• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Elliptic Cauchy matrices
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
June 5, 2026
Neural Network Maps as a Method for Constructing Mathematical Models
Scientists from HSE University–Nizhny Novgorod and the Institute of Physics Belgrade, Serbia, are jointly exploring the application of machine learning techniques and neural networks to the study of nonlinear dynamics. Natalya Stankevich, Leading Research Fellow at the Laboratory of Topological Methods in Dynamics of the Faculty of Informatics, Mathematics, and Computer Science at HSE University–Nizhny Novgorod, spoke to the HSE News Service about this international project.
June 5, 2026
‘In the Age of Technology, It Is Interesting to Look into the Past and Think about What We Can Take from It
Polina Tabakova decided to apply for a Philology degree at HSE in Nizhny Novgorod because she grew up in Mari El and did not want to move far away from the Russian forests. In an interview for the Young Scientists of HSE University project, she spoke about the genre of the campus novel, the existential drama of Kolobok, and a blackout version of Eugene Onegin.
June 5, 2026
HSE Scientists Develop Method to Compress Large Language Models Without Losing Quality
Researchers from the AI and Digital Science Institute at the HSE Faculty of Computer Science have developed a new compression method for large language models such as GPT and LLaMA that reduces their size by 25–36% without additional training or significant loss of accuracy. This is the first approach to use mathematical transformations—specifically, rotations of model weights—to make models more amenable to compression with structured matrices. The study results have been published in ACL Findings 2025. The code is available on GitHub.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Elliptic Cauchy matrices

Functional Analysis and Its Applications. 2024. Vol. 58. No. 3. P. 289–298.
Zabrodin A., Vadim Prokofev

Some identities that involve the elliptic version of the Cauchy matrices are presented
and proved. They include the determinant formula, the formula for the inverse matrix, the matrix
product identity and the factorization formula.

Research target: Mathematics
Language: English
DOI
Keywords: elliptic functionsmatrix identities
Publication based on the results of:
Representation theory of vertex algebras and quantum groups with applications to knot theory, integrable systems, geometry of moduli spaces, and enumerative invariants (2024)
Similar publications
Wave dynamics within the Whitham-Ostrovsky equation
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
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
A model exhibiting all possible types of hyperbolic chaos on the 2-torus
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
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
Generalizing the Brady-Yong Algorithm: Efficient Fast Hough Transform for Arbitrary Image Sizes
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
Universal Comparison Methodology for Hough Transform Approaches
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
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
Формальная группа Бухштабера и эллиптические функции малых уровней
Ustinov A., Математические заметки 2017 Т. 102 № 1 С. 96–108
In the paper, we suggest a method for finding relations concerning series defining the Buchstaber formal group. This method is applied to the cases in which the exponent of the group is an elliptic function of level n=2,3, and 4. An algebraic relation for the series defining the universal Buchstaber formal group is also proved. ...
Added: October 7, 2025
Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System
Prokofiev V., Zabrodin A., Mathematical Physics Analysis and Geometry 2023 Vol. 26 No. 3 Article 20
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By ...
Added: December 4, 2023
Применение прямого алгоритмического поиска решений на ОУЭФ
Шагай М. А., Флегонтов А. В., В кн.: Некоторые актуальные проблемы современной математики и математического образования. Материалы научной конференции "Герценовские чтения - 2022".: СПб.: РГПУ им. А.И. Герцена, 2022.
This article deals with classes of equations - the Weierstrass orbit, the tangent orbit, and the elliptic integral orbit, -  whose solutions have a special structure. Through a finite set of special functions, all solutions are constructed by the method of differential "puzzles" after applying the algorithmic direct method. ...
Added: February 6, 2023
A General Harmonic Solution in Dilaton Electrodynamics: An Exact Expression for the Fields and the Generalized Lorentz Force
Mosharev P., Кечкин О. В., Moscow University Physics Bulletin 2020 Vol. 75 No. 5 P. 427–433
An exact expression is obtained for harmonic fields in Maxwell electrodynamics with dilatons in terms of elliptic Jacobi functions and elliptic Legendre integrals. The case of centrally symmetric fields is considered individually and effective charges of all three types, that is, electric, magnetic, and dilaton charges, are calculated. An expression is given for the generalized ...
Added: September 28, 2021
Odd supersymmetric Kronecker elliptic function and Yang–Baxter equations
A. Levin, M. Olshanetsky, A. Zotov, Journal of Mathematical Physics 2020 Vol. 61 P. 103504
We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application, we construct odd supersymmetric extensions of the elliptic R-matrices, which satisfy the classical and the associative Yang–Baxter equations. ...
Added: November 10, 2020
Квазиперенормируемые квантовые теории поля
Semenov-Tian-Shansky K. M., Поляков М. В., Смирнов А. О. et al., Теоретическая и математическая физика 2019 Т. 200 № 2 С. 290–309
Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity, analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions of nonlinear recurrence relations relevant for field ...
Added: September 29, 2020
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit