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Determinants in quantum matrix algebras and integrable systems
Theoretical and Mathematical Physics. 2021. Vol. 207. P. 626–639.
Gurevich D., Saponov P. A.
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from \cite{G}. We establish relations between these determinants and the so-called column-(row-)determinants, often used in the theory of integrable systems. Also, we generalize the quantum integrable spin systems from \cite{CFRS} by using generalized Yangians, related to couples of compatible braidings. We demonstrate that such quantum integrable spin systems are not uniquely determined by the "quantum coordinate ring" of the basic space V. For instance, the "quantum plane" xy=qyx gives rise to two different integrable systems: rational and trigonometric ones.
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
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
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
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
Kazimirov D., Rybakova E., Vitalii V. Gulevskii et al., IEEE Access 2025 Vol. 13 P. 20101–20132
The Hough (discrete Radon) transform (HT/DRT) is a digital image processing tool that has become indispensable in many application areas, ranging from general image processing to neural networks and X-ray computed tomography. The utilization of the HT in applied problems demands its computational efficiency and increased accuracy. The de facto standard algorithm for the fast ...
Added: May 28, 2026
Kazimirov D., Vitalii Gulevskii, Kroshnin A. et al., Mathematics 2026 Article 1136
The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations, or task-oriented, relying on application-specific criteria that do not fully capture algorithmic properties. This paper ...
Added: May 28, 2026
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
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
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
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
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
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
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
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
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
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
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
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
Pavel Pyatov, Ogievetsky O., / Series arXiv "math". 2025. No. arXiv:2511.12282.
For a family of the orthogonal O(k) type Quantum Matrix algebras we establish an analogue of the Cayley-Hamilton theorem. The form of the Cayley-Hamilton identity is different in three cases. First, the cases of odd ( k=2 ell -1) and even ( k=2 ell) heights are different. Second, for even height orthogonal Quantum Matrix algebra ...
Added: November 21, 2025
Гуревич Д. И., Saponov P. A., Соколов В. В., Успехи математических наук 2023 Т. 78 № 4(472) С. 203–204
An algorithm is proposed for constructing symmetrizers in quantum matrix algebras. ...
Added: August 6, 2024
Gurevich D. I., Petrova V., Saponov P. A., Journal of Geometry and Physics 2022 Vol. 179 Article 104606
By using the notion of quantum double we introduce analogs of partial derivatives on a Reflection Equation algebra, associated with a Hecke symmetry of GL(N) type. We construct the matrix L=MD, where M is the generating matrix of the Reflection Equation algebra and D is the matrix composed of the quantum partial derivatives and prove that the matrices M, D and ...
Added: August 27, 2022
Гуревич Д. И., Saponov P. A., Теоретическая и математическая физика 2021 Т. 207 № 2 С. 261–276
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column- or row-determinants, often used in the theory of integrable systems. Also, we generalize the quantum integrable spin systems from [CFRS] by using generalized Yangians, related to couples of ...
Added: August 27, 2022
Ogievetsky O., Pyatov P. N., Journal of Geometry and Physics 2021 Vol. 165 Article 104211
We establish the analogue of the Cayley–Hamilton theorem for the quantum matrix algebras of the symplectic type. We construct the algebra in which the quantum characteristic polynomial acquires a factorized form. The low-dimensional examples and the classical limit are discussed. ...
Added: March 18, 2021
Pyatov P. N., Ogievetsky O., / Series math "arxiv.org". 2020.
We establish the analogue of the Cayley--Hamilton theorem for the quantum matrix algebras of the symplectic type. ...
Added: January 26, 2021