Let us introduce n ( 2) mappings fi (i=1,2,,n) defined on complete linear metric spaces (Xi-1, ρ) (i=1,2,,n), respectively, and let fi:Xi-1 Xi be completely continuous on bounded convex closed subsets Xi-1(0) Xi-1, (i=1,2,,n 0), such that fi(Xi-1(0)) Xi(0). Moreover, let us introduce n set-valued mappings Fi : Xi-1 Xi (Xi)(the family of all non-empty closed compact subsets of Xi), (i=1,2,,n 0). Here, we have a fixed point theorem on the successively recurrent system of set-valued mapping equations: xi Fi(xi-1, fi(xi-1)), (i=1,2,,n 0). This theorem can be applied immediately to analysis of the availability of system of circular networks of channels undergone by uncertain fluctuations and to evaluation of the tolerability of behaviors of those systems. In this paper, mathematical situation and detailed proof are discussed, about this theorem.
Mitsunori MAKINO Shin'ichi OISHI Masahide KASHIWAGI Kazuo HORIUCHI
A type of infinite dimensional homotopy method is considered for numerically calculating a solution curve of a nonlinear functional equation being a Fredholm operator with index 1 and an A-proper operator. In this method, a property of so-called A-proper homotopy plays an important role.
A mathematical theory is proposed, based on the concept of functional analysis, suitable for operation of network systems extraordinarily complicated and diversified on large scales, through connected-block structures. Fundamental conditions for existence and evaluation of system behaviors of such network systems are obtained in a form of fixed point theorem for system of nonlinear mappings.
Yoshihiro KANEKO Shoji SHINODA Kazuo HORIUCHI
A file transmission net N is a directed communication net with vertex set V and arc set B such that each arc e has positive cost ca(e) and each vertex u in V has two parameters of positive cost cv(u) and nonnegative integral demand d(u). Some information to be distributed through N is supposed to have been written in a file and the written file is denoted by J, where the file means an abstract concept of information carrier. In this paper, we define concepts of file transfer, positive demand vertex set U and mother vertex set M, and we consider a problem of distributing d(v) copies of J through a file transfer on N from a vertex v1 to every vertex v in V. As a result, for N such that MU, we propose an O(nm+n2 log n) algorithm, where n=|V| and m=|B|, for synthesizing a file transfer whose total cost of transmitting and making copies of J is minimum on N.
Takao SOMA Shin'ichi OISHI Yuchi KANZAWA Kazuo HORIUCHI
This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.
Kiyotaka YAMAMURA Shin'ichi OISHI Kazuo HORIUCHI
An iterative decomposition method with mesh refinement strategies is presented for the numerical solution of nonlinear two-point boundary value problems. It is shown that this method is more efficient than the traditional finite difference methods and shooting methods.