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Editor-in-Chief

**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

Partners

**Summaries of the Issue**

### REVIEW PAPER

TRENDS IN THE DEVELOPMENT OF DETONATION ENGINES
FOR HIGH-SPEED AEROSPACE AIRCRAFTS AND THE PROBLEM
OF TRIPLE CONFIGURATIONS OF SHOCK WAVES.
Part I. Research of detonation engines
Bulat Pavel V, Denissenko Petr V., Volkov Konstantin N.

1

We consider current problems of improving propulsion systems of highly supersonic air-space vehicles. In the first part, we review historic developments and list the landmark scientific papers. Classification of detonation engines is presented with detailed consideration of rotation detonation engines and continuous detonation engines. Experimental results on detonation, which are of particular importance for the design of detonation engines, are discussed. The second part of the paper provides an overview of the development in detonation theory, mathematical modelling, and numerical simulation. We focus on the interference of shock waves with formation of triple points, regular and irregular reflection of shock waves, existence of multiple solutions and the resulting appearance of hysteresis. The relevance and importance of triple shock wave configurations for the development of new types of air intakes and detonation jet engines is demonstrated.

### OPTICAL ENGINEERING

SPECIAL ASPECTS OF INITIAL OPTICAL SCHEME SELECTION FOR DESIGN OF NON-IMAGING OPTICAL SYSTEMS
Anitropov Roman V, Benitez Pablo , Vladimir N. Vasiliev, Zaitceva Anastasiya S., Letunovskaya Marina V. , Livshits Irina Leonidovna, Stafeev Sergey K.

22

Subject of Research. The research results, structural composition analysis and the parametric synthesis of the projected imaging and non-imaging optical systems were presented. We made an attempt to use the gained experience about imaging systems while designing non-imaging systems, by adapting the composition theory for the calculations of non-imaging systems. Several patterns were revealed, which provide a deeper understanding of the design process of non-imaging optical systems; measures of its optimization were proposed. Method. We investigated the applicability of the theory of composition and synthesis of non-imaging optical systems. The main provisions of the theory of composition are based on the division of all available optical elements in four types depending on their functionality, which corresponds to a modular design. Similar items were identified in non-imaging optical systems and adaptation of composition theory to their design became possible. Main Results. General design patterns of imaging and non-imaging optical systems were studied. Classification of systems, components, as well as technical and generic characteristics of imaging and non-imaging optical systems was determined. Search mechanism of the initial optical system by means of structural and parametric synthesis of non-imaging optical system was formalized. The basic elements were determined included in non-imaging systems and their classification by functionality was done. They were subdivided into basic, corrective, wide angle and high aperture ones. The rules for formation of these elements and their composition were determined: surface reflecting, refracting, spherical and nonspherical elements with total internal reflection. The foundations of composition theory for non-imaging optical systems were laid. The approbation of this method was carried out on the example of the illumination system calculation for surgical room. A 3D model of an illumination optical system for surgical room was obtained, consisting of three identical domes. The illuminator designed with the use of the proposed methodology showed high energy efficiency (92.3%). Practical Relevance. The results can find application in optical design of non-imaging systems having various functionality, for example, illuminators, concentrators, etc. and can provide import substitution of similar foreign devices. The results can be useful by engineers specializing in the design and/or operation of non-imaging optical systems.

APPLICATION OF CHEMOMETRICS FOR ANALYSIS OF BIOAEROSOLS
BY FLOW-OPTICAL METHOD
Khudyakov Evgeniy S., Kochelaev Evgeniy A., Volchek Andrey O., Dmitry O. Kirsanov, Jahatspanian Igor E.

