Кафедра "Комп'ютерна математика і аналіз даних"

Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/7570

Офіційний сайт кафедри http://web.kpi.kharkov.ua/kmmm

Кафедра "Комп'ютерна математика і аналіз даних" заснована в 2002 році.

Кафедра входить до складу Навчально-наукового інституту комп'ютерних наук та інформаційних технологій Національного технічного університету "Харківський політехнічний інститут", забезпечує підготовку бакалаврів і магістрів за проектно-орієнтованою освітньою програмою за напрямом науки про дані "DataScience".

У складі науково-педагогічного колективу кафедри працюють: 3 доктора наук: 1 – технічних, 1 – фізико-математичних, 1 – педагогічних; 15 кандидатів наук: 10 – технічних, 4 – фізико-математичних, 1 – педагогічних; 3 співробітників мають звання професора, 9 – доцента.

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Analysis of efficiency of the bioinspired method for decoding algebraic convolutional codes
(Технологический центр, 2019) Panchenko, Sergii; Prykhodko, Sergii; Kozelkov, Sergii; Shtompel, Mykola; Kosenko, Viktor; Shefer, Oleksandr; Dunaievska, О. I.
It has been shown that convolutional codes are widely used, along with various decoding methods, to improve the reliability of information transmission in wireless telecommunication systems. The general principles of synthesis and the parameters and algebraic non-systematic convolutional codes with arbitrary coding rate and maximum achievable code distance have been shown. The basic stages of the bioinspired method for decoding algebraic convolutional codes using a random shift mechanism have been presented. It has been shown that the essence of the presented decoding method implies applying the procedure of differential evolution with the heuristically determined parameters. In addition, this method uses information about the reliability of the adopted symbols to find the most reliable basis for the generalized generator matrix. The mechanism of random shift for the modification of the accepted sequence is additionally applied for the bioinspired search based on various most reliable bases of a generalized generator matrix. The research results established that the bioinspired method for decoding algebraic convolutional codes ensures greater efficiency compared with the algebraic decoding method in the communication channel with additive white Gaussian noise. Depending on the parameters of the algebraic convolutional code and the necessary error coefficient, the energy gain from encoding ranges from 1.6 dB to 3 dB. It was shown that the presented bioinspired decoding method can be used for convolutional codes with a large code constraint length. In doing so, the presented method for decoding algebraic convolutional codes is less efficient than the Viterbi decoding method and turbo codes at a sufficient number of decoding iterations.
Analysis of operating modes of single-phase current source rectifier with rectangular-stepped pulse-width modulation
(Технологический центр, 2018) Krasnov, Oleksii; Liubarskyi, Borys; Bozhko, Vladimir; Petrenko, Оleksandr; Dubinina, Oksana; Nuriiev, Ramil
The operating modes of the single-phase active current-source rectifier in the case of rectangular-stepped pulse-width modulation and load in the form of DC traction motor are investigated. The single-phase bridge rectifier circuit with a discharge diode is considered. The mathematical model of the rectifier is developed and the main ratios for pulse-width modulation with rectangular-stepped modulating signal are determined. On the computer model, electromagnetic processes at three modulation frequencies (900, 1,200, 1,800 Hz) are studied. The features of the effect of the modulation depth and frequency on the rectifier power factor and the total harmonic voltage and current distortion in the mains supply are determined. The DC motor for today remains the main type of the traction motor of the 25 kV, 50 Hz AC mainline electric locomotives of alternating current in Ukraine and in some other countries. To power such motors, diode or thyristor rectifiers are used. At the same time, it is known that converters on fully controlled semiconductor devices provide higher power efficiency. The studies allow determining what values of modulation frequency and depth provide a high power factor (more than 0.9) and minimum total harmonic voltage and current distortion distortions in the mains supply. This allows finding rational approaches to the selection of power circuits and control algorithms for active converters in the traction electric drive of electric locomotives. The efficiency of increasing the power factor and reducing the total harmonic voltage and current distortion can be achieved, first of all, by reducing the power consumption for traction of trains. According to the set of selected comparison criteria, the active current-source rectifier with a modulation frequency of 1,200 Hz is the most suitable for implementation in the traction electric drive of the electric locomotive. Provision of high power characteristics in a wide range of traction loads can be achieved in the multi-zone circuit of such a converter.
Determining parameters of electromagnetic radiation for energoinformational disinfection of wool in its pretreatment
(Технологический центр, 2017) Kosulina, N.; Cherenkov, A.; Pirotti, E.; Moroz, S.; Chorna, M.
