Computer Tools in Education

In memory of Yuriy Borisovich Senichenkov

Sergey Pozdniakov — 2025-05-07

On the Solvability and Special Solutions of Parametric Pell Equations

Nikolai Osipov — 2025-04-27

The paper investigates a family of solutions of second-order parametric Pell equations of the general form: x² −mx y + y² = B, where m and B are some parameters. An optimal algorithm for solving such equations is found as an alternative to the traditional method. The proposed method allows not only to solve equations of this type for specific values of the parametersm and B, but also to investigate some equations of this class for solvability
as a whole. In the particular case of equations of a special type, sequences of natural numbers are identified —the parameters of the equation, for which it is totally unsolvable.

Cogger and Yu Method: an Open Computer Implementation and Solution of Ranking Problems

Vladimir A. Parkhomenko — 2025-05-07

Cogger and Yu method for evaluation weights and ranking alternatives is considered. Based on this pairwise comparison method, an open source decision support system is developed. pagebreak The architecture of the developed application is presented, unit tests are conducted, including examples from publications and specially generated test cases. An example by V.V. Podinovsky, illustrating the incorrectness of hierarchy analysis method, showed, from our point of view, an acceptable result by Cogger and Yu method. The experiment is confirmed on a new original problem, showing the closeness of the results of Cogger and Yu method and criteria importance theory. The problem of ranking level generation algorithms for computer games in two-dimensional space is solved.

An Educational Model of the Movement of a Car on a Turn

Alexander Liapzev — 2025-04-27

A mathematical model of the movement of a car in a turn is proposed. The movement of the car is described based on modeling the dry friction force acting on the wheels of the car, so that it takes into account the characteristic features associated with the rolling of the wheel and corresponds to the Coulomb-Amonton law when the wheels are locked. A mathematical model of car movement is derived from the laws of mechanics, representing a system of 6 1st-order differential equations, including a number of parameters characterizing
movement. The numerical solution of a system of equations can be obtained quite simply by students using standard procedures available in mathematical environments designed for mathematical modeling (MATLAB, Octave, etc.).The study of the model’s solutions is actually a computational experiment and allows, despite the simplicity of the model, to identify some qualitative features of the car’s movement that manifest themselves in practice.

On Modularity in AI-Aided Music Systems

Gleb Rogozinski — 2025-05-07

Recently, music creation systems utilizing artificial intelligence have been rapidly advancing. The swift growth of machine learning methods has already led to the emergence of numerous powerful solutions in the fields of sound synthesis, generative technologies, music information retrieval, and other areas. The availability of computational resources is driving progress in the development of solutions for processing raw audio. Decomposing tasks can reduce the complexity of proposed solutions, ensuring improved quality at each stage of production.

Design and Implementation of a Blockchain-based Self-Directed Learning Process Evaluation Traceability Platform

Wenlong Yi — 2025-05-08

This study proposes a blockchain-based self-directed learning process evaluation traceability platform to address issues in current self-directed learning evaluation systems, including insufficient transparency, single evaluation subjects, low student participation, and nonstandardized evaluation criteria. The platform, designed based on a self-directed learning ability influence factor model, utilizes blockchain’s immutability to achieve secure storage, transparent recording, and trusted sharing of learning data. Comprising blockchain and application layers, the platform enables users to monitor the entire learning process and trace data through its interface. Multi-dimensional test results demonstrate the platform’s usability and reliability in high-concurrency scenarios. This study enriches self-directed learning evaluation and learning analytics theories. It provides new possibilities for integrating blockchain technology with digital education, significantly promoting educational evaluation reform and high-quality education development.

Characteristic of indexing in the PostgreSQL database management system

Natalia Grafeeva — 2025-04-26

The article discusses the features of the indexing process in the PostgreSQL database. The authors conducted a review and comparative analysis of indexes of various types, demonstrated examples of effective use of indexes. Based on the obtained results, conclusions about indexing as one of the means of optimizing SQL queries were drawn.