Кафедра прикладної математики (ПМ)

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About one class of the problems of optimal stochastic control of hybrid dynamical systems
(Econtechmod. An International Quarterly Journal, 2016) Тевяшев, А. Д.; Матвиенко, О. И.
A new class of the problems of optimal stochastic control of hybrid dynamical systems different from well-known ones by the introduction of additional extreme and probabilistic constraints on the phase variables is studied in the present work. The mathematical formulation and approximate method of solution of the examined class of the problems are presented in this work. The effectiveness of the use of this class of the problems is illustrated on the example of one of the largest water main of Ukraine.
About one problem of optimal stochastic control of the modes of operation of water mains
(Econtechmod. An International Quarterly Journal, 2015) Tevyashev, A.; Matviyenko, O.
The problem of increasing of the efficiency of operation of the water mains in modern conditions while the transition to a three-tier tariff for the electricity is examined in the present work. An effective method for solving this problem, based on the use of specific features of the water mains as stochastic objects operating in the stochastic environment is offered. The mathematical formulation of the problems of optimal stochastic control of the modes of operation of the water main with probabilistic constraints on the phase variables is presented. A new strategy for the optimal stochastic control of the modes of operation of the water main, the use of which has allowed to develop an effective method for solving the examined problem is proposed in the present work. It is shown that the transition from the classical deterministic problems of control of the modes of operation of the water mains to stochastic ones, provides a significant (up 9%) decrease of financial expenses for the electricity.
Air object recognition by the normalized contour descriptors
(ХНУРЕ, 2021) Єсілевський, В. С.; Тевяшев, А. Д.; Колядін, А. В.
This paper consider research into the methods for recognizing the type of an air object on a digital image acquired from video monitoring system. A method has been proposed that is applied on a feature vector built on the basis of a Fourier transform for the sequence of coordinates of its two-dimensional contour. This makes it easier to solve the classification problem owing to a more compact arrangement of the multidimensional feature vectors for similar air objects. The architecture of an air situation video monitoring system has been suggested, which includes an image preprocessing module and a module of neural network. Preprocessing makes it possible to identify an object’s contour and build a sequence of normalized descriptors, which are partially independent of the spatial position of the object and the contour processing technique. Proposal method is easy in realization and do not require significant computational resources due take into consideration the specificity of recognizing objects in 3 dimensional. This research has shown that the reported results make it easier to train a neural network and reduce the hardware requirements for solve the task of air situation video monitoring.
Air Objects Recognition by the Phase Correlation Method
(Друкарня Мадрид, 2020) Yesilevskyi, V. S.; Tevyashev, A. D.; Koliadin, A.
The article considers a method for determining the type of an air object on a digital image by comparing it with standard images using the phase correlation method.
An Statistical Analysis of Queries Receipt Flows in E-Governance Systems
(ХНУРЕ, 2018) Sazonov, K.; Alkilani, M.; Kobziev, V.
The statistical approach to analyzing the flow of requests in e-governance systems is described. The function and density of the generalized distribution of the time interval between the receipt of requests is given. Two of the three possible boundary distributions do not allow the scale parameter to be evaluated as a dispersion. Описаний статистичний підхід до аналізу потоків запитів у системах електронного урядування. Наведено функцію та щільність узагальненого розподілу інтервалу часу між надходженням запитів. Два з трьох можливих граничних розподілів не дозволяють оцінювати параметр масштабу у вигляді дисперсії.
Analysis of the properties of ordinary levy motion based on the estimation of stability index
(Sofia : ITHEA, 2014) Kirichenko, L.; Shergin, V.
The work proposes a method for estimating the stability index of alpha-stable distributions by using moments of fractional order. Provided numerical modeling has fully justified all of the results. Comparative analysis of the efficiency among the proposed method of estimating the stability index and widely used methods was performed. Proposal method is much simpler, far more faster and substantially less memory required. Estimation of generalized Hurst exponent from time series of the ordinary Lévy process was performed. Multifractal fluctuation analysis method and evaluation based on stability index estimation were compared. The results of numerical modelling showed that proposed method for estimating the fractal properties of the ordinary Lévy process, based on stability index estimation via fractional order moments is a much more accurate.
Artificial intelligence in educational mathematics: opportunities and threats
(KNPU, 2023) Манчинська, Н. Б.