Угнетение инфекционных микроорганизмов в кипах шерсти возможно при помощи электромагнитного излучения (ЭМИ) с параметрами: частота 36 ГГц, мощность 0,5 кВт, экспозиция 3 мин. Энергоинформационные параметры были определены в результате теоретических и экспериментальных исследований процесс взаимодействия ЭМИ с инфекционными микроорганизмами.
Effect of deformation degree under quasihydroextrusion at 77K on the structure and properties of CuCrZr alloy
(Харківський національний університет імені В. Н. Каразіна, 2019) Belyaeva, A. I.; Khaimovich, P. A.; Galuza, A. A.; Kolenov, I. V.; Savchenko, Alla Aleksandrovna; Shul`gin, N. A.
Influence of the parallelepiped form localized defects on ellipsometry data: scale modeling
(Institute of Nuclear Physics Polish Academy of Sciences, 2021) Galuza, A. A.; Kolenov, I.; Savchenko, A.
Influence of the parallelepiped form localized defects on ellipsometry data: scale modeling
(Institute of Nuclear Physics, 2021) Galuza, A. A.; Kolenov, I.; Savchenko, Alla Aleksandrovna
Ця стаття присвячена проблемі аналізу еліпсометричних даних поверхні з локалізованими дефектами (різні фази, пухирі, зерна тощо).
Mathematical model of the development of a single twin layer inmetal crystals
(Національний технічний університет "Харківський політехнічний інститут", 2021) Bosin, Mark Yevgenovych; Gomozov, Yevgen Pavlovych; Drygach, Tetyana Grygorivna
By analyzing the experimental data available in the scientific literature, a mathematical model of the development of a singletwin layer in metal crystals has been obtained. The model has the form of a differential equation, the order of which is determined by the required accuracy of obtaining the results associated with the solution of this equation. Even in the linear approximation of one of the main parameters of the phenomenological model, the latter gives qualitatively the same dependences of the development of single twins under different loading conditions compared to the experiment. Despite a large number of experimental works devoted to twinning, there is still no rigorous quantitative theory of the development of twinning layers in different media and under different conditions. However, in these works, the mathematical approach was demonstrated only inrelation to elastic twins. This work is an introduction to the creation of a quantitative theory of twinning in metal crystals. Comparisons with the experimental results of the proposed phenomenological model were limited in this work to the task of demonstrating the performance of the model in thesense of predicting the most specific effects of the development of twins under various conditions and loading modes. In particular, the model implies the effect of loss and subsequent restoration of hardening by twin boundaries during stress pulsations, the Bauschinger effect upon a change in the sign of the applied voltage, and a number of other effects observed experimentally on a number of different metal crystals.
Matlab модель генератора ЭКГ сигнала на основе частотного преобразования
(НТУ "ХПИ", 2018) Шишкин, Михаил Анатольевич; Бутова, Ольга Анатольевна; Фетюхина, Людмила Викторовна; Ахиезер, Елена Борисовна; Дунаевская, Ольга Игоревна
Предложен метод построения Matlab/Simulink модели генератора электрокардиографического сигнала на основе анализа частотного спектра и формирования соответствующих компонент, реализующих суперпозицию сигналов необходимых гармонических составляющих. Целью работы является синтез такого блока с изменяемыми параметрами, который бы мог использоваться в качестве источника сигнала при имитационном моделировании различных кардиологических систем. В ходе работы были получены решения, позволяющие генерировать кардиографический сигнал наиболее часто встречающихся патологий, моделировать вариабельность сердечного ритма и влияние наиболее распространённых помех.
Methodology of project-based learning for training junior students in applied mathematics: general scheme of the educational process
(IOP Publishing Ltd, 2023) Akhiiezer, O. B.; Haluza, O. A.; Savchenko, A. O.; Lyubchyk, Leonid Mykhailovych; Protsay, N. T.; Aslandukov, M. O.
An original methodology of the project-based learning for junior students of the specialty applied mathematics is proposed in the paper. A complete step-by-step diagram (as a BPMN diagram) of the process of the project-based learning as a business process with a description of the specifi actions of all its participants is given. The paper specifid and clearly describes all the main aspects of the work on the project, starting from the criteria that the project problem must satisfy, and ending with the form of project defense. The roles of both students within the project team and all teachers are described in detail. Special attention is paid to all documents accompanying the work on the project, which should be submitted by the project team. The results of the article may be useful to those teams of teachers who are just starting to work on the implementation of project-based learning into the educational process for the specialty of applied mathematics or related ones.
