1989 年度実績報告書

多変数関数論と解析的微分方程式の研究

研究課題

研究課題/領域番号	63460006
研究機関	九州大学
研究代表者	梶原壌二九州大学, 理学部, 教授 (90037169)
研究分担者	吉田正章九州大学, 理学部, 助教授 (30030787) 田中俊一九州大学, 理学部, 教授 (00028127) 加藤十吉九州大学, 理学部, 教授 (60012481) 塩浜勝博九州大学, 理学部, 教授 (20016059) 白谷克巳九州大学, 理学部, 教授 (80037168)
キーワード	Uniform Approximation / Good Boundary / Global Solution / Numerical Analysis / Resident Theorem / Monodromy / K3 surface / Hypergeometric Equation
研究概要	代表者の梶原は無限次元の複素解析を行い、整関数による一様近似と自己同型群が境界において良い挙動をすれば、境界の一部の把握が全貌の把握を導くことを示し、更に、Z、W変数の正則な微分作用素SPに対して合成SPが全射であるための条件を、SPの助変数空間における局所性に帰着させ、フラッタ-解析で求められる複素係数方程式の実根を留数計算より導出した。吉田は種々の複素構造に対応する線型偏微分方程式を研究、数種の代数多様体の族を記述する方程式を発見し、構造を解明した。塩浜は非負曲率完備多様体上の局所凸集合の位相に関するBurago-Zalgallerの結果を更に精密化し、Gromall-CheegerのSoul Thearemを一般化して、凸集合の位相構造に関する最終的な結果を得た。西川はコンパクト多様体上のリ-マン葉層構造の基底的微分形式のなす複体上に定義される熱作用素に対してその基本解を構成し、ドラムーホッジ型の分解定理に新たな証明を与えた。坂内はassociation schemeの指数表を解明し、山崎は荷重0の非正則アイゼンシュタイン級数との重畳を取ることにより、ジ-ゲルカスプ形式に対称平方を拡張し、ディリクレ級数の解析的性質を導いた。藤野は閾値機構をもつオ-トマトンを定義し、挙動解析を行い、挙動圏のサイクル型及び組数に関する有効な公式を見出し、洞は有限生成可換リ-群の無限直積上の定常積測度及び無限対称群不変測度について、群作用に関する準不変性を調べ、拡張されたl_p空間を用いることによって準不変な作用(平行移動)全体のなす集合を評価し、実及び複素数列空間上の測度の対角型変換に関する準不変性を研究した。大塚はde BruznのName-Free Expressionに関して研究し、λ-calculusと違ってその正確な定式化がなされていなかったものを、始めて定式化することに成功し、λ-calculusとの対比を行った。

研究成果
(42件)

すべてその他

すべて文献書誌 (42件)

