ID (降順)
JaLCDOI 10.18926/fest/48237 Basic Reproductive Ratio for Epdiemic Models (Review) 住田 正憲| 梶原 毅| We review some fundamental results on the basic reproductive ratio of models in epidemiology following several documents. We present the general denition of the basic reproductive ratio and the threshold theorem of for the stability of the disease free equilibrium. All results for non-negative matrices and non singular M-matrices which we need in the denition of the basic reproductive ratio and the proof of the threshold theorem are also presented. All parts of the review are self-contained, and all parts of the proof are given explicitly. Basic reproductive ratio epidemic model Non negative matrix M-matrix 岡山大学環境理工学部研究報告 2012-03 17巻 1号 1 6 2185-3347 Japanese publisher
JaLCDOI 10.18926/fest/19724 梶原 毅| In this paper, we contruct Hilbert C* -bimodules for continuous graphs whose vertexes are countable 1-dimensiona tori, and show some uniquness property of the C* -representatiion of these bimodules. Hilbert bimodule C* -algebras continous graph 岡山大学環境理工学部研究報告 1999-02-26 4巻 1号 77 80 1341-9099 English publisher
JaLCDOI 10.18926/fest/11610 佐々木 徹| 石川 洋文| 梶原 毅| 渡辺 雅二| We treat the problem of water pollution by the method of a mathematical model. We illustrate the method of analysis with Kojima Lake. We analyze in-flow and out-flow of the lake, compute numerical solutions of the governing equations of the water flow and the pollutant. The simulation leads to the conclusion concerning the figure of Kojima Lake. Kojima lake Water analysis Finite element method 岡山大学環境理工学部研究報告 1996-03 1巻 1号 47 53 1341-9099 English publisher
JaLCDOI 10.18926/fest/11608 梶原 毅| This paper contains some remarks supplementary to the previous paper [KW] concerning Hilbert C*-bimodules given from bundle constructions and a example given by this construction concerning the product type action on C*-algebras. Hilbert bimodule bundle tensor product 岡山大学環境理工学部研究報告 1996-03 1巻 1号 43 46 1341-9099 English publisher
JaLCDOI 10.18926/fest/11560 佐々木 徹| 梶原 毅| 石川 洋文| We have computed the phase of spreading contaminations in Kojima Lake by using the upwind-type finite element method. We have treated the two cases: the pollutant flows from the Sasagase river and from the Kurashiki River. We see that the upwind-type finite element method is effective in both cases, when the diffusion constant is quite small. Upwind-type Finite element method Kojima Lake 岡山大学環境理工学部研究報告 1998-01-14 3巻 1号 31 36 1341-9099 English publisher
JaLCDOI 10.18926/fest/11558 梶原 毅| In this paper, we define coaction crossed product of Hilbert C*-bimodule by finite groups. We show that resulting bimodule is of finite type, and compute indices of them. We present a Takesaki-Takai duality theorem which is some non-commutative generalization of abelian groups case in [KW2]. Hilbert bimodule Coaction Crossed product 岡山大学環境理工学部研究報告 1998-01-14 3巻 1号 25 29 1341-9099 English publisher
JaLCDOI 10.18926/fest/11557 Mathematical analysis of virus infectious diseases by ordinary differential equations 佐々木 徹| 梶原 毅| Some mathematical models describing interaction of virus and cells in vivo are reviewed. Similar models using systems of ordinary differential equations can be used for the analysis of dynamics of virus and cells for different kinds of virus. Models for human immunodeficiency virus, hepatitis C virus and hepatitis B virus are treated here. Although models are similar, different approximations can reduce the systems to the explicitly solvable forms. The solutions obtained here can be used to estimate biological parameters. Virus Mathematica models HIV HCV HBV 岡山大学環境理工学部研究報告 2000-02-29 5巻 1号 23 30 1341-9099 Japanese publisher
JaLCDOI 10.18926/fest/11553 Mathematical analysis of pathogenesis of viral hepatitis. 佐々木 徹| 梶原 毅| Simple mathematical models are considered to explain the pathogenesis of viral hepatitis. Dynamics of populations of liver cells and two virus strains are analyzed qualitatively. This analysis suggests the possibility that the viral mutation causes the hepatitis from the state of carrier. hepatitis mathematical model mutation 岡山大学環境理工学部研究報告 2000-02-29 5巻 1号 7 11 1341-9099 Japanese publisher
