Computer Tools in Education

In Memory of Andrey Nikolaevich Terekhov

2026-04-17T22:41:54+00:00

On July 31, 2025, Andrey Nikolaevich Terekhov passed away. He was a Doctor of Physical and Mathematical Sciences, Professor, founder of the Department of System Programming at St. Petersburg State University, member of the Academic Council of St. Petersburg State University, member of the Public Council under the Committee on Informatization and Communications of the Government of St. Petersburg, as well as a renowned scientist and IT entrepreneur.

Effective Solution for the Traveling Salesman Problem on Randomly Distributed Data

2026-04-16T23:16:01+00:00

In this study, we present a method and its implementations for the traveling salesman problem considering matrices with a uniform random distribution of path costs. The method is a modification of the branch-and-bound method with specific heuristics. Data generation and validation used for this study are discussed. The mathematical study of the problem being solved can probably be considered complete as early as the 1970s; even earlier, an approach to its solution in the form of the branch- and-bound method was described. The purpose of this paper is to describe such a heuristic implementation of the branch-and-bound method, which with almost a single probability gives the optimal solution to a random problem in an acceptable time. We call random variants of the problem, in which each cell of the traveling salesman matrix for a problem instance represents a realization of a uniformly distributed random variable. It is important to note that approaches to the heuristic solution of a random variant differ significantly from approaches to geometric and pseudogeometric variants. In our opinion, we have achieved our goal: thus, the maximum time to obtain a solution for 100 random problem instances of dimension 99 did not exceed 2 minutes, while the exact solution was always found; the last thing was verified by the fact that the branch-and-bound method was always counted to completion. In the paper, we provide a brief description of the heuristics used for this purpose, the most important of which is the construction of the so-called sequence of right-hand subproblems.

Investigation of the Efficiency of the Phase-Based Method Based on Gabor Filter Banks for Audio Recovery from Video Recordings

2026-04-16T23:16:23+00:00

This paper addresses the problem of passive acoustic signal recovery through the analysis of video sequences of vibrating objects. Sound waves propagating through a medium exert varying pressure on physical objects, inducing microscopic vibrations of their surfaces. The amplitude of such vibrations typically amounts to fractions of a pixel (10−3 -- 10−2 pixels), posing a challenge for detection via classical computer vision methods based on optical flow.
This study extends the "visual microphone" approach proposed in [1]. Based on computer vision principles [3], the Fourier transform shift property serves as the theoretical foundation, mathematically linking spatial object displacement to a linear phase shift. With the general mathematical model being preserved, the frequency- spatial decomposition stage is modified. Specifically, this research evaluates the efficiency of a custom implementation of a complex Gabor filter bank (in contrast to the Steerable Pyramid used in the original work).
An optimized C++ software implementation of the algorithm is presented. The proposed solution employs convolution via the Fast Fourier Transform (FFT) and batch parallel frame processing (OpenMP), yielding signicantly higher computational efficiency compared to naive spatial convolution.
A comparative analysis regarding robustness to sensor noise [18] is conducted, demonstrating the superiority of the phase-based approach over intensity-based methods using experimental data. Results obtained with a high-speed camera (2200 fps) confirm the feasibility of recovering acoustic information within the bandwidth limited by the Nyquist frequency [15, 16] and capturing tonal signals from lightweight objects at a distance of several meters. Furthermore, the impact of incoherent sensor noise is effectively mitigated through spatial weighting and filtering.

Study of coefficients of finite Dirichlet series vanishing at some zeros of Riemann's zeta function

2026-04-18T13:21:09+00:00

In 2013, Yu. V. Matiyasevich numerically studied finite Dirichlet series vanishing at multiple non-trivialzeros of the Riemann zeta function. He fixed the first coefficient of these series to 1 and observedthat the initial coefficients of the considered Dirichlet series closely resemble those of the alternating zeta function.This study was extended by fixing multiple coefficients of such finite Dirichlet series, and patterns were identified in the remaining initial coefficients. Specifically, these coefficients approximate the coefficients of the product ζ(s) · Σ^f+1_k=1 b_k k^-s , where f denotes the number of fixed coefficients, and the b_k values are determined from the series coefficients.The results of this analysis provide new insights into the relationship between the Riemann zeta function and number theory.

Animation of a satellite’s orientation in free flight

2026-04-17T21:45:38+00:00

This article presents an animation of the orientation of a freely rotating rigid body. The animation algorithm is based on an exact solution of the Euler equations.

Modification of Collocation Methods for the Numerical Solution of Functional Differential Equations

2026-04-19T13:04:59+00:00

This paper presents a generalization of collocation methods for numerical integration to the case of ﬁrst- and second-order functional-differential equations. The integration schemes for collocation methods are derived using Newton’s polynomial interpolation on Lobatto partitions applied to the right-hand sides of the functional-differential equations. The effectiveness of the modiﬁed collocation methods is illustrated using a planar model of the Moon’s motion with tidal effects determined by the Moon’s position on a shifted time scale with a delay. Numerical experiments show that the modiﬁed collocation method provides accuracy comparable to the generalized Adams method, with a signiﬁcantly larger integration step and, accordingly, a smaller computational effort.

Prospects for using the ontology description language ONTOL V2 in automating the knowledge veriﬁcation procedure

2026-04-17T23:21:53+00:00

This paper examines the prospects for using the ontology description language ONTOL V2, which is a modiﬁed version of the ONTOL V1 language developed to automate the process of verifying the knowledge of engineering students. The necessity of transitioning from modeling to metamodeling is substantiated. An example of automating a laboratory work on user interfaces is provided and analyzed.

Modeling Interdisciplinary Connections and Assessing Their Effectiveness in Educational Technologies

2026-04-17T23:44:11+00:00

It is known that the structure of an educational technology largely determines the quality and cost of education. Despite many years of practical experience in using educational technologies, the improvement of these technologies continues to the present day. One of the most effective and low-cost methods for improving the educational process is the use of adequate mathematical models. One such model that allows us to rethink educational technology and derive practical recommendations based on it is the matrix model of learning.

Computational triangulation in the digital age of mathematics teacher education: an example

2026-04-18T00:06:30+00:00

What is triangulation? Whereas the very idea of triangulation can be traced back to the 6^th century B.C. as a method of indirect measurements of distances and heights [1], nowadays, different subject matters use this term when scholarly attempts to make research rigorous can be described as a construction of a triangle. Most notably, triangulation has been used by sociologists as a way of taking a look at a certain experimental outcome from at least two different perspectives, by connecting three points – the outcome as the focus of research and two alternative perspectives – thus forming a triangle. When there are more than two alternative perspectives, more than one triangle can be constructed. These ideas stem from the works of sociologists [2-6]. In the cited works, different types of triangulation have been considered including methodological triangulation [2], theoretical triangulation [5], “triangulation between methods and triangulation within a method” [6, p. 217, italics in the original], and triangulation by data sources [5].