# 003. Факультет інформатики

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Item 9th Workshop on Cloud Technologies in Education: Report(2022) Kiv, Arnold; Semerikov, Serhiy; Shyshkina, Mariya; Striuk, Andrii; Striuk, Mykola; Yechkalo, Yuliia; Mintii, Iryna; Nechypurenko, Pavlo; Kalinichenko, Olga; Kolgatina, Larisa; Vlasenko, Kateryna; Amelina, Svitlana; Semenikhina, OlenaThis is an introductory text to a collection of selected papers from the 9th Workshop on Cloud Technologies in Education (CTE 2021) which held in Kryvyi Rih, Ukraine, on the December 17, 2021. It consists of short introduction, papers’ review and some observations about the event and its future.Item A competency-based approach to the systematization of mathematical problems in a specialized school(2021) Vlasenko, Catherine; Lovianova, Iryna; Armash, Tatiana; Sitak, Iryna; Kovalenko, DariaThe issue of searching for new methodological approaches to the systematization that will encourage the increase of students motivation to learn mathematics under the competency-based approach is considered in this article. The research analyzes the existing works on the increase in students motivation to learn Mathematics, in particular, the use of cross-curricular connections while forming students competency. Competency-based problems, systematized according to the topic of the 10th grade Functions, their features and graphics, were determined as the tools to measure students competency and a method to form their motivation to learn mathematics. The use of such methods as the initial research and information gathering, systematization and structural analysis of the problems, data processing allowed the authors of the article to systematize the problems for school subjects of the 10th grade that demonstrate cross-curricular connections of Mathematics with other learning subjects and allow showing the advantages of the mathematical modeling in researching real processes. The research shows the realization of cross-curricular connections in time and such connections as parallel learning, perspective connections, use of the mathematical modeling method are shown. An experiment was held in order to prove the e ciency of implementing a system of the problems to demonstrate the use of the function in di erent tasks of natural subjects. The results proved that the implemented system of problems considerably in uences the increase in students motivation to learn mathematics.Item A Comprehensive Program of activities to develop sustainable core skills in novice scientists(2021) Vlasenko, Catherine; Rovenska, Olga; Chumak, Olena; Lovianova, Iryna; Achkan, VitalyThis paper is aimed at studying scientific communication as an integral part of a scientists activity. The authors of this article analysed the development of informational technologies, which gave rise to a new paradigm of scientific communication Research 2.0. In the present study the analysis of research papers, describing models of scientific communication is done. The findings allow to define the structure and content of a comprehensive program of activities, connected to scientific communication in compliance with the Scientific Communication Life Cycle Model. In order to implement the program, aimed at developing core skills through scientific communication of scientists, a target audience, comprising postgraduate students and young researchers in Mathematics and TeachingMethods was engaged. A five-stage program of activities, which was developed, prompted scientific activity of young researchers and gave them an opportunity to learn about means of presenting research results, elements of management, mechanisms for applying the findings. A constructive description of each module of the program is done, actions and a strategy are described, communication between participants and tutors through the platform Higher School Mathematics Teacher is arranged in this research. In order to assess the efficiency of implementing the program, Researcher Development Framework (RDF) is used. The study also presents the results of the activity of young researchers, who were engaged in the program. Following the change in the phase of the development of researchers characteristic features and in compliance with RDF, a conclusion is made about a positive impact of the program on the development of career skills of young scientists, their interaction skills, awareness of professional behavior procedure.Item A Logical-Algebraic Approach to Revising Formal Ontologies: Application in Mereotopology(2024) Aranda-Corral, Gonzalo; Borrego-Díaz, Joaquín; Chávez-González, Antonia; Gulayeva, NataliyaIn ontology engineering, reusing (or extending) ontologies poses a significant challenge, requiring revising their ontological commitments and ensuring accurate representation and coherent reasoning. This study aims to address two main objectives. Firstly, it seeks to develop a methodological approach supporting ontology extension practices. Secondly, it aims to demonstrate its feasibility by applying the approach to the case of extending qualitative spatial reasoning (QSR) theories. Key questions involve effectively interpreting spatial extensions while maintaining consistency. The framework systematically analyzes extensions of formal ontologies, providing a reconstruction of a qualitative calculus. Reconstructed qualitative calculus demonstrates improved interpretative capabilities and reasoning accuracy. The research underscores the importance of methodological approaches when extending formal ontologies, with spatial interpretation serving as a valuable case study.Item About Big Matrix Inversion(2021) Malaschonok, Gennadi; Tchaikovsky, IgorМатеріал доповіді учасників 4-ої Міжнародної конференції "Комп'ютерна алгебра", 28–29 червня 2021 р., Москва.Item About one problem for equation of fractal diffusion with argument deviation(2017) Drin, Iryna; Drin, Svitlana; Drin, YaroslavМатеріал VI-ї