| Project/Area Number |
19740078
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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 |
Basic analysis
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| Research Institution | Okayama University of Science |
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Principal Investigator |
HIBINO Masaki Okayama University of Science, 工学部, 准教授 (10441461)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,690,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | 関数方程式論 / 複素解析 / 発散級数 / 総和可能性 / 解析接続 / 関数空間論 / 縮小写像 / 収束羃級数 / 総合可能性 |
|---|
| Research Abstract |
We studied first-order partial differential equations with singular points. Firstly, we gave conditions which ensure the existence and the uniqueness of formal power series solutions centered at the singular point, in forms of those for eigenvalues of some matrix determined by equations. Moreover, we gave conditions which assure the convergence of the formal solution. Secondly, we considered the linear equations called of nilpotent type, whose formal solution diverges, and we gave conditions under which the divergent solution is summable, in forms of global conditions (analytic continuation property, growth conditions or decreasing conditions) for coefficients of equations.
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