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On Solving Multicriteria Decision Making Problems Based on Pairwise Comparisons 基于两两比较的多准则决策问题求解
Computer Tools in Education Pub Date : 2020-06-27 DOI: 10.32603/2071-2340-2020-2-27-58
N. Krivulin, Temirlan Abildaev, Vladlena D. Gorshechnikova, D. Kapatsa, Elizaveta A. Magdich, Anastasia A. Mandrikova
{"title":"On Solving Multicriteria Decision Making Problems Based on Pairwise Comparisons","authors":"N. Krivulin, Temirlan Abildaev, Vladlena D. Gorshechnikova, D. Kapatsa, Elizaveta A. Magdich, Anastasia A. Mandrikova","doi":"10.32603/2071-2340-2020-2-27-58","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-2-27-58","url":null,"abstract":"Problems known in the literature are considered for evaluating ratings of alternatives based on pairwise comparisons. To solve the problems, three methods are used, including the traditional method of of analysis of hierarchies by T. Saaty and the method of weighted geometric means, as well as the new method of minimax log-Chebyshev approximation, for which the solution is obtained using the apparatus and methods of tropical (idempotent) mathematics. Comparison of the solutions obtained shows that the use of different methods does not always lead to the same or close results. If the results of different methods differ significantly the choice of one of them for making a decision does not seem entirely justified. On the contrary, the coincidence or similarity of these results can be considered as some additional argument in favor of choosing one of them as a solution close to the optimum.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116332889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On circular sections of a quadric surface 在二次曲面的圆形截面上
Computer Tools in Education Pub Date : 2020-03-31 DOI: 10.32603/2071-2340-2020-4-59-68
A. Seliverstov
{"title":"On circular sections of a quadric surface","authors":"A. Seliverstov","doi":"10.32603/2071-2340-2020-4-59-68","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-4-59-68","url":null,"abstract":"A brief overview of the history of conic sections is given. Circular sections of ellipsoids and hyperboloids with planes passing through the center of the surface are considered. In general, there are two such secant planes. Generalizing the concept that arose in rigid-body mechanics, a straight line passing through the center of an ellipsoid is called the Galois axis if the orthogonal plane intersects this ellipsoid along a circle. Let us consider the pencil of planes passing through the intermediate principal axis of a triaxial ellipsoid. Each section of an ellipsoid with such a plane is an ellipse, one of the axes of which coincides with the intermediate principal axis of the ellipsoid. When the secant plane rotates around the intermediate principal axis of the ellipsoid, the length of the other axis of the ellipse continuously changes, taking values between the lengths of the minor and major axes of the ellipsoid. Therefore, some such section is a circle whose diameter is the intermediate principal axis of the ellipsoid. A triaxial ellipsoid has two such sections. They transform into each other when mirrored relative to the plane passing through the intermediate and other principal axes of the ellipsoid. Both Galois axes are orthogonal to the intermediate principal axis of the triaxial ellipsoid, and for a non-sphere ellipsoid of rotation, both Galois axes coincide with one axis and are orthogonal to the other principal axes of the ellipsoid. A method for constructing Galois axes from the known principal axes of an ellipsoid is proposed. This construction serves as one of the natural examples of geometric problems. In addition, the Galois axis can be correctly defined not only for the ellipsoid (for which it was originally introduced), but also for some other classes of centrally symmetric surfaces, including hyperboloids.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115382009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Source code plagiarism analysis and visualization for programming course 源代码抄袭分析和可视化编程课程
Computer Tools in Education Pub Date : 2020-03-31 DOI: 10.32603/2071-2340-2020-4-79-92
Аndrey Tsibin, E. Efimchik
{"title":"Source code plagiarism analysis and visualization for programming course","authors":"Аndrey Tsibin, E. Efimchik","doi":"10.32603/2071-2340-2020-4-79-92","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-4-79-92","url":null,"abstract":"The problem of unfair borrowing in the academic environment is still relevant. Unfair borrowing, or plagiarism, is found today in various forms of academic activity, ranging from semester papers of students to dissertations of scientists. The development of communications and the global nature of interaction have led to a wide availability of materials that are easy to copy. This leads to the fact that it becomes easier for students to find a solution than to compose it. A separate problem is the unfair borrowing in the works of students of educational institutions, which they perform in