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Noncommutative geometry and Painleve equations
Okounkov A., Rains E.
Priority areas:
mathematics
Language:
English
Keywords: Painleve equations
Bershtein M., Shchechkin A., Letters in Mathematical Physics 2019 Vol. 109 No. 11 P. 2359-2402
Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé equation is equal to the series of 𝑐=1 Virasoro conformal blocks. We study similar series of 𝑐=−2 conformal blocks and relate it to Painlevé theory. The arguments are based on Nakajima–Yoshioka blowup relations on Nekrasov partition functions. We also study series of ...
Added: October 21, 2019
Parusnikova A., Vasilyev A. V., / Cornell University. Series arXiv "math". 2017. No. 1702.05758.
In this paper we present a family of values of the parameters of the third Painlevé equation such that Puiseux series formally satisfying this equation -- considered as series of z^{2/3} -- are series of exact Gevrey order one. We prove the divergence of these series and provide analytic functions which are approximated by them ...
Added: February 21, 2017
Bezrukavnikov R., Kazhdan D., Representation Theory 2015
Geometry of second adjointness for p-adic groups. ...
Added: July 27, 2015
M.A. Bershtein, A.I.Shchechkin, Communications in Mathematical Physics 2015 Vol. 339 No. 3 P. 1021-1061
In 2012, Gamayun, Iorgov, and Lisovyy conjectured an explicit expression for the Painlevé VI τ function in terms of the Liouville conformal blocks with central charge c = 1. We prove that the proposed expression satisfies Painlevé VI τ function bilinear equations (and therefore prove the conjecture). The proof reduces to the proof of bilinear ...
Added: August 14, 2015
Levin A., Olshanetsky M., Zotov A., Journal of Physics A: Mathematical and Theoretical 2016 Vol. 49 No. 39 P. 1-24
In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on the R-matrix description which provides Lax pairs in terms of quantum and classical R-matrices. First, we prove that for relativistic (and non-relativistic) tops, such Lax pairs with spectral parameters follow from the associative Yang–Baxter equation and its ...
Added: September 17, 2016
Parusnikova A., Vasilyev A., Journal of Mathematical Sciences 2019 Vol. 241 No. 3 P. 318-326
We examine asymptotic expansions of the third Painlevé transcendents for αδ ≠ 0 and γ = 0 in the neighborhood of infinity in a sector of aperture <2π by the method of dominant balance). We compare intermediate results with results obtained by methods of three-dimensional power geometry. We find possible asymptotics in terms of elliptic ...
Added: October 26, 2019
Bershtein M., Shchechkin A., Letters in Mathematical Physics 2019 Vol. 109 No. 11 P. 2359-2402
Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé equation is equal to the series of c=1 Virasoro conformal blocks. We study similar series of c=−2 conformal blocks and relate it to Painlevé theory. The arguments are based on Nakajima–Yoshioka blowup relations on Nekrasov partition functions. We also study series of ...
Added: August 31, 2020
Iorgov N., Lisovyy O., Tykhyy Y. et al., Constructive Approximation 2014 Vol. 39 No. 1 P. 255-272
We outline recent developments relating Painlev ́e equations and 2D conformal field theory. Generic tau functions of Painlev ́e VI and Painlev ́e III_3 are written as linear combinations of c= 1 conformal blocks and their irregular limits. This provides explicit combinatorial series representations of the tau functions, and helps to establish connection formula for ...
Added: August 14, 2015
Parusnikova A., Vasilyev A. V., Journal of Dynamical and Control Systems 2019 Vol. 25 No. 4 P. 681-690
In this paper, we study the third Painlevé equation with parameters γ = 0, αδ ≠ 0. The Puiseux series formally satisfying this equation (after a certain change of variables) asymptotically approximate of Gevrey order one solutions to this equation in sectors with vertices at infinity. We present a family of values of the parameters δ = −β^2/2 ≠ 0 such that ...
Added: June 4, 2019
Bershtein M., Shchechkin A., / Cornell University. Series math "arxiv.org". 2018.
Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé equation equals to the series of c=1 Virasoro conformal blocks. We study similar series of c=−2 conformal blocks and relate it to Painlevé theory. The arguments are based on Nakajima-Yoshioka blow-up relations on Nekrasov partition functions.
We also study series of q-deformed c=−2 ...
Added: November 22, 2018
Gavrylenko P., Lisovyy O., / arXiv.org. Series arXiv.org "math-ph". 2017. No. 1705.01869.
We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $\Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painlev\'e III equation of type $D_8$ (radial sine-Gordon equation). In particular, ...
Added: May 5, 2017
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240
We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019
Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
Added: February 2, 2017
ООО Фирма "Элист", 2014
В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...
Added: October 17, 2014
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
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
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
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018