The integration of artificial intelligence (AI) in mathematics education offers new learning opportunities but also presents challenges such as academic integrity violations, misinformation, and student over-reliance on technology. Misuse of AI can result in a lack of genuine understanding. Educators must guide students to use AI responsibly, verifying its outputs and avoiding cheating. Emphasizing logical thinking, analysis, and creativity, teachers should employ diverse assessment methods to accurately evaluate student knowledge and skills, ensuring AI enhances rather than replaces learning.
Challenges for universities to online technologies implementation in the conditions of war in Ukraine
(2024) Sytnykova, Y.; Petrenko, T.; Bezkorovaina, O.; Ptushka, A.
The experience of online education in Ukraine during wartime is unique. After the Russian-Ukrainian war beginning, in a month of so-called "holidays", in spring 2022, from April, 1, by the order of the Ministry of Education and Science of Ukraine and the rectors' orders of universities, online education started. The classes were online, and it was difficult to overcome the war stress, but the experience of the pandemic taught everyone to work with online technologies such as Zoom, Meet, and Google Classroom. Teaching students online was carried out as online as offline with the university platforms like Moodle and others for offline learning, they contained all educational materials from the previous two years of the pandemic, tasks, quizzes, and tests. The purpose of the research is to identify pedagogical, psychological, and technical challenges for teaching university students during the war in Ukraine with the survey method. The survey was conducted online with 65 university lecturers and 122 students from 5 universities in Kharkiv, Ukraine. The pedagogical, psychological, and technical difficulties were analyzed. The questions were aimed at studying such aspects as 1) pedagogical and psychological difficulties: the teachers/students' readiness for online teaching/learning, 2) pedagogical difficulties: the procedures of online teaching/learning and technologies, in particular, methods, forms, means of giving/mastering knowledge, 3) psychological and technical difficulties faced both by teachers and students. The results are as follows. The acquired teaching and learning experience with online technologies helped to establish online education in wartime positively in general. The main pedagogical difficulties were overcome with basic methods (online and offline), teaching forms such as lectures, seminars, and practical classes online, and offline, and, finally, different tools/means/platforms (video/audio recordings, corresponding emails, social networks, Moodle platform, etc.). The psychological state of both teachers and students in the circumstances of online education was also examined. The most common psychological difficulties with online learning were connected with external ones as constant shelling, and air alarms as with internal ones as stress, anxiety, worries, depression, burnout, sadness, and frustration. The technical difficulties were connected to blackouts, lack of Internet connection, power outages, evacuation, changes in living and working conditions, relocations, and the impossibility of using laboratory equipment. The conclusion is despite all online difficulties, the quality of teaching did not change significantly, thanks to the clear understanding that it is a necessity to teach and learn online.
Changing Trends in Teaching Computer Vision at Ukrainian Universities in the Age of Artificial Intelligence
(International Journal of Emerging Technologies in Learning, 2024) Yesilevskyi, V.; Kyt, M.
In recent years, professional education in computer vision and artifcial intelligence (AI) has witnessed transformative changes, a process signifcantly accelerated by the COVID-19 pandemic, which catalyzed the shift towards online learning formats. In Ukraine, as in many other countries, universities have rapidly adapted their curricula to align with these new realities. The onset of martial law in Ukraine further entrenched online learning as the dominant mode of education. Additionally, there has been a noticeable shift in research activities towards projects tailored to the defense sector, unfolding against the backdrop of signifcant global advancements in AI for computer vision. This article explores the impact of these shifts and the “Artifcial Intelligence Development Concept” introduced by the Ministry of Digital Transformation of Ukraine on the quality and methodologies of computer vision education. It scrutinizes specifc training courses in this domain, along with the literature used in the educational process. The exploration includes how deep neural network technologies such as TensorFlow, PyTorch, OpenCV, and Python libraries are being integrated into computer vision curricula, reﬂecting the latest advancements in the feld. It also examines the needs of Ukrainian startups and companies specializing in computer vision projects, analyzing how curricula are evolving to meet the specifc requirements of modern software developers. Furthermore, the article proposes directions for the further development of online education in computer vision teaching in Ukraine.
Chat technologies in teaching mathematics disciplines in higher education: a correct using strategy
(2024) Sytnykova, Yu. V.
