Кафедра штучного інтелекту та математичного моделювання
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Item type:Наукова стаття, Latex system in distance learning of the probability theory(2023-11-20) Hubal, HalynaArticle discusses the main issues for writing interactive mathematical tests in the LaTeX system. The LaTeX system is convenient to use for writing interactive mathematical tests in distance learning. We use the eqExam package, the AcroTeX eDucation Bundle package, the turnthepage package in order to write interactive mathematical tests, for example tests on the probability theory. For this, we create (tasks) of the “True/False” type, the “Short Answer” type, the “Essay” type (“Specifying a Definition”, “Justification of a Theoretical Hypothesis”) and the “Multiple Choice” type.Item type:Наукова стаття, 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, HalynaA 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.Item type:Наукова стаття, Analysis of approaches to the study of limits of sequences and functions and the use of information technologies(2024-01-25) Hubal, HalynaArticle 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.Item type:Наукова стаття, ОПТИМАЛЬНА ПОБУДОВА МАТЕМАТИЧНИХ ТАБЛИЦЬ І ВИЗНАЧНИКІВ МАТРИЦЬ У СИСТЕМІ LATEX(Луцьк: ЛНТУ, 2025-02-12) Губаль, Галина МиколаївнаУ статті здійснено оптимальну побудову математичних таблиць і визначників матриць у системі LaTeX. Створено нові команди (макроси), які будують математичні таблиці, в яких значення першого рядка автоматично заповнюються і здійснюється умовний друк значень другого рядка; записують введені матриці в пам’ять та виводять записані матриці; генерують визначники матриць шляхом виключення заданого рядка і заданого стовпця.Item type:Наукова стаття, Digital technologies as a powerful toolkit for improving the quality of students' mathematical training(Kraków, 2025) Hubal, HalynaThe 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.Item type:Наукова стаття, Improvement of references and footnotes in mathematical and other texts by creating macros in the LaTeX programming language(2023-09-01) Hubal, HalynaThe LaTeX programming language considered in this article is used to represent mathematical and other texts in scientific research. Many LaTeX packages provide advanced code-formatting features. Expanding the LaTeX programming language with macros automates the performance of a large number of tasks. In this research, the author programs in the LaTeX system when creating new macros. New macros created by the author improve adding references to everything that can be numbered and improve adding different types of footnotes in texts. Source codes of these new macros are given in this article. These macros can be embodied in a LaTeX style file, and they expand the capabilities of LaTeX.Item type:Наукова стаття, Mathematical study of the stability of fixed points of systems of differential equations describing biochemical processes rates(Lutsk: LNTU, 2022-08-12) Hubal, HalynaMathematical study of the stability of fixed points of systems of differential equations describing biochemical processes rates is performed in the article. A system of differential equations for deviations is constructed, which describes the behavior of the system near the fixed point. An analysis of the general solution of the system of differential equations describing biochemical processes rates is made. The behavior of the systems near fixed points is investigated by the method of small perturbations. The conditions of existence of the limit cycle of the system of differential equations are investigated. For the cases when the system of differential equations cannot have an analytical solution, integrated curves are constructed by qualitative research. Phase trajectories of the system of differential equations describing biochemical processes rates are constructed. The definition of the nature of the stability of fixed points is considered and investigated.Item type:Наукова стаття, Вдосконалення створення таблиць і деяких обчислень на мові програмування LATEX для математичних досліджень(Луцьк: ЛНТУ, 2024-07-01) Губаль, Галина МиколаївнаУ статті розглядається система LaTeX. Виконано автоматизацію створення даних у математичних дослідженнях за допомогою створених нових макросів у системі LaTeX на мові програмування LaTeX. Створено нові макроси, які генерують матриці випадкових чисел, розмірності яких можна ввести на етапі виконання макросів, які обчислюють і друкують суми введеної кількості доданків, піднесених до заданого степеня, які друкують рядки введених таблиць при заданій умові, які обчислюють і друкують суму елементів рядків і стовпців введених таблиць.Item type:Наукова стаття, Information technologies in teaching probability theory to foreign students in English in higher education institutions(Oxford, 2025) Hubal, HalynaThe 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.Item type:Наукова стаття, 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, SvitlanaThe 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.