30

Subject of Research. The informativity of detection channels for bioaerosol analyzer is investigated. Analyzer operation is based on flow-optical method. Method. Measurements of fluorescence and the light scattering of separate bioaerosol particles were performed in five and two spectral ranges, correspondingly. The signals of soil dust particles were registered and used as an imitation of background atmospheric particles. For fluorescenceinduction of bioaerosol particles we used light sources: a laser one with a wavelength equal to 266 nm and 365 nm LED source.Main Results. Using chemometric data processing the classification of informative parameters has been performed and three most significant parameters have been chosen which account for 72% of total data variance. Testing has been done using SIMCA and k-NN methods. It has been proved that the use of the original and the reduced sets of three parameters produces comparable accuracy for classification of bioaerosols. Practical Relevance. The possibility of rapid detection and identification of bioaerosol particles of 1-10 microns respirable fraction (hindering in the human respiratory system) by flow-optical method on a background of non-biological particles is demonstrated. The most informative optical spectral ranges for development of compact and inexpensive analyzer are chosen.

APPROACH TO AUTOMATION OF LENS COMPONENTS CENTERING
FOR ASSEMBLING OF DIFFERENT DESIGN OBJECTIVES
Pimenov Aleksey Yu.

39

Subject of Research.Existing adjustment methods of lens objectives in two mechanical designs have been analyzed, the main ways of centering error compensation have been considered. The algorithm of automated search of optical elements position has been developed based on the existing methods of centering for compensation of residual decentering. The methods of joint application of this algorithm and centering machine “Trioptics Opticentric” have been suggested. Method. Centering errors of the objective lens components are measured on the centering machine. Aberrations of optical system are calculated by using the received data of centering errors entered to the objective mathematical model. For the calculation of aberration compensation, iteration algorithm of searching of optical elements optimal position is used. The image quality is analyzed for each obtained realization of the optical system. The result of program performance is data matrix about optical components location such that compensation of residual aberrations occurs. Based on the obtained information the system assembling is carried out with the use of centering machine “Trioptics Opticentric”. Main Results. Computer modeling of centering errors for 100 lens apochromatic objectives of drop-in mountings lens design has been carried out. The coma of object axial point image has been chosen as quality estimation criterion. The developed algorithm has been applied for the worst realization of the optical system. In this case the value of integral coma of object axial point image has been decreased by two orders and reduced practically to zero. It is noted that the modeling of adjustment process via using the algorithm of automated search enables to predict the possibility of objective assembly with required quality parameters. Practical Relevance. The received results can be applied on the lines of automated assembly of modern lens objectives.

METHOD FOR CREATION OF SPHERICAL PANORAMAS FROM IMAGES
OBTAINED BY OMNIDIRECTIONAL OPTOELECTRONIC SYSTEMS
Lazarenko Vasiliy P., Djamiykov Todor S., Korotaev Valery Viktorovich, Yaryshev Sergey Nikolaevich

46

Subject of Study. The key feature of spherical panoramas is the maximum possible angle of view (360 × 180 degrees). Omnidirectional optical-electronic systems are able to produce images that show most of this space, but these images are different from the canonical spherical panoramas. This paper proposes a method of converting the circular images obtained by omnidirectional optical systems, to canonical spherical panoramic images with the use ofcalibration procedure of omnidirectional optical-electronic system. Method. The process of spherical panoramas creation consists of three steps.The first step includesthe forming of virtual surface in the object space corresponding to a field of view of the spherical panorama. The surface is defined by the three-dimensional array of pixels.At the second step the coordinates of images of these points in the plane of the detectorare specified. At the third step pixel-by-pixel forming of the output imageisperformed from the original omnidirectional image with the use of coordinates obtained at the second step. Main Results. We have considered the geometric projectionmodel of spherical panoramas. The algorithm has been proposed calculating the three-dimensional array of pixels, characterizing the field of view of a spherical panorama and convenient for practical usage. The developed method is designed to work with omnidirectional optical-electronic systems both with catadioptric optical systems and with fisheye lens. Experimental results confirming the validity of this method are presented. The reprojection mean-square error was equal to 0.794 px. Practical Relevance. The proposed method can be applied in technologies of creating of virtual tours or panoramas of streets where spherical panoramic images are the standard for storing visual information. The method may also find its application in various fields of robotics, orientation and navigation of space vehicles and UAVs.

