1992 年度実績報告書

一部実施要因計画の構築と解析の研究

研究課題

研究課題/領域番号	04640232
研究機関	広島大学
研究代表者	桑田正秀広島大学, 総合科学部, 教授 (10144891)
研究分担者	吉田清広島大学, 総合科学部, 教授 (80033893) 水田義弘広島大学, 総合科学部, 教授 (00093815) 西浦康政広島大学, 総合科学部, 教授 (00131277) 久保泉広島大学, 総合科学部, 教授 (70022621) 江口正晃広島大学, 総合科学部, 教授 (30037220)
キーワード	分散分析 / curvature / 球対称解 / continuum theory / 白色雑音 / サドルポイント近似 / 等長埋め込み / ポランシャル
研究概要	1.実験計画における最適性の理論の新しい導入、色々の最適性の理論の共有の性質、2つの最適性間の双対的関係等が明らかになった。水準数が2、3と一般のsの場合の分散分析と検定統計量が求まり、2水準の場合の頑健性について一部明らかになった。 2.分布関数の新しい近似法と片側検定における符号付き対数尤度比や正規化変換を行った統計量の漸近展開、平面上の点配置型パターンをギブス分布でモデル化する際のポテンシャル関数の尤度推定量の漸近的性質、また「誕生日問題」を不等生起確率の場合に拡張した公式と近似式が求まった。ガウス型白色雑音の汎関数の解析のためのHida‐Calculusについて、特に有限次元的なHida超汎関数の完全な特徴付が与えられた。 3.3次正定値対称行列空間のzonal多項式の係数を決定し、G=SU(n,1)の場合Ad表現に対するHarish‐ChandraのC関数の行列成分を求めた。グリーン関数とソボレフ関数の超平面上でのp‐乘積分の性質、反応拡散系に現れるInterfacial Patternsの安定性と分岐等、Nerve Equationに現れるEvans functionとSLEP equationの関係を論じた。 4.p‐Laplace方程式の球対称解を求め、superlinear elliptic方程式の正値解の非存在とsingular Emden‐Fowler型方程式の正値解の存在を示した。 5.群論的に単純化するためGauss方程式を一般化し、Riemann多様体が等長に埋め込めるための新しい条件を見いだし、現在まで求まっている対称空間の局所等長埋め込みの次元に関する表を作成した。 6.expansive homeomorphismの性質、許容する連続体の条件を求めた。グラフのshift mapがexpansiveになるinverse limitは平面を4つ以上に分けることを示し、ベキ空間とホイットニー連続体の最近までの結果を論じた。

研究成果

(24件)

すべてその他

すべて文献書誌 (24件)

[文献書誌] Masahide Kuwada: "Analysis of variance of balanced fractional factorial designs" Discrete Math.116. (1993)
[文献書誌] Masahide Kuwada: "Robustness of balanced fractional 2^mfactorial designs derived from simple arrays" Discrete Math.116. (1993)
[文献書誌] Yoshifumi Hyodo (共著者:M.Kuwada): "Analysis of variance of balanced fractional s^m factorial designs of resolvtion Vp.6" J.Statist.Plann.Inference.
[文献書誌] Yoshio Agaoka: "A table on the codimension of local isometric imbeddings of Riemannian symmetric spaces" Mem.Fac.Integrated Art.& Soi.,Hiroshima Univ.,Ser.IV,Science Report.18. 1-10 (1992)
[文献書誌] Hiroyuki Usami: "Nonexistence results of entire solutions for superlinear elliptic ineoualities" J.Math.Anal.Appl. 164. 59-82 (1992)
[文献書誌] Masaaki Eguchi (共著者:M.Miyamoto R.Wada): "An explicit expression of the Harish-Chandra C-function of SU(n,1)associated to Ad(K) representation" Proc.Japan Acad.68. 232-236 (1992)
[文献書誌] Hiroyuki Usami: "Positive solutions of singular Emden-fowler type systems" Hiroshima Math.J.22. (1992)
[文献書誌] Hisao Kato: "Expansive homeomorphisms in continuum theory" Topology Appl.45. 223-243 (1992)
[文献書誌] Hisao Kato: "Embeddability into the plane and movability on inverse limits of graphs whose shift maps are expansive" Topology Appl.43. 141-156 (1992)
[文献書誌] Hisao Kato (共著者:K.Kawamura): "A class of continua which admit no expansive homeomorphisms" Rocky Mountain J.Math.22. 645-651 (1992)
[文献書誌] 加藤久男: "巾空間とWhitney連続体の幾何学的構造" 数学. 44. 229-244 (1992)
[文献書誌] Izumi Kubo (共著者:H.‐H.Kuo): "Fourier transform and cylindrical Hida distributions" Stochastic Processes. 191-200 (1993)
[文献書誌] Ryuei Nishii: "Saddlepoint approximation for the distribution function of the mean of random variables" Hiroshima Math.J.22. 177-183 (1992)
[文献書誌] Ryuei Nishii: "Optimality in experimental designs" Discrete Math.116. (1993)
[文献書誌] Ryuei Nishii (共著者:T.Yanagimoto): "Normal approximation to the distribution of the sample mean in the exponential family" Proc.3rd Pacific Statistical Conference. (1993)
[文献書誌] Yasumasa Nishiura: "Coexistence of infinitely many stable solutions to reaction diffusion systems in the singular limit" Dynamics Reported.
[文献書誌] Yasumasa Nishiura: "Coalescence,repulsion,and nonuniqueness for singular limit reaction diffusion systems" Proc.International Taniguchi Symposium on Nonlinear Partial Differential Eguations and Applications.
[文献書誌] T.Ikeda(共著者:Y.Nishiura): "Pattern selection for two breathers" SIAM J.Appl.Math.
[文献書誌] Shigeru Mase: "Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood eslimator of potential fanctions" Probab.Theory and Rel Fields. 92. 51-67 (1992)
[文献書誌] Shigeru Mase: "Aprroximations to the birthday problem with unegual occurrence probabilities and their application to the surname problew in Japan" Ann.Inst. Statist.Math.44. 479-499 (1992)
[文献書誌] Yoshihiro mizuta: "Growth properties of p‐th hyperplane means of Green potentials in a half space" J.Math.Soc.Japan. 44. 1-12 (1992)
[文献書誌] Yoshihiro Mizuta: "Spherical means of Beppo Levi functions" Math.Nachr.158. 241-262 (1992)
[文献書誌] Kiyoshi Yoshida: "On oscillation and decay of solutions for some ordinary differential systems" Funkcialaj Ekvacioj.
[文献書誌] A.Kowata (共著者:R.Wada): "Zonal polynomials on the space of 3×3 positive define symmetric matrices" Hiroshima Math.J.22. 433-443 (1992)

