| Project/Area Number |
24340031
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Meiji University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TATE Tatsuya 東北大学, 理学系研究科, 教授 (00317299)
HIGUCHI Yusuke 昭和大学, 教養部, 講師 (20286842)
AHARA Kazushi 明治大学, 総合数理学部, 教授 (80247147)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥12,090,000 (Direct Cost: ¥9,300,000、Indirect Cost: ¥2,790,000)
Fiscal Year 2014: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
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| Keywords | tight frame / quasicrystal / 2次元結晶 / 離散幾何解析学 / 結晶構造 / 複素2次曲面 / 有理点 / 準結晶 / 位相的結晶 / タイト・フレーム / 標準的実現 |
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| Outline of Final Research Achievements |
Motivated by the recent development in systematic design of crystal structures by both mathematicians and crystallographers, we studied interesting relationships among seemingly irrelevant subjects; say, standard crystal models, tight frames in the Euclidean space, rational points on Grassmannian, and quadratic Diophantine equations. Thus our view is quite a bit different from the traditional one in mathematical crystallography. The central object in this study was what we call crystallographic tight frames, which are, in a loose sense, considered a generalization of root systems. We also studied near quasi crystals pf Poisson's type.
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