1998 Fiscal Year Final Research Report Summary
| Project/Area Number |
07404002
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
MATUMOTO Takao Fac.Sci., HIROSHIMA UNIVERSITY Prof., 理学部, 教授 (50025467)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIURA Yasumasa Hokkaido U., RIES,Prof., 電子科学研究所, 教授 (00131277)
MUTA Taizo Fac.Sci., Prof., 理学部, 教授 (80025353)
FUJIKOSHI Yasunori Fac.Sci., Prof., 理学部, 教授 (40033849)
HARADA Koichi Fac.Int.Arts Sci., Prof., 総合科学部, 教授 (90124114)
SAEKI Osamu Fac.Sci., Assoc.Prof., 理学部, 助教授 (30201510)
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| Project Period (FY) |
1995 – 1998
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| Keywords | Visible geometry / 3- amd 4-manifolds / Information geomtry / Comutational geometry / Boundary surface / Deformation of surfaces / 2-dimensional knot |
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| Research Abstract |
We are seeking how to study the applied geometry, by organizing the applied geometry seminar and symposium "Visible Geometry". The new topics and methods in the study of curves and surfaces in 3-space, the structure of the boundary surface and its move, the structure of 3-dimensional or 4-dimensional manifolds, dynamical approach, algebraic and algorithmic approach to geometry, information geometric aspect are the main contents of our recent study.
Matumoto investigates the deformation of generic surfaces in 3-space by the visible geometric methods with applications to the study of surfaces in 4-space especially of the 2-dimensionza1 knots, besides the study of information and computational geometry. Agaoka classified the tilings of the sphere by the rectangle triangles. Saeki is interested in the global study of the manifolds and mappings from the view point of singularity theory, and found a new topological meaning of curvature and tangential developping surface of the curve in 3-spac
… More
e. Yoshida found a relation between the boundary and characteristic classes. Nakayama extends the notion of Lyapunov function and studied the space of orbits. Doi handles the counting problem of plane curves. Harada defined the curvature for the discrete data to approximate efficiently by a polygonal curve and proposed a method to remove the unnecessary data. Tabata is working on the finite element analysis with some geometric considerations. Nishiura improves the softwear to pursue the branching solutions and studies the self-replicating dynamics. Irie studies the time evolution of space-structure and strategy for a population dynamics. Muta investigated the quantum theoretic phase structures in the curved spacetime. Tanisaki studied the geometric structure of quantum group by D-module. Imaoka studies some algorithms for the various invariants in topology. In information geometric aspects Matumoto characterized the statistical manifold by two point function and Fujikoshi studies the asymptotic expansions and error estimates in statistics. Less
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