2000 Fiscal Year Annual Research Report

リーマン面の単射正則写像の研究と流体力学への応用-古典的単葉関数論の現代的意義

Research Project

Project/Area Number	11440048
Research Institution	Hiroshima University
Principal Investigator	柴雅和広島大学, 工学部, 教授 (70025469)
Co-Investigator(Kenkyū-buntansha)	水田義弘広島大学, 総合科学部, 教授 (00093815) 金子新広島大学, 工学部, 教授 (10038101) 伊藤雅明広島大学, 工学部, 助教授 (10116535) 米谷文男京都工芸繊維大学, 工芸学部, 教授 (10029340) 徳永宏京都工芸繊維大学, 工芸学部, 教授 (10027906)
Keywords	リーマン面 / 等角的埋め込み / 流体力学 / 単葉関数 / 正則写像 / モジュラス / 理想境界 / 解析接続
Research Abstract	年度目標は抽象・具象の2方向に進められた.代表者と伊藤とはRankineの卵を拡張して「Weierstrassのζ-関数が惹き起こすトーラス上の流れ」を数値解析的手法も援用して調べ,流体力学的・複素解析的な性質を明らかにした.これに平行して代表者は,新概念「理想境界を越える解析接続」を導入し,古典的な解析接続をRiemann面論や流体力学の立場から研究した.これらはイタリアで開かれた国際研究集会で報告した.Schmiederは単葉正則関数の具体的性質を研究した.水田は,擬等角写像の研究を視野に入れ,Sobolevの定理をSobolev-Orlicz関数にまで拡張し境界値の存在について論じた.米谷はRiemann面の変動に伴うAhlfors-Rauch型変分公式の高次元複素多様体への拡張を試み,増本は閉Riemann面のホモロジー類の極値的長さの間の代数的関係を考察した.太田は離散Painleve方程式系に対する幾何学的構成を行いBacklund変換について調べた.伊藤は,主因子分析に関する佐藤との共同研究を進め,偏差分方程式の保存密度を求める数値解析的な研究を行った.岩瀬は測定下限と検出下限を伴ったデータ解析を数理的に研究し,樋口は影響関数の観点からのロバスト性を考察してパラメータの決定方法を研究した.一般力学系との関連では,那須がBoyle-Maassの予想をテキスタイルシステムを用いて証明しその結果をさらに拡張し,鄭は可微分力学系のエルゴード論的研究を行い非可逆写像のエントロピーについて調べた.流体力学との関連では,金子が海峡部に発生する潮流渦の時空間発展を実験データとNavier-Stokes方程式との同化を通して力学的に再現し,長町は数理物理学と解析性との関連を追及し.徳永は航空工学などで重要な多重連結領域内の流れを圧力1価の条件下で解析した.

Research Products

(28 results)

All Other

All Publications (28 results)

