1996 年度実績報告書

非線形解析とその応用

研究課題

研究課題/領域番号	07454021
研究機関	千葉大学
研究代表者	吉田英信千葉大学, 理学部, 教授 (60009280)
研究分担者	河原田秀夫千葉大学, 工学部, 教授 (90010793) 剣持信幸千葉大学, 教育学部, 教授 (00033887) 蔵野正美千葉大学, 教育学部, 教授 (70029487) 安田正美千葉大学, 理学部, 教授 (00041244) 高木亮一千葉大学, 理学部, 教授 (00015562)
キーワード	非線形解析 / 相分離現象 / 最適制御問題 / 横断ハウスドルフ次元 / パーコレーションモデル / ディリクレ問題
研究概要	1.昨年に引続き、各分担者の専門の分野における非線形な現象について、いろいろなシンポジュウや研究集会等に出席して、全国の多くの研究者との討論等を通じて、これまでに為されてきた数々の研究についての情報を収集・整理した。それらを他分野の分担者と共に数度にわたって検討し、同一、類似のものに、整理、分類した。また、一同で、同一、類似の現象がどの分野においてどのように研究されてきたかを整理・検討した。これらの結果を踏まえて、分担者が研究成果としてまとめ、論文等として公表された。こうして、始めに計画された今回のプロジェクトの目的はほぼ達成されたと思う。 2.非線形の問題は、最近になってようやく研究され始めたばかりであり、我々の得た成果・情報は、非線形現象の多様さに比べて、微々たるものであることがこの共同研究を通じて痛感された。今回、他分野の分担者の助けと援助によって、各自の研究方法の上に、従来とは異なる視点が加えられ、個人の限界を打破する突破口とならんとしつつある。今回の研究を通して、単独では得られない新しい視点と観点が得られ、改めて共同研究の大切さを実感させられた。 3.各大学、各研究機関において、私たちと同様な主旨で、非線形問題が扱われつつある。分担者の度々の出張によって、多くの役立つ情報が得られたが、更に、外国を含むより広範な研究者からの助言とアドヴァイスが必要不可欠であることがわかった。この意味において、今年度より科研で外国出張が認められるようになったことは大変に喜ばしいことである。 4.次年度以降も今回と同様の内容と目的をもって、継続的にこの種のプロジェクトを組んで研究を続けることの必要性を痛感した。今回の得られた有形無形の成果を無駄にすることのないよう、今後も継続に取り組んで行きたい。2年間に渡っての財政的支持に対して心より感謝したい。

研究成果
(35件)

すべてその他

すべて文献書誌 (35件)

