| Project/Area Number |
13640214
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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 | Shimane University |
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Principal Investigator |
YAMASAKI Maretsugu Shimane Univ., Science and Engineering, Professor, 総合理工学部, 教授 (70032935)
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| Co-Investigator(Kenkyū-buntansha) |
SUGIE Jitsuro Shimane Univ., Science and Engineering, Professor, 総合理工学部, 教授 (40196720)
FURUMOCHI Tetsuo Shimane Univ., Science and Engineering, Professor, 総合理工学部, 教授 (40039128)
AIKAWA Hiroaki Shimane Univ., Science and Engineering, Professor, 総合理工学部, 教授 (20137889)
秦野 薫 島根大学, 教育学部, 教授 (40033873)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | infinite network / Hardy's inequality / eigen-value problem / discrete Laplacian / Martin boundary / Sierpinski Gadket / integro-difference equations of Voltera's type / complementarity problem / 離散ラプラシアン / 固有値問題 / ソボレフ・ポアンカレ不等式 / 変分法 / 差分方程式 |
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| Research Abstract |
1. Inequalities on networks have played important roles in the theory of networks. We study several famous inequalities on networks such as Wirtinger's inequality, Hardy's inequality, Poincare-Sobolev's inequality and the strong isoperimetric inequality, etc. These inequalities are closely related to the smallest eigen value of weighted, discrete Laplacian. We discuss some relations between these inequalities and the potential-theoretic magnitude of the ideal boundary of an infinite network.
2. Martin boundary plays important roles both in the theory of harmonic functions and the study of geometric figure of domains. We determine Martin boundary of a uniform John domain. Our results are applied to the study of Sierpinski Gasket.
3. We study some properties of the solutions of integro-difference equations of Voltera's type. In particular, we focus the boundedness property and the periodicity of solutions.
4. We attempt to obtain more useful information from the output of the verification method proposed by Alefeld, Chen and Potra. We use the Faekas lemma to check the nonexistence of solutions of inear complementarity problems.
5. As an integrated research of the theory of infinite networks and their applications, we submit a lecture note related this field.
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