On eigenvalues of banded matrices
(Інститут математики НАН України, 2019) Akhiiezer, O. B.; Dunaievska, О. I.
In the paper, asymptotics for eigenvalues of Hermitian, compact operators, generated by infinite, banded matrices is obtained in terms of the asymptotics of their matrix entries. Analogues for banded matrices of Gershgorin’s disks theory are discussed.
Optical constants of surface layer on gadolinium gallium garnet: ellipsometric study
(Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 1999) Belyaeva, A. I.; Galuza, A. A.; Grebennik, T. G.; Yuriyev, V. P.
A multiple angle ellipsometric method is used for measurements of thin film layers on substrates. The method evaluates fundamental optical constants and thicknesses of the film layers. Dielectric func tions of the surface layers on the gadolinium gallium garnet (GdGaG) substrate – commonly used substrate material for rare-earth ferrogarnets (ReFeG) films, have been determined. The thickness and origin of the surface layer on the GdGaG substrate was found out. It is shown that the dielectric properties of microscopically rough layers with thicknesses ~ of 20 to 35 nm can be accurately modeled in the homogeneous thin layer approximation, but not in the effective-medium one. The precision of data was confirmed by comparing different simulations. Agreement to the third decimal point for refraction index was shown. Errors for thicknesses were not more than 3%.
Optimization of thermal modes and cooling systems of the induction traction engines of trams
(Технологический центр, 2017) Liubarskyi, Borys; Petrenko, Оleksandr; Iakunin, Dmytro; Dubinina, Oksana
We developed a procedure for the optimization of thermal modes and parameters of the cooling system of induction traction engines of tram carriages. The procedure includes the following basic steps. The optimization of operating modes of an induction traction drive by the criterion of effectiveness of its work under different modes. The optimization of motion modes of a tram carriage along a track section with the assigned motion schedule and profile based on the curves of the motion of a tram carriage, optimal by the criterion of energy consumption, using the method of Hamilton-Jacobi-Bellman. The optimization of parameters of the cooling fan of traction engines by the criterion of efficiency of a cooling system using the Weyl method by the generalized golden section. It is proposed to conduct determining of operating modes of a traction drive in advance based on the solution to the problem of conditional optimization of its modes. In order to determine the optimal operating modes of a traction drive, we selected a combined method: global search is executed by genetic algorithm with a one-point crossover and by selection on the principle of roulette. At the final stage of an optimization procedure, optimum refining is carried out using the Nelder-Mead method. When a tram carriage moved along a track section, we defined the following. We determined the optimal modes of motion of the tram carriage T-3 VPA with induction traction engines for a track section with the assigned motion schedule. It was found that, compared with the basic design, efficiency of the cooling system increased by 27.6 %, which corresponds to a reduction in the proposed criterion of efficiency. Based on the results of modeling a traction engine with an optimal fan, it was established that the largest overheating is observed in the frontal part of the stator winding. The temperature is 139.6 °C at second 3363 from starting the motion and it does not exceed a permissible value of 140 °C.
Pedagogical acme-technology of formation of responsibility among leader-professionals during the process of professional education
(Національний технічний університет "Харківський політехнічний інститут", 2020) Dubinina, Oksana; Ihnatiuk, Olha; Sereda, Nataliia V.
The article is devoted to the problem of formation of responsibility among leader-professionals during the process of professional education at the university. The authors note that the solution to this problem is possible by developing a special pedagogical acme-technology. The paper presents characteristics of structural components of proposed technology (concept, content, procedural parts, software and methodology). In the course of this study, the pedagogical conditions for the formation of responsibility among leaderprofessionals were determined. The results of this study on the establishment of the influence of factor units on the responsibility formation of future leader-professionals in the process of their professional education at the university are discussed.
Probabilistic estimation of stability of solutions of optimization problems
(Research and Scientific Group, Poland, 2018) Dunaievska, О. I.
The issues of stability of solution of optimization problems are considered on the example of transportation problem of linear programming, in which the transportation costs are random variables with a known distribution density. The complexity of solving such optimization problems by classical methods is substantiated. It is proved that the problem of estimating stability admits an analytic solution if the optimal solution of the problem is sought using the matrix minimum method. This solution is based on the search for the probability that characterizes the level of stability of solving the optimization problem. The corresponding computational procedure is described. An example is considered that illustrates it graphically.
