| Project/Area Number |
22740077
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | High Energy Accelerator Research Organization |
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Principal Investigator |
OISHI-TOMIYASU Ryoko 大学共同利用機関法人高エネルギー加速器研究機構, 物質構造科学研究所, 特任助教 (30518824)
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 結晶構造解析 / 粉末指数付け / ブラベー格子 / 二次形式 / 簡約理論 / 粉末未知構造解析 / 位相問題 / 平均テータ級数 / 多項式計画問題 / 大域的最適化 / 半正定値計画法 |
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| Research Abstract |
Our study aims to create new application of mathematics to crystallography. A number of successful results were gained as a result, in both theoretical and practical aspects. Firstly, new algorithms and software were developed for error-stable Bravais lattice determination (BLD) and powder auto-indexing. As proved in several published papers, they are theoretically well-founded, error-stable and very prompt compared to all the existing methods. With regard to BLD, it was also proved that it is impossible to improve our algorithm as long as a similar methodology is adapted. Therefore, it may be said that the new software have decisive advantages in crystallography. In addition, a new method for ab-initio crystal structure determination was developed in order to enumerate all the solutions of so called "phase problem". For the method, additional study about its practical application is still necessary.
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