| Project/Area Number |
17540138
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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 | Hiroshima Institute of Technology |
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Principal Investigator |
KUBO Izumi Hiroshima Institute of Technology, Faculty of Environmental Studies, Professor (70022621)
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| Co-Investigator(Kenkyū-buntansha) |
YAGUCHI Hirotake Mie University, Faculty of Education, Professor (40157970)
YOKOTA Hisashi Shibaura Institute of Technology, Faclty of Engineering, Professor (90210616)
IKEDA Satoshi Miyazaki University, Faculty of Engineering, Associate Professor (70282796)
NAKATA Toshio Fukuoka University of Education, Faculty of Education, Associate Professor (10304693)
HONDA Tatsuhiro Hiroshima Institute of Technology, Faculty of Engineering, Associate Professor (20241226)
浅井 暢宏 愛知教育大学, 教育学部, 講師 (60399029)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,570,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Chaos / Dynamical System / Random Generator / Distributed Processing / Random Algorithm / Infinite Dimensional Stochastic Analysis / Renormalization / Fractional Expansion / Renomalization |
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| Research Abstract |
Yaguchi and Kubo proposed a nonrecursive pseudorandom number generator based on chaos theory. They investigated its efficiency and improved nature of random numbers in points of theoretical and statistical view. Ikeda and Kubo evaluated cover times of random walks of a token on finite graphs. Such a problem is deeply connected with algorithms of distributed processing. Their idea is to introduce transition probabilities determined by local information, for example using Gibbs measure whose potential is given by degrees of neighbor nodes. Thus they shortened cover times extremely from the case of the usual transition of equi-probabilities. Nakata investigated the coupon collector's problem, which appears in random algorithms of distributed processing. His idea is to introduce coupons with bonuses. He showed distributions of success times and their limit distributions for the extended case. He also discussed imbedding of the Markov chains into time continuous processes. He also showed li
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mit distributions for problems of balls and urns. Yokota observed the efficiency of random algorithms for support systems of mathematical learning, which can recognize mathematical formulas drawn by hands. He obtained a patent (P06P005221) by the system. He also investigated fractional expansion, which appears often in chaos theory. He discussed periodicity of fractional expansion in algebraic fields. Honda proved growth order and covering theorem of univalent functions on the unit ball with respect to any norm of C^n. He discussed starlike mappings and convex mappings on the balls. Furthermore, he obtained some results on growth order and of bolomorpliic functions on open balls of complex Banach spaces and extended Bohr theorem to Banach spaces. Asai, who joined into the project in 2007, had researched with Kubo the multiplicative renormalization method to obtained orthogonal polynomials of one variable, which was inspired by the white noise calculus. He applied the results to one mode interacting Fock spaces. Kubo investigated the method more deeply. Less
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