The current trends in the dialogue technologies utilizing in higher education is considered, new realities in the use of chat technologies to improve the educational process are highlighted. The advantages and disadvantages of implementing chat technologies based on ChatGPT in a studying mathematical disciplines are emphasized. Conclusions are drawn about the further correct implementation of chat technologies in higher education.
Classification of Multifractal Time Series by Decision Tree Methods
(КНУ, 2018) Булах, В. А.; Кіріченко, Л. О.; Радівілова, Т. А.
The article considers classification task of model fractal time series by the methods of machine learning. To classify the series, it is proposed to use the meta algorithms based on decision trees. To modeling the fractal time series, binomial stochastic cascade processes are used. Classification of time series by the ensembles of decision trees models is carried out. The analysis indicates that the best results are obtained by the methods of bagging and random forest which use regression trees.
Classification of time realizations using machine learning recognition of recurrence plots
(AISC, 2021) Кіріченко, Л. О.; Радівілова, Т. А.; Зінченко, П. П.
In the article,the machine learning classification of time realizations using the recurrence plot visualization is considered. Every time realization is converted intoa matrix of recurrence states and it is presented as a black-and-white image. The resulting images of realizations are classified using deep neural networks. A deep residual neural network is used as an image classifier. The binary classifi-cation of EEG realizationsis carried out. The result of the binary classification is the detection of an epileptic seizure. The data for the experiment are records of brain activity containing 178 values. The results of the studyshow that the consi-dered method has a high classification accuracy. The proposed classification ap-proach can be readily used in practice.
Comparative Analysis of Noisy Time Series Clustering
(2019) Кіріченко, Л. О.; Радівілова, Т. А.; Ткаченко, А. Є.
A comparative analysis of the clustering of sample time series was performed. The clustering sample contained time series of various types, among which atypical objects were present. In the numerical experiment, white noise with different variance was added to the time series. Clustering was performed by k-means and DBSCAN methods using various similarity functions of time series. The values of the quality functionals were quantitative measures of the quality of clustering. The best results were shown by the DBSCAN method using the Euclidean metric with a Complexity Invariant Distance. The method allows to separate a cluster with atypical series at different levels of additive noise. The results of the clustering of real time series confirmed the applicability of the DBSCAN method for detecting anomaly.
Comparative analysis of the complexity of chaotic and stochastic time series
(Zaporizhzhia National Technical University, 2014) Kirichenko, L. O.; Kobitskaya, Yu. A.; Habacheva, A. Yu.
The new approach to the recognition mechanism of the time series generating process based on the results of the entropy and the recurrent analysis is proposed. The comparative analysis of the realizations properties of chaotic and stochastic processes with different correlation structure was carried out. It is shown that the derived set of information characteristics allows to distinguish the realizations of deterministic chaotic and fractal random processes. Depending on complexity measures of time series of process parameters were obtained. The information characteristics dependencies from the process parameters were obtained. The results of bioelectric signals and financial time series study are presented. Предложен новый подход к распознаванию механизма процесса, породившего временной ряд, базирующийся на результатах энтропийного и рекуррентного анализа. Проведен сравнительный анализ свойств реализаций хаотических и стохастических процессов, имеющих различную корреляционную структуру. Показано, что полученное множество характеристик информационной сложности позволяет различать реализации детерминированных хаотических и фрактальных случайных процессов. Получены зависимости информационных характеристик от параметров процессов. Приведены результаты исследования биоэлектрических сигналов и финансовых рядов.
Comparison of classifiers based on the decision tree
(ХНУРЕ, 2021) Федоров, Д. П.
The main purpose of this work is to compare classifiers. Random Forest and XGBoost are two popular machine learning algorithms. In this paper, we looked at how they work, compared their features, and obtained accurate results from their robots.
Computer Modeling Wind Turbine Blades with Optimal Parameters
(2023) Стрельнікова О. О.; Сєрікова О. М.; Дегтярьов К. Г.
The objective of this paper is to develop effective methods of weight optimization for wind turbine blades. New mathematical model based on the application of boundary element method is proposed. Hypersingular integral equations are used to determine the dynamic pressure on the blade. A new version of the nonlinear programming method, based on the usage of adaptive management of optimization procedures, is elaborated. As computer simulation results, the wind turbine blade is obtained with minimal weight.
Computer simulation of free and forced vibration ofcompound fuel tanks
(2023) Стрельнікова, О. О.; Сєрікова, О. М.; Choudhary, N.
