Кафедра штучного інтелекту та математичного моделювання

Постійне посилання на фондhttps://repository.lntu.edu.ua/handle/123456789/57

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Higher Mathematics
(Lutsk: LNTU, 2024) Hubal, Halyna
Methodical instructions developed according to the current author's curriculum of the academic discipline "Higher Mathematics" to strengthen students' knowledge and skills and to provide methodical assistance in mastering the discipline materials.
Methods of functional analysis for the discrete velocity model of the BBGKY hierarchy of equations of symmetric systems of particles interacting as hard spheres
(Singapore, Republic of Singapore: International Center of Scientific Research, 2025) Hubal, Halyna
A dynamic symmetric system of particles interacting as hard spheres was considered in the article. Such systems are used in a number of scientific areas such as mathematical physics, theoretical physics, mathematical biology, mathematical economics, chemistry, and modern nanotechnology. It was proved that the functional series of the cumulant representation of the solution of the discrete velocity model of the Cauchy problem for the BBGKY hierarchy of equations with initial data having the chaos property converge in the norm of the space of sequences of summable functions. Under the condition of low densities, it was proved the existence and uniqueness of the solution of a closed evolution equation obtained from the solution of the Cauchy problem for the BBGKY hierarchy of equations, which is important for deriving the generalized kinetic equation.
Analysis of approaches to the study of limits of sequences and functions and the use of information technologies
(2024-01-25) Hubal, Halyna
Article analyzes approaches to the study of limits of sequences and functions and the use of information technologies. The theorem on the limit of an intermediate sequence is of great importance when investigating the convergence of sequences and when calculating the limits of sequences. It is developed an algorithm for applying this theorem that is illustrated with examples. An example of calculating the limit of a function with a geometric interpretation of the obtained result is considered. The possibility of completing the calculation of limits at infinity, using the program code written by the author in the LaTeX programming language, is considered.
Digital technologies as a powerful toolkit for improving the quality of students' mathematical training
(Kraków, 2025) Hubal, Halyna
The article considers the application and impact of digital technologies on improving the quality of students’ mathematical training. It is shown the advantages of using digital technologies. It is described the features of deepening students’ knowledge through digital technologies.
Information technologies in teaching probability theory to foreign students in English in higher education institutions
(Oxford, 2025) Hubal, Halyna
The article presents some features of teaching probability theory to foreign students in English in higher education institutions in Ukraine. The article emphasizes the importance of using information technologies both for teaching probability theory and for understanding this discipline by foreign students. Examples of using the LaTeX system in creating educational materials and test tasks are given.
Psychological Aspects of the Decision-Making Process: The Influence of Personal Characteristics on Choice Strategies in the Face of Instability
(2024-12-28) Hubal, Halyna; Fomina, Iryna; Drozd, Lidia; Arkhypova, Tetiana; Sobkova, Svitlana
The aim of the article is to empirically find out the specifics of the correlation between the decision-making process and the personal qualities of representatives of various professions in the face of social instability. The study used the Melbourne Decision Making Questionnaire (MDMQ) and the Freiburg Personality Inventory (FBI). The hypothesis that decision-making processes are related to personal qualities and differ among representatives of different professions in the face of social instability was confirmed. It was found that the respondents mostly prefer a rational way of making decisions. However, a fifth of the respondents are characterized by the dominance of the avoidance strategy. No persons with pronounced procrastination were found. Doctors and programmers have emotional control and reduced aggressive reactions in the decision-making process. Social orientation of life choices is typical for teachers. IT specialists often use the avoidance strategy. Conclusions: In general, the peculiarities of decision-making strategies in the conditions of war are determined, which can be extrapolated to similar situations of military instability on the planet. The obtained results can be used in the process of developing programmes of professional development and psychological assistance of individuals in times of war. Research prospects may be the study of the gender aspect of decision-making.
Digital Technologies in the Process of Teaching STEM Disciplines: Challenges and Prospects
(2024-03-28) Hubal, Halyna; Siasiev, Andrii; Sipii, Volodymyr; Syrmamiikh, Iryna; Burtovyi, Serhii
The modern integration of digital technologies into the educational process requires additional study, given the opportunities that this process opens up. The purpose of the article is to study the use of digital technologies in STEM educ ation through the prism of researching the main challenges and prospects. To achieve this goal, the methods of questionnaires and interviews were used. In particular, 65 teachers of higher education institutions were interviewed, whose opinions became the basis for forming a generalised picture of the study. The results show that modern teachers actively use digital technologies in STEM education. The average level of digital technology use among STEM teachers is high: 43 people (65%) use technology at grade levels 4 and 5. However, this intensive use of digital technologies in STEM education raises both challenges and opportunities. In particular, today's teachers often face limited access to the necessary technical infrastructure, which can limit their ability to implement digital tools. Poor quality of internet connection can affect the smoothness and efficiency of using online resources. Insufficient training of teachers in the use of digital technologies is also a significant challenge. Incre asing the availability of digital resources for teachers will make learning more accessible and diverse. Cooperation between universities and technology companies also opens up new opportunities for the development of STEM education. The conclusions emphasise that such interaction facilitates the exchange of experience, access to advanced technologies and resources, and creates conditions for the implementation of joint projects and programmes.
