К 90-летию со дня рождения Б.С. Гельруда

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К 90-летию со дня рождения Б.С. Гельруда

Математика в школе. 2020. № 7. С. 69–80.

Peresetsky A., Брайнин В. Б., Волков С. Е., Каленков С. Г., Левит В. И., Медведева Н. Н., Сагарадзе В. В., Файншмидт Е. М., Шейдвассер (Таран) В. М.

Research target: Mathematics Education

Priority areas: mathematics

Language: Russian

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LLM Difficulty Prediction Across Three L2 Task Types and Two Examination Forms

Lyu M., Omopekunola M., Wang F., / Series 2026.aimecon-wip.55 "Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con)". 2026.

Large language models (LLMs) have been proposed as a substitute for field trials in itemdifficulty estimation, but evidence about where they succeed is usually drawn from a single test form. We compare LLM difficulty predictions across three task types that make different language demands, grammar cloze, semantic cloze and reading comprehension, on two operational Grade ...

Added: October 5, 2026

Научно-методическое сопровождение реализации образовательных стратегий и региональных концепций (программ) развития образования: преодоление разрыва между цифровыми вызовами, новыми грамотностями, рисками образовательного неравенства и практикой школы

Денисенко И. С., Petrenko O., Vasilyeva T., Киров: Межрегиональный центр инновационных технологий в образовании, 2026.

Монография посвящена преодолению разрыва между стратегическими целями развития образования и повседневной практикой школы. Научно-методическое сопровождение рассматривается как управленческий механизм перевода образовательных инициатив в устойчивые изменения педагогических и управленческих практик. Представлена эмпирически апробированная модель научно-методического сопровождения, основанная на цикле: данные — интерпретация — гипотеза — педагогическая проба — анализ — корректировка или закрепление практики. Эмпирическая база включает ...

Added: October 5, 2026

Проект "Учитель-партнер" как инструмент обеспечения преемственности школьного и вузовского образования

Vradiy N., Давыдова Е. А., Просвещение. Иностранные языки 2026

В статье рассматривается проект «Учитель-партнер» как модель взаимодействия школы и вуза, объединяющая олимпиадную подготовку школьников, профориентацию и методическую поддержку учителей иностранного языка. ...

Added: October 5, 2026

Non vitae, sed scholae discimus: работают ли выпускники-педагоги в школе?

Милицына П. С., Rozhkova K., Roshchin S. et al., Высшее образование в России 2026 № 8-9 С. 94–115

Привлечение и удержание молодых педагогов в школах является одним из важнейших вопросов для преодоления проблемы кадрового дефицита в системе образования. В статье анализируются особенности трудоустройства выпускников российских вузов педагогических специальностей выпуска 2021–2022 гг. На основе тотальных административных данных выявлены факторы, влияющие на вероятность их первоначального трудоустройства в школу и последующего закрепления в профессии. Результаты показывают, ...

Added: October 5, 2026

Explicit Formula for Inverse and Determinant in Geometric Algebras over Odd-dimensional Vector Spaces

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

On Practical Aspects of Constructing Quasi-Cyclic Subfield Subcodes of Dual Elliptic Codes and Their Application in McEliece-type Cryptosystems

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

Graphon spin systems as exactly solvable models

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

Роль и место преподавателя в экосистеме университетского предпринимательства: российский опыт

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

Планетарное зацепление трилистника

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

Беляевская, Е.С., Нисская, А.К. (2026). Поддержка просоциального поведения в дошкольном возрасте: подходы, практики, обобщающая модель. Современная зарубежная психология, 15(3), 89–97. https://doi.org/10.17759/jmfp.2026150309

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

A quantum–analogue formalism for modeling supraliminal information processing

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

Рецензия на книгу: Быстрова И. В. Британский союзник: организация военно-экономических поставок в СССР в 1941–1945 гг. Документальное исследование. М.: Весь мир, 2022. 576 с.

Gorelov R., Территория: журнал исторических исследований 2026 Т. 2 № 1 С. 200–211

Added: October 1, 2026

Кейсы российских университетов. Выпуск 5, 2024 – 2025

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

Консервативные энтропийно и энергетически корректные разностные методы для одномерных квазигазодинамических систем уравнений

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

On some arithmetic conditions of recurrent sequences modulo prime p

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

Long-time behaviour of dynamical systems driven by bounded mixing noises

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

Markovian reduction and exponential mixing in total variation for random dynamical systems

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

Нормативные и правовые аспекты использования технологий искусственного интеллекта в системе высшего образования Китая

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

Bounds on the derivatives of the log-cumulative distribution function of the multivariate normal distribution

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

Asymptotics of Spectrum and Quantum Averages of the Hydrogen Atom in a Magnetic Field Near the Upper Boundaries of Spectral Clusters

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

Pairings on the algebra of Laurent series over a ring

Levashev V., / Series arXiv "math". 2026. No. 2609.06010.

We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...

Added: September 24, 2026

Iterative construction of the R-matrices in arbitrary dimensions

Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.

We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter. By analyzing the ...

Added: September 24, 2026

On static manifolds with boundary admitting a nowhere-vanishing static potential

Medvedev V., / Series arXiv "math". 2026.

We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...

Added: September 19, 2026

Vague stimulating ideas, images and metaphors in scientific thinking: researchers' work with horizons of unclear knowledge

Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.

Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...

Added: September 15, 2026