1992 年度 実績報告書

一部実施要因計画の構築と解析の研究

研究代表者

桑田 正秀 広島大学, 総合科学部, 教授 (10144891)

研究成果

[文献書誌] Masahide Kuwada: "Analysis of variance of balanced fractional factorial designs" Discrete Math.116. (1993)

[文献書誌] Masahide Kuwada: "Robustness of balanced fractional 2^mfactorial designs derived from simple arrays" Discrete Math.116. (1993)

[文献書誌] Yoshifumi Hyodo (共著者:M.Kuwada): "Analysis of variance of balanced fractional s^m factorial designs of resolvtion Vp.6" J.Statist.Plann.Inference.

[文献書誌] Yoshio Agaoka: "A table on the codimension of local isometric imbeddings of Riemannian symmetric spaces" Mem.Fac.Integrated Art.& Soi.,Hiroshima Univ.,Ser.IV,Science Report.18. 1-10 (1992)

[文献書誌] Hiroyuki Usami: "Nonexistence results of entire solutions for superlinear elliptic ineoualities" J.Math.Anal.Appl. 164. 59-82 (1992)

[文献書誌] Masaaki Eguchi (共著者:M.Miyamoto R.Wada): "An explicit expression of the Harish-Chandra C-function of SU(n,1)associated to Ad(K) representation" Proc.Japan Acad.68. 232-236 (1992)

[文献書誌] Hiroyuki Usami: "Positive solutions of singular Emden-fowler type systems" Hiroshima Math.J.22. (1992)

[文献書誌] Hisao Kato: "Expansive homeomorphisms in continuum theory" Topology Appl.45. 223-243 (1992)

[文献書誌] Hisao Kato: "Embeddability into the plane and movability on inverse limits of graphs whose shift maps are expansive" Topology Appl.43. 141-156 (1992)

[文献書誌] Hisao Kato (共著者:K.Kawamura): "A class of continua which admit no expansive homeomorphisms" Rocky Mountain J.Math.22. 645-651 (1992)

[文献書誌] 加藤 久男: "巾空間とWhitney連続体の幾何学的構造" 数学. 44. 229-244 (1992)

[文献書誌] Izumi Kubo (共著者:H.‐H.Kuo): "Fourier transform and cylindrical Hida distributions" Stochastic Processes. 191-200 (1993)

[文献書誌] Ryuei Nishii: "Saddlepoint approximation for the distribution function of the mean of random variables" Hiroshima Math.J.22. 177-183 (1992)

[文献書誌] Ryuei Nishii: "Optimality in experimental designs" Discrete Math.116. (1993)

[文献書誌] Ryuei Nishii (共著者:T.Yanagimoto): "Normal approximation to the distribution of the sample mean in the exponential family" Proc.3rd Pacific Statistical Conference. (1993)

[文献書誌] Yasumasa Nishiura: "Coexistence of infinitely many stable solutions to reaction diffusion systems in the singular limit" Dynamics Reported.

[文献書誌] Yasumasa Nishiura: "Coalescence,repulsion,and nonuniqueness for singular limit reaction diffusion systems" Proc.International Taniguchi Symposium on Nonlinear Partial Differential Eguations and Applications.

[文献書誌] T.Ikeda(共著者:Y.Nishiura): "Pattern selection for two breathers" SIAM J.Appl.Math.

[文献書誌] Shigeru Mase: "Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood eslimator of potential fanctions" Probab.Theory and Rel Fields. 92. 51-67 (1992)

[文献書誌] Shigeru Mase: "Aprroximations to the birthday problem with unegual occurrence probabilities and their application to the surname problew in Japan" Ann.Inst. Statist.Math.44. 479-499 (1992)

[文献書誌] Yoshihiro mizuta: "Growth properties of p‐th hyperplane means of Green potentials in a half space" J.Math.Soc.Japan. 44. 1-12 (1992)

[文献書誌] Yoshihiro Mizuta: "Spherical means of Beppo Levi functions" Math.Nachr.158. 241-262 (1992)

[文献書誌] Kiyoshi Yoshida: "On oscillation and decay of solutions for some ordinary differential systems" Funkcialaj Ekvacioj.

[文献書誌] A.Kowata (共著者:R.Wada): "Zonal polynomials on the space of 3×3 positive define symmetric matrices" Hiroshima Math.J.22. 433-443 (1992)

1992 年度実績報告書

桑田正秀広島大学, 総合科学部, 教授 (10144891)

[文献書誌] 加藤久男: "巾空間とWhitney連続体の幾何学的構造" 数学. 44. 229-244 (1992)