LINE-FIELD SWEPT-SOURCE OPTICAL COHERENCE TOMOGRAPHY SYSTEM FOR NEAR INFRARED SPECTRAL REGION
Gurov Igor P, Margaryants Nikita B., Pimenov Aleksey Yu.

54

Subject of Research.The system for line-field swept-source optical coherence tomography (OCT) for near infrared spectral range is considered. In this connection, for tomograms visualization, frequency of signal acquisition not less than 20 kHz is needed. It is inaccessible for 2D photo sensitive arrays. In order to solve this problem, it has been proposed to use the line array of photo detectors, which frame registration frequency reaches tens of kilohertz. Method. Peculiarity of the method consists in using illumination of an object under investigation by light intensity distribution in the form of line for providing maximum energy efficiency of optical system. In addition, it becomes possible to obtain B-scans without a need in lateral object scanning that increases the rate of formation and imaging of tomograms. Main Results. The OCT optical system using a high-speed array of photodetectors has been developed; aberration analysis has been carried out. Experimental investigations based on Linnik micro interferometer optical scheme has been carried out. Tomograms of different samples have been obtained. Practical Relevance. Тhe obtained results can be accepted as a basis for creation of compact high performance OCT system without lateral mechanical scanning.

### AUTOMATIC CONTROL AND ROBOTICS

BACKSTEPPING ALGORITHM FOR LINEAR SISO PLANTS
UNDER STRUCTURAL UNCERTAINTIES
Furtat Igor Borisivich, Nekhoroshikh Artem N.

61

The robust algorithm is proposed for parametric and structurally uncertain linear plants under external bounded disturbances. The structural uncertainty is an unknown dynamic order of the model of plants. The developed algorithm provides plant output tracking for a smooth bounded reference signal with a required accuracy at a finite time. It is assumed that only scalar input and output of the plants are available for measurement, but not their derivatives. For the synthesis of the control algorithm we use a modified backstepping algorithm. The synthesis of control algorithm is separated into rsteps, where ris an upper bound of the relative degree of control plant model. At each step we synthesize auxiliary controls that stabilize each subsystem about a zero. At the last step we synthesize a basic control law, which provides output tracking for smooth reference signal. It is shown that for the implementation of the algorithm we need to use only one filter of the control signal and the simplified control laws obtained by application of the real derivative elements. It allows simplifying significantly the calculation and implementation of the control system. Numerical examples and results of computer simulation are given, illustrating the operation of the proposed scheme.

RESEARCH OF FREE MOTION TRAJECTORIES FEATURES OF CONTINUOUS SYSTEM DEFINED AS A CONSECUTIVE CHAIN OF IDENTICAL FIRST-ORDER APERIODIC LINKS
Vunder Nina A., Nuyya Olga S, Peshcherov Ruslan O, Ushakov Anatoly Vladimirovich

68

It is stated that the model of desired behavior has found a widespread usage in the theory and practice of control system design, with the state matrix having a binomial Newton placement of eigenvalues. A structural representation of these systems in the case of the transfer functions approach application leads to a system defined as a consecutive chain of identical first-order aperiodic links. Such model of the desired system behavior has the transient response of the system, which is characterized by the absence of overshoot, that is particularly valuable in the unique technological equipment control. Situation varies considerably when the control system with a binomial placement of eigenvalues has a nonzero initial state. Such situation may arise in the case of an unexpected power fail interrupt of the system electrical components followed by its recovery. This problem is especially important for remote online control of continuous plant in the case of the normal functioning disruption of the channel environment and its restoration in the future. The system in a form of consecutive chain of identical first-order aperiodic links mathematically has a three-parametric set as a module of the negative real eigenvalue, its multiplicity equal to the system dimension and aperiodic link gain. It was found that the three-parametric system may have trajectory emissions at any of negative eigenvalue module. The paper results are illustrated by the computer experiment.

