Keiichi Miyajima

Partial Differentiation on Normed Linear Spaces R n

Partial Differentiation on Normed Linear Spaces Rn Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].

Riemann Integral of Functions from R into Real Normed Space

Riemann Integral of Functions from R into Real Normed Space In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].

The Product Space of Real Normed Spaces and its Properties

The Product Space of Real Normed Spaces and its Properties In this article, we define the product space of real linear spaces and real normed spaces. We also describe properties of these spaces.

Contracting Mapping on Normed Linear Space

Summary In this article, we described the contracting mapping on normed linear space. Furthermore, we applied that mapping to ordinary differential equations on real normed space. Our method is based on the one presented by Schwarz [29].

Riemann Integral of Functions from R into n-dimensional Real Normed Space

Riemann Integral of Functions from R into n-dimensional Real Normed Space In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].

Stochastic modeling of growth processes of bacteria colony and simulation studies

In the various fields of engineering including fluid, chemical, and biological engineering, we will observe many kinds of spatio-temporal patterns. For example, in the Belouzov-Zhabotinsky reaction, a target and a spiral ones are observed, which denote spatio-temporal oscillation of concentration of chemical substances. The analyses of such patterns are important problems of engineering. Up to date, excellent works in analyses of pattern formations have been performed, however, models in such analyses were considered in a deterministic framework. So, we cannot analyze influence of disturbances such as impurities in chemical substances and unexpected change of environmental situations on pattern formations using such deterministic models. In this paper, focusing our attention on the bacteria colony patterns and taking disturbances into consideration, we will propose the stochastic model of the growth processes of bacteria called Bacillus subtilis and study influence of disturbances on created bacteria patterns through simulation experiments.

The Sum and Product of Finite Sequences of Complex Numbers

The Sum and Product of Finite Sequences of Complex Numbers This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].

Behavior analyses of two-phase Stefan problems with anisotropy modeled by the stochastic phase field model

The purpose of this paper is to study a Stefan problem with anisotropy under a random disturbance. The Stefan problem is a typical example of a free boundary problem. Some mathematical models of the Stefan problem have been proposed in the past, which are generally classified into a Stefan type and a phase field one. The classical Stefan model ignores some of basic physical phenomena such as supercooling, superheating and surface tension, so we adopt the phase field model, which can include such basic physical phenomena and anisotropy in the model. In this paper, taking consideration of the influence of the random fluctuation of the temperature on the crystal growth, we propose the stochastic phase field model. And the crystal growth processes in the Stefan problem are numerically analyzed using the proposed stochastic phase field model.

Integral manifold andH? control in weak nonlinear systems

For a weak nonlinear system the authors obtained sufficient conditions for locking the solution of a differential equation system of the weak nonlinear type within a stable integral manifold, while satisfying the saddle point conditions of the optimal control evaluation function. The resulting solution can be used as a state feedback solution for the problem of H∞ regulator in weak nonlinear systems. By using the P solution of a Riccati matrix, sufficient conditions for obtaining the state feedback rule were derived from the results of discussion relating to the integral manifold. Then, the effectiveness of feedback of the weak nonlinear type was confirmed by simulation in a simple system. In addition, the Lyapunov function was used to evaluate stability of a closed-loop system obtained based on this feedback rule.

Optimizing fuzzy logic with genetic algorithm

We consider the existence of an optimal solution and the convergency of a genetic algorithm when it is used for optimizing fuzzy logic. The existence of an optimal solution is assured by the compactness of the the set of membership functions that defines the rules of the fuzzy logic. The convergency of the algorithm is assured by the compactness and the modification of the algorithm.