| Project/Area Number |
09440082
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
KONISHI Sadanori KYUSHU UNIVERSITY, Graduate School of Mathematics, Professor, 大学院・数理学研究院, 教授 (40090550)
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| Co-Investigator(Kenkyū-buntansha) |
TABATA Masahisa KYUSHU UNIVERSITY, Graduate School of Mathematics, Professor, 大学院・数理学研究院, 教授 (30093272)
NAKAO Mitsuhiro,t. KYUSHU UNIVERSITY, Graduate School of Mathematics, Professor, 大学院・数理学研究院, 教授 (10136418)
YANAGAWA Takashi KYUSHU UNIVERSITY, Graduate School of Mathematics, Professor, 大学院・数理学研究院, 教授 (80029488)
MAESONO Yoshihiko KYUSHU UNIVERSITY, Faculty of Economics, Associate Professor, 大学院・経済学研究院, 助教授 (30173701)
FUKUMOTO Yasuhide KYUSHU UNIVERSITY, Graduate School of Mathematics, Associate Professor, 大学院・数理学研究院, 助教授 (30192727)
笛田 薫 九州大学, 大学院数理学研究科, 助手 (50253399)
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| Project Period (FY) |
1997 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥10,800,000 (Direct Cost: ¥10,800,000)
Fiscal Year 2000: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1999: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1997: ¥3,600,000 (Direct Cost: ¥3,600,000)
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| Keywords | Nonlinear modeling / Chaotic time series / Information-theoretic criteria / Numerical verification / Finite element analysis / Motion and expansion of a vortex ring / Resampling methods / Nonlinear multivariate analysis / 識別・判別問題 / 地球マントル対流有限要素近似 / 共鳴不安定性 / 情報量規準 / 楕円型固有値問題の精度保証 / ブーストラップ法 / 表面張力 / スプライン / 非線形反応 / 並列数値計算 / 地球環境シミュレーション / 完全不積文系 / 非線形時系列 / 非線形モデル / 多次元離散データ / 特異摂動法 / 情報量・エントロピー |
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| Research Abstract |
Modeling and model evaluation are crucial issues in scientific data analysis. Models are used for understanding the structure of system or process and for making trustworthy predictions in various fields of natural and social sciences. The data contain the information about the system under consideration and the objective of statistical analysis is to express this information in an understandable form using a statistical model. We also make inferences about the unknown aspects of random phenomena and seek an understanding of causal relationships. Now the wide availability of fast and inexpensive computers enables us to construct various types of nonlinear models for analyzing data with complex structure. Through this research project we have investigated the problem of constructing various types of nonlinear models and obtained the results in the following : (1) Model evaluation and selection criteria ; information-theoretic criterion which enables us to evaluate various types of nonli
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near statistical models. (2) Nonlinear modeling based on kernel, spline, neural network. (3) Defining the embedding dimension and delay time in the chaotic time series with additive dynamic noise. (4) The estimation of the Lyapunov exponent for the nonlinear autoregressive time series models. (5) Techniques for the numerical vertification of solutions of differential equations. (6) A method to estimate the guaranteed error bounds of the finite element solutions for the Stokes problem. (7) Mathematical model of the earth's mantle movement. (8) A finite element analysis for a thermal convection problem with the infinite Parandl number on the earth's mantle convection. (9) The motion and expansion of a viscous vortex ring ; various dynamical aspects, such as formation, traveling speed, waves, instability, interactions. (10) The motion of an axisymmetric vortex ring of small cross-section in a viscous in compressible fluid. (11) Theory for normalizing transformations of asymptotic U-statistics. (12) The use of Weighted bootstrap methods. Less
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