### MATERIAL SCIENCE AND NANOTECHNOLOGIES

SPECTRAL CHARACTERISTICS OF MID-INFRARED LIGHT-EMITTING DIODES BASED ON InAs (Sb,P)
Zhumashev Nariman K., Munbaev Karim Djafarovich, Bazhenov Nikolay L., Stoyanov Nikolay D., Kizhaev Sergei S., Gurina Tatiana I., Astakhova Anastasiia P., Tchernyaev Anton V., Molchanov Sergei S. , Lipsanen Harri K., Salikhov Khafiz M. , Bougrov Vladislav E.

76

Subject of Study.We consider spectral characteristics of mid-infrared light-emitting diodes with heterostructures based on InAs(Sb,P) emitting at T=300 K in the wavelength range 3.4–4.1 micrometers. The aim of the study was to search for the ways of increasing the diode efficiency. Methods. The heterostructures were grown from metal-organic chemical compounds with the use of vapor-phase epitaxial technique. The spectra were recorded under pulse excitation with the use of computer-controlled installation employing MDR-23 grating monochromator and a lock-in amplifier. InSb photodiode was used as a detector. Comparative study of electroluminescence spectra of the diodes was carried out at the temperatures equal to 300 K and 77 K. We compared the obtained data with the calculation results of the band diagrams of the heterostructures. Main Results. As a result of comparative study of the electroluminescence spectra of the diodes recorded at 300 K and 77 K we have established that increasing of their efficiency is hindered by substantial influence of Auger recombination. For the first time at 77 Кwe have observed the effect of stimulated emission from InAsSb active layer in light-emitting structures made of InAs/InAsSb/InAsSbP. For heterostructures with quantum wells InAs/(InAs/InAsSb)/InAsSbP we have found out that at 77 Кthe carrier recombination occurs outside quantum wells, which points out to the insufficient carrier localization in the active layer. Thus, we have shown that the efficiency of mid-infrared light-emitting diodes based on InAs(Sb,P) can be increased via suppression of Auger-recombination and improvement of carrier localization in the active region. Practical Relevance. The results of the study can be used for development of heterostructures for mid-infrared light-emitting diodes.

SIMULATION OF SENSING ELEMENT OF TEMPERATURE SENSOR
BASED ON SILICATE GLASS WITH SODIUM NANOPARTICLES
Bochkareva Elizaveta S., Sidorov Alexander Ivanvich

85

Computational simulation methods were used to show that silicate glasses with sodium nanoparticles, which possess plasmon resonance at 405 nm wavelength, can be used as sensing elements in temperature sensors. The modeling was performed in a dipole quasistatic approximation taking into account the dispersion of sodium optical constants in solid and liquid states, and also the temperature dependence of sodium material density in a liquid phase. It was shown that for the temperature less than 373 K the glasses with sodium nanoparticles can be used for creation of temperature sensors of emergency situations with the threshold switching during the transition of sodium from solid to liquid state. The temperature measurement at higher temperatures can be performed either on the spectral shift of the plasmon absorption band, or on the change of its amplitude. The calculations have shown that the temperature sensitivity of spectral position of the plasmon absorption band of sodium nanoparticles in glass is 0.017 nm/K for the temperature region equal to 373-973K; and the temperature sensitivity of the plasmon absorption band amplitude is 0.3 %/K.

### COMPUTER SCIENCE

(IN-) PRIVACY IN MOBILE APPS. CUSTOMER OPPORTUNITIES (in Engl.)
Chemerkin Yury S., Kuzmenko Tatiana I.

