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On Mathematical Visualization in Education
Communications in Computer and Information Science. 2020. Vol. 1140. No. 1. P. 11–27.
Editor of translation: V. Sukhomlin
This article treats the use of modern information technologies in the classroom educational process. It emphasizes the need to combine symbolic and visual mathematics, describes the problems associated with this issue, provides a review of the existing systems and a list of the requirements a modern mathematical visualization system must meet. The article is conceived as a manifesto for the use of mathematical visualization in education. The article then goes on to describe the developments of the authors' research group. The functionality of visualmath.ru website is described. This resource contains an ample collection of visual and text modules for teachers to create presentations based largely on visual materials. The most important part of the article is the description of fast and powerful JavaScript visulatization libraries developed specifically for the project: Skeleton and Grafar. The former is designed to display two-dimensional graphs, while the latter visualizes three-dimensional objects with transparency and illumination effects. Both libraries are capable of processing large element sets in near-real time. In conclusion, selected examples of visualizations created using the libraries use are provided, including the ones used in courses on mathematical analysis and analytical geometry.
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Линская Ю. В., Вестник Санкт-Петербургского университета. Серия 14. Право 2023 № 4 С. 844–853
The article examines the concept of “educational service” in the context of the public discussion that has arisen about the possibility of its use in relation to education and educational relations. The current situation with the gradual abandonment of the term in the current educational legislation is considered, which corresponds to the provisions of the ...
Added: June 5, 2026
Издательство Санкт-Петербургского университета, 2023.
his book analyzes the application of Federal Law "On Education in the Russian Federation" over a ten-year period. The authors demonstrate the effect of the law's provisions defining new or updated institutions. Particular attention is paid to e-learning and new distance learning technologies, which are being actively implemented and discussed in Russian society due to ...
Added: June 5, 2026
Линская Ю. В., Вестник Санкт-Петербургского университета. Серия 14. Право 2025 Т. 16 № 2 С. 439–455
The purpose of this article is to compare the higher education systems in the Russian Federation and the People’s Republic of China (PRC), the specifics of legal regulation and government programs to support higher education. In recent years, the two countries have been developing dynamic cooperation and partnership in almost all spheres of life, including ...
Added: June 5, 2026
Адамский А. И., Kolachev N., Подболотова М. И. et al., М.: МГПУ, 2026.
Монография раскрывает концептуальный и технологический аспекты задачномодульного подхода к построению образовательной программы магистратуры, опосредованного использованием искусственного интеллекта для автоматизации оценивания компетентности обучающихся. Издание предназначено для руководителей и преподавателей магистратуры, ориентировано на подготовку кадров для сферы образования. Может быть использовано в качестве учебного материала для слушателей курсов повышения квалификации и профессиональной переподготовки. ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Seul: PMLR, 2026.
Added: June 4, 2026
Kazakov A., Shilov O. M., Mints D. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...
Added: June 3, 2026
Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162
Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...
Added: June 2, 2026
Obukhov A., Вершок О., Володина В. et al., Исследователь/Researcher 2025 № 3-4 С. 300–339
The article synthesizes the field notes of participants from the “Sociocultural Psychology and Anthropology” expedition group of Vernadsky School No. 1553 during their trip to Buryatia in the summer of 2025. Research was conducted in the Ulyunkhan Ulus in the upper reaches of the Barguzin River, with the final conference held in Tankhoy on the ...
Added: June 2, 2026
Obukhov A., Исследователь/Researcher 2025 № 3-4 С. 83–131
The article describes the experience of preparing and conducting a student research expedition to Buryatia as part of
the HSE University “Rediscovering Russia” program, themed “Man in Harmony with Nature: Interaction of Schools in the Republic of Buryatia with Protected Areas”. The expedition was prepared and carried out in cooperation with the D. Banzarov Buryat State ...
Added: June 2, 2026
Obukhov A., Кириллова К. Б., Исследователь/Researcher 2025 № 3-4 С. 26–48
This article investigates the phenomenon of enduring informal multi-age communities contributing to adolescent upbringing. The conditions for the establishment and the factors ensuring the endurance of such communities are identified through the example of three organizations: the “Nadezhda” unit, the Children and Youth Organization “Ostrov Sokrovishch” (Treasure Island), and the “Karavella” (Caravel) unit. As for ...
Added: June 2, 2026
Obukhov A., Исследователь/Researcher 2025 № 3-4 С. 10–15
The introductory article to the journal issue titled “Nature and Culture of Buryatia”, which presents the results of several
expeditions conducted in the Republic of Buryatia and Irkutsk Oblast, provides a preliminary overview of the key research problems addressed in the published materials. It contains an overview of the main topic—Nature and Culture of Buryatia—as well ...
Added: June 2, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026