Третий тип динамики и гомоклинические траектории Пуанкаре

Hypergraphs provide a natural framework for representing neurophysiological interactions distributed across sets of sensors. A key methodological question is how hyperedges should be defined from frequency-resolved electroencephalography/magnetoencephalography (EEG/MEG) data. We demonstrate a construction strategy in which hyperedges are obtained from canonical coherence (caCOH), an extension of coherence that estimates coupling between multidimensional signal spaces. To ...

Added: August 18, 2026

Global shifted potentials for moduli stacks of sheaves on Calabi-Yau four-folds

Borisov D., Katzarkov Ludmil, Sheshmani A. et al., American Journal of Mathematics 2026 Vol. 148 No. 4 P. 1075–1101

It is shown that there are globally defined Lagrangian distributions on the stable loci of derived \mathrm{Quot}-stacks of coherent sheaves on Calabi--Yau four-folds. Dividing by these distributions produces perfectly obstructed smooth stacks with globally defined -1-shifted potentials, whose derived critical loci give back the stable loci of smooth stacks of sheaves in global Darboux form. ...

Added: August 18, 2026

Вырождение графа, описывающего комплексную структуру

Богатырев А. Б., Математический сборник 2023 Т. 214 № 3 С. 106–119

Рассматривается клеточное разбиение пространства модулей вещественных кривых рода 2 с отмеченной точкой на единственном вещественном овале. Клетки перечисляются определенными графами, веса которых описывают комплексную структуру на кривой. Показано, что стягивание ребра графа приводит к корневой особенности естественного отображения из весов графа в пространство модулей кривых. ...

Added: August 14, 2026

Число компонент уравнений Пелля–Абеля с примитивным решением заданной степени

Богатырев А. Б., Gendron Q., Успехи математических наук 2023 Т. 78 № 1 С. 209–210

Уравнение Пелля-Абеля — это функциональное уравнение вида P²-DQ² = 1, с заданным многочленом D, свободным от квадратов, и неизвестными многочленами P и Q. Мы показываем, что пространство уравнений Пелля-Абеля с фиксированными степенями D и примитивным решением P является комплексным многообразием. Мы описываем его связные компоненты с помощью эффективно вычислимого инварианта. ...

Added: August 14, 2026

Stiefel filters

Богатырев А. Б., Transactions of the Moscow Mathematical Society 2024 Vol. 85 No. 2 P. 323–337

The best uniform rational approximation of the Sign function on two intervals separated by zero was explicitly found by E. I. Zolotarëv in 1877. The natural extension of this problem to three bands was solved by E. Stiefel in 1961. We indicate the solutions overlooked by the prominent geometer and study their properties. ...

Added: August 14, 2026

Вариационная формула в модели Шоттки римановых поверхностей

Богатырев А. Б., Успехи математических наук 2026 Т. 81 № 3(489) С. 159–160

Предложена простая и эффективно реализуемая формула для изменения абелевых интегралов (включая их периоды) при вариации образующих классической группы Шоттки, представляющей риманову поврехность. ...

Added: August 14, 2026

The space of solvable Pell-Abel equations

Gendron Q., Compositio Mathematica 2025 Vol. 161 No. 7 P. 1483–1511

A Pell–Abel equation is a functional equation of the form P^2-DQ^2=1 , with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell–Abel equations with the degrees of D and of the primitive solution P fixed is a complex manifold. We describe its connected components ...

Added: August 14, 2026

Generative geospatial modelling with geometric algebra

Yu Z., Wang J., Wang Z. et al., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2026 Vol. 384 P. 1–16

The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, ...

Added: August 13, 2026

О замыкающих ординалах инфинитарных вероятностных исчислений

Speranski S. O., Математические заметки 2026 Т. 120 № 3 С. 470–483

We show that, in terms of closure ordinals, many infinitary calculi for ‘first-order’ logics of probability (i.e., for languages similar to those in [Abadi & Halpern 1994]) are as hard as possible: the corresponding closure ordinals coincide with the least non-constructive ordinal, denoted by $\omega_1^{\mathrm{CK}}$. ...