Robust model predictive control of constrained supply networks via invariant ellipsoids technique
(2013) Lyubchyk, Leonid; Dorofieiev, Yuri; Nikulchenko, Artem
The problem of robust control strategy synthesis for distributed supply network under demand uncertainty, time delays and state and control constraints is considered. An invariant ellipsoids approach is used for robust control problem solving, since the uncertain demands are regarded as an external disturbance. On the base Model Predictive Control approach, the designed control law implements in the form of linear feedback signal based on mismatch between the current state and safety stock level and provides external disturbances effect suppression with simultaneous robust stabilization of closed-loop system. Via invariant ellipsoids technique the considered problem was presented in the terms of Linear Matrix Inequalities and a solution of corresponding semi-definite optimization problem was also obtained. As an example, the three-tier supply network with ve nodes robust control problem is considered.
Selective invariant multivariable control system design based on inverse model approach
(Consulting Company Consilium Sp. z o.o. Warsaw, Poland, 2015) Lyubchyk, Leonid; Kostyuk, Olga
The problem of disturbance rejection in multivariable control systems is considered. It has been shown that different two-degree-of-freedom control structures used for immeasurable disturbance estimation and compensation may be treated as a particular case of a general Inverse Model Control approach. The decomposition of the problem into the separate disturbance estimation and compensation is suggested. Moreover the connection between inverse model design problems and unknown input observer theory has been established in order to give a practical way to inverse model parameterization and design. The properties of closed-loop selective invariant control system with model-based controllers have been also investigated with the aim of attainable accuracy estimation.
Simulation of the formation of innovative engineering industry cluster
(Publishing House "Education and Science", 2015) Akhiezer, Elena; Dunaievska, О. I.; Mekhovich, Sergey; Heliarovska, Oksana
Surface energy anisotropy for the low-index crystal surfaces of the textured polycrystalline BCC tungsten: experimental and theoretical analysis
(National Science Center "Kharkov Institute of Physics and Technology", 2017) Belyaeva, A. I.; Savchenko, A. A.; Galuza, A. A.; Kolenov, I. V.
Summarizing the experimental and theoretical trends observed on the changes in surface microstructure and topography resulting from surface energy anisotropy for the low-index crystal surfaces of the polycrystalline bcc tungsten under sputtering is done. A brief summary of the most closely related work is included. The experimental results have been discussed in the framework of the various theoretical methods. Emphasis was placed on the problems which are existing up to now. It is shown that the absence of a common trend in the ordering of the (100), (110), and (111) surface energies amongst the various theoretical models is a problem yet to be satisfactorily discussed. It is shown experimentally that for polycrystalline textured tungsten (bcc metal), the order of the three low-index surface energies is γ(111) > γ(100) > γ(110).
Teaching and Learning Math Behind Computer Science with the Help of GeoGebra and Python
(2016) Pikalova, Valentyna
The paper is focused on topics where mathematics and computing are most relevant to each other, emphasizing the bridges between theory and practice. Topics include sets, relations, elementary graph theory, asymptotic notation and growth of functions, permutations and combinations, discrete probability. The main tools in order to support and compare problem-solving technique are GeoGebra and Python. The main goal is not only to combine an appreciation of mathematical reasoning with an understanding of computing but enrich both of them through interdisciplinary approach.
The optical characteristics of contaminating films on Mo, SS and Cu mirror samples exposed in plasma devices
(National Science Center "Kharkov Institute of Physics and Technology", 2008) Bondarenko, V. N.; Belyaeva, A. I.; Galuza, A. A.; Konovalov, V. G.; Kudlenko, A. D.; Ryzhkov, I. V.; Shtan, A. F.; Solodovchenko, S. I.; Voitsenya, V. S.
The optical methods with the use of in-vessel first mirrors (FMs) are expected to occupy an important place in the diagnostic complex of the future fusion reactor ITER. As the surface of FMs will be subjected to physical sputtering by high-energy D and T charge-exchange atoms, this can lead to a decline in the initial FM reflectance. The second factor of FM reflectance deterioration is the redeposition of contaminants on the mirror surface. In the paper, optical indices and thickness values of the films deposited on Mo and SS mirrors in the tokamak TRIAM-1M as well as on SS and Cu mirrors in the torsatron URAGAN-3M were studied by ellipsometry at the wavelength λ=632.8 nm. The spectral reflectance at normal incidence of light for all the samples was measured in the wavelength range λ=253–650 nm. The optical parameters of TRIAM-1M films were determined as the film was progressively removed by deuterium plasma ions in the stand DSM-2.