JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 51(36) 2018年9月 [査読有り]
We introduce a class of recursions defined over the d-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations satisfy th...
Ryo Kamiya   Masataka Kanki   Takafumi Mase   Tetsuji Tokihiro   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 51(35) 2018年8月 [査読有り]
Coprimeness property was introduced to study the singularity structure of discrete dynamical systems. In this paper we shall extend the coprimeness property and the Laurent property to further investigate discrete equations with complicated patter...
Ryo Kamiya   Masataka Kanki   Takafumi Mase   Tetsuji Tokihiro   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 51(12) 2018年3月 [査読有り]
We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional ...
JOURNAL OF THEORETICAL BIOLOGY 437 141-148 2018年1月 [査読有り]
We investigate an integrate and fire model for two cardiomyocytes interacting with each other. A feature of the model is to incorporate the refractory periods of the cardiomyocytes as well as the influence of firing of adjacent cells. The present ...
Masataka Kanki   Takafumi Mase   Tetsuji Tokihiro   
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 14 2018年 [査読有り]
In this article we investigate the coprimeness properties of one and two-dimensional discrete equations, in a situation where the equations are decomposable into several factors of polynomials. After experimenting on a simple equation, we shall fo...
Journal of the Physical Society of Japan 55(5) 1420-1423 1986年
We find a systematic procedure constructing the 2D and 3D “periodic” Penrose tilings, which tend to the infinite Penrose tilings. The electronic states in the 2d Penrose tiling are studied by using this sequence. We observe that the spectral measu...