1993 Fiscal Year Final Research Report Summary
Dynamics and topologocal entropy
| Project/Area Number |
04640192
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Science University of Tokyo |
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Principal Investigator |
TOGAWA Yoshio Science University of Tokyo Faculty of Science and Technology, 理工学部, 助教授 (20112899)
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| Co-Investigator(Kenkyū-buntansha) |
SUYARI Hiroki Science University of Tokyo Faculty of Science and Technology, 理工学部, 助手 (70246685)
WATANABE Noboru Science University of Tokyo Faculty of Science and Technology, 理工学部, 講師 (70191781)
SHIMOIDA Hiroo Science University of Tokyo Faculty of Science and Technology, 理工学部, 教授 (00112897)
MIYAZAWA Masakiyo Science University of Tokyo Faculty of Science and Technology, 理工学部, 教授 (80110948)
OHYA Masanori Science University of Tokyo Faculty of Science and Technology, 理工学部, 教授 (90112896)
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| Project Period (FY) |
1992 – 1993
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| Keywords | Entropy Theory / Quantum Mechanics / Chaos / Topological Entropy / Mutual Entropy / Genetic Analysis / Queue Network / Rate conservation |
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| Research Abstract |
Entropy Theory has been begun bu Clausius, Boltzmann and Shannon, von Neumann constructed the mathematical framework of quantum mechanics and quantum entropy. Now many authors have made many reseraches in this field. This project could get the following results : (1) The dependencty of parameters of topological entropy are discussed in the dynamics which the solutions approaches to the boundary in chaos. (2) The conditions for the stability of the circuit for the image processing are obtained. (3) The error probabilities are formulated and the comparison fo the efficiency of optical modulations are discussed with mutual entropy. (4) The applications of the mutual entropy to the Gaussian channel are discussed. (5) The maximization the entropy in quantum system and the properties pf the fuzzy entropy are discussed. (6) For the sake of the alinment of genes we applied DP matcing and compared the usual methods. (7) Multiple alignment of genes are applied to the genetic analysis. (8) The stochastic processes are proposed to apply RGSMP (Reallocatable Generalized Semi-Markov Process) and its properties are investigated. (9) Under the mathematical assumption of the stationay distribution of RGSMP the state transition of RGSMP is discussed. (10) The moment in infinite channel queues are computed and discussed to the applications to burst arrival queues. (11) The discussions on rate conservation are summarized and some fundamental formulas of the stochastic processes are derived from the rate conservation.
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