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## On matrix Painleve-4 equations

Nonlinearity. 2022. Vol. 35. No. 12. P. 6528-6556.

Bobrova I., Sokolov V.

Using the Painleve–Kovalevskaya test, we find several polynomial matrix

systems, which can be regarded as non-commutative generalisations of the

Painleve-4 equation. For these systems isomonodromic Lax pairs are presented.

Limiting transitions that reduce them to known matrix Painleve-2 equations are

found.

Bobrova I., Sokolov V., Journal of Nonlinear Mathematical Physics 2023 Vol. 30 No. 2 P. 646-662

All Hamiltonian non-abelian Painlevé systems of P1−P6 type with constant coefficients are found. For P1−P5 systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new P′3 and P5 systems thus obtained, we find isomonodromic Lax pairs for them. ...

Added: December 23, 2022

I. A. Bobrova, Sokolov V. V., Journal of Geometry and Physics 2023 Vol. 191 Article 104885

We find all non-abelian generalizations of P1 - P6 Painleve systems such that the corresponding autonomous system obtained by freezing the independent variable is integrable. All these systems have isomonodromic Lax representations. ...

Added: June 21, 2023

Anoshin V. I., Beketova A., Parusnikova A. et al., Computational Mathematics and Mathematical Physics 2023 Vol. 63 No. 1 P. 86-95

The second member of the fourth Painlevé hierarchy is considered. Convergence of certain power asymptotic expansions in a neighborhood of zero is proved. New families of power asymptotic expansions are found. Computations are carried out using a computer algebra system. Reference to a code that can be used for computing the Gevrey order of the ...

Added: March 30, 2023

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

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: October 21, 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

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

Anoshin V. I., Beketova A., Parusnikova A. et al., Programming and Computer Software 2022 Vol. 48 No. 1 P. 30-35

Asymptotic behavior and asymptotic expansions of solutions to the second term of the fourth Painlevé hierarchy are constructed using power geometry methods [1]. Only results for the case of general position—for the equation parameters β,δ≠0β,δ≠0—are provided. For constructing asymptotic expansions, a code written in a computer algebra system is used. ...

Added: February 5, 2022

I. A. Bobrova, Journal of Mathematical Physics 2023 Vol. 64 No. 10 Article 101702

In this paper, we discuss a connection between different linearizations for non-abelian analogs of the second Painlevé equation. For each of the analogs, we listed the pairs of the Harnard-Tracy-Widom (HTW), Flaschka-Newell (FN), and Jimbo-Miwa (JM) types. A method for establishing the HTW-JM correspondence is suggested. For one of the non-abelian analogs, we derive the ...

Added: October 6, 2023

Bobrova I., Mazzocco M., Journal of Geometry and Physics 2021 Vol. 166 Article 104271

In this paper we study the so-called sigma form of the second Painleve hierarchy. To obtain this form, we use some properties of the Hamiltonian structure of the second Painleve hierarchy and of the Lenard operator. ...

Added: September 25, 2021

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

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

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.

We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...

Added: March 9, 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

Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016

Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291

The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...

Added: December 7, 2013

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014

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

Турунцева М., Астафьева Е., Баева М. et al., Научный вестник ИЭП им. Гайдара.ру (электронный журнал) 2015 № 3(85) С. 3-33

В статье представлены расчеты прогнозных значений различных экономических показателей Российской Федерации во II–III кварталах 2015 г., построенные на основе моделей временных рядов, структурных эконометрических уравнений и моделей, построенных с использованием результатов конъюнктурных опросов. ...

Added: June 18, 2015