The new analytical method and computer technology are elaborated for numerical simulation of free and forced vibrations of compound fuel tanks in launch vehicles at different stages of mission: at overloads and in microgravity, with considering the liquid sloshing impacts.
Construction of a Stochastic Model for a Water Supply Network with Hidden Leaks and a Method for Detecting and Calculating the Leaks
(Eastern-European Journal of Enterprise Technologies, 2019) Тевяшев, А. Д.; Матвієнко, О. І.; Никитенко, Г. В.
Розроблена стохастична модель водопровідної мережі з витоками, яка в порівнянні із запропонованими раніше моделями (без урахування витоків) більш адекватно описує процеси транспорту і розподілу води в системах водопостачання. При математичному моделюванні водопровідних мереж виникають труднощі, пов'язані з величезною розмірністю реальних водопровідних мереж, обмеженістю інформаційних ресурсів і оперативних даних, що не дозволяє досить адекватно оцінити параметри технологічного обладнання і структуру водопровідної мережі. Тому для реальної водопровідної мережі по її диктуючих точках будується еквівалентна схема, для якої проводяться всі подальші розрахунки. Задача побудови схеми еквівалентної водопровідної мережі складається з трьох задач: ідентифікації структури, параметрів і стану водопровідної мережі. Запропонований метод виявлення витоків заснований на порівнянні зміни величини напору на насосних станціях і в диктуючих точках водопровідної мережі. На базі стохастичної моделі водопровідної мережі з витоками розроблений метод розрахунку величини витоків, який полягає в наступному: знаючи напір води у вузлах еквівалентної водопровідної мережі і приблизні діаметри витоків у вузлах проводиться розрахунок нових значень напорів у вузлах еквівалентної водопровідної мережі. Далі знову розраховується величина витоку, знаючи новий напір у вузлі і діаметр витоків. Зробивши кілька таких ітерацій приходимо до висновку, що починаючи з деякого кроку величина витоків і напори у вузлах еквівалентної водопровідної мережі перестають змінюватися. Знаючи величину витоку і напір у кожному вузлі еквівалентної водопровідної мережі, визначаємо дійсний діаметр свищів у кожному вузлі. Запропонований метод виявлення розрахунку величини витоків не вимагає фінансових витрат або використання додаткового обладнання, він може застосовуватися у Водоканалах для виявлення і розрахунку величини витоків.
Data Mining methods for detection of collective anomalies in time series
(Національна академія Національної гвардії України, 2021) Кіріченко, Л. О.; Кобзєв, В. Г.; Федоренко, Є. Д.
The paper considers the approach to the detection of collective anomalies in time series, based on the use of clustering methods, in particular the method of k-means, as well as the effectiveness of their application.
Development of a video processing module for the task of air object recognition based on their contours
(ХНУРЕ, 2022) Yesilevskyi, V.; Koliadin, A.; Sereda, O.
The subject of research in the article is the module of automatic segmentation and subtraction of the background, which is created, based on the sequential application of methods of image preprocessing and modified method of interactive segmentation of images and implemented in the system of optical monitoring of the air situation. The aim of the work is to develop an image segmentation module to increase the efficiency of recognition of an air object type on a video image in the system of visual monitoring of the air environment by means of qualitative automatic segmentation. To solve this problem, a modified interactive algorithm in the mode of automatic selection of an object in the image, which allows more accurately, without the participation of the operator, to determine the foreground pixels of the image for further recognition of the type of airborne object. The following tasks are solved in the article: the analysis of existing methods of binarization of color images for semantic segmentation of images, which are used in image recognition systems; the development of a pipeline of methods for automatic segmentation of images in the system of optical monitoring of the air environment. In the work, the following methods are used: methods of digital image processing, methods of filtering and semantic segmentation of images, methods of graph analysis. The following results are obtained: the results of image processing with the proposed module of segmentation and background subtraction confirm the performance of the module procedures. The developed pipeline of methods included in the module demonstrates correct segmentation in 93% of test images in automatic mode without operator participation, which allows us to conclude about the effectiveness of the proposed module. Conclusions: The implementation of the developed module of segmentation and background subtraction for the system of optical monitoring of the air environment allowed to solve the problem of segmentation of video images for further recognition of aerial objects in the system of optical monitoring of the air environment in automatic mode with a high degree of reliability, thus increasing the operational efficiency of this system.

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