Математический сборник

We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...

Added: October 17, 2026

Turbulent Exchange Tensor in the Atmospheric Boundary Layer: An Inverse-Problem Approach Using Radiosonde Wind Observations with High Vertical Resolution

Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51

An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...

Added: October 16, 2026

Diversity of chaos with additional zero Lyapunov exponents in heterogeneous ensemble of quasi-periodic and chaotic systems

Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309

We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...

Added: October 16, 2026

A Reproducible Microscopy Acquisition Pipeline and Microscopy-Aware Attention for Classification, Detection, and Segmentation of Microorganisms

Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330

Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...

Added: October 14, 2026

On Calculation of Robustness and Stability of Formal Concepts Based on Delta Measure

Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992

The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...

Added: October 14, 2026

Shrimps as a fundamental object of nonlinear dynamics. Overview, properties and quasi-periodic generalization

Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592

Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...

Added: October 14, 2026

Poincaré series of valuations on functions over a subfield of complex numbers

Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22

For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...

Added: October 13, 2026

Wave scattering by a sloping beach of an arbitrary angle. Revisited: regular solution

Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4

In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...

Added: October 12, 2026

Дифференциальная геометрия и топология. Курс лекций

Gusein-Zade S., М.: МЦНМО, 2026.

Книга содержит курс лекций по дифференциальной геометрии и топологии, читавшихся автором на механико-математическом факультете МГУ в разные годы. В дополнениях приводятся некоторые сюжеты (связности в расслоениях, теорема Фробениуса, производные Ли и др.), которые были включены в курс в отдельные годы либо содержались в аналогичных курсах лекций в Независимом московском университете. Для студентов математических и физических специальностей. ...

Added: October 12, 2026

О воспроизводимости анализа временных рядов на основе матричных профилей

Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66

The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...

Added: October 9, 2026

Теория вероятностей и математическая статистика. Олимпиадные задачи

М.: Юрайт, 2026.

The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...

Added: October 9, 2026

Человеко-машинная система анализа и улучшения качества условий проживания населения

Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913

The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...

Added: October 9, 2026

Linear dependencies, polynomial factors in the Duke–Erdős forbidden sunflower problem

Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124

We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...

Added: October 8, 2026

Modulational Instability and Wave Dynamics in the Rotated Modified Gardner–Whitham Equation

Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245

This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...

Added: October 8, 2026

Автоматизированное построение математических теорий

Люксембург А. А., УРСС, 2005.

Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...

Added: October 7, 2026

Decision support system for improving the quality of life of the population

Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595

Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...

Added: October 7, 2026

Space-Time Fluctuations in a Quasi-static Limit

Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7

We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...

Added: October 6, 2026

Примеры гамильтоново-минимальных лагранжевых подмногообразий в Gr(r,n)

Tyurin N. A., Известия РАН. Серия математическая 2025 Т. 89 № 2 С. 146–160

In the paper one presents a generalization of A. E. Mironov construction of Hamiltonian minimal and minimal lagrangian submanifolds to the case of an algebraic variety which admits a Kahler–Einstein metric, symmetric with respect to a toric action of Tk. As an application one presents examples of Hamiltonian minimal lagrangian submanifolds in the Grassmanian Gr(r,n). ...

Added: April 17, 2025

О действиях торов и кватернионных торов на произведениях сфер

Ayzenberg A., Гугнин Д. В., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 326 С. 5–14

Изучаются действия торов (стандартных компактных торов, а также их кватернионных аналогов) на произведениях сфер. Доказано, что пространство орбит некоторого специального действия тора на произведении сфер гомеоморфно сфере. Аналогичное утверждение для вещественного тора Zn2Z2n было доказано вторым автором в 2019 г. Результат также распространен на произвольные компактные топологические группы; таким образом, получено обобщение всех перечисленных выше результатов о произведениях ...

Added: January 16, 2025

Многообразия с действием тора сложности 1, имеющие конечное число орбит группы автоморфизмов

Gayfullin S., Chunaev D., Фундаментальная и прикладная математика 2023 Т. 24 № 4 С. 47–59

In this work we obtain sufficient conditions for a variety with a torus action of complexity one to have finite number of automorphism group orbits. ...

Added: December 2, 2023

О гомотопическом разложении фактора момент–угол-комплекса и его приложениях

Limonchenko I., Solomadin G., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 317 С. 132–156

In this paper we prove that the quotient of any real or complex moment-angle complex by any closed subgroup in the naturally acting compact torus on it is equivariantly homotopy equivalent to the homotopy colimit of a certain toric diagram. For any quotient we prove an equivariant homeomorphism generalizing the well-known Davis-Januszkiewicz construction for quasitoric ...

Added: October 15, 2022

Limit points and additive group actions

Arzhantsev I., Ricerche di Matematica 2024 Vol. 73 No. 2 P. 715–724

We show that an effective action of the one-dimensional torus G_m on a normal affine algebraic variety X can be extended to an effective action of a semi-direct product G_m⋌G_a with the same general orbit closures if and only if there is a divisor D on X that consists of G_m-fixed points. This result is applied to the study of orbits of the automorphism group Aut(X) on X. ...

Added: August 16, 2021

Lie algebras of vertical derivations on semiaffine varieties with torus actions

Arzhantsev I., Liendo A., Stasyuk T., Journal of Pure and Applied Algebra 2021 Vol. 225 No. 2 P. 106499

Let X be a normal variety endowed with an algebraic torus action. An additive group action alpha on X is called vertical if a general orbit of alpha is contained in the closure of an orbit of the torus action and the image of the torus normalizes the image of alpha in Aut(X). Our first result in this paper ...

Added: July 29, 2020