Added: August 12, 2026

Data-Efficient Unsupervised Recalibration of Calorimeter Sensor Arrays Using Wasserstein Adversarial Learning

Ali S., Bocharnikov V., Ratnikov F. et al., Sensors 2026 Vol. 26 No. 16 Article 5024

Large distributed sensor arrays require repeated recalibration as radiation damage, material aging, gain variation, and readout drift alter channel responses. We studied a high-granularity calorimeter as a large sensor array and addressed unsupervised recalibration from two unpaired datasets: a nominal reference response and an aged response with attenuated cell-wise signals. Aging was modeled by a ...

Added: August 11, 2026

Maps preserving two small values of λ-th upper scrambling index

Kulev Y., Maksaev A., Promyslov V., Linear Algebra and its Applications 2026 Vol. 730 P. 51–72

The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This ...

Added: August 7, 2026

On the Matchings-Jack and Hypermap-Jack Conjectures for Labelled Matchings and Star Hypermaps

Kanunnikov A., Promyslov V., Vassilieva E., Electronic Journal of Combinatorics 2024 Vol. 31 No. 3 Article P3.6

Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the b-conjecture) are two major open questions relating Jack symmetric functions, the representation theory of the symmetric groups and combinatorial maps. They show that the coefficients in the power sum expansion of some Cauchy sum for ...

Added: August 7, 2026

From hyperbolic to complex Euler integrals

Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96

Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...

Added: August 4, 2026

Flexibility criterion for affine horospherical varieties

Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146

In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...

Added: August 3, 2026

О полуортогональных разложениях производных категорий диаграммных схем

Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129

Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...

Added: August 3, 2026

Mathematical methods of reinforcement learning

Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90

Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...

Added: August 3, 2026

A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147

We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...

Added: July 31, 2026

Квадратичный закон взаимности и его обобщения

Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75

This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...

Added: July 30, 2026

Three Algorithms for Merging Hierarchical Navigable Small World Graphs

Ponomarenko A., / Series Computer Science "arxiv.org". 2025.

This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...

Added: July 30, 2026

Cross-influence of two societies in deterministic evolutionary game

Shchur L., Antonov D., Burovski E., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2026 Vol. 36 No. 10 Article 2650132

We present a simple model that simulates the possible influence of one society on another. Specifically, two societies evolve deterministically according to the well-known Nowak-May spatial game with the addition of mutual influence through connections that reflect the current states of the societies. This may be related to the influence of a global information resource ...

Added: April 20, 2026

Политическое в пространстве турбулентного мира

Гаман-Голутвина О.В., Сморгунов Л. В., Полис. Политические исследования 2023 № 1 С. 7–10

The object of consideration in the article is the sources of global turbulence and the understanding of this topic within the framework of modern political science. Among the sources of turbulence are the natural environment and its pulsations, which can destabilize social systems; anthropogenic impact on nature, climate and large ecosystems; unstable demography and powerful ...

Added: December 8, 2025

Chaotic dynamics in an overlapping generations model: Forecasting and regularization

Tatyana A. Alexeeva, Kuznetsov N., Mokaev T. et al., Chaos, Solitons and Fractals 2025 Vol. 196 Article 116371

Irregular dynamics (especially chaotic) is often undesirable in economics because it presents challenges for predicting and controlling the behavior of economic agents. In this paper, we used an overlapping generations (OLG) model with a control function in the form of government spending as an example, to demonstrate an effective approach to forecasting and regulating chaotic ...

Added: April 20, 2025

Смешанная динамика: элементы теории и примеры

Gonchenko S., Гонченко А. С., Kazakov A. et al., Известия высших учебных заведений. Прикладная нелинейная динамика 2024 Т. 32 № 6 С. 722–765

Основной целью работы является представление недавних результатов, полученных в математической теории динамического хаоса и связанных с открытием его новой третьей формы, так называемой смешанной динамики. Этот тип хаоса сильно отличается от двух его классических форм — консервативного и диссипативного хаоса, и главное его отличие состоит в том, что аттракторы и репеллеры могут пересекаться, не совпадая ...

Added: December 1, 2024