| Project/Area Number |
22540224
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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 |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Yoshimasa 京都大学, 大学院・情報学研究科, 教授 (50172458)
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| Co-Investigator(Renkei-kenkyūsha) |
KATO Tsuyoshi 京都大学, 大学院・情報学研究科, 教授 (20273427)
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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 |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可積分系 / 離散可積分系 / 超離散可積分系 / 古典直交多項式 / 双直交関数系 / 一般化固有値問題 / 国際情報交換 / アルゴリズム / 応用数学 / 数理工学 / 直交多項式 / 量子力学 |
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| Research Abstract |
By using the theory of orthogonal polynomials and the theory of Hirota’s tau-functions, we study the system of bi-orthogonal functions with the help of the classical orthogonal functions and the nonautonomous discrete integrable systems. In this study, we have succeeded in deriving the discrete integrable systems associated with skew-orthogonal polynomials and making clear the relationship between the Padeinterpolations and the solutions of the elliptic Painleve equations in terms of elliptic hypergeometric functions. A stable numerical algorithm for the generalized eigenvalue problem of a tri-diagonal matrix pencil is introduced from the nonautonomous discrete integrable systems related to the classical biorthogonal rational functions.
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