90

Subject of Study. The paper presents the results of an investigation of cross-platform mobile applications. This paper focuses on a cross-platform app data investigation in purpose of creating a database that helps to make decisions from data privacy viewpoint. These decisions refer to knowledge about mobile apps that are available to the public, especially on how consumer data is protected while it is stored locally or transferred via network as well as what type of data may leak. Methods. This paper proposes a forensics methodology as a cornerstone of an app data investigation process. The object of research is an application data protection under different security control types among modern mobile OS. The subject of research is a modification of forensics approach and behavioral analysis to examine application data privacy in order to find data that are not properly handled by applications which lead to data leakages, defining protection control type without forensics limits. In addition, this paper relies on using the simplest tools, proposing a limit to examine locally stored data and transmitted over the network to cover all data, excluding memory and code analysis unless it is valuable (behavioral analysis). The research methods of the tasks set in the paper include digital forensics approach methods depending on data conception (at-rest, in-use/memory, in-transit) with behavioral analysis of application, and static and dynamic application code analysis. Main Results. The research was carried out for the scope of that thesis, and the following scientific results were obtained. First, the methods used to investigate the privacy of application data allow considering application features and protection code design and flaws in the context of incomplete user awareness about the privacy state due to external activity of the developer. Second, the knowledge set about facts of application data protection that allows making a knowledge database to implement the missing privacy and security protection control and provide the privacy requirements (keeping the users informed about possibility to avoid untrusted usage cases). Practical Relevance. Practical relevance of the received results is the following: first, the set of knowledge facts about each examined application to privacy score per application, per application category (IM, travel, etc.), per OS, etc; second, the developed method under the forensics approach can be used to carry out analysis of the application data privacy in relation to the specified requirements including audit, reconfiguring EMM application policiesand reasons for theircommissioning.

PRINCIPLES OF INDICATION FOR EN-ROUTE FLIGHT PATHS
OF THE AIRCRAFT ON THE SCREEN OF ON-BOARD DISPLAY DEVICES
Markelov Vladimir V., Kostishin Maksim O. , Zharinov Igor Olegovich, Nechaev Vladimir A., Zakoldaev Danil A.

96

Subject of Research.We consider the principles and algorithms for construction of en-route flight paths of an aircraft (airplane) in a horizontal plane for their subsequent display on the navigation situation indicators in the cockpit. Navigation situation indicatorsaredisplay devices designed on the basis of flat liquid crystal panel. Methods. Flight trajectory display by on-board multifunction indicators is performed by successive drawing of graphic primitives available in the library and defined in accordance with an array of data to display the route. An array of data is generated by on-board software complex based on the information provided in the flight task and the corresponding «Jeppesen» database or analogous one. Formation of the array is carried out by bringing the set of trajectory paths to the format of three typical trajectories described. In addition, each of the types of trajectories has a standard description of the algorithm for calculating the parameters that make up an array of data to display.Main Results.The algorithms of forming and calculating the amounts of data of routing paths required for their construction and display on the multifunction indicators applied in avionics.Practical Relevance.These novel routing algorithms for constructing trajectory paths unify algorithms of generating information for display on the navigation situation indicators and optimize a set of calculated data for flight control at the trajectory in the horizontal plane.

ERROR CORRECTION METHOD FOR SEQUENCING DATA
WITH INSERTIONS AND DELETIONS
Alexandrov Anton V., Shalyto Anatoly Abramovich

108

Subject of Research.A method for error correction for sequencing reads of a haploid organism with insertions and deletions was developed. It was tested on two libraries: a synthesized dataset for Escherichia coli bacterium and a real dataset of reads for Pseudomonas stutzeri. Method. The method is based on using k-mers but only for finding reads that are close to each other. For the close reads a consensus string is created which is then used for correcting errors in the initial reads. Main Results. The algorithm is implemented as a separated program. The program has been tested on both real and synthesized data. The method performance is higher than that of the other known methods (N50 metric was used as well as total contig length and maximal contig length as metrics for comparison). Practical Relevance. The method can be used together with known genome assembly methods not suitable for application with the reads containing insertion and deletion errors.

CHOICE OF OPTION FOR IMPLEMENTATION OF THE MULTILEVEL SECURE ACCESS TO THE EXTERNAL NETWORK
Kolomoitcev Vladimir S.

