1991 Fiscal Year Final Research Report Summary
Metrics on complex manifold
| Project/Area Number |
01540036
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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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 Institute of Technology |
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Principal Investigator |
KATO Akikuni Nagoya Institute of Technology Department of Mathematics Assistant Professor, 工学部, 助教授 (20024226)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAZATO Makoto Nagoya Institute of Technology Department of Mathematics Assistant Professor, 工学部, 助教授 (00015900)
KURATA Masahiro Nagoya Institute of Technology Department of Mathematics Assistant Professor, 工学部, 助教授 (10002164)
HASEGAWA Yoshihei Nagoya Institute of Technology Department of Mathematics Assistant Professor, 工学部, 助教授 (10022675)
TAKEMOTO Fumio Nagoya Institute of Technology Department of Mathematics Assistant Professor, 工学部, 助教授 (50022645)
MATSUURA Shozo Nagoya Institute of Technology Department of Mathematics Professor, 工学部, 教授 (20024151)
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| Project Period (FY) |
1989 – 1991
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| Keywords | Generalized length / L-torsion / L-coprimary decomposition / Measure-preserving diffeomorphism / Hitting time distribution / Generalized diffusion process |
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| Research Abstract |
Our results can be divided into three parts ; (I) concerning commutative algebra, (II) concerning differential topology, and (III) concerning probability theory.
(I) A. Kato considers modules over a commutative ring R, then he studies modules modulo submodules of a generalized length zero. Fixing a generalized length L, the concepts of L-torsion, L-coannihilator, L-nilpotent, and L-coprimary module can be considered. Especially he gives a L-coprimary decomposition of a module modulo a submodule whose L equals zero.
(II) M. Kurata proves the following ; for measure-preserving diffeomorphisms of closed manifolds, there are families of locally invariant manifolds corresponding to Lyapunov exponents less than, where being non-negative.
(III) Y. Hasegawa develops a potential theory on a certain hypersurface S of infinite dimensional real sequences space E. M. Yamazato characterizes the class of hitting time distributions of single points of generalized diffusion processes.
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