2001 年度実績報告書

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

研究課題

研究課題/領域番号	11440048
研究機関	広島大学
研究代表者	柴雅和広島大学, 大学院・工学研究科, 教授 (70025469)
研究分担者	水田義弘広島大学, 総合科学部, 教授 (00093815) 金子新広島大学, 大学院・工学研究科, 教授 (10038101) 伊藤雅明広島大学, 大学院・工学研究科, 助教授 (10116535) 米谷文男京都工芸繊維大学, 工芸学部, 教授 (10029340) 増本誠山口大学, 理学部, 助教授 (50173761)
キーワード	ワイアシュトラスのゼータ関数 / 流体力学 / トーラスのモジュラス / 流れのエネルギー / リーマン面 / 等角的埋め込み / 理想境界の大きさ / 理想境界を越える解析接続
研究概要	代表者は理想境界を越える解析接続を定義し,等角的埋め込みやAbelの定理との関連を示した.また,伊藤(雅)と共に,Weierstrassのゼータ関数による流れと一様流との重ね合わせとして得られるトーラス上の流れのエネルギーを調べた.これら2件はポルトガルでの国際会議で柴と伊藤(雅)がそれぞれ発表した.さらにSchmiederと共同で,開リーマン面を閉リーマン面に等角的に埋め込んで実現される理想境界の大きさ(特にその下限)について調べた. 応用流体力学の立場からは徳永と金子が研究したが,金子は流速分布計で得た海流データを解析を行った.物理学との関係については,幾つかの新しい非線形可積分発展方程式系の構成と解析を大田が行い,公理論的場の量子論における局所化された観測量の作る代数の定義可能性や核定理に関する応用上有用な問題を長町が扱った.岩瀬は低濃度を特徴とする特性量の統計的推定方法を開発し,佐藤は流体力学などを活用して降下化学物質のデータから気象条件や地形の特性を見出した.税所は反射壁確率過程の近似方法とその応用に関する研究を行った.伊藤(浩)はトーラスの代数幾何学的側面について,また樋口は確率微分方程式について,それぞれ本研究の遂行に貢献した.水田は,多調和関数に対してLiouville型定理やBocher型定理を示し,P・調和測度の存在や単調関数の境界値の存在についても調べた.那須は記号力学系の自己同型の力学系に関するBoyleとMaasの予想を証明し,1次元可微分力学系に対して鄭は小さなLiapunov指数を持つ反発周期軌道の個数の増大率を上から評価した.増本はリーマン面の曲線族の極値的長さと拡張された意味での中間値の定理との関連を論じ,米谷はリーマン面上のAhlfors-Rauch型変分公式を複素多様体の変形問題に応用し,Denjoy領域の等角写像に関する注意も与えた.

研究成果
(30件)

すべてその他

すべて文献書誌 (30件)

[文献書誌] M.Ito: "Nonlinearity of energy of Rankine flows"Nonlinear Analysis, Theory, Methods & Applications. 47. 5467-5477 (2001)
[文献書誌] G.Schmieder: "On the size of the ideal boundary of a finite Riemann surface"Ann. Univ. Marie Curie-Sklodwske, Sekt. A. 55. 175-180 (2001)
[文献書誌] 伊藤雅明: "トーラス上のランキン流れとそのエネルギー"京都大学数理解析研究所講究録. 1223. 1-9 (2001)
[文献書誌] M.Ito: "Superpositions of a uniform flow on a torus and the flow described by the Weierstrass ξ function"Real and Complex Analysis. Proc. 5^<th> Japan-Korea Workshop held at Hiroshima Univ. (ed. by M. Furushima et al.). (2002)
[文献書誌] X-H.Zhu: "Kuroshio stream path variation and its associated velocity structures south of Shikoku"Japan. Geophys. Res. Lett.. 28・24. 4615-4618 (2001)
[文献書誌] A.Kaneko: "Repeat meridional survey of the western North Pacific subtropical gyre by a VOS ADCP during 1997 to 1998"Japan. Geophys. Res. Lett.. 28・18. 3429-3432 (2001)
[文献書誌] Y-M.Chung: "Topological entropy for differential maps of intervals"Osaka J. Math.. 38. 1-12 (2001)
[文献書誌] F.Maitani: "Ahlfors-Rauch type variational formulas on complex manifolds"Mem. Fac. Eng. And Design Kyoto Inst. Tech.. 49. 19-36 (2001)
[文献書誌] H.Ishida: "Conformal imbeddings of Denjoy domains"Acta Human. Sci. Univ. Sangio Kyotiensis. 30. 1-7 (2001)
[文献書誌] M.Masumoto: "A theorem of Schmieder-Shiba on compact continuations of