1991 Fiscal Year Annual Research Report

実体,2次形式と多様体

Research Project

Project/Area Number	03640065
Research Institution	Hiroshima University
Principal Investigator	岩上辰男広島大学, 総合科学部, 助教授 (50015567)
Co-Investigator(Kenkyū-buntansha)	水田義弘広島大学, 総合科学部, 教授 (00093815) 間瀬茂広島大学, 総合科学部, 助教授 (70108190) 桑田正秀広島大学, 総合科学部, 教授 (10144891) 加藤久男広島大学, 総合科学部, 助教授 (70152733) 江口正晃広島大学, 総合科学部, 教授 (30037220)
Keywords	Lelekの問題 / リンキング形式 / 等長埋め込み / L.Cohnの予想 / EmdenーFowler型方程式 / 細連続性 / サドルポイント法 / 特異極限
Research Abstract	1.実体の2次形式に関して、準ピタゴラス体の概念を拡張したnーピタゴラス体を研究し,準ピタゴラス体(n=1)において成り立つ多くの結果が一般の場合に成り立つことを確認したが,それらの体のヴィット環およびk群の構造に関する決定的な結果を得るに至っていない。 2.多様体に関して,Lelekの問題の肯定解,1次元連続体の拡大同相写像関する問題の部分解を与えた。また,4次元球面に埋め込まれた閉曲面に対し,その補空間に二重被覆空間のホモロジ-群とリンキング形式に関する特徴づけを行なった。さらに,リ-マン多様体の局所等長埋め込みの障害となる新たな量を導入し,それをいくつかの対称空間に応用して,等長埋め込みの余次元に関する評価を改良した。 3.L.Cohnの予想がSL(3.IR),SL(4.IR)の場合に正しいことを証明した。また,対称空間のある巾零多様体上の正則関数が,ある種の微作用素の固有関数に一意的に拡張できることを証明した。 4.特異EmdenーFowler形方程式の解,ある4階楕円型式方程式の正値解,ある楕円型不等式の解(の非存在)について多くの結果が得られた。 5.調和関数の境果値の存在,半空間でのグリ-ンポテンシャルに関する超平面上での積分値の境界挙動,ベッポ-レビ関数の連続性,ポテシシャルの細連続性を研究し,多くの新たな結果を得た。 6.分解能Vの部分釣合い型ー部実銭2^<m1+m2>要因計画の分散分析と仮説検定を行なった。また,指数型分布族に従う標本分析の分布関数を近似するためのサドルポイント法を提案し,その漸近的性質を調べた。さらに、平面中の点群をギブス分布でモデル化したとき,ポテンシャル関数の最尤推定量が漸近的に有効となるための条件を求めた。 7.Phase field modelからStefan modelへの特異極限における進行波解の漸近収束を研究して多くの新たな結果を得た。

Research Products
(27 results)

All Other

All Publications (27 results)

