Theory of Dynamical Systems
| Project/Area Number |
60460002
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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 |
代数学・幾何学
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| Research Institution | Nagoya University |
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Principal Investigator |
SHIRAIWA Kenichi Nagoya Univ., College of General Education, Prof., 教養部, 教授 (80023521)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAKE Katsuya Nagoya Univ., College of General Education, Prof., 教養部, 教授 (20023632)
OZAWA Masanao Nagoya Univ., College of General Education, Assoc. Prof., 教養部, 助教授 (40126313)
SATO Ken-iti Nagoya Univ., College of General Education, Prof., 教養部, 教授 (60015500)
SHIOTA Masahiro Nagoya Univ., College of General Education, Assoc. Prof., 教養部, 助教授 (00027385)
IKEGAMI Giko Nagoya Univ., College of General Education, Assoc. Prof., 教養部, 助教授 (00023614)
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| Project Period (FY) |
1985 – 1986
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| Project Status |
Completed (Fiscal Year 1986)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1986: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | Dynamical Systems / Singular Perturbation / Quantum Mechanics / Operator Rings / Conditional Expectations / 観測過程 / 単峰な確率分布 / 出生死亡過程 |
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| Research Abstract |
This project is supported partly by the Grant-in-Aid for Scientific Research (B) from 1985 to 1986. We have obtained the following results in the second year of the project.
1. G. Ikegami obtained a necessary and sufficient (graph theoretic) conditions for an electrical circuit to be regular and a partial results of the second part of the Hilbert's 16th problem. Further, he continued his study of the fundamental theory of singular perturbations.
2. M. Shiota proved that a <C^r> mapping (1 <<!=> r< <infinite> ) between analytic Nash manifolds can be approximated arbitrarily closely by analytic Nash mappings.
3. K. Sato studied a unimodal processes with independent increments and obtained a generalization of the Johnson-Rogers' inequality. Some applications of the above results were made.
4. M. Ozawa studied <AW^*> -algebras and solved Kaplansky's conjecture. Also, he obtained a necessary and sufficient conditions for measuring processes to have a non-negative amount of information and solved the Groenewold's conjecture.
5. K. Miyake unified both the Hilbert's Theorem 94 and the Principal Ideal Theorem by using Artin's splitting modules. And generalizing the above results, he analyses the Capitulation Problem and observed that it should be considered in the theory of nilpotent extensions of algebraic number fields.
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Report
(1 results)
Research Products
(11 results)
