| Project/Area Number |
23340025
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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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 University |
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Principal Investigator |
KIGAMI Jun 京都大学, 情報学研究科, 教授 (90202035)
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| Co-Investigator(Kenkyū-buntansha) |
KAMEYAMA Atsushi 岐阜大学, 工学部, 教授 (00243189)
AIKAWA Hiroaki 北海道大学, 理学研究科, 教授 (20137889)
ITO Syunji 東邦大学, 理学部, 訪問教授 (30055321)
HINO Masanori 大阪大学, 大学院・基礎工学研究科, 教授 (40303888)
SHISHIKURA Mitsuhiro 京都大学, 大学院・理学研究科, 教授 (70192606)
KUMAGAI Takashi 京都大学, 数理解析研究所, 教授 (90234509)
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| Co-Investigator(Renkei-kenkyūsha) |
OSADA Hirofumi 九州大学, 大学院・数理学研究院, 教授 (20177207)
KOTANI Motoko 東北大学, 大学院・理学研究科, 教授 (50230024)
HATTORI Tetsuya 慶応義塾大学, 経済学部, 教授
TAKAHASHI Satoshi 奈良女子大学, 人間文化研究科, 准教授 (70226835)
KUWADA Kazumasa 東京工業大学, 大学院・理学研究科, 准教授 (30432032)
WAKANO Isao 京都大学, 大学院・情報学研究科, 講師 (00263509)
KUBO Masayoshi 京都大学, 大学院・情報学研究科, 講師 (10273616)
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| Project Period (FY) |
2011-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥18,590,000 (Direct Cost: ¥14,300,000、Indirect Cost: ¥4,290,000)
Fiscal Year 2013: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2012: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2011: ¥7,020,000 (Direct Cost: ¥5,400,000、Indirect Cost: ¥1,620,000)
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| Keywords | フラクタル / 解析学 / 確率論 / 力学系 / ラプラシアン / 熱核 |
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| Research Abstract |
In this project, we have studied internal structure of fractal sets from the broad viewpoint of analysis, geometry and algebra. In particular, we have considered stochastic processes and potential theory on fractals, which are thought of as models of objects in the nature. For instance, we have obtained conditions to ensure the existence of scaling relation of space-time on the heat conductance on fractals. Moreover, we have studied equilibrium state of heat on spaces with infinitely many holes and obtained a condition for the equilibrium state to be smooth.
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