[文献書誌] H.Yoshida: "A type of uniqueness for the Dirichlet problem on a half-space with continuous data," Pacific J. Math.172. 591-609. (1996)
[文献書誌] H.Yoshida,I.Miyamoto,: "Solutions of the Dirichlet problem on a cone with continuous data" Journal of the Mathematical Society of Japan. 50(1)(to appear). (1998)
[文献書誌] H.Yoshida,I.Miyamoto: "Harmonic functions in a cone which vanish on the boundary," MATHEMATISCHE NACHRICHTEN. (to appear).
[文献書誌] R.Takagi,H.S.Kim: "On the type number of real hypersurfaces in P_n (C)" Tsukuba J. Math.第20巻第2号. 349-356 (1996)
[文献書誌] R.Takagi,Y-W:Choe H.S.Kim,I-B.Kim: "Rigidity theorems for real hypersurfaces in a complex pojective space" Hokkaido Math. J.第25巻第3号. 433-451 (1996)
[文献書誌] R.Takagi,H.S.Kim: "Certain real hypersurfaces of a complex space form" Kyungpook Math. J.第35巻第3号. 591-606 (1996)
[文献書誌] J.Wang & M.Taguri: "Jackknifing : higher order accurate confidence intervals" Journal of the Japan Statistical Society. Vol.26. No.1. 69-82 (1996)
[文献書誌] 汪金芳,田栗正章: "ブートストラップ法--2標本問題からの考察" 統計数理,. 第44巻,1号. 3-18 (1966)
[文献書誌] M.Yasuda,J.Li: ""Egoroff's Theorem on Fuzzy measure spaces"," Journal of Lanzhou University (Natural Sciences). 32. 19-22 (1996)
[文献書誌] M.Yasuda,J.Li: ""Two properties of Fuzzy set functions deduced from Fuzzy number-valued Fuzzy integral"," Journal of Lanzhou University (Natural Sciences). 32. 23-27 (1996)
[文献書誌] M.Yasuda,Y.Kadota,M.Kurano.: ""Utility-optimal Stopping in a denumerable Markov Chain"" Bulletin of Infomatics and Cybernetics. Vol.28, No.1. 15-21 (1996)
[文献書誌] M.Yasuda,Y.Kadota,M.Kurano.: ""A Utility Deviation in discounted Markov decision Processes with Genaral Utility"" Bulletin of Infomatics and Cybernetics. Vol.28, No.1. 71-78 (1996)
[文献書誌] N.Kenmochi,M.Niezgodka: "Viscosity approach to modelling non-isothermal diffusive phase separation" Japan J. Industrial Appl. Math.13. 135-169 (1996)
[文献書誌] N.Kenmochi,A.Damlamian: "Asymptotic behavior and periodic forcing in time for the solutions of a nonlin ear system representing a phase change with dissipation" Proceedings of the 1st World Congress of Nonlinear Analysts. Vol.III. 2281-2288 (1996)
[文献書誌] N.Kenmochi,J.Shirohzu A.Kadoya,N.Kato: "Optimal control on the lateral boundary for a phase separation model with constraint" Pitman Research Motes Math. Ser.Vol.363. 98-110 (1996)
[文献書誌] N.Kenmochi: "Global attractors of the semigroup associated to a phase-field model with constraint" Pitman Research Motes Math. Ser.Vol.363. 111-125 (1996)
[文献書誌] N.Kenmochi: "Attractors of semigroups associated with nonlinear systems for diffusive phase separation" Abst. Appl. Anal.1. 169-192 (1996)
[文献書誌] N.Kenmochi,I.Pawlow: "Controlled Czochraralski crystal growth" J. SICE. 35. 944-950 (1996)
[文献書誌] 腰越秀之、河原田秀夫: "Approximation of boundary values for Maxwell equations by use of fictitious domain method," 統計数理研究所共同研究リポート85. 29-38 (1996)
[文献書誌] H.Kawarada,H.Koshigoe A.Sasamoto: "On penetration phenomenon of magnetic field into superconducting material" Advance in Math. Sci. and Appl.Vol.6. 125-133 (1996)
[文献書誌] H.Kawarada,H.Koshigoe A.Sasamoto: "Mathematical Model for Penetration Phenomenon of Magnetic Field into Superconductor" Theoretical and Applied Mechanics. Vol.45. 59-63 (1996)
[文献書誌] M.Nagisa,S.Wada: "An extension of the mean ergodic theorem," Math. Japon.(to appear).
[文献書誌] M.Nagisa: "Stable rank of some full group C^★-algebras of groups obtained by the free product" Internat. J. Math.(to appear).
[文献書誌] M.Nagisa,S.Wada: "Averages of operators and their positivity," Proc. A. M. S.(to appear).
[文献書誌] I.Miyamoto,Y.Okuyama: "On Norlund summability of Legendre series" Math. Japonica. (to appear).
[文献書誌] Y.Hino,S.Murakami T.Yoshizawa,: "Almost periodic solutions of abstract functional differential equations with infinite delay" Proceeding of WCNA96,. (to appear).
[文献書誌] Y.Hino,S.Murakami T.Yoshizawa,: "Existence of almost periodic solutions of some functional differential equations with infinite delay in a Banach space" Tohoku Mathematical Journal,. (to appear).
[文献書誌] Y.Hino and S.Murakami: "Existence of an almost periodic solutions of abstract linear functional differential equations with infinite delay" Dynamic Systems and Applications. 5-3. 385-398 (1996)
[文献書誌] Y.Hino and S.Murakami: "Stabilities in linear integro differential equations" Lecture Notes in Numerical and Applied Analysis. 15. 31-46 (1996)
[文献書誌] Ryuichi ISHIMURA Yasunori OKADA: "The micro-support of the complex defined by a convolution operator in tube domains,Singularities and differential equations" Institute of Math. Polish Acad.,Warszawa,. 33. 105-114 (1996)
[文献書誌] Hideki Tanemura: "Critical behavior for a continuum percolation model" Japan-Russia Symposium on Probability Theory and Mathematical Statistics. 485-495 (1996)
[文献書誌] Hideki Tanemura.: "A system of infinitely many mutually reflecting Brownian balls" Probab. Theory Relat. Fields. 104. 399-426 (1996)
[文献書誌] Konno,Y.Shiraishi,T.: "On construction of improved estimators in mutlple-design multivariate linear models under general restriction" Annals of Institute of Mathematical Statistics. 47. 665-674 (1996)
[文献書誌] Konno,Y.Kariya,T.Strawderman,W.E.: "Double shrinkage estimators in the GMANOVA model" Journal of multivariate anaysis. 56. 245-258 (1996)
[文献書誌] Konno,Y.Kubokawa,T.A.K.Md.E.Saleh: "Shrinkage estimators in a mixed MANOVA and GMANOVA model" Statistics & Decisions. 17(to appear). (1997)