[Publications] Yoshio Agaoka,E.Kaneda: "An estimate on the codimesion of local isometric imbeddings of compact Lie groups."
[Publications] G.Caginalp,Y.NiShiura: "The Existence of Travelling Waves for Phase Field Equations and Convergence to Sharp Interface Models in the Singular Limit." Quart.Appl.Math.49. 147-162 (1991)
[Publications] Masaaki Eguchi: "The explicit representation of the determinant of HarishーChandra's Cーfunction in SL(3,IR)and SL(4,IR)cases." Hirroshima Math.J.22. (1992)
[Publications] D.Hilhorst,M.Mimura,Y.Nishiura: "A Free Boundary Problem Arising in Some ReactingーDiffusion System" Proc.of the Royal Society of Edinburgh. 118. 355-378 (1991)
[Publications] Hisao Kato,A.Koyama,E.D.Tymchatyn: "Mappings with zero surjective span." Houston J.Math. 17. 325-333 (1991)
[Publications] Hisao Kato: "On expansiveness of shift homeomorphisms of inverse limits of graphs." Fund.Math.137. 201-210 (1991)
[Publications] Hisao Kato: "Expansive homeomorphisms and indecomposability." Fund.Math.139. 49-57 (1991)
[Publications] Hisao Kato: "A note on continuous mappings and property of J.L.Kelley." Proc.A.M.S.112. 1143-1148 (1991)
[Publications] A.Kowata,R.Wada: "Zonal polynomials on the space of 3×3 positive definite symmetric matices." Hiroshima Math.J.
[Publications] Masahide Kuwada: "An analysis of variance of partially balanced fractinal 2^<m1+m2> factorial designs of resolution V." J.Japan Statist.Soc.21. 43-59 (1991)
[Publications] Shigeru Mase: "Approximations to the birthday problem with unequal occurrence probabilities and their application to the surname problem in Japan." Ann.of Inst.Stat.Math.(1992)
[Publications] Shigeru Mase: "Uniform LAN condition of planar Gibbsian point processes and optimality of Maximum Likelihood Estimator of Potential Functions." Probability Theory and Related Fields. (1992)
[Publications] 間瀬茂,上田修功: "モルフォロジ-と画像解析[1]" 電子情報通信学会誌. 74. 166-174 (1991)
[Publications] Yoshihiro Mizuta: "Boundary limits of harmonic functions in OrliczーSobolev classes." Proceedings ICPT Nagoya.
[Publications] Yoshihiro Mizuta: "Growth propeties of pーth hyperplane means of Green potentーials in a half space." J.Math.Soc.Japan. 44. (1992)
[Publications] Yoshihiro Mizuta: "Continuity properties of potentials and BeppoーLeviーDeny functions." Hiroshima Math J.23. (1993)
[Publications] Yoshihiro Mizuta: "Finite limits of potentials." Analysis.
[Publications] Ryuei Nishii: "Optimality of optimal designs." Discrete Mathematics. (1992)
[Publications] Ryuei Nishii: "Saddlepoint approximation for the distribution function of the mean of random variables." Hiroshima Math.J.(1992)
[Publications] Yasumasa Nishiura: "Singular Limit Approach to Stability and Bifurcation for Bistable Reaction Diffusion Systems." Rocky Mountain J.of Math.21. 727-767 (1991)
[Publications] Yasumasa Nishiura,G.Caginalp: "Convergence of Travelling Waves for Phase Equations to Sharp Interface Models in the Singular Limit." Patterns and dynamics in Reactive Media,The IMA Volumes in Mathematics and its Applications.37. 151-157 (1991)
[Publications] Mituhiro Sekine: "On homology of the double covering over the exterior of a surface in 4ーsphere." Hiroshima Math.J.21. 419-426 (1991)
[Publications] 上田修功,間瀬茂: "モルフォロジ-と画像解析[2]" 電子情報通信学会誌. 74. 271-279 (1991)
[Publications] Hiroyuki Usami: "On positive decaying solutions of singuler EmdenーFowlerーtype equations." Nonlinear Anal.16. 795-803 (1991)
[Publications] Hiroyuki Usami: "On bounded positive entire solutions of forth order semilinear elliptic equations." Japan J.Math.17. 11-36 (1991)
[Publications] Hiroyuki Usami: "Nonexistence results of entire solutions for superlinear elliptic inequalities." J.Math.Anal.Appl.164. 59-82 (1992)
[Publications] Ryoko Wada,A.Kowata: "Holomorphic functions on the nilpotent subvariety of symmetric spaces." Hiroshima Math.J.21. 263-266 (1991)

1991 Fiscal Year Annual Research Report

実体,2次形式と多様体

Principal Investigator

岩上 辰男 広島大学, 総合科学部, 助教授 (50015567)

Research Products

[Publications] Yoshio Agaoka,E.Kaneda: "An estimate on the codimesion of local isometric imbeddings of compact Lie groups."

