2006 Fiscal Year Final Research Report Summary
The Study of caloric morphism
| Project/Area Number |
17540144
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Ibaraki University |
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Principal Investigator |
SHIMOMURA Katsunori Ibaraki University, College of Science, Associate Professor, 理学部, 助教授 (00201559)
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| Co-Investigator(Kenkyū-buntansha) |
HORIUCHI Toshio Ibaraki University, College of Science, Professor, 理学部, 教授 (80157057)
SUZUKI Noriaki Nagoya University, Graduate School of Mathematics, Associate professor, 大学院・多元数理科学研究科, 助教授 (50154563)
NISHIO Masaharu Osaka City University, Graduate School of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
ANDO Hiroshi Ibaraki University, dollage of Science, Lecturer, 理学部, 講師 (60292471)
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| Project Period (FY) |
2005 – 2006
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| Keywords | caloric morphism / Appell transformation / heat equation / 熱方程式 |
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| Research Abstract |
The purpose of this research is the study of the caloric morphism (the transformation which preserve the solution of the heat equation), focusing on the explicit determination of the morphism.
We obtained the following results in the term of the project.
1. We have determined the caloric morphism for constant curvature spaces.
2. We determined all the caloric morphism between two semi-euclidean spaces with different radial metrics. As a result, we found a new type of caloric morphism in this setting, whose space mapping is the mixture of the similarity and the inversion.
3. We made the list of fundamental caloric morphisms between two semi-euclidean spaces with different radial metrics. And we gave a representation of all the caloric morphism as a composition of the fundamental caloric morphisms.
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