1990 Fiscal Year Final Research Report Summary
Mathematical Analysis of Stochastic and Dynamic Systems
| Project/Area Number |
01460007
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University |
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Principal Investigator |
FUJIKOSHI Yasunori Department of Mathematics, Professor, 理学部, 教授 (40033849)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUMOTO Takao Department of Mathematics, Associate Professor, 理学部, 助教授 (50025467)
MAEDA Fumi-yuki Department of Mathematics, Professor, 理学部, 教授 (10033804)
KUSANO Takasi Department of Mathematics, Professor, 理学部, 教授 (70033868)
MIMURA Masayasu Department of Mathematics, Professor., 理学部, 教授 (50068128)
TAKENAKA Shigeo Department of Mathematics, Associate Professor, 理学部, 助教授 (80022680)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Stochastic System and Dynamic System / Growth Curve Model / Fractal Set / Hausdorff Dimension / Reaction Diffusion System / Monge-Ampere Equation / Martin Boundary / Knot |
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| Research Abstract |
We have investigated about stochastic systems and dynamic systems related to various fields of natural science and technology. We used mathematical tools from several fields, for instance, theory of probability, statistics, differential equation, functional analysis, geometry, numerical analysis and so on. We also applied our results to statistical physics and biological physics.
1. Stochastic System :
(1) Y. Fujikoshi : Asymptotic Expansions in Mathematical Statistics, Statistical Testing of the Growth Curve Model.
(2) H. Totoki : Hausdorff Dimension of Random Fractals, Cross Product of Random Dynamics.
2. Mathematical and Numerical Analysis of Dymanical Systems :
(1) M. Mimura etc : Stability and Bifurcations in Bistable Reaction Diffusion Systems.
(2) T. Kusano : Existence Theorem of Solutions for Monge-Ampere Equation.
(3) S. Oharu : Non-linear Perturbation of Semi-groups.
(4) F.-Y. Maeda : Martin Boundary of Harmonic Space.
3. Geometric Approach of Dynamic Systems :
(1) T. Matsumoto : Condition of Triviality for Knots of a Certain Kind.
(2) K. Okamoto : Kirillov-Kostant Theory and Feymnann's path integral. These results are closely related to applied mathematics, for example, mathematical physics and biophysics.
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