Irreducibility and hypertranscendence of non-linear difference equations
Project/Area Number |
24840005
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Research Category |
Grant-in-Aid for Research Activity Start-up
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Allocation Type | Single-year Grants |
Research Field |
Global analysis
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Research Institution | Yamagata University |
Principal Investigator |
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Project Period (FY) |
2012-08-31 – 2014-03-31
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Project Status |
Completed (Fiscal Year 2013)
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Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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Keywords | 離散パンルヴェ方程式 / 既約性 / 超越性 / 代数的差分方程式 / パンルヴェ方程式 / 分解可能拡大 / 差分代数 / 差分方程式 |
Research Abstract |
There are special second-order algebraic difference equations called discrete Painleve equations. The equation called d-Painleve equation of type D7(1) is one of them. Its irreducibility in the sense of decomposable extension was proved. The irreducibility implies that the transcendental function solution cannot be built from rational functions by reiterating algebraic operations and the taking of solutions of linear difference equations or first-order algebraic difference equations. A standard form of difference Riccati equations for any transforming operator was also studied.
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Report
(3 results)
Research Products
(11 results)
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[Presentation] 倍角公式と代数的独立性2013
Author(s)
西岡斉治
Organizer
2013函数方程式論サマーセミナー
Place of Presentation
リゾートホテル阿蘇いこいの村, 熊本県
Year and Date
2013-08-09
Related Report
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