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Cayley–Hamilton theorem for orthogonal quantum matrix algebras
Journal of Geometry and Physics. 2026. Vol. 224. Article 105798.
Ogievetsky O., Pyatov P. N.
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 we derive two versions of the Cayley-Hamilton theorem, one for its positive component O^+(2\ell) and another one for the negative component O^-(2\ell). In each case we introduce the spectral parameterization of the coefficients of the Cayley-Hamilton identity by the `eigenvalues' of the quantum matrices.
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.
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Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
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Ilyashenko Y., Shilin I., Stanislav Minkov, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106
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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 ...
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Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
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Морозов С. В., 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 ...
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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 ...
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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 ...
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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 ...
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Gurevich E., Saraev I., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 19–56
In this paper, we consider a class of gradient-like ows without heteroclinic
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Aleskerov F. T., Khutorskaya O., Stepochkina A. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
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Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
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Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
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It is known that for every continuous real-valued
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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
Ogievetsky O., Pavel Pyatov, Journal of Geometry and Physics 2026 Vol. 219 Article 105718
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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