2013 Fiscal Year Final Research Report
Research on the multifractal decompositions of mutual-recursive sets
| Project/Area Number |
23540170
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
YASUGI Mariko 京都産業大学, 名誉教授 (90022277)
MORI Takakazu 京都産業大学, 理学部, 教授 (00065880)
HOSONO Yuzo 京都産業大学, 理学部, 教授 (50008877)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 数理モデル / 確率論 / フラクタル / マルチフラクタル / スピングラス |
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| Research Abstract |
On the fractal set defined by a system of contraction similarities, we consider two probability measures induced by these contractions. The multifractal decompositions of the fractal with respect to these probability densities are investigated and the Hausdorff dimensions of these decompositions are given. For that purpose we introduced a probability measure with two parameters (q,s). Furthermore we studied the spin-glass phenomena of multifractal structures and the related gauge-invariance. We extend these results to mutual-recursive sets.
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