[Publications] M.Shiba: "Analytic continuation beyond the ideal boundary"Kokyuroku, Res.Inst.Math.Sci., Kyoto Univ.. 1155. 120-127 (2000)
[Publications] M.Shiba: "Some function-theoretic properties of the hyperbolic metric and a new construction of fundamental domains"Kokyuroku, Res.Inst.Math.Sci., Kyoto Univ.. 1163. 1-8 (2000)
[Publications] M.Shiba: "Analytic continuation beyond the ideal boundary"Real and Complex Analysis, Proc.the third Japan-Korea Workshop, Ewha Womans University, Seoul, Korea (ed.by S.Y.Lee). 26-35 (2000)
[Publications] M.Shiba: "Ideal fluid flows on a noncompact Riemann surface and analytic continuation beyond the ideal boundary"Real and Complex Analysis, Proc.the fourth Japan-Korea Workshop, Hiroshima University (ed.by M.Furushima et al.). 34-49 (2001)
[Publications] M.Shiba: "Analytic continuation beyond the ideal boundary"to appear in "Analytic continuations and its applications" (ed.by S.Saitoh et al.). (2001)
[Publications] G.Schmieder: "On the Mobius distance"Annales UMCS, Sec.A. 54・11. 125-131 (2000)
[Publications] Y.M.Chung: "Topological entropy for differentible maps of intervals"to appear in Osaka J.Math.. 38. (2001)
[Publications] T.Futamura: "A generalization of the Liouville theorem to polyharmonic functions"to appear in J.Math.Soc.Japan. 53. (2001)
[Publications] Y.Mizuta: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 25. 457-465 (2000)
[Publications] Y.Mizuta: "Differentiability and Holder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)
[Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue of Sobolev classes"to appear in Revue Roumaine Math.Pures Appl.. 45. (2000)
[Publications] M.Nasu: "Endomorphisms of expansive systems on compact metric spaces and the pseudoorbit tracing property"Trans.Amer.Math.Soc.. 352. 4731-4757 (2000)
[Publications] J.J.C.Nimmo: "Applications of Darboux tranformations to the self-dual Yang-Mills equations"Theor.Math.Phys.. 122・2. 239-246 (2000)
[Publications] Y.Ohta: "Determinant and Pfaffian solutions for discrets soliton equations"CRM Proc.Lecture Notes. 25. 339-345 (2000)
[Publications] 岡田泰典: "渦度・流れ関数法と移動格子法によるジャーナル・ベアリング流れの動的解析"日本機械学会論文集(B編). 66・643. 641-646 (2000)
[Publications] J-H.Park: "Assimilation of coastal acoustic tomography data into a barotropic ocean model"Geophysical Res.Lett.. 27・20. 3373-3376 (2000)
[Publications] T.Futamura: "A generalization of Bocher's theorem for polyharmonic functions"to appear in Hiroshima Math.J.. 31. (2001)
[Publications] T.Futamura: "Existence of functions in weighted Sobolev spaces"to appear in Nagoya Math.J..
[Publications] M.Ito: "Nonlinearity of energy of Rankine flows on a torus"to appear in J.Nonlinear Analysis : Ser.A.
[Publications] K.Iwase: "Estimation of the fifth percentile using a subset of order statistics"Proc.the International Cconference on Mesurement and Multivariate. 2. 218-220 (2000)
[Publications] 岩瀬晃盛: "SQC今さらこんなこと(その1〜その12)その1"標準化と品質管理. 53・4. 69-73 (2000)
[Publications] 岩瀬晃盛: "SQC今さらこんなこと(その1〜その12)その12"標準化と品質管理. 54・3. 97-101 (2000)
[Publications] F.Maitani: "Ahlfors-Rauch type variational formulas on complex manifolds"Mem.Fac.Engi.Des.Kyoto Inst.Tech.. 49. 17-38 (2001)
[Publications] M.Masumoto: "Hyperbolic lengths and conformal embeddings of Riemann surfaces"Israel J.Math.. 116. 77-92 (2000)
[Publications] A.Ramani: "Discrete integrable systems from continuous Painleve equations through limiting procedures"Nonlinearity. 13・4. 1073-1086 (2000)
[Publications] A.Ramani: "Linearizable mappings and the low-growth criterion"J.Phys.A : Math.Gen.. 33・31. L287-L292 (2000)
[Publications] H.Tokunaga: "Numerical simulation of unsteady incompressible flow along multi-element aerofoil by unstrucrured grid coupled with finite volume and vorticity-stream function method"Numerical Grid Generation in Computational Field Simulations (ed.by B.K.Soni, et al., ISGG, Chateau Whsitler Resort, Canada). 25-28 (2000)
[Publications] 柴雅和: "森北出版(株)"関数論講義. 283 (2000)

2000 Fiscal Year Annual Research Report

リーマン面の単射正則写像の研究と流体力学への応用-古典的単葉関数論の現代的意義

Principal Investigator

柴 雅和 広島大学, 工学部, 教授 (70025469)

Research Products

[Publications] M.Shiba: "Analytic continuation beyond the ideal boundary"Kokyuroku, Res.Inst.Math.Sci., Kyoto Univ.. 1155. 120-127 (2000)

[Publications] M.Shiba: "Some function-theoretic properties of the hyperbolic metric and a new construction of fundamental domains"Kokyuroku, Res.Inst.Math.Sci., Kyoto Univ.. 1163. 1-8 (2000)

