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On polynomially integrable planar outer billiards and curves with symmetry property
Mathematische Annalen. 2018. Vol. 372. P. 1481-1501.
Glutsyuk A., Shustin E.
We show that every polynomially integrable planar outer convex billiard is elliptic. We also
prove an extension of this statement to non-convex billiards.
Hutsalyuk A., Liashyk A, Pakuliak S. Z. et al., Nuclear Physics B 2017 Vol. 923 P. 277-311
We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of Bethe parameters. We also obtain recursions for ...
Added: October 26, 2017
Glutsyuk A., / Cornell University. Series "Working papers by Cornell University". 2021. No. 2104.01362.
Reflection in strictly convex bounded planar billiard acts on the space of oriented lines and preserves a standard area form. A caustic is a curve C whose tangent lines are reflected by the billiard to lines tangent to C. The famous Birkhoff conjecture states that the only strictly convex billiards with a foliation by closed ...
Added: November 4, 2021
V. A. Poberezhny, Journal of Mathematical Sciences 2013 Vol. 195 No. 4 P. 533-540
We consider systems of linear differential equations discussing some classical and modern results in the Riemann problem, isomonodromic deformations, and other related topics. Against this background, we illustrate the relations between such phenomena as the integrability, the isomonodromy, and the Painlevé property. The recent advances in the theory of isomonodromic deformations presented show perfect agreement ...
Added: February 14, 2014
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., Nuclear Physics B 2018 Vol. 926 P. 256-278
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(m|n)-invariant R-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system ...
Added: September 13, 2018
Gontsov R. R., V.A. Poberezhnyi, Helminck G. F., Russian Mathematical Surveys 2011 Vol. 66 No. 1 P. 63-105
This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable ...
Added: September 27, 2013
A.V.Zabrodin, Zotov A. V., Liashyk A. et al., Theoretical and Mathematical Physics 2017 Vol. 192 No. 2 P. 1141-1153
We discuss the correspondence between models solved by the Bethe ansatz and classical integrable systems of the Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric six-vertex model parameterized by trigonometric(hyperbolic) functions. ...
Added: October 26, 2017
Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2013. No. 18/13.
We review the modern theory of isomonodromic deformations, considering linear systems of
differential equations. On that background we illustrate the natural relations between
such phenomena as integrability, isomonodromy and Painlev\'{e} property. The recent
advances in the theory of isomonodromic deformations we present show perfect agreement to
that approach. ...
Added: March 31, 2014
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., Russian Mathematical Surveys 2017 Vol. 72 No. 1 P. 33-99
Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians in terms of the current generators of the Yangian double . The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the ...
Added: October 26, 2017
Liashyk A., Slavnov N. A., Journal of High Energy Physics 2018 Vol. 06 No. 018 P. 1-31
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl_3-invariant R-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We prove that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters. They thus do become on-shell vectors provided ...
Added: September 13, 2018
Lyashik A., Pakuliak S. Z., Ragoucy E. et al., Journal of Statistical Mechanics: Theory and Experiment 2019 Vol. 2019 No. 4 P. 1-23
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(N)-invariant R-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix. The second type is associated to a monodromy matrix closely related to the inverse of the monodromy matrix. We show that these two types of ...
Added: June 6, 2019
Bialy M., Fierobe C., Glutsyuk A. et al., Arnold Mathematical Journal 2022 Vol. 8 P. 411-422
This is a collection of problems composed by some participants of the workshop “Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM on October 4–8, 2021. ...
Added: February 1, 2024
V.A.Vassiliev, Arnold Mathematical Journal 2020 Vol. 6 No. 2 P. 291-309
V. Arnold’s problem 1987–14 from his Problems book asks whether there exist bodies with smooth boundaries in R^N (other than the ellipsoids in odd-dimensional spaces) for which the volume of the segment cut by any hyperplane from the body depends algebraically on the hyperplane. We present a series of very realistic candidates for the role ...
Added: August 17, 2020
Glutsyuk A., / Cornell University. Series "Working papers by Cornell University". 2019.
For a given closed convex planar curve γ with smooth boundary and a given p>0, the string construction yields a family of curves Γp for which γ is a caustic. The action of the reflection Tp on the tangent lines to γ≃S1 induces its action on the tangency points: a circle diffeomorphism p:γ→γ. We say ...
Added: November 12, 2019
Glutsyuk A., Journal of Fixed Point Theory and Applications 2022 Vol. 24 No. 2 Article 35
For a given closed convex planar curve γ with smooth boundary and a given p>0, the string construction yields a family of curves Γp for which γ is a caustic. The action of the reflection Tp on the tangent lines to γ≃S1 induces its action on the tangency points: a circle diffeomorphism Tp:γ→γ. We say ...
Added: November 4, 2021
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., SciPost Physic (Нидерланды) 2018 Vol. 4 No. 006 P. 1-30
We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra U_q(gl_n). We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, ...
Added: September 13, 2018
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