Міжнародної науково-практичної конференції "Проблеми інформатики та комп'ютерної техніки (ПІКТ-2017)", 5-8 жовтня 2017 року.Item Accurate classification for Automatic Vehicle Type Recognition based on ensemble classifiers(2019) Shvai, Nadiya; Hasnat, Abul; Meicler, Antoine; Nakib, AmirIn this work, a real world problem of the vehicle type classification for Automatic Toll Collection (ATC) is considered. This problem is very challenging because any loss of accuracy even of the order of 1% quickly turns into a significant economic loss. To deal with such problem, many companies currently use Optical Sensors (OS) and human observers to correct the classification errors. Herein, a novel vehicle classification method is proposed. It consists in regularizing the problem using one camera to obtain vehicle class probabilities using a set of Convolutional Neural Networks (CNN), then, uses the Gradient Boosting based classifier to fuse the continuous class probabilities with the discrete class labels obtained from OS. The method is evaluated on a real world dataset collected from the toll collection points of the VINCI Autoroutes French network. Results show that it performs significantly better than the existing ATC system and, hence will vastly reduce the workload of human operators.Item Algebraic and algorithmic classification of matrix algorithms [electronic resourse](2021) Malaschonok, GennadiDue to the growing size of the matrices used in applications, it is useful to carefully distinguish between some groups of matrix algorithms. We propose to use algebraic classi cation as the main way to group matrix algorithms. From an algorithmic point of view, we propose to highlight the class of block-recursive algorithms. These algorithms make it possible to ensure a uniform load of a computing cluster, to solve the problem of protecting against failure of its individual nodes, and, in addition, they have the complexity of matrix multiplication.Item The algorithm for knowledge assessment based on the Rusch model(2022) Kostikov, Alexander; Vlasenko, Kateryna; Lovianova, Iryna; Volkov, Sergii; Avramov, EvgenyIn this paper the algorithm for adaptive testing of students’ knowledge in distance learning and an assessment of its effectiveness in the educational process has been proposed. The paper provides an overview of the results of the application of modern test theory, a description and block diagram of the proposed algorithm and the results of its application in the real educational process. The effectiveness of using this algorithm for the objective assessment of students’ knowledge has been experimentally shown.Item All-path convexity: two characterizations, general position number, and one algorithm(2024) Haponenko, Vladyslav; Kozerenko, SergiyWe present two characterizations for the all-path convex sets in graphs. Using the first criterion, we obtain a new characterization of connected block graphs and compute the general position number in a graph with respect to the all-path convexity. The second criterion allows us to provide a new algorithm for testing a set on all-path convexity.Item Analysis of the Shape of Wave Packets in the "Half Space–Layer–Layer with Rigid Lid" Three-Layer Hydrodynamic System(2022) Avramenko, Olga; Lunyova, МariiaWe study the process of propagation of weakly nonlinear wave packets on the contact surfaces of a "half space–layer–layer with rigid lid" hydrodynamic system by the method of multiscale expansions. The solutions of the weakly nonlinear problem are obtained in the second approximation. The condition of solvability of this problem is established. For each frequency of the wave packet, we construct the domains of sign constancy for the coefficient for the second harmonic on the bottom and top contact surfaces. The regularities of wave formation are determined depending on the geometric and physical parameters of the hydrodynamic system. We also analyze the plots of the shapes of deviations of the bottom and top contact surfaces typical of the constructed domains of sign-constancy of the coefficient. We discover the domains where the waves become ∪ - and ∩ -shaped and reveal a significant influence of wavelength on the shapes of deviations of the contact surfaces of the analyzed hydrodynamic system.Item The analytical view of solution of the first boundary value problem for the nonlinear equation of heat conduction with deviation of the argument(2023) Drin, Yaroslav; Drin, Iryna; Drin, SvitlanaIn this article, for the first time, the first boundary value problem for the equation of thermal conductivity with a variable diffusion coefficient and with a nonlinear term, which depends on the sought function with the deviation of the argument, is solved. For such equations, the initial condition is set on a certain interval. Physical and technical reasons for delays can be transport delays, delays in information transmission, delays in decision-making, etc. The most natural are delays when modeling objects in ecology, medicine, population dynamics, etc. Features of the dynamics of vehicles in different environments (water, land, air) can also be taken into account by introducing a delay. Other physical and technical interpretations are also possible, for example, the molecular distribution of thermal energy in various media (solid bodies, liquids, etc.) is modeled by heat conduction equations. The Green’s function of the first boundary value problem is constructed for the nonlinear equation of heat conduction with a deviation of the argument, its properties are investigated, and the formula for the solution is established.Item An approach to modeling elections in bipartisan democracies on the base of the "state-probability of action" model(2024) Dosyn, Dmytro; Oletsky, OleksiyAn approach to constructing the two-level behavioral "state-probability of action" model and to getting appropriate matrices "state-probability of choice" for the case of two competing