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## Graduate School of Science and Engineering

Science of Environment and Mathematical Modeling

### Laboratory of Mathematics for Information

#### Staff

#### Main Research Topics

<1> Stability of ordinary differential equations/difference equations and price-adjustment equations:

Michio Morishima (1977) performed numerical calculation of price-adjustment difference equations for price equilibrium of two commodities in order to estimate the eventual stability. Iterative calculations were performed on the relative price (%) of one commodity, and 25,000 to 30,000 were plotted. (Fig. 1)

Michio Morishima (1977) performed numerical calculation of price-adjustment difference equations for price equilibrium of two commodities in order to estimate the eventual stability. Iterative calculations were performed on the relative price (%) of one commodity, and 25,000 to 30,000 were plotted. (Fig. 1)

<2> Fuzzy differential equations/optimization:

The curves of solutions for fuzzy differential equations which show ambiguous information are drawn from left to right (Fig. 2). The solution methods for bridge optimal location problems with fuzzy hourly traffic volumes (round numbers) of A, B, C, D, Ln, and Rm will solve variational inequalities (Fig. 3).

The curves of solutions for fuzzy differential equations which show ambiguous information are drawn from left to right (Fig. 2). The solution methods for bridge optimal location problems with fuzzy hourly traffic volumes (round numbers) of A, B, C, D, Ln, and Rm will solve variational inequalities (Fig. 3).

<3> Chaos/fractal analysis:

The wings of the Gumowski-Mira are the focus on research into the nature of chaos and randomness (Fig. 4)

The wings of the Gumowski-Mira are the focus on research into the nature of chaos and randomness (Fig. 4)

<4> DNA computing:

The properties of the chemical reactions of four types of DNA bases are used and optimization theory is applied for devising new computing principles.

The properties of the chemical reactions of four types of DNA bases are used and optimization theory is applied for devising new computing principles.

<5> Rough information image processing analysis:

Redundant information occurs when image processing data is handled in a significantly large space. The objective of this research is to develop algorithms with faster computing speeds to take advantage of the large number of zero values even though the number of computing increases.

Redundant information occurs when image processing data is handled in a significantly large space. The objective of this research is to develop algorithms with faster computing speeds to take advantage of the large number of zero values even though the number of computing increases.

#### Research Contents

The average rate of change can be calculated by taking the displacement of an object as minute changes over time. The limiting operation can be used to obtain the differential (coefficient) from the average rate of change. We are engaged in research that applies this differential concept to various fields.

The purpose of our research is analysis of the stability and chaos (complex behavior that is difficult to predict) of trajectories for ordinary differential equations where differentiation is considered on a continuous time axis and difference equations at discrete times and then applying these results. In particular, our aim is to apply these results to price stabilization analysis in economic theory.

Also, when the environment surrounding people is modeled, information analysis is needed that incorporates ambiguous meanings (fuzziness) such as "roughly, about" if objectively performing numerical analysis of subjectivity and skilled and experienced intuition. We are also involved in the analysis of fuzzy differential equations that have ambiguity and research into the fuzzy optimization such as bridge location problems that take into account ambiguous road traffic volumes.

The purpose of our research is analysis of the stability and chaos (complex behavior that is difficult to predict) of trajectories for ordinary differential equations where differentiation is considered on a continuous time axis and difference equations at discrete times and then applying these results. In particular, our aim is to apply these results to price stabilization analysis in economic theory.

Also, when the environment surrounding people is modeled, information analysis is needed that incorporates ambiguous meanings (fuzziness) such as "roughly, about" if objectively performing numerical analysis of subjectivity and skilled and experienced intuition. We are also involved in the analysis of fuzzy differential equations that have ambiguity and research into the fuzzy optimization such as bridge location problems that take into account ambiguous road traffic volumes.

#### Keywords

- Fuzzy differential equation
- Fuzzy optimization
- Qualitative theory of ordinary differential equation
- Chaos/fractal analysis

- Price adjustment difference equation
- Optimized DNA computing
- Sparse decomposition and wavelet transformation