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Creating New Mathematics by Schoolchildren
Doklady Mathematics. 2023. Vol. 107. No. 1. P. S132–S136.
A. L. Semenov, Soprunov S. F., Ivanov-Pogodaev I. A.
The paper discusses an example of an educational project in modern mathematics in which school students create mathematics that is new to them. The mathematical results produced by the students in the theory of definability also have an “absolute” novelty, i.e., are the basis for professional publications. The described course was based on recent results of this article’s authors in the theory of definability. The new results were obtained by a group of 10 schoolchildren from different regions of Russia.
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Sorokin P., Morozova E., Goshin M. E. et al., Высшее образование в России 2026 Т. 35 № 3 С. 63–89
The purpose of this study is to empirically identify the potential of contemporary educators involved in university entrepreneurship support initiatives as potential drivers of ecosystem development. This is achieved through an analysis of their key individual characteristics, professional experience, pedagogical practices, and the institutional context of the university environment. To this end, based on a ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Nisskaya A., Беляевская Е. С., Современная зарубежная психология 2026 Т. 3 № 15 С. 89–97
Context. The preschool period is a critical stage for the development of prosocial behavior. Children begin to understand the feelings of others, and the foundations of empathy and mutual assistance are formed. Situation-specific expressions of care can develop into more stable forms when children are embedded in a system of social relationships. However, the specific characteristics ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
М.: Национальный исследовательский университет "Высшая школа экономики", 2026.
The next collection “Cases of Russian Universities” contains cases developed in the master’s program “Management in Higher Education,” which has been offered since 2011 by the Institute of Education at the National Research University Higher School of Economics. The program is intended for university staff aiming for a managerial career or seeking to develop their ...
Added: October 1, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are
reduced to discrete-time random dynamical systems generated by time-one maps, so that
the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Мичурина А. А., Гуманитарные науки и образование 2026 Т. 17 № 3 С. 82–87
China pays special attention to the application of artificial intelligence (AI) technologies in various spheres of life, including education. The integration of AI into the field of education carries many opportunities. At the same time, this process is associated with a large number of risks, which raises the issue of the need for legal regulation ...
Added: October 1, 2026
Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1174–1178
Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...
Added: September 30, 2026
Dvoinin A., Развитие личности 2025 № Спецвыпуск С. 17–20
The article outlines A.M. Dvoinin’s personal reminiscences of his teacher, the prominent psychologist Valeria Sergeevna Mukhina ...
Added: September 30, 2026
Beldiev I., Тимашёв Д. А., Алгебра и анализ 2026 Т. 38 № 5 С. 1–10
An algebraic variety X is called a homogeneous space if there exists a transitive regular action of an algebraic group on X. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number. ...
Added: September 30, 2026
Ravedovskaya U., Didenko A., Филатова А. А., Journal of Teaching English for Specific and Academic Purposes 2025 Vol. 13 No. 3 P. 529–538
Emergence of generative artificial intelligence (GenAI) is revolutionizing teaching and evaluation in higher education. Early adopters have already demonstrated how large language model (LLM) conversational agents can serve as on-demand tutors, yet empirical evidence regarding their effectiveness in facilitating conceptual learning in non-computational domains is scant. Based on constructivist learning theory, this paper presents a ...
Added: September 18, 2026
Selskiy A., Физическое воспитание и студенческий спорт 2024 Т. 3 № 3 С. 227–231
Physical education and the corresponding subject in educational programs are traditionally considered as the tools for mastering skills directly related to sport and its certain disciplines. Meanwhile, within the competency-based education approach, physical education can be understood in a much wider context, as a source of development of soft skills and even cognitive abilities. This ...
Added: June 23, 2026
Zobnina M., Rozhkov A., Королева В. А. et al., М.: Национальный исследовательский университет "Высшая школа экономики", 2024.
Книга представляет собой практическое руководство для преподавателей, ориентированное на организацию и проведение курсов по предпринимательству в вузах. В ней представлены ключевые аспекты методики преподавания, включая стратегии, методы обучения, управление конфликтами, а также разнообразные формы и инструменты занятий, такие как лекции, семинары, кейс-метод, геймификация и предпринимательские мастерские. Особое внимание уделяется разработке эффективных практических заданий для студентов, ...
Added: November 23, 2025
Mikhailova A., Вопросы образования 2024 № 2 С. 139–169
Action research - that is “learning how to do something by doing it" - is a way to change teachers’ beliefs through practice. 15 teachers from three primary and secondary schools conducted their own action research. After a preliminary training, teachers independently designed and conducted lessons using digital tools to stimulate students’ active learning. During ...
Added: September 19, 2024
Posicelskaya M. A., Rudchenko T. A., Semenov A., Mathematics in School 2023 Vol. 2 No. 115 P. 7–12
The problem of values is becoming more central in education today than ever before. The main questions facing the teacher today:
• What value system will the student form as a result of education?
• What values are the driving motive for a student in the learning process? ...
Added: March 14, 2024