Station rotation model of blended learning in higher education: achieving a balance between online and in-person instruction
(2024) Yukhymenko, Violetta; Borysova, Svitlana; Bazyl, Olena; Hubal, Halyna; Barkar, Uliana
The purpose of the article is to empirically test the effectiveness of the model of teaching with rotating stations in a mixed format on the basis of a survey conducted among teachers of higher education institutions in Ukraine. The study uses a mixed-methodology approach to collect qualitative and quantitative data from 65 teachers during the first semester of the 2023-2024 academic year. The main instruments are questionnaires and interviews among teachers who have used the Station Rotation Model. The responses were processed using descriptive statistics and comparative analysis to identify any significant differences in the results. The results emphasise the need for careful selection of a platform for distance learning and the acquisition of skills in creating e-resources. The results of the study provide practical recommendations for the implementation of the model in the Ukrainian higher education context. This is important for Ukrainian higher education institutions looking for optimal methods of blended learning. The findings of the study highlight the positive attitude of teachers to the proposed model, which promotes the individualisation of learning and development of digital competence. However, implementation requires additional time and advanced digital skills of teachers. The average score of the model's effectiveness (approximately 4.046) and the percentage distribution in scores 4 (47.69%) and 5 (30.77%) indicate a high level of acceptance of this approach by modern teachers. The recommendations are based on the individual experience of teachers, indicating the variability in the choice of the optimal means of communication with students. The study contributes to the understanding of the effectiveness of the blended learning model and will help to optimise its wider implementation.
Evaluation of the effectiveness of decision-making algorithms in the management of renewable energy sources: A case study of Ukraine
(2025) Siasiev, Andrii; Dudnikov, Serhii; Nikolaienko, Dmytro; Hubal, Halyna; Bondarchuk, Oleg
The integration of renewable energy sources in Ukraine requires advanced decision-making algorithms to address various challenges, including energy forecasting, resource optimization, and grid stability. The existing algorithms exhibit limitations in accuracy and efficiency, necessitating the development of innovative approaches to enhance performance in this regard. This work evaluated the performance of existing algorithms and developed two new algorithms: the enhanced forecasting algorithm (EFA) and the dynamic resource optimization algorithm (DROA). Data from a hybrid energy system comprising solar, wind, and battery storage was used for analysis. The algorithms were assessed based on forecasting accuracy, economic efficiency, and system stability. Moreover, key metrics like mean absolute percentage error (MAPE) and operational cost reductions were used for the evaluation in the current work. According to the analysis results, the EFA achieved a 54% improvement in forecasting accuracy and reduced MAPE to 5.8%. The DROA enhanced resource optimization, resulting in a 56% reduction in energy losses and an 18% decrease in operational costs. System stability was improved, and grid frequency fluctuations were reduced by 67%. These results demonstrated the superiority of these new algorithms over existing methods. This work highlighted advanced algorithms' critical role in optimizing Ukraine's renewable energy systems. The EFA and DROA demonstrated significant potential for operational and economic benefits. This is possible with improved energy forecasting, reduced losses, and enhanced grid stability. Future research endeavors should focus more on applications and explore additional performance metrics to optimize energy systems in this regard.
The impact of CAD software on the teaching of engineering graphics: a systematic review
(International University of Sarajevo, 2025) Koziar, Mykola; Hubal, Halyna; Burchak, Ihor; Botviniev, Maksym; Saveliev, Dmytro
Introduction. Incorporating CAD and BIM in the engineering graphics learning environment has revolutionized teaching methods by providing richer visualization, analysis, and collaboration tools. Despite this, there are still big differences in the adoption and ability rates and levels of CAD and BI across regions and institutions. Methods. For PRISMA, 45 studies were used for comparison from 2020-2024. Studies selected for the review had to meet inclusion criteria about CAD and BIM awareness and competency, challenges, and fit within the engineering education curriculum. The data were combined qualitatively and quantitatively, and the discoveries were classified into major themes. Results. CAD applications like AutoCAD are more widely adopted in the BIM industry than in BIM applications like Revit, especially in development areas. Challenges to BIM adoption include high costs, lack of policies, and 2D drafting. Countries with developed BIM industries are the most effective and integrate educational curricula, highlighting the importance of industry alignment in promoting CAD and BIM technologies. Conclusion. This research suggests that frameworks for implementing BIM integration require a uniform set of best practices, more access to information, and demonetization and curriculum development to fill shortcomings. Even with CAD at the core, BIM advances must be looked for following the industry's needs and put into practice. Further research should be directed toward developing ways to overcome and advance the existing technology gaps.

Кафедра штучного інтелекту та математичного моделювання

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