[Publications] G.Caginalp,Y.NiShiura: "The Existence of Travelling Waves for Phase Field Equations and Convergence to Sharp Interface Models in the Singular Limit." Quart.Appl.Math.49. 147-162 (1991)

[Publications] Masaaki Eguchi: "The explicit representation of the determinant of HarishーChandra's Cーfunction in SL(3,IR)and SL(4,IR)cases." Hirroshima Math.J.22. (1992)

[Publications] D.Hilhorst,M.Mimura,Y.Nishiura: "A Free Boundary Problem Arising in Some ReactingーDiffusion System" Proc.of the Royal Society of Edinburgh. 118. 355-378 (1991)

[Publications] Hisao Kato,A.Koyama,E.D.Tymchatyn: "Mappings with zero surjective span." Houston J.Math. 17. 325-333 (1991)

[Publications] Hisao Kato: "On expansiveness of shift homeomorphisms of inverse limits of graphs." Fund.Math.137. 201-210 (1991)

[Publications] Hisao Kato: "Expansive homeomorphisms and indecomposability." Fund.Math.139. 49-57 (1991)

[Publications] Hisao Kato: "A note on continuous mappings and property of J.L.Kelley." Proc.A.M.S.112. 1143-1148 (1991)

[Publications] A.Kowata,R.Wada: "Zonal polynomials on the space of 3×3 positive definite symmetric matices." Hiroshima Math.J.

[Publications] Masahide Kuwada: "An analysis of variance of partially balanced fractinal 2^<m1+m2> factorial designs of resolution V." J.Japan Statist.Soc.21. 43-59 (1991)

[Publications] Shigeru Mase: "Approximations to the birthday problem with unequal occurrence probabilities and their application to the surname problem in Japan." Ann.of Inst.Stat.Math.(1992)

[Publications] Shigeru Mase: "Uniform LAN condition of planar Gibbsian point processes and optimality of Maximum Likelihood Estimator of Potential Functions." Probability Theory and Related Fields. (1992)

[Publications] 間瀬 茂,上田 修功: "モルフォロジ-と画像解析[1]" 電子情報通信学会誌. 74. 166-174 (1991)

[Publications] Yoshihiro Mizuta: "Boundary limits of harmonic functions in OrliczーSobolev classes." Proceedings ICPT Nagoya.

[Publications] Yoshihiro Mizuta: "Growth propeties of pーth hyperplane means of Green potentーials in a half space." J.Math.Soc.Japan. 44. (1992)

[Publications] Yoshihiro Mizuta: "Continuity properties of potentials and BeppoーLeviーDeny functions." Hiroshima Math J.23. (1993)

[Publications] Yoshihiro Mizuta: "Finite limits of potentials." Analysis.

[Publications] Ryuei Nishii: "Optimality of optimal designs." Discrete Mathematics. (1992)

[Publications] Ryuei Nishii: "Saddlepoint approximation for the distribution function of the mean of random variables." Hiroshima Math.J.(1992)

[Publications] Yasumasa Nishiura: "Singular Limit Approach to Stability and Bifurcation for Bistable Reaction Diffusion Systems." Rocky Mountain J.of Math.21. 727-767 (1991)

[Publications] Yasumasa Nishiura,G.Caginalp: "Convergence of Travelling Waves for Phase Equations to Sharp Interface Models in the Singular Limit." Patterns and dynamics in Reactive Media,The IMA Volumes in Mathematics and its Applications.37. 151-157 (1991)

[Publications] Mituhiro Sekine: "On homology of the double covering over the exterior of a surface in 4ーsphere." Hiroshima Math.J.21. 419-426 (1991)

[Publications] 上田 修功,間瀬 茂: "モルフォロジ-と画像解析[2]" 電子情報通信学会誌. 74. 271-279 (1991)

[Publications] Hiroyuki Usami: "On positive decaying solutions of singuler EmdenーFowlerーtype equations." Nonlinear Anal.16. 795-803 (1991)

[Publications] Hiroyuki Usami: "On bounded positive entire solutions of forth order semilinear elliptic equations." Japan J.Math.17. 11-36 (1991)

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

[Publications] Ryoko Wada,A.Kowata: "Holomorphic functions on the nilpotent subvariety of symmetric spaces." Hiroshima Math.J.21. 263-266 (1991)

岩上辰男広島大学, 総合科学部, 助教授 (50015567)

[Publications] 間瀬茂,上田修功: "モルフォロジ-と画像解析[1]" 電子情報通信学会誌. 74. 166-174 (1991)

[Publications] 上田修功,間瀬茂: "モルフォロジ-と画像解析[2]" 電子情報通信学会誌. 74. 271-279 (1991)