the framework of practical programming courses. As in the case of text, it is possible to detect plagiarism manually only in the smallest subsamples of data. Fortunately, today there are quite a large number of systems that allow you to automatically identify the similarity of the source code. Moreover, there are tools that allow you to aggregate the results of the search for plagiarism by several different systems, which also increases the likelihood of detecting cases of unfair borrowing. At the same time, the use of these tools is still not so widespread in educational institutions. This article describes the process of plagiarism analysis built for use in practical programming courses, as well as a tool for interactive graph visualization of the results of plagiarism analysis.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134435969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Visualization of Functional Dependences in Dynamic Geometry Systems 动态几何系统中函数依赖的可视化
Computer Tools in Education Pub Date : 2020-03-31 DOI: 10.32603/2071-2340-2020-4-93-112
V. Dubrovskii
{"title":"Visualization of Functional Dependences in Dynamic Geometry Systems","authors":"V. Dubrovskii","doi":"10.32603/2071-2340-2020-4-93-112","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-4-93-112","url":null,"abstract":"We describe various methods of visualization of functions and geometric transformations encountered in school mathematics by means of the dynamic geometry systems such as MathKit, The Geometer’s Sketchpad, and GeoGebra and their usage scenarios in the spirit of modern trends in education. Novel opportunities for teaching and learning functions and their properties based on computer models are discussed. The focus is on specifically computerized interpretations of functions, in particular, the so-called dynagraphs, in which parallel axes of arguments and values are used, and the correspondence given by the function is found when the argument-point moves along its axis.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126947352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Mobile Application to Demonstrate the Basic Concepts of Radio Electronics 演示无线电电子学基本概念的移动应用程序
Computer Tools in Education Pub Date : 2020-03-30 DOI: 10.32603/2071-2340-2020-1-49-57
Lev E. Shurinov, I. Petrushin, S. Knizhin
{"title":"A Mobile Application to Demonstrate the Basic Concepts of Radio Electronics","authors":"Lev E. Shurinov, I. Petrushin, S. Knizhin","doi":"10.32603/2071-2340-2020-1-49-57","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-1-49-57","url":null,"abstract":"In the process of studying the basics of the theory of signal transmission and acquaintance with the elements of electrical circuits it is important to demonstrate the mechanism of their work. For this, as a rule, a special laboratory workshop is required, inaccessible during lectures. The developed mobile application “SAoS” works in an interactive mode and does not require special programming skills. It allows the simulation of signals and operations on them using generators, adders, multipliers and various filters included in the structural diagram. The received signal is displayed in the form of an oscillogram and an amplitude spectrum.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129159872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal Algebras of Binary Operations of Rank 3 秩3二元运算的极小代数
Computer Tools in Education Pub Date : 2020-03-30 DOI: 10.32603/2071-2340-2020-1-38-48
Dmitry Eremenko
{"title":"Minimal Algebras of Binary Operations of Rank 3","authors":"Dmitry Eremenko","doi":"10.32603/2071-2340-2020-1-38-48","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-1-38-48","url":null,"abstract":"В работе рассматривается задача нахождения минимальных алгебр бинарных операций ранга 3. Решение данной задачи является первым шагом для построения решетки алгебр бинарных операций ранга 3. Построение такой решетки — один из вопросов универсальной алгебры, в частности теории решеток. В статье описывается алгоритм нахождения минимальных алгебр, который основан на свойстве идемпотентности операций, порождающих минимальные алгебры. Данный алгоритм был реализован на языке Python. Результаты работы алгоритма представлены в табличном виде.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124460225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Method for Reducing Iteration in Algorithms for Building Minimal Additive Chains 构建最小可加链算法中的一种减少迭代的方法
Computer Tools in Education Pub Date : 2020-03-28 DOI: 10.32603/2071-2340-2020-1-5-18
A. M. Kotochigov, A. Suchkov
