2004 Fiscal Year Final Research Report Summary
Study of Complex and vector potential theory
| Project/Area Number |
14540173
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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 | Nara Women's University |
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Principal Investigator |
YAMAGUCHI Hiroshi Nara Women's University, Faculty of Science, Department of Mathematics, Professor, 理学部, 教授 (20025406)
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| Co-Investigator(Kenkyū-buntansha) |
MIYATAKE Sadao Nara Women's University, Graduate School of Humanities and Sciences, Professor, 大学院・人間文化研究科, 教授 (10025447)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Pseudoconvexity / Complex manifold / Riemann surfaces / Non-linear partial diff. equation / Non-complession fluid / Bifurcation analysis / Kolomogorov Flow / Hamilton Flow |
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| Research Abstract |
Field of function theory : We study how the potential quantity of Riemann surface R(+) or domains D(+) of a complex manifold move when they (R(+) or D(+)) move function-theoretically with complex parameter t, and we find that they move subharmonically for t.
Field of potential theory : We introduced the nature of equilibrium magnetic vector potential based on the electric solenoid in 1R^3, and we apply it to research Poincare's remark on Dirschlt problem's alternating method.
Field of Non-linear partial differential equations : Based on Riemann's original paper in 1860 concerning non-linear wave equation, we generalized it to the diagonalle non-linear partial differential equation and solve them with initialvalue conditions.
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