Multilateral research on the role of limiting recursive functions in the computability problem
| Project/Area Number |
20540143
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
YASUGI Mariko Kyoto Sangyo University, 名誉教授 (90022277)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Takakazu 京都産業大学, 理学部, 教授 (00065880)
KOBAYASHI Satoshi 京都産業大学, コンピュータ理工学部, 教授 (70234820)
TSUJII Yoshiki 京都産業大学, 理学部, 教授 (90065871)
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| Co-Investigator(Renkei-kenkyūsha) |
HAYASHI Susumu 京都大学, 大学院・文学研究科, 教授 (40156443)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 極限再帰関数 / 実効的一様位相 / 計算可能確率分布 / Fine計算可能関数 / 数学基礎論 / 極限再帰性 / 列計算可能性 / 極限再帰の数学の体系 / マルチフラクタル / 数理哲学 / 実効的収束 / 2次元Fine可積分関数 / フラクタル / 実効的一様性 / 単調有界性原理 / 計算可能分布 / Fine可積分関数 / グラフ有向集合 / 形式的体系の解釈 / 計算機上の実現 |
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| Research Abstract |
A function whose value is obtained somewhere in the course of an infinite process of computations is called a limiting recursive function. The theory of limiting recursive functions plays an important role when one observes mathematics from the standpoint of "computation". We have applied it to the computability theory in mathematics, and compared this method with the method of uniform topology, in which a Euclidean discontinuous function turns continuous. We have further devised how to implement a part of this theory on the computer.
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Report
(4 results)
Research Products
(47 results)