115

We study the optimal way for design of access scheme called "Direct Connection. This scheme provides a secure access to external network resources, and consists of several groups of routers and two kinds of firewalls. The scheme is considered in view of the fact that the system has got common areas of removing threats in the channel for different means of protection. Parameters of average residence time of request in the system and its reliability were obtained for each variant of access scheme. Based on the results, comparison of the ways of design for access scheme was carried out between themselves and with the standard access scheme (with onefirewall). It was found out that design of access scheme with a single group of routers for the whole system has better performance and reliability than the other variants of "Direct Connection" access scheme.

SYNTHESIS OF THE SECONDARY STRUCTURE OF ALGEBRAIC BAYESIAN NETWORKS: AN INCREMENTAL ALGORITHM AND STATISTICAL ESTIMATION OF ITS COMPLEXITY
Zotov Mikhail A., Levenets Daniil G., Tulupyev Aleksander L, Zolotin Andrei A.

122

An improved algorithm for the synthesis of the secondary structure of algebraic Bayesian networks represented by a minimal join graph is proposed in the paper. The algorithm differs from the previously offered one so that it relies on the incremental principle, uses specially selected edges and, finally, eliminates redundant edges by a greedy algorithm. The correct operation of the incremental algorithm is mathematically proved. Comparison of the computational complexity of the new (incremental) algorithm implementation and two well-known (greedy and direct) is made by means of statistical estimates of complexity, based on the sample values of the runtime ratio of software implementations of two compared algorithms. Theoretical complexity estimates of the greedy and direct algorithms have been obtained earlier, but are not suitable for comparative analysis, as they are based on the hidden characteristics of the secondary structure, which can be calculated only when it is built. To minimize the influence of random factors at calculating the ratio average program runtime is used obtained by N launches on the same set of workloads. The sample values of ratio is formed for M sets of equal power K. According to the sample values the median is calculated, as well as the other statistics that characterize the spread: borders of the 97% confidence interval along with the first and the third quartiles. Sets of loads are stochastically generated according to the specified parameters using the algorithm described in the paper. The stochastic algorithms generating a set of loads with given power, as well as collecting the statistical data and calculating of statistical estimates of the ratio of forward and greedy algorithm to the incremental algorithm runtimes is described in the paper. A series of experiments is carried out in which N is changed in the range 1, 2 ... 9, 10, 26, 42 ... 170.They have showed that the incremental algorithm speed exceeds the forward and greedy ones, moreover in the 10-170 load sets power range this finding is statistically significant (97% level). The results of experiments are visualized using a graphs library Highcharts. The developed incremental algorithm is designed for application in problems solving of algebraic Bayesian networks machine learning.

### ENGINEERING AND TECHNOLOGIES

EFFECT OF MICROPHONES NON-IDENTITY
ON THE MICROPHONE ARRAYS CHARACTERISTICS
Perelygin Sergey V., Krivosheikin Anatoly V

133

Subject of Research. The paper deals with known methods that ensure microphone channels matching in a microphone arrays.The authors have developed the new calculation method of the sensitivities difference of the microphones having an effect on interfering signal suppression in the problem of broadband signals spatial separation.Methods. Theoretical and experimental studies are based on the use of the discrete Fourier transform apparatus, methods of computational mathematics, mathematical modeling. Main Results. We have proposed analytical expressions in a closed form and theoretical dependences, linking the degree of the interfering signal suppression with the microphones sensitivities difference. Simulation, performed in MATLAB environment (version 7), has confirmed the validity of theoretical results. In the course of modeling the authors have obtained experimental dependence of the interfering signal suppression on the microphones sensitivities difference. This dependence gives the possibility to define a tolerance on a difference between microphones frequency responses, which guarantees the required interfering signal suppression at the useful signal selection. Practical Significance. The results can be applied in the design of the device which separates target speaker's speech from noise of a mixture of voices.