[文献書誌] T.Honda et J.Kajiwara: "Sur un theoreme d'Akio Kodama" Memoirs of the Faculty of Science Kyushu University. 44. (1989)
[文献書誌] J.Kajiwara,M.Nishihara,S.Ogai and N.Sugawara: "Uniform Approximation of Continuous Functions and 〓^∞-Functions" Resultate der Mathematik. 18. (1990)
[文献書誌] J.Kajiwara and M.Kajiwara: "Numerical Analysis and Resudue theorem" Memoirs of the Faculty of Science Kyushu University. 45. (1990)
[文献書誌] K.Shiohama,Y.Otsu and T.Yamaguchi: "A new version of differentiable sphere theorem" Invent.Math.98. 219-228 (1989)
[文献書誌] K.Shiohama and T.Yamaguchi: "Positively curved manifolds with restricted diameters" “Geometry of Manifolds"Perspectives in Math.,Academic Press. 8. 345-350 (1989)
[文献書誌] K.Shiohama and M.Tanaka: "An isoperimetric problem for infinitely connected complete open surfaces" “Geometry of Manifolds"Perspectives in Math., Academic Press. 8. 317-343 (1989)
[文献書誌] K.Shiohama,T.Shioya and M.Tanaka: "Mass of rays on complete open surfaces" Pacific J.Math.(1990)
[文献書誌] A.Hora: "On a Banach Space of Functions Associated with a Homogeneous Additive Process" Publications of the Research Institute for Math.Sci.Kyoto Univ.24. (1988)
[文献書誌] A.Hora: "Quasi-Invariant Measures on Commutative Lie Groups of Infinite Product Type" Research Institute for Math.Sci.Kyoto Univ.654. (1989)
[文献書誌] A.Kudo and K.Yanagi: "概不偏検定" 日本SASユ-ザ-会論文集. 167-169 (1989)
[文献書誌] E.Bannai: "Association schemesの指数表とsubschemes" 代数学分科会報告集. (1989)
[文献書誌] E.Bannai,Shen Hao,S-Y.Song and H.Z.Wei: "Character Tables of Certain Association Schemes Coming from Finite Unitary and Symplectic Groups"
[文献書誌] E.Bannai,N.Kawanaka and Sung-Yell Song: "The Character Table of the Hecke Algebra H(GL_<2n>(F_q),Sp_<2n>(F_q))"
[文献書誌] E.Bannai and Sung-Yell Song: "The Character Tables of Paige's Simple Moufang Loops and Their Relationship to the Character Tables of PSL(2,q)" Proc.London Math.Soc.58. 209-236 (1989)
[文献書誌] E.Bannai and T.Ito: "On Distance-regular Graphs with Fixed Valency,IV" Europ.J.Combinatorics. 10. 137-148 (1989)
[文献書誌] E.Bannai,A.C.Kim and M.Kiyota: "On The Number of Elements which are not N-th Powers in Finite Groups" Communications in Algebra. 17(11). 2865-2870 (1989)
[文献書誌] E.Bannai: "On Spherical t-designs(a survey)" 代数的組合せ論報告集. (1989)
[文献書誌] E.Bannai: "Subschemes of some association schemes"
[文献書誌] E.Bannai and S.G.Hoggar: "Tight t-Designs and Squarefree Integers" Europ.J.Combinatorics. 10. 113-135 (1989)
[文献書誌] H.Sato: "Convergence of sum and product of a martingale difference sequence" Hiroshima Math.Jour.18. 69-72 (1988)
[文献書誌] H.Sato: "On the absolute Continuity of Infinite Product Measure and Its Convolution" Probab.Th.Rel.Fields. 81. 609-627 (1989)
[文献書誌] H.Sato: "Uniform Integrabilities of an Additive Martingale and its Exponential"
[文献書誌] H.Shimauchi: "関数近似における最適復旧について" 中村学園研究紀要. 21. (1989)
[文献書誌] K.Matsumoto: "種数3のある超楕円曲線族に対する2変数モジュラ-函数"
[文献書誌] K.Matsumoto,T.Sasaki and M.Yoshida: "The Monodromy of the period map of a 4-parameter family of k3 surfaces and the Aomoto-Gel'fand hypergeometric function of type(3,6)"
[文献書誌] K.Sakurai and M.Yoshida: "Fuchsian Systems Associated with the P^2(F_2)-Arrangement" Siam J.Math.Anal.20. 1490-1499 (1989)
[文献書誌] M.Takase: "ドイツ数学史の構想" 数学セミナ-. (1989)
[文献書誌] M.Hara,T.Sasaki and M.Yoshida: "Tensor Products of Linear Differential Equations--a study of exterior products of hypergeometric equations" Funkcialaj Ekvacioj.32. 453-477 (1989)
[文献書誌] N.Furukawa: "Max型関数の最適化アルゴリズムによる非線形方程式の一数値解析法" 講演アブストラクト. (1990)
[文献書誌] N.Furukawa: "Higher-Order Variational Sets,Variational Derivatives and Higher-Order Necessary Conditions in Abstract Math.Programming" Bull.of Informatics and Cybernetics. 23. (1988)
[文献書誌] R.Fukuda: "On the Strong Integrability of Sub-Gaussian Vectors"
[文献書誌] S.Fujino: "閾値機構を持つオ-トマトンの挙動解析"
[文献書誌] S.Fujino: "記憶を持つセル・オ-トマトンについて"
[文献書誌] S.Fujino: "オ-トマトン・ネットワ-ク並列処理に関する実験数学的考察"
[文献書誌] S.Fujino: "正方配列有界セル・オ-トマトンCA_2ーX(m)の挙動解析(II)"
[文献書誌] S.Nishikawa: "Heat Conduction for Riemannian Foliations" Bull.of the American Mathematical Society. 21ー2. 265-267 (1989)
[文献書誌] S.Nishikawa: "Transversal Infinitesimal Automorphisms of Harmonic Foliations on Complete Manifolds" Ann.Global Anal.Geom.7ー1. 47-57 (1989)
[文献書誌] T.Yamazaki: "Jacobi forms and a Mass relation for Eisenstein series(II)" J.Fac.Sci.Univ.Tokyo Sect.IA,Math.36ー2. 373-386 (1989)
[文献書誌] T.Honda: "Sur un Theoreme de Type D'akio Kodama" Memoirs of the Fac.of Sci.Kyushu University. 44ー2. 61-66 (1989)
[文献書誌] Y.Sueyoshi: "A Characterization of Number Fields by p-Closed Extensions" Journal of Number Theory. 28ー2. 145-151 (1988)
[文献書誌] Y.Sueyoshi: "Explicit reciprocity laws on relative Lubin-Tate groups"
[文献書誌] K.Shiohama(Edited): "Geometry of Manifolds,Perspectives in Mathematics" Academic press,Boston-New-York-Berkeley-London-Sydney-Tokyo-Toronto, (1989)

