| Project/Area Number |
21540193
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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 | University of Hyogo |
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Principal Investigator |
UMEDA Tomio 兵庫県立大学, 大学院・物質理学研究科, 教授 (20160319)
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| Co-Investigator(Renkei-kenkyūsha) |
IWASAKI Chisato 兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
HOSHIRO Toshihiko 兵庫県立大学, 大学院・物質理学研究科, 教授 (40211544)
FUJIIE Setsuro 兵庫県立大学, 大学院・物質理学研究科, 准教授 (00238536)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 関数方程式 / スペクトル理論 / 固有関数 / 相対論的効果の数学的解明 / 量子力学の数学的研究 / 国際研究者交流（イギリス） / 国際情報交換（フランス） / 解析学 / 数理物理学 / 数理物理 / スペクトル解析 |
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| Research Abstract |
We investigated mathematical properties of energies of Dirac operators, which play fundamental roles in quantum mechanics, describing states of tiny particles like atoms. We found a few of new mathematical phenomena on threshold energies which are considered to be clues in theoretical explanations of the electron-positron pair creation. We also found an infinite series of functions, which play significant roles in the theoretical treatments of stability of matter. In addition, we discovered a mathematical phenomenon in connection with some important inequalities and with some important functions at threshold energies.
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