| Project/Area Number |
22540181
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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 | Kanazawa University |
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Principal Investigator |
TOHGE Kazuya 金沢大学, 電子情報学系, 教授 (30260558)
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| Co-Investigator(Renkei-kenkyūsha) |
MORI Seiki 山形大学, 理学部, 教授 (80004456)
SHIMOMURA Shun 慶應義塾大学, 理工学部, 教授 (00154328)
ISHIZAKI Katsuya 日本工業大学, 工学部, 教授 (60202991)
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| Project Period (FY) |
2010 – 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: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | ネバンリンナ理論 / 有理型函数 / max-plus代数 / 超離散方程式 / トロピカル・ネバンリンナ理論 / max-plus 代数 / 正則曲線 / 値分布論 / 差分方程式 / トロピカル数学 / (q-)差分方程式 / ディオファントス近似 / Nevanlinna理論 / Bank-Laine予想 / 微分方程式 / 零点分布 / 指数多項式 |
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| Research Abstract |
R. Nevanlinna’s theory describes the value distribution of meromorphic functions in the plane. We have successfully transplanted it to a theory describing the value distribution of piecewise linear and continuous functions on the real line in the max-plus algebra. As an application, we can find some results on piecewise linear continuous solutions which correspond to those on meromorphic solutions to complex differential equations. Especially, some growth formulas for an ultra-discretized entire function are obtained in terms of the coefficients of its tropical series expansion.
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