1989 年度 実績報告書

多変数関数論と解析的微分方程式の研究

研究代表者

梶原 壌二 九州大学, 理学部, 教授 (90037169)

研究成果

[文献書誌] T.Honda et J.Kajiwara: "Sur un theoreme d'Akio Kodama" Memoirs of the Faculty of Science Kyushu University. 44. (1989)

[文献書誌] J.Kajiwara,M.Nishihara,S.Ogai and N.Sugawara: "Uniform Approximation of Continuous Functions and 〓^∞-Functions" Resultate der Mathematik. 18. (1990)

[文献書誌] J.Kajiwara and M.Kajiwara: "Numerical Analysis and Resudue theorem" Memoirs of the Faculty of Science Kyushu University. 45. (1990)

[文献書誌] K.Shiohama,Y.Otsu and T.Yamaguchi: "A new version of differentiable sphere theorem" Invent.Math.98. 219-228 (1989)

[文献書誌] K.Shiohama and T.Yamaguchi: "Positively curved manifolds with restricted diameters" “Geometry of Manifolds"Perspectives in Math.,Academic Press. 8. 345-350 (1989)

[文献書誌] K.Shiohama and M.Tanaka: "An isoperimetric problem for infinitely connected complete open surfaces" “Geometry of Manifolds"Perspectives in Math., Academic Press. 8. 317-343 (1989)

[文献書誌] K.Shiohama,T.Shioya and M.Tanaka: "Mass of rays on complete open surfaces" Pacific J.Math.(1990)

[文献書誌] A.Hora: "On a Banach Space of Functions Associated with a Homogeneous Additive Process" Publications of the Research Institute for Math.Sci.Kyoto Univ.24. (1988)

[文献書誌] A.Hora: "Quasi-Invariant Measures on Commutative Lie Groups of Infinite Product Type" Research Institute for Math.Sci.Kyoto Univ.654. (1989)

[文献書誌] A.Kudo and K.Yanagi: "概不偏検定" 日本SASユ-ザ-会論文集. 167-169 (1989)

[文献書誌] E.Bannai: "Association schemesの指数表とsubschemes" 代数学分科会報告集. (1989)

[文献書誌] E.Bannai,Shen Hao,S-Y.Song and H.Z.Wei: "Character Tables of Certain Association Schemes Coming from Finite Unitary and Symplectic Groups"

[文献書誌] E.Bannai,N.Kawanaka and Sung-Yell Song: "The Character Table of the Hecke Algebra H(GL_<2n>(F_q),Sp_<2n>(F_q))"

[文献書誌] E.Bannai and Sung-Yell Song: "The Character Tables of Paige's Simple Moufang Loops and Their Relationship to the Character Tables of PSL(2,q)" Proc.London Math.Soc.58. 209-236 (1989)

[文献書誌] E.Bannai and T.Ito: "On Distance-regular Graphs with Fixed Valency,IV" Europ.J.Combinatorics. 10. 137-148 (1989)

