Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Masuda, Tetsu"'
A cluster algebra is an algebraic structure generated by operations of a quiver (a directed graph) called the mutations and their associated simple birational mappings. By using a graph-combinatorial approach, we present a systematic way to derive a
Externí odkaz:
http://arxiv.org/abs/2303.06704
The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from the discre
Externí odkaz:
http://arxiv.org/abs/1908.10060
In this paper, we consider the discrete power function associated with the sixth Painlev\'e equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is em
Externí odkaz:
http://arxiv.org/abs/1705.00445
We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric \tau functions for the sixth Painlev\'e equation. The original definition of the discrete power function imposes s
Externí odkaz:
http://arxiv.org/abs/1105.1612
Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda lattice equ
Externí odkaz:
http://arxiv.org/abs/1102.1829
Autor:
Masuda, Tetsu
Publikováno v:
SIGMA 5 (2009), 035, 30 pages
We present the $\tau$-functions for the hypergeometric solutions to the $q$-Painlev\'e system of type $E_7^{(1)}$ in a determinant formula whose entries are given by the basic hypergeometric function ${}_8W_7$. By using the $W(D_5)$ symmetry of the f
Externí odkaz:
http://arxiv.org/abs/0903.4102
Akademický článek
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Hypergeometric solutions to the q-Painlev\'e equations are constructed by direct linearization of disrcrete Riccati equations. The decoupling factors are explicitly determined so that the linear systems give rise to q-hypergeometric equations.
C
C
Externí odkaz:
http://arxiv.org/abs/nlin/0501051
Hypergeometric solutions to seven q-Painlev\'e equations in Sakai's classification are constructed. Geometry of plane curves is used to reduce the q-Painlev\'e equations to the three-term recurrence relations for q-hypergeometric functions.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/nlin/0403036
We present a simple heuristic method to derive the Painlev\'e differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.
Comment: 9 pages w
Comment: 9 pages w
Externí odkaz:
http://arxiv.org/abs/nlin/0403009