[Publications] M.Shiba: "Analytic continuation beyond the ideal boundary"Real and Complex Analysis, Proc.the third Japan-Korea Workshop, Ewha Womans University, Seoul, Korea (ed.by S.Y.Lee). 26-35 (2000)

[Publications] M.Shiba: "Ideal fluid flows on a noncompact Riemann surface and analytic continuation beyond the ideal boundary"Real and Complex Analysis, Proc.the fourth Japan-Korea Workshop, Hiroshima University (ed.by M.Furushima et al.). 34-49 (2001)

[Publications] M.Shiba: "Analytic continuation beyond the ideal boundary"to appear in "Analytic continuations and its applications" (ed.by S.Saitoh et al.). (2001)

[Publications] G.Schmieder: "On the Mobius distance"Annales UMCS, Sec.A. 54・11. 125-131 (2000)

[Publications] Y.M.Chung: "Topological entropy for differentible maps of intervals"to appear in Osaka J.Math.. 38. (2001)

[Publications] T.Futamura: "A generalization of the Liouville theorem to polyharmonic functions"to appear in J.Math.Soc.Japan. 53. (2001)

[Publications] Y.Mizuta: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 25. 457-465 (2000)

[Publications] Y.Mizuta: "Differentiability and Holder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)

[Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue of Sobolev classes"to appear in Revue Roumaine Math.Pures Appl.. 45. (2000)

[Publications] M.Nasu: "Endomorphisms of expansive systems on compact metric spaces and the pseudoorbit tracing property"Trans.Amer.Math.Soc.. 352. 4731-4757 (2000)

[Publications] J.J.C.Nimmo: "Applications of Darboux tranformations to the self-dual Yang-Mills equations"Theor.Math.Phys.. 122・2. 239-246 (2000)

[Publications] Y.Ohta: "Determinant and Pfaffian solutions for discrets soliton equations"CRM Proc.Lecture Notes. 25. 339-345 (2000)

[Publications] 岡田泰典: "渦度・流れ関数法と移動格子法によるジャーナル・ベアリング流れの動的解析"日本機械学会論文集(B編). 66・643. 641-646 (2000)

[Publications] J-H.Park: "Assimilation of coastal acoustic tomography data into a barotropic ocean model"Geophysical Res.Lett.. 27・20. 3373-3376 (2000)

[Publications] T.Futamura: "A generalization of Bocher's theorem for polyharmonic functions"to appear in Hiroshima Math.J.. 31. (2001)

[Publications] T.Futamura: "Existence of functions in weighted Sobolev spaces"to appear in Nagoya Math.J..

[Publications] M.Ito: "Nonlinearity of energy of Rankine flows on a torus"to appear in J.Nonlinear Analysis : Ser.A.

[Publications] K.Iwase: "Estimation of the fifth percentile using a subset of order statistics"Proc.the International Cconference on Mesurement and Multivariate. 2. 218-220 (2000)

[Publications] 岩瀬晃盛: "SQC今さらこんなこと(その1〜その12)その1"標準化と品質管理. 53・4. 69-73 (2000)

[Publications] 岩瀬晃盛: "SQC今さらこんなこと(その1〜その12)その12"標準化と品質管理. 54・3. 97-101 (2000)

[Publications] F.Maitani: "Ahlfors-Rauch type variational formulas on complex manifolds"Mem.Fac.Engi.Des.Kyoto Inst.Tech.. 49. 17-38 (2001)

[Publications] M.Masumoto: "Hyperbolic lengths and conformal embeddings of Riemann surfaces"Israel J.Math.. 116. 77-92 (2000)

[Publications] A.Ramani: "Discrete integrable systems from continuous Painleve equations through limiting procedures"Nonlinearity. 13・4. 1073-1086 (2000)

[Publications] A.Ramani: "Linearizable mappings and the low-growth criterion"J.Phys.A : Math.Gen.. 33・31. L287-L292 (2000)

[Publications] 柴雅和: "森北出版(株)"関数論講義. 283 (2000)

柴雅和広島大学, 工学部, 教授 (70025469)