Algebra and Model Theory 14. Val. 14.

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Algebra and Model Theory 14

Vol. 14. Novosibirsk : Издательство НГТУ, 2023.

Under the general editorship: A. G. Pinus, E. N. Poroshenko, S. V. Sudoplatov

The 15th International Summer School-Conference “Problems Allied to
Model Theory and Universal Algebra” was held on 21–29 of June 2023 at
Novosibirsk State Technical University NETI and at the camping center
“Erlagol” in Altai mountains. The School was organized by Algebra and
Mathematical Logic Department of Novosibirsk State Technical University
(NSTU NETI) and Sobolev Institute of Mathematics of Siberian Branch of
Russian Academy of Sciences (IM SB RAS) . The School was supported
by Grant of NSTU (C23-2) and by Grant of International Mathematical
Center in Akademgorodok. This was the first time when the schoolconference
included both online and offline parts. For this reason there were
participants from rather many countries. At the school-conference, there
were participants from Russia, Kazakhstan, Uzbekistan, Canada, China,
Greece, Hungary, Italy, Oman, Poland. They made 41 talks. Within the
school-conference, the discussions on actual problems on Algebra, Model
Theory and related subjects were held. Information about the conference is
posted on the conference website https://erlagol.ru.

Замкнутые классы инфинитарных функций и их приложения в теории ультрафильтров

Н. Л. Поляков, В кн.: Algebra and Model Theory 14Vol. 14.: Novosibirsk: ., 2023. С. 102–112.

The Galois theory for closed classes of infinitary functions and some of its applications in the theory of ultrafilters are considered. ...

Added: November 23, 2023

Research target: Mathematics

Language: English

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Keywords: алгебра algebra model theory теория моделей

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

EEG evidence for reproducible neural states during Buddhist Highest Yoga Tantra meditation

Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560

Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...

Added: July 29, 2026

Произведения Масси и соотношения в когомологиях алгебр Стинрода

Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153

In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2. As part of a demonstration ...

Added: July 28, 2026

Three-dimensional magnetization textures as quaternionic functions

Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234

Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications. Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and reason about. Here we build analytical representation for such ...

Added: July 28, 2026

Nonlinear Neumann eigenvalues in outward cuspidal domains with weighted measure

Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91

We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...

Added: July 27, 2026

On the (p,q)-Eigenvalues of the No-Flux p-Laplacian

Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618

We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...

Added: July 27, 2026

Local Fault-Tolerant Routing in 3D Mesh NoCs using Single-Hop Rollback

Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536

This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...

Added: July 23, 2026

Kolmogorov Operators and Their Applications

Singapore: Springer, 2024.

Included in the following conference series: INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop Conference proceedings info: INdAM 2022 Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields. This volume collects a selection of the talks given at the Cortona meeting by ...

Added: July 17, 2026

Existence and uniqueness results for strongly degenerate McKean-Vlasov equations with rough coefficients

Veretennikov A., Pascucci A., Rondelli A., Stochastic Processes and their Applications 2026 Vol. 199 Article 104978

We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness. ...

Added: July 17, 2026

О сильных решениях многомерных СДУ с диагональными матрицами диффузии

Veretennikov A., Ляппиева А. А., Теория вероятностей и ее применения 2026 Т. 71 № 2 С. 295–304

Установлен новый результат о сильной единственности для многомерного СДУ с невырожденной диффузией и частично нерегулярным сносом. Его можно рассматривать как комбинированный вариант на темы Ямада и Ватанабэ (1971), Звонкина (1974) и первого автора настоящей статьи (1980). ...

Added: July 17, 2026

Об условиях для центральной предельной теоремы Добрушина для неоднородных цепей Маркова

Veretennikov A., Нуриева А. И., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 525 С. 24–30

Предложено новое достаточное условие в задаче о центральной предельной теореме в схеме серий для неоднородных цепей Маркова, с возможностью того, что минимум эргодического коэффициента Маркова–Добрушина может быть ближе к нулю, чем в основном условии Добрушина. ...

Added: July 17, 2026

О частных производных модифицированных полиномов Бернштейна–Станку для функций нескольких переменных

Veretennikov A., Мазутский Н. М., Математический сборник 2025 Т. 216 № 7 С. 3–27

Целью работы является доказательство аппроксимации смешанных производных второго порядка для функции нескольких переменных в норме L1 такими же производными модифицированных полиномов Бернштейна–Станку при минимальной возможной регулярности. ...

Added: July 17, 2026

О законе больших чисел для неодинаково распределенных слабо зависимых слагаемых

Ахмярова А. Т., Veretennikov A., Теория вероятностей и ее применения 2025 Т. 70 № 2 С. 211–227

В работе предложены новые версии слабого закона больших чисел (ЗБЧ) для слабо зависимых слагаемых (вообще говоря, разнораспределенных) как при наличии математического ожидания каждого из них, так и без такового. Одним из основных условий в первом из трех рассматриваемых случаев, в котором развиваются идеи из статьи Ю. Ш. Чау 1971 г., является равномерная интегрируемость слагаемых по Чезаро в духе работ по ЗБЧ для ...

Added: July 17, 2026

On weak existence of solutions of degenerate McKean-Vlasov equations

Veretennikov A., Stochastics and Dynamics 2024

A new weak existence result for degenerate multi-dimensional stochastic McKean–Vlasov equation is established under relaxed regularity conditions. ...

Added: July 17, 2026

Алгебра для студентов-математиков. Часть 1 (новое издание)

Gorodentsev A. L., М.: МЦНМО, 2025.

Книга представляет собой первую часть интенсивного двухгодичного курса алгебры для студентов, профессионально изучающих математику и физику. Основу курса составляют лекции, читавшиеся на факультете математики Высшей школы экономики и в Независимом московском университете, а также материалы сопровождавших их семинарских занятий. В книге также приводится большое количество задач и упражнений. Новое издание отличается от издания 2013 года: материал ...

Added: February 24, 2026

Алгебра для студентов-математиков. Часть 2

Gorodentsev A. L., М.: МЦНМО, 2025.

Книга представляет собой вторую часть интенсивного двухгодичного курса алгебры для студентов, профессионально изучающих математику и физику. Основу курса составляют лекции, читавшиеся на факультете математики Высшей школы экономики и в Независимом московском университете, а также материалы сопровождавших их семинарских занятий. В книге также приводится большое количество задач и упражнений. ...

Added: February 22, 2026