alternatives has been suggested. The top level is directly connected to probabilities of choice between alternatives. States of the model are connected to grades of pairwise comparisons. For getting rows of the matrix on this basis transitive scales are offered to be applied, but not only. It appears important to distinguish values of preferences themselves and probabilities of choice related to them. For this reason, another parameter standing for decisiveness of agents has been introduced. The bottom level is related to separate criteria influencing a choice. A way to applying such a model for modeling voting in a bipartisan democracy has been suggested. Within this context, a problem of equilibrium between two alternatives, when no alternative has advantages over the other, is of great importance. Some sufficient conditions for equilibrium between two alternatives have been postulated in the paper, they significantly rely upon properties of symmetry. The illustrating example of modeling elections in an imaginary country has been provided. Voters in this example are to make a choice between two candidates on the base of comparing them by some given criteria. In the initial example the equilibrium between alternatives holds. Then an issue how agents of influence could change the situation in a desirable direction is discussed.Item Attempts at Computing Gröbner Bases without S-polynomials whenever Possible(2017) Akritas, Alkiviadis G.; Malaschonok, GennadiIn this note we lay down some thoughts on computing Grobner bases using subresultant polynomial remainder sequences (prs’s) to eliminate variables. In this way we try to minimise 5-polynomial computations and, if possible, to completely avoid them. A personal note to us by Bruno Buchberger - at the Polynomial Computer Algebra conference (PCA-2015) in St. Petersburg, Russia - served as the motivation for our effort.Item Balance function generated by limiting conditions(2023) Morozov, DenysThis article conducts an analysis of the inherent constraints governing the formation of the price function that describes the interaction between two markets. The research not only identifies these constraints but also obtains an explicit form of the specified function. The key factors considered in constructing the price function are defined in the article. Through analyzing these constraints and their impact on market interaction, a formula for the price function is provided. This approach not only reveals the essence of natural constraints in forming the price function but also provides a contextual foundation for negotiations shaping a fair exchange price for the interaction process between two markets. This offers a theoretical basis for modeling and solving similar problems arising during practical economic activities. Two economies, Economy 1 and Economy 2, producing goods X and Y with linear Production Possibility Curve (PPC) graphs, are under consideration. The cost of producing one unit of good X relative to Y is denoted as 𝑅1 for Economy 1 and 𝑅2 for Economy 2. Exchange between economies occurs in a market, where the possible exchange is Δ𝑥 units of X for Δ𝑦 = 𝑅market ·Δ𝑥 units of Y, and vice versa. If 𝑅1 is less than 𝑅2, Economy 1 specializes in the production of X, and Economy 2 specializes in Y, fostering mutually beneficial trade. For mutually beneficial exchange on the market with a price 𝑅market, it is necessary and sufficient that 𝑅1 ≤ 𝑅market ≤ 𝑅2. The article also explores the concept of a fair exchange price, specifying conditions for symmetry, reciprocity, and scale invariance. Notably, it indicates that the unique solution satisfying these conditions is 𝑓(𝑅1,𝑅2) = √ 𝑅1 · 𝑅2. In the context of balanced exchange, where economies gain equal profit per unit of the acquired good, the balanced exchange price 𝑅market[𝑏𝑎𝑙𝑎𝑛𝑐𝑒] is determined as 𝑅market = √ 𝑅1 · 𝑅2. This serves as a fair price, meeting the aforementioned conditions of symmetry, reciprocity, and scale invariance. In the provided example with 𝑅1 = 2 and 𝑅2 = 8, the article examines the mutually beneficial interval for 𝑅market and computes the balanced and fair exchange price.Item The boundary problem by variable t for equation of fractal diffusion with argument deviation(2017) Drin, I.; Drin, Svitlana; Drin, Y.For a quasilinear pseudodifferential equation with fractional derivative by time variable t with order a e (0,1), the second derivative by space variable x and the argument deviation with the help of the step method we prove the solvability of the boundary problem with two unknown functions by variable t.Item Calculations on a Cluster with Distributed Memory: Matrix Decomposition and Inversion in the Commutative Domain(2017) Malaschonok, G.; Ilchenko, E.Матеріал виступу на XIV Мiжнародній науково-практичній конференцiї "Теоретичнi та прикладнi аспекти побудови програмних систем (TAAPSD'2017)", Київ, 4-8 грудня 2017 року.Item The cauchy problem for quasilinear equation with nonstationary diffusion coefficient(2023) Drin, Yaroslav; Drin, Iryna; Drin, SvitlanaThe initial problem for the heat conduction equation with the inversion of the argument are considered and Green’s function are determined. The theorem declared that the Poisson’s formula determines the solution of the Cauchy problem considered and proved.Item Commuting sets for topological set operators(2021) Antoshyna, Kateryna; Kozerenko, SergiyProceedings of the "Algebraic and Geometric Methods of Analysis", May 25-28, 2021 Odesa, Ukraine.Item Complexity of the problem of verifying the coordination mechanism in a system of software support of network collaboration(Springer New York, 2008) Glybovets, Mykola; Hlomozda, DmytroThe problem of verifying the coordination mechanism in a system of software support of network collaboration is considered. This problem is demonstrated to be similar to the agent verification problem. It is proved that the problem of verifying the coordination mechanism is co-complete.