Algebra and model theory 2025. Volume 16

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Algebra and model theory 2025. Volume 16

Издательство НГТУ, 2025.

Under the general editorship: M. Shahryari, S. V. Sudoplatov

The 17th International Summer School-Conference “Problems Allied to Model Theory and Universal Algebra” was held on 19–26 of June 2025 at Sobolev Institute of Mathematics, Novosibirsk State Technical University NETI and at the Camping Center “Erlagol” in Altai mauntains. 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 International Mathematical Center in Akademgorodok and by Faculty of Applied Mathematics and Computer Science of NSTU NETI. The school-conference included both online and in-person talks. At the school-conference, there were participants from Russia, Kazakhstan, Uzbekistan, China, Iran, Oman, France, Greece, Hungary, Poland. They made 50 talks. Within the school-conference, the discussions on actual problems on Model Theory, Algebra and related subjects were held. Information about the conference is posted on the conference website https://erlagol.ru.

О ДВУХ РАЗЛИЧНЫХ ТИПАХ ОРДИНАЛЬНЫХ ИТЕРАЦИЙ ВНУТРЕННИХ ФУНКТОРОВ

Polyakov N. L., В кн.: Algebra and model theory 2025. Volume 16.: ., 2025. С. 134–139.

In [1], the concept of a skew limit ultrapower of ordinal rank of an arbitrary model $\mathfrak M$ with respect to an ultrafilter $\mathfrak u$ was introduced for a model-theoretic characterization of some natural preorders on the set of ultrafilters on the set $\beta\omega$. We will show that this concept admits broad generalizations that can ...

Added: November 24, 2025

Research target: Mathematics

Language: English

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Keywords: algebra model theory logic and model theory

Algebra and model theory 2025. Volume 16

On structural stability of 3-diffeomorphisms with the Smale solenoid attractor–repeller dynamics

Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107

We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...

Added: June 4, 2026

Об эквивалентности по надстройке декартовых произведений регулярных гомеоморфизмов с гомеоморфизмами Данжуа

Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89

Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...

Added: June 3, 2026

Случайные блуждания на симметрических пространствах некомпактного типа ранга 1

Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162

Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...

Added: June 2, 2026

Electrical networks and data analysis in phylogenetics

Gorbounov Vassily, Kazakov A., Data Analytics and Topology 2025 Vol. 1 No. 1 P. 33–45

A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set. For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...

Added: May 28, 2026

Non-linear in-band interference cancellation on base of conjugate gradients method

Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6

This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...

Added: May 26, 2026

New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart”

Yu.S. Ilyashenko, S. Minkov, I. Shilin, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106

In this paper, new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological invariant of two arithmetic progressions, both perturbed and unperturbed, on the ...

Added: May 26, 2026

ADDITIVE AUTOMORPHISMS OF REGULAR MATRIX GRAPH

Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6

The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...

Added: May 25, 2026

Coping with AI errors with provable guarantees

Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856

AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...

Added: May 23, 2026

Overcoming the Curse of Dimensionality with Synolitic AI

Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84

High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...

Added: May 23, 2026

Stable On-the-Fly Learning for Dynamic Neural Networks With Delayed Inputs

Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392

This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...

Added: May 22, 2026

Analysis of the alternating minimization method for low-rank canonical polyadic decomposition in the Chebyshev norm

Stanislav Morozov, Calcolo 2026 Vol. 63 No. 2 Article 23

The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...

Added: May 22, 2026

B-facets in Dimension 4

Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 Article 18

A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...

Added: May 21, 2026

The VCG Mechanism, the Core, and Assignment Stages in Auctions

Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 Article 106192

The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...

Added: May 20, 2026

Upper bounds for Steklov eigenvalues of a hypersurface of revolution

Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407

In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...

Added: May 19, 2026

On smooth Fano threefolds with coregularity zero

Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84

We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...

Added: May 18, 2026

Классификация градиентно-подобных потоков без гетероклинических пересечений на четырехмерных многообразиях

Gurevich E., Saraev I., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 19–57

In this paper, we consider a class of gradient-like ows without heteroclinic intersections, dened on closed manifolds of dimension four. We show that for such ows, the problem of complete topological classication can be reduced to the combinatorial problem of distinguishing special framed graphs describing the mutual arrangement of invariant manifolds and the action of the ow on a wandering ...

Added: May 18, 2026

Алгебра и теория чисел

Ustinov A., Алфутова Н. Б., МЦНМО, 2022.

The book is a collection of problems in mathematics, designed primarily for high school students with advanced study of mathematics, interested in exact sciences. It will also be useful for mathematics teachers and students studying mathematics in higher educational institutions. A significant part of the material can be used to prepare for written and oral ...

Added: January 21, 2025

Международная конференция МАЛЬЦЕВСКИЕ ЧТЕНИЯ 13–17 ноября 2023 г. Тезисы докладов

[б.и.], 2023.

Proceedings of the international conference "Mal'tsev Meeting 2023" ...

Added: November 30, 2024

Model Theory and Algebra 2024

-, 2024.

Added: November 18, 2024

Algebra and Model Theory 14

Novosibirsk: ., 2023.

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 ...

Added: November 23, 2023

Градуированные компоненты присоединенной алгебры Ли прямоугольной группы Кокстера

Veryovkin Y., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 318 С. 31–42

The lower central series of a right-angled Coxeter group RCK and the corresponding graded Lie algebra L(RCK) associated with the lower central series of a right-angled Coxeter group are studied. Relations are obtained in the graded components of the Lie algebra L(RCK). A basis of the fourth graded component of L(RCK) for groups with at most four generators is described. ...

Added: November 23, 2023

Алгебра. 7 класс. Учебник

Мордкович А. Г., Семенов П. В., Александрова Л. А. et al., М.: Просвещение, 2021.

The textbook is written in accordance with GEF LLC and is included in the a long line of textbooks for grades 7-9; supports time-new models of studying algebra: basic and advanced. Outline-theoretical material is accompanied by a detailed looking at a large number of examples, practical tasks presented at three levels of difficulty. At the ...

Added: January 30, 2023

Алгебра. 8 класс. Учебник

Мордкович А. Г., Семенов П. В., Александрова Л. А. et al., М.: Просвещение, 2021.

Added: January 30, 2023

Алгебра. 9 класс. Учебник

Мордкович А. Г., Семенов П. В., Александрова Л. А. et al., Просвещение, 2021.

The textbook is written in accordance with GEF LLC and is included dit into a complete line of algebra tutorials for 7-9 grades. Its priority content and methodological line is functional-graphic, key mi concepts - mathematical language and mathematical del. The presentation of the theoretical material is accompanied detailed consideration of a large number of examples. At the end of each chapter, ...

Added: January 30, 2023