[文献書誌] E.Bannai,A.C.Kim and M.Kiyota: "On The Number of Elements which are not N-th Powers in Finite Groups" Communications in Algebra. 17(11). 2865-2870 (1989)

[文献書誌] E.Bannai: "On Spherical t-designs(a survey)" 代数的組合せ論報告集. (1989)

[文献書誌] E.Bannai: "Subschemes of some association schemes"

[文献書誌] E.Bannai and S.G.Hoggar: "Tight t-Designs and Squarefree Integers" Europ.J.Combinatorics. 10. 113-135 (1989)

[文献書誌] H.Sato: "Convergence of sum and product of a martingale difference sequence" Hiroshima Math.Jour.18. 69-72 (1988)

[文献書誌] H.Sato: "On the absolute Continuity of Infinite Product Measure and Its Convolution" Probab.Th.Rel.Fields. 81. 609-627 (1989)

[文献書誌] H.Sato: "Uniform Integrabilities of an Additive Martingale and its Exponential"

[文献書誌] H.Shimauchi: "関数近似における最適復旧について" 中村学園研究紀要. 21. (1989)

[文献書誌] K.Matsumoto: "種数3のある超楕円曲線族に対する2変数モジュラ-函数"

[文献書誌] K.Matsumoto,T.Sasaki and M.Yoshida: "The Monodromy of the period map of a 4-parameter family of k3 surfaces and the Aomoto-Gel'fand hypergeometric function of type(3,6)"

[文献書誌] K.Sakurai and M.Yoshida: "Fuchsian Systems Associated with the P^2(F_2)-Arrangement" Siam J.Math.Anal.20. 1490-1499 (1989)

[文献書誌] M.Takase: "ドイツ数学史の構想" 数学セミナ-. (1989)

[文献書誌] M.Hara,T.Sasaki and M.Yoshida: "Tensor Products of Linear Differential Equations--a study of exterior products of hypergeometric equations" Funkcialaj Ekvacioj.32. 453-477 (1989)

[文献書誌] N.Furukawa: "Max型関数の最適化アルゴリズムによる非線形方程式の一数値解析法" 講演アブストラクト. (1990)

[文献書誌] N.Furukawa: "Higher-Order Variational Sets,Variational Derivatives and Higher-Order Necessary Conditions in Abstract Math.Programming" Bull.of Informatics and Cybernetics. 23. (1988)

[文献書誌] R.Fukuda: "On the Strong Integrability of Sub-Gaussian Vectors"

[文献書誌] S.Fujino: "閾値機構を持つオ-トマトンの挙動解析"

[文献書誌] S.Fujino: "記憶を持つセル・オ-トマトンについて"

[文献書誌] S.Fujino: "オ-トマトン・ネットワ-ク並列処理に関する実験数学的考察"

[文献書誌] S.Fujino: "正方配列有界セル・オ-トマトンCA_2ーX(m)の挙動解析(II)"

[文献書誌] S.Nishikawa: "Heat Conduction for Riemannian Foliations" Bull.of the American Mathematical Society. 21ー2. 265-267 (1989)

[文献書誌] S.Nishikawa: "Transversal Infinitesimal Automorphisms of Harmonic Foliations on Complete Manifolds" Ann.Global Anal.Geom.7ー1. 47-57 (1989)

[文献書誌] T.Yamazaki: "Jacobi forms and a Mass relation for Eisenstein series(II)" J.Fac.Sci.Univ.Tokyo Sect.IA,Math.36ー2. 373-386 (1989)

[文献書誌] T.Honda: "Sur un Theoreme de Type D'akio Kodama" Memoirs of the Fac.of Sci.Kyushu University. 44ー2. 61-66 (1989)

[文献書誌] Y.Sueyoshi: "A Characterization of Number Fields by p-Closed Extensions" Journal of Number Theory. 28ー2. 145-151 (1988)

[文献書誌] Y.Sueyoshi: "Explicit reciprocity laws on relative Lubin-Tate groups"

[文献書誌] K.Shiohama(Edited): "Geometry of Manifolds,Perspectives in Mathematics" Academic press,Boston-New-York-Berkeley-London-Sydney-Tokyo-Toronto, (1989)

1989 年度実績報告書

梶原壌二九州大学, 理学部, 教授 (90037169)