| Project/Area Number |
19740053
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Future University-Hakodate (2007, 2009)
Sapporo Medical University (2008) |
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Principal Investigator |
YURA Fumitaka Future University-Hakodate, システム情報科学部, 准教授 (90404805)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,590,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | 離散数学 / ソリトン系 / 有限体 / 応用数学 / 数理物理 / ソリトン / 箱玉系 |
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| Research Abstract |
We have clarified the existence of soliton system on sequential cellular automata (CA) by the reduction to discrete hungry Lotka-Volterra equation and have analyzed the reason why this model can involve such integrable system as this one.
The (filter-type) CAs which consist of finite states are considered. As a result, finite-field-valued soliton systems are obtained. There exist several studies on integrable systems over finite fields in the past, however, it seems probable that soliton systems over finite fields have not been shown as far as we know. This novel system could give seminal development in integrable systems because the algebraic structure of finite fields is different from that of real numbers and max-plus algebra.
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