{"title":"A Method for Reducing Iteration in Algorithms for Building Minimal Additive Chains","authors":"A. M. Kotochigov, A. Suchkov","doi":"10.32603/2071-2340-2020-1-5-18","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-1-5-18","url":null,"abstract":"Optimization of algorithms for computing the values of polynomials, more precisely, of monomials, is equivalent to the problem of constructing for a given number a minimal additive chain. To search for such chains, no algorithms are known except brute force. The increase in the complexity of the brute force algorithm is very large. Among chains of the same length there are a lot of equivalent ones, that is, those ending with the same number. The article provides a sufficient criterion for the equivalence of chains and shows how the use of the criterion reduces the procedure for the formation of all additive chains of a fixed length.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114971874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge 在数学知识的各种表示形式的背景下，数学对象的数字表示
Computer Tools in Education Pub Date : 2020-03-28 DOI: 10.32603/2071-2340-2020-58-86
S. Adlaj, Sergey N. Pozdniakov
{"title":"Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge","authors":"S. Adlaj, Sergey N. Pozdniakov","doi":"10.32603/2071-2340-2020-58-86","DOIUrl":"https://doi.org/10.32603/2071-2340-2020-58-86","url":null,"abstract":"This article is devoted to a comparative analysis of the results of the ReMath project (Representing Mathematics with digital media), devoted to the study of digital representations of mathematical concepts. The theoretical provisions and conclusions of this project will be analyzed based on the theory of the information environment [1], developed with the participation of one of the authors of this article. The analysis performed in this work partially coincides with the conclusions of the ReMath project, but uses a different research basis, based mainly on the work of Russian scientists. It is of interest to analyze the work of the ReMath project from the conceptual positions set forth in this monograph and to establish links between concepts and differences in understanding the impact of computer tools (artifacts) on the process of teaching mathematics. At the same time, the authors dispute the interpretation of some issues in Vygotsky’s works by foreign researchers and give their views on the types and functions of digital artifacts in teaching mathematics.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130359923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chemoinformatics: Applications of Computer Science in the Analysis of Chemical Structures (on the Example of Cadmium Sulfide) 化学信息学:计算机科学在化学结构分析中的应用(以硫化镉为例)
Computer Tools in Education Pub Date : 2019-12-28 DOI: 10.32603/2071-2340-2019-4-44-54
A. Maksimov, Arsenii D. Zavalishin, M. Abramov, A. Tulupyev
{"title":"Chemoinformatics: Applications of Computer Science in the Analysis of Chemical Structures (on the Example of Cadmium Sulfide)","authors":"A. Maksimov, Arsenii D. Zavalishin, M. Abramov, A. Tulupyev","doi":"10.32603/2071-2340-2019-4-44-54","DOIUrl":"https://doi.org/10.32603/2071-2340-2019-4-44-54","url":null,"abstract":"The article is aimed at demonstrating the practical application of graph theory as a subsection of the theoretical foundations of computer science in solving one of the interdisciplinary problems — describing the structure of the cadmium sulfide molecule using methods and indices of chemoinformatics. The article presents the results of calculations of the atom-bond connectivity index (ABC), of the geometric and arithmetic index GA, of the generalized Randic index, GA5 and ABC4, of the Zagreb indices for the chemical graph of cadmium sulfide (CdS). Topological indices for cadmium sulfide are considered for the first time, although the task of calculating these indices is not new in itself. The relevance of the results is emphasized by the fact that cadmium sulfide is widely used in various fields, such as optoelectronics, photodetectors, photoresistors, etc.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124993667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constructive Tasks as a Tool of Invasive and Non-invasive Assessment of Knowledge 建设性任务作为侵入性和非侵入性知识评估的工具
Computer Tools in Education Pub Date : 2019-09-30 DOI: 10.32603/2071-2340-2019-3-96-104
A. Chukhnov
{"title":"Constructive Tasks as a Tool of Invasive and Non-invasive Assessment of Knowledge","authors":"A. Chukhnov","doi":"10.32603/2071-2340-2019-3-96-104","DOIUrl":"https://doi.org/10.32603/2071-2340-2019-3-96-104","url":null,"abstract":"Constructive tasks are very important and appear in every branch of mathematics. This work is devoted to some experiments with constructive tasks held within the education and assessment process. Firstly, some remote constructive tasks were given to students within a course of Mathematical Logic and Theory of Algorithms. The tasks served only as a support tool and students were not obliged to solve them. Secondly, tasks of the same types were given to elder students which had already passed the course with an additional request to log their intellectual activity while solving the tasks. The third experiment was held during the written exam. Constructive tasks which were given to the students appeared as “the reverse” to the tasks they had solved during the semester.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124776351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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