JaLCDOI 10.18926/fest/11524 Speeds of travelling wave solutions in a mathematical model of some infectious disease in predator-prey system 梶原 毅| 沖田 知毅| In this paper we construct a simple mathematical model for infectious disease in a pradator-prey system, and study the speeds of travelling wave solutions of this model. We present a method of estimation of speeds and make a numerical study about this matter. Travelling wave Infectious disease 岡山大学環境理工学部研究報告 2001-02-28 6巻 1号 17 23 1341-9099 Japanese publisher
JaLCDOI 10.18926/fest/11515 Stability analysis of mathematical models of infectious disease 村瀬 晶子| 佐々木 徹| 梶原 毅| Dynamics of infectious disease in vivo is described by coupled differential equations. Stability analysis of the complicated systems is difficult without computer calculation, while stability analysis is, in general, important to investigate qualitative behaviour of models. Liu analyzes stability of systems describing HIV dynamics in vivo with a symbolic calculation software. The same method is used for stability analysis of a mathematical model of malaria. mathematical model infectious disease dynamics in vivo stability analysis symbolic calculation 岡山大学環境理工学部研究報告 2002-03-22 7巻 1号 17 21 1341-9099 Japanese publisher
JaLCDOI 10.18926/fest/11495 A note on the effect of quadratic term on final pattern in Turing model 山内 憲一| 梶原 毅| The effect of the quadratic term on the final pattern in Turing model is disscussed numerically. Turing models are non linear reaction diffusion equations. Linear analysis for wave length is very useful to find evolving waves. But when a quadratic term appear in the equation, an initial wave can disappears and changes drastically to a spot which is independent of linear analysis. Turing instability Reaction Diffusion equation Quadratic term 岡山大学環境理工学部研究報告 2003-03 8巻 1号 19 22 1341-9099 Japanese publisher
JaLCDOI 10.18926/fest/11483 On Persistence in Dynamical Systems (Review) 佐々木 徹| 梶原 毅| Some important results on persistence are reviewed. These results concern the behavior of the orbits approaching the boundary. The orbits restrict the flow on the boundary, if one of them approaches more than one invariant set. A typical example is a model for cyclic competition, where the heteroclinic cycle can be the ω-limit set. Thus the persistence can be reduced to some conditions on the boundary flow. persistence ordinary differential equation dynamical system 岡山大学環境理工学部研究報告 2005-02-28 10巻 1号 13 21 1341-9099 Japanese publisher
JaLCDOI 10.18926/fest/11481 梶原 毅| 佐々木 徹| An elementary proof of permanence for a simple mathematical model proposed by Nowak and Bangham. In many papers, permanence property is proved by theorems established by the general theory of dynamical system. In this paper, we present an elementary proof only using differential inequalities and the theory of linear differential equations with constant coefficients. Permanence dynamical system pathogen 岡山大学環境理工学部研究報告 2005-02-28 10巻 1号 9 11 1341-9099 English publisher
JaLCDOI 10.18926/fest/11455 Iuchi Takuma| 梶原 毅| Qualitative analysis for the model of HIV infection in vivo presented by Perelson and Nelson are developed. The local stability analysis is done for the interior equilibrium, and it is shown that, for some paramter value, the interior equilibrium can be unstable and a Hopf bifurcation can occur. It is shown that the boundary equilibrium is globally asymptotically stable. Last, it is shown that this system is permanent. HIV Mathematical model Stability Liapunov function 岡山大学環境理工学部研究報告 2004-02-27 9巻 1号 45 51 1341-9099 English publisher
JaLCDOI 10.18926/fest/11426 Hydrodynamic and structural simulation by a particle approach 守田 利昌| 梶原 毅| This paper is a research report concerning the hydrodynamic simulation and the structural simulation by a particle approach. The proposal particle method model is introduced in this report, and the calculation example by the calculation code which uses the proposal model is shown. The high possibility of the particle method is shown by calculation examples which is difficult to solve by FDM and FEM. It is shown by caliculation examples of both the hydrodynamic and the structure analysis problems that the proposal model enables us to treat the fluid and the structure in a unified way. Particle Simulation Hydrodynamic analysis Structural analysis 岡山大学環境理工学部研究報告 2006-03-15 11巻 1号 19 26 1341-9099 Japanese publisher