1996 年度 実績報告書

非線形解析とその応用

研究代表者

吉田 英信 千葉大学, 理学部, 教授 (60009280)

研究成果

[文献書誌] H.Yoshida: "A type of uniqueness for the Dirichlet problem on a half-space with continuous data," Pacific J. Math.172. 591-609. (1996)

[文献書誌] H.Yoshida,I.Miyamoto,: "Solutions of the Dirichlet problem on a cone with continuous data" Journal of the Mathematical Society of Japan. 50(1)(to appear). (1998)

[文献書誌] H.Yoshida,I.Miyamoto: "Harmonic functions in a cone which vanish on the boundary," MATHEMATISCHE NACHRICHTEN. (to appear).

[文献書誌] R.Takagi,H.S.Kim: "On the type number of real hypersurfaces in P_n (C)" Tsukuba J. Math.第20巻第2号. 349-356 (1996)

[文献書誌] R.Takagi,Y-W:Choe H.S.Kim,I-B.Kim: "Rigidity theorems for real hypersurfaces in a complex pojective space" Hokkaido Math. J.第25巻第3号. 433-451 (1996)

[文献書誌] R.Takagi,H.S.Kim: "Certain real hypersurfaces of a complex space form" Kyungpook Math. J.第35巻第3号. 591-606 (1996)

[文献書誌] J.Wang & M.Taguri: "Jackknifing : higher order accurate confidence intervals" Journal of the Japan Statistical Society. Vol.26. No.1. 69-82 (1996)

[文献書誌] 汪金芳,田栗正章: "ブートストラップ法--2標本問題からの考察" 統計数理,. 第44巻,1号. 3-18 (1966)

[文献書誌] M.Yasuda,J.Li: ""Egoroff's Theorem on Fuzzy measure spaces"," Journal of Lanzhou University (Natural Sciences). 32. 19-22 (1996)

[文献書誌] M.Yasuda,J.Li: ""Two properties of Fuzzy set functions deduced from Fuzzy number-valued Fuzzy integral"," Journal of Lanzhou University (Natural Sciences). 32. 23-27 (1996)

[文献書誌] M.Yasuda,Y.Kadota,M.Kurano.: ""Utility-optimal Stopping in a denumerable Markov Chain"" Bulletin of Infomatics and Cybernetics. Vol.28, No.1. 15-21 (1996)

[文献書誌] M.Yasuda,Y.Kadota,M.Kurano.: ""A Utility Deviation in discounted Markov decision Processes with Genaral Utility"" Bulletin of Infomatics and Cybernetics. Vol.28, No.1. 71-78 (1996)

[文献書誌] N.Kenmochi,M.Niezgodka: "Viscosity approach to modelling non-isothermal diffusive phase separation" Japan J. Industrial Appl. Math.13. 135-169 (1996)

[文献書誌] N.Kenmochi,A.Damlamian: "Asymptotic behavior and periodic forcing in time for the solutions of a nonlin ear system representing a phase change with dissipation" Proceedings of the 1st World Congress of Nonlinear Analysts. Vol.III. 2281-2288 (1996)

