O_{3}SINGLE CRYSTALS GROWN FROM THEIR OWN MELT Guzilova Lyubov I., Maslov Victor N., Aifantis Katerina E, Romanov Alexey E, Nikolaev Vladimir I546

The results of microhardness measurements of β-Ga2O3 single crystals for (001) crystallographic face are reported. The crystals were grown by the free crystallization with the "Garnet-2M" equipment. Microhardness values were determined by the Vickers method at varying loads. A four-sided diamond pyramid was used as an indenter. The average value of gallium oxide microhardness was equal to 8.91 GPa. We have carried out comparison of the values obtained with the microhardness for the other wide bandgap semiconductors - epitaxial GaN layers grown on 6H-SiC and GaP layers grown on GaP:S. The findings are usable for machining process development of β-Ga2O3 single crystal substrates. In particular, silicon carbide and electrocorundum may be recommended for β-Ga2O3 machine processing.