CVClient
Profile Information
- Affiliation
- Faculty of Engineering Department of Mathematical Engineering, Musashino University
- Degree
- Master of Engineering(Kyoto University)Doctor of Engineering(Graduate School, Kyoto University)
- J-GLOBAL ID
- 201701011554992865
- researchmap Member ID
- B000271159
Research History
11-
Jun, 2006 - Present
-
Apr, 2005 - Mar, 2014
-
Apr, 2002 - Mar, 2005
Education
3-
Apr, 1964 - Mar, 1968
Committee Memberships
14-
Nov, 2009 - Mar, 2013
-
Dec, 2010 - Nov, 2011
-
Aug, 2006 - Sep, 2011
-
May, 2009 - Apr, 2011
-
Apr, 2010 - Mar, 2011
Awards
3-
May, 2012
-
Apr, 2010
-
Apr, 2006
Papers
177-
Journal of Mathematical Physics, 54(2) 23504, Feb 5, 2013We present the singularity analysis of the ultradiscrete analogue of linearisable mappings of Quispel-Roberts-Thompson (QRT) type. The ultradiscretisation method used here is one which keeps track of signs and thus can be applied without the positivity restrictions of the classical ultradiscretisation approach. We show that in all cases the mappings possess confined singularities. The same is true for two non-autonomous equations, which are equally linearisable in the discrete case. We construct explicitly the solutions of the ultradiscrete mappings analysed here. © 2013 American Institute of Physics.
-
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(36) 365202-365202, Sep, 2012We examine a class of second-order mappings which can be integrated by reduction to a linear equation. These mappings have been identified in our previous works where we have precisely shown how to obtain their linearization. The mappings belonging to this class are referred to as 'linearizable mappings of the third kind'. We construct their explicit solution and obtain, for all of them, an invariant of QRT aspect but which is non-autonomous. We show that some of these 'third-kind' mappings are related to another class of linearizable mappings, known as mappings of Gambier type, from which they are obtained through a (discrete) derivative with respect to a parameter.
-
Direct ultradiscretization of Ai and Bi functions and special solutions for the Painleve II equationJOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(15) No.15, Apr, 2012Ultradiscrete Ai and Bi functions are directly derived through the ultradiscrete limit from q-difference analogues of the Ai and Bi functions, respectively. An infinite number of identities among the number of restricted partitions are obtained as by-products. A direct relationship between a class of special solutions for the ultradiscrete Painleve II equation and those of the q-Painleve II equation which have a determinantal structure is also established.
-
JOURNAL OF MATHEMATICAL PHYSICS, 53(2) 023510-023510, Feb, 2012Ultradiscrete singularity confinement test, which is an integrability detector for ultradiscrete equations with parity variables, is applied to various ultradiscrete equations. The ultradiscrete equations exhibit singularity structures analogous to those of the discrete counterparts. Exact solutions to linearisable ultradiscrete equations are also constructed to explain the singularity structures. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3682229]
Misc.
24-
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 43(31), Aug, 2010We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation of an exponential evolution operator. We apply our method to a host of systems for which there exist discretization results obtained by what we call the 'intuitive' method and compare the discretizations obtained. A discussion of our method as compared to one of the Mickens is also presented. Finally we apply our method to a system of coupled Riccati equations with emphasis on the preservation of the integrable character of the differential system.
-
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 42(28) 282002, Jul, 2009We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We present the Miura transformations between the various equations involved, including the more familiar potential form of the lattice mKdV.
-
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 42(28) 282002, Jul, 2009We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We present the Miura transformations between the various equations involved, including the more familiar potential form of the lattice mKdV.
-
CHAOS SOLITONS & FRACTALS, 40(1) 491-496, Apr, 2009We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it delay-difference scheme. We show that, as a function of the delay (which corresponds to the Period of infectiveness) the percentage of non-infected population varies over a wide range. We present also a variant of our model where the recovery rate follows a Poisson law and obtain it discrete version of the SIR model. We estimate the percentage of non-infected population in the two models, show that they lead to almost the same values and present an explanation of this fact. The second model is based oil the assumption that the infection is spread by carriers. Under the hypothesis that the carriers are relatively long-lived, and that the number of the infected ones is a relatively small fraction of the total population of potential carriers, we show that the model reduces to the same version of the discrete SIR obtained by our first model. (C) 2007 Elsevier Ltd. All rights reserved.
-
CHAOS SOLITONS & FRACTALS, 40(1) 491-496, Apr, 2009We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it delay-difference scheme. We show that, as a function of the delay (which corresponds to the Period of infectiveness) the percentage of non-infected population varies over a wide range. We present also a variant of our model where the recovery rate follows a Poisson law and obtain it discrete version of the SIR model. We estimate the percentage of non-infected population in the two models, show that they lead to almost the same values and present an explanation of this fact. The second model is based oil the assumption that the infection is spread by carriers. Under the hypothesis that the carriers are relatively long-lived, and that the number of the infected ones is a relatively small fraction of the total population of potential carriers, we show that the model reduces to the same version of the discrete SIR obtained by our first model. (C) 2007 Elsevier Ltd. All rights reserved.