[文献書誌] N.Kenmochi,J.Shirohzu A.Kadoya,N.Kato: "Optimal control on the lateral boundary for a phase separation model with constraint" Pitman Research Motes Math. Ser.Vol.363. 98-110 (1996)

[文献書誌] N.Kenmochi: "Global attractors of the semigroup associated to a phase-field model with constraint" Pitman Research Motes Math. Ser.Vol.363. 111-125 (1996)

[文献書誌] N.Kenmochi: "Attractors of semigroups associated with nonlinear systems for diffusive phase separation" Abst. Appl. Anal.1. 169-192 (1996)

[文献書誌] N.Kenmochi,I.Pawlow: "Controlled Czochraralski crystal growth" J. SICE. 35. 944-950 (1996)

[文献書誌] 腰越秀之、河原田秀夫: "Approximation of boundary values for Maxwell equations by use of fictitious domain method," 統計数理研究所共同研究リポート85. 29-38 (1996)

[文献書誌] H.Kawarada,H.Koshigoe A.Sasamoto: "On penetration phenomenon of magnetic field into superconducting material" Advance in Math. Sci. and Appl.Vol.6. 125-133 (1996)

[文献書誌] H.Kawarada,H.Koshigoe A.Sasamoto: "Mathematical Model for Penetration Phenomenon of Magnetic Field into Superconductor" Theoretical and Applied Mechanics. Vol.45. 59-63 (1996)

[文献書誌] M.Nagisa,S.Wada: "An extension of the mean ergodic theorem," Math. Japon.(to appear).

[文献書誌] M.Nagisa: "Stable rank of some full group C^★-algebras of groups obtained by the free product" Internat. J. Math.(to appear).

[文献書誌] M.Nagisa,S.Wada: "Averages of operators and their positivity," Proc. A. M. S.(to appear).

[文献書誌] I.Miyamoto,Y.Okuyama: "On Norlund summability of Legendre series" Math. Japonica. (to appear).

[文献書誌] Y.Hino,S.Murakami T.Yoshizawa,: "Almost periodic solutions of abstract functional differential equations with infinite delay" Proceeding of WCNA96,. (to appear).

[文献書誌] Y.Hino,S.Murakami T.Yoshizawa,: "Existence of almost periodic solutions of some functional differential equations with infinite delay in a Banach space" Tohoku Mathematical Journal,. (to appear).

[文献書誌] Y.Hino and S.Murakami: "Existence of an almost periodic solutions of abstract linear functional differential equations with infinite delay" Dynamic Systems and Applications. 5-3. 385-398 (1996)

[文献書誌] Y.Hino and S.Murakami: "Stabilities in linear integro differential equations" Lecture Notes in Numerical and Applied Analysis. 15. 31-46 (1996)

[文献書誌] Ryuichi ISHIMURA Yasunori OKADA: "The micro-support of the complex defined by a convolution operator in tube domains,Singularities and differential equations" Institute of Math. Polish Acad.,Warszawa,. 33. 105-114 (1996)

[文献書誌] Hideki Tanemura: "Critical behavior for a continuum percolation model" Japan-Russia Symposium on Probability Theory and Mathematical Statistics. 485-495 (1996)

[文献書誌] Hideki Tanemura.: "A system of infinitely many mutually reflecting Brownian balls" Probab. Theory Relat. Fields. 104. 399-426 (1996)

[文献書誌] Konno,Y.Shiraishi,T.: "On construction of improved estimators in mutlple-design multivariate linear models under general restriction" Annals of Institute of Mathematical Statistics. 47. 665-674 (1996)

[文献書誌] Konno,Y.Kariya,T.Strawderman,W.E.: "Double shrinkage estimators in the GMANOVA model" Journal of multivariate anaysis. 56. 245-258 (1996)

[文献書誌] Konno,Y.Kubokawa,T.A.K.Md.E.Saleh: "Shrinkage estimators in a mixed MANOVA and GMANOVA model" Statistics & Decisions. 17(to appear). (1997)

1996 年度実績報告書

吉田英信千葉大学, 理学部, 教授 (60009280)