QUALITY CONTROL AUTOMATED LASER-ULTRASONIC METHOD FOR SOLDER JOINTS OF NOZZLES OF CHAMBERS IN LIQUID ROCKET ENGINES
Sergeev Dmitry S, Fedorov Alexei V, Barinov Andrei V., Astredinova Nadezhda V.

139

The paper deals with the problem of quality control for solder joints of nozzles of chambers in liquid rocket engines (LRE). The nozzle of LRE chamber is a responsible product, operating in conditions of high pressure and temperature gradient, having a complex geometric shape and consisting of a large number of milled channels. The analysis of existing methods for solving the problem of quality control of solder joints in LRE nozzles of chambers is carried out. The necessity of the development of an automated laser-ultrasonic control method of solder joints in LRE nozzles of chambers is proved. The analysis of existing automated ultrasonic means of control and the factors affecting control accuracy is carried out. The prototype hardware has been designed for the automated laser ultrasonic nondestructive quality testing of solder joints of LRE nozzles. For software control of the sensor movement mechanism for scanning the inner surface of LRE chamber nozzles and its positioning, the usage of three-layer neural network is proposed. An adaptive algorithm of automated quality control of solder joints has been worked out. A method for the integrated assessment of the quality of solder joints of LRE chambers is suggested. In the process of research methodology was developed for automated measurement of geometrical characteristics of defects and quality control of solder joints in LRE nozzles of chambers. The approbation of the developed method was carried out on three-coordinate automated stand.

### MODELING AND SIMULATION

ROBUST MODIFICATION OF THE LASSO METHOD FOR GENOME-WIDE
ASSOCIATION STUDY IN VIEW OF TARGET PHENOTYPE VALUES
Utkin Lev V., Zhuk Yulia A., Coolen Frank

150

A modification of the Lasso method used for genome-wide association study by examples of double haploid lines of barley is proposed for taking into account the additional information about target values of the phenotype which is defined by some feature of plants. From a statistical point of view, a linear regression problem is studied. It is proposed to formalize the additional information about features of plants as intersection of two sets of weights assigned to the training set elements. The first set of weights is produced by means of the interval contamination model. The second set is formed by the pair-wise comparisons of phenotype values. The obtained intersection is convex and is totally defined by its extreme points. This feature allows reducing the Lasso method with sets of weights to a finite set of standard Lasso methods. Results of numerical experiments have showed that the modification provides the better accuracy measures in comparison with the standard Lasso when the training set is small.

BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES
Makeev Ilya V., Igor Yu. Popov, Irina V. Blinova

161

Stokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to axisymmetric flows for the case when viscosity is a function of radius. We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Examples of such benchmarking are presented. The advantage of this benchmarking approach is the ability to test numerical algorithms for variable viscosity and density gradients. We suggest numerical scheme of multigrid algorithm for solving Stokes and continuity equations with variable viscosity in a spherical coordinate system. Calculations are performed on a sequence of orthogonal staggered grids. The quality of the numerical scheme was verified by comparing the numerical solution with the analytical solution of the test problem.

INFORMATIONAL MODEL OF MENTAL ROTATION OF FIGURES
Lyakhovetskiy Vsevolod A. , Potapov Alexey Sergeevich, Krumina Gunta

168

Subject of Study.The subject of research is the information structure of objects internal representations and operations over them, used by man to solve the problem of mental rotation of figures. To analyze this informational structure we considered not only classical dependencies of the correct answers on the angle of rotation, but also the other dependencies obtained recently in cognitive psychology. Method.The language of technical computing Matlab R2010b was used for developing information model of the mental rotation of figures. Such model parameters as the number of bits in the internal representation, an error probability in a single bit, discrete rotation angle, comparison threshold, and the degree of difference during rotation can be changed. Main Results.The model reproduces qualitatively such psychological dependencies as the linear increase of time of correct answers and the number of errors on the angle of rotation for identical figures, "flat" dependence of the time of correct answers and the number of errors on the angle of rotation for mirror-like figures. The simulation results suggest that mental rotation is an iterative process of finding a match between the two figures, each step of which can lead to a significant distortion of the internal representation of the stored objects. Matching is carried out within the internal representations that have no high invariance to rotation angle. Practical Significance.The results may be useful for understanding the role of learning (including the learning with a teacher) in the development of effective information representation and operations on them in artificial intelligence systems.

WENO SCHEMES FOR SOLUTION OF UNSTEADY ONE-DIMENSIONAL
GAS DYNAMICS TEST PROBLEMS
Bulat Pavel V, Volkov Konstantin N.

174

Creation of test solutions is an essential element in the general design contents for numerical methods aimed at integration of Euler equations. We consider numerical solution of Euler equations describing flows of inviscid compressible gas and allowing continuous and discontinuous solutions. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solutions of Riemann problem. Monotonic correction of derivatives makes it possible to avoid new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the loss of accuracy. Calculations with the use of WENO schemes allow obtaining accurate and monotonic solution with the presence of both weak and strong gas dynamical discontinuities.

### INFORMATION TECHNOLOGIES IN EDUCATION

AUTOMATED CONTROL SIMULATION OF PROFESSIONAL SKILLS FORMATION FOR PRODUCTION SYSTEM OPERATOR
Fayzrakhmanov Rustam A., Polevshchikov Ivan S.

181

Subject matter.We propose a mathematical model of the automated control of the professional skills formation for the trainee through exercises using computer training complex. Its distinctive features are: automatic receipt of the integral quality index of exercising on the basis of certain indicators of quality assessment in terms of trainee’s estimation fuzziness in the performance of exercises for each such indicator at different points in time; automatic gradual introduction of each quality indicator, tips and warnings in the process of repeated exercise performing in order to acquire quickly the ability of self-trained quality of their work; automatic control of the dynamics of the gradual forming of skills during repeated exercising. Method. The study used the basics of control theory, the fuzzy-set theory, analytic hierarchy process, mathematical modeling of iterative learning, modeling using Petri nets. Main Results. We have developed an original mathematical model of the automated control of the process of formation of professional skills for the future operators of industrial processes in the performance of practical exercises with the use of the computer training complex. Practical Significance. The proposed mathematical model and appropriate methodology can be applied to create computer-aided training of operators of different processes.

### BRIEF PAPERS

STUDY OF OPTICAL AND LUMINESCENT PROPERTIES
OF POTASSIUM-ALUMINA-BORATE GLASS DOPED WITH Cr

^{3+}IONS Gorbachev Andrey D., Nikonorov Nikolay V. , Stepanov Sergey A., Nuryev Rustam K., Shirshnev Pavel S.191

Potassium-alumina-borate glass doped with chromium ions have been synthesized and investigated, and results are presented. We have synthesized glass of 25K2O-25Al2O3-50B2O3 speciation with addition of 0.2 weight per cent of Cr. It was found out, that heat treatment induces changes in absorption and photoluminescence spectra. According to x-ray diffraction measurements, it has been shown that Al4B2O9 nanocrystalls have been obtained. The average diameter of nanocrystalls is 15 nm. Luminescence spectra have shown that Cr3+ ions are in an octahedral crystalline surrounding of the alumina ions similar to the spectrum of ruby crystal. A conclusion has been done that nanocrystalls of Al4B2O9: Cr3+ are obtained, most probably, in the researched glass. Synthesized material can be used as the base for fiber amplifier in data-transmission systems and as an active substance for medical lasers.

SPEAKER-DEPENDENT FEATURES FOR SPONTANEOUS SPEECH RECOGNITION
Medennikov Ivan P.

195

This paper presents the results of the study on improving robustness to the acoustic variability of the speech signal for spontaneous speech recognition system. The method is proposed to constructing high-level bottleneck features using deep neural network adapted to a speaker and to acoustic environment with i-vectors. The proposed method provides 11,9% relative reduction of word error rate in Russian spontaneous telephone speech recognition task.