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Одномерная проблема Римана на эллиптической кривой
Математические заметки. 2017. Т. 101. № 1. С. 91-100.
Matveeva A., Poberezhny V. A.
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and an explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.
Publication based on the results of:
Poberezhny V. A., Matveeva A., Journal of Geometry and Physics 2017 Vol. 114 P. 384-393
We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is ...
Added: October 26, 2016
Takasaki K., Takebe T., Теоретическая и математическая физика (Российская Федерация) 2012 Vol. 171 No. 2 P. 683-690
We briefly review a recursive construction of hbar-dependent solutions of the Kadomtsev-Petviashvili hierarchy. We give recurrence relations for the coefficients X_n of an ħ-expansion of the operator X = X_0 + hbar X_1 + hbar^2 X_2 + ... for which the dressing operator W is expressed in the exponential form W = exp(X/hbar). The wave ...
Added: June 22, 2012
V A Poberezhnyi, R R Gontsov, Russian Mathematical Surveys 2008 Vol. 63 No. 4 P. 603-639
A counterexample to Hilbert's 21st problem was found by Bolibrukh in 1988 (and published in 1989). In the further study of this problem he substantially developed the approach using holomorphic vector bundles and meromorphic connections. Here the best-known results of the past that were obtained by using this approach (both for Hilbert's 21st problem and ...
Added: September 28, 2013
Takasaki K., Takebe T., Analysis and Mathematical Physics 2012 No. 2 P. 171-214
A construction of general solutions of the hbar-dependent Toda hierarchy is presented. The construction is based on a Riemann–Hilbert problem for the pairs (L, M) and (L_, M_) of Lax and Orlov-Schulman operators. This Riemann–Hilbert problem is translated to the language of the dressing operators W and W_. The dressing operators are set in an ...
Added: June 22, 2012
Serge Lvovski, Moscow Mathematical Journal 2019 Vol. 19 No. 3 P. 597-613
We show that if we are given a smooth non-isotrivial family of curves of genus 1 over C with a smooth base B for which the general fiber of the mapping J : B → A 1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting ...
Added: August 30, 2019
Netay I. V., Savvateev A. V., Bulletin of the Korean Mathematical Society 2017 Vol. 54 No. 5 P. 1597-1617
The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely ...
Added: April 11, 2018
Vyugin I. V., Дудникова Л. А., Математический сборник 2024 Т. 215 № 2 С. 3-20
The paper is devoted to the study of holomorphic vector bundles with logarithmic connections on a compact Riemann surface and the application of the results obtained to the study of the question of positive solvability of the Riemann–Hilbert problem on a Riemann surface. We give an example of a representation of the fundamental group of a ...
Added: March 5, 2024
Takebe T., Kuroki G., Journal of Physics A: Mathematical and Theoretical 2001 Vol. 34 No. 11 P. 2403-2413
We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonisation technique. ...
Added: August 14, 2014
Buryak A., Moscow Mathematical Journal 2023 Vol. 23 No. 3 P. 309-317
An algorithm to determine all the Gromov–Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov–Witten invariants in terms of the stationary ones. In the case of an ...
Added: November 20, 2023
Lebedev P. A., Nesterenko A., Черновик статьи 2014
В работе предложен алгоритм вычисления явного вида эндоморфизма эллиптической кривой, который может использоваться для ускорения операций по вычислению кратной точки. Приведены детали авторской реализации и результаты её производительности. В статье впервые представлены решения поставленной задачи для степени соответствующего многочлена Гильберта выше пятой. ...
Added: October 23, 2014
Takebe T., International Journal of Modern Physics A 2004 Vol. 19, May suppl. P. 418-435
Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model. ...
Added: August 14, 2014
Serge Lvovski, Springer, 2020
This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they ...
Added: October 27, 2020
Buff X., Goncharuk Nataliya, Journal of Modern Dynamics 2015 Vol. 9 P. 169-190
We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let f: R/Z -> R/Z be a (real) analytic orientation preserving circle diffeomorphism and let omega in C/Z be a parameter with positive imaginary part. Construct a complex torus by glueing the two boundary components of the annulus { z ...
Added: October 10, 2013
Malygina E., Кунинец А. А., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83-105
We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes constituting error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove ...
Added: March 19, 2024
Matveeva A., Poberezhny V. A., Mathematical notes 2017 Vol. 101 No. 1 P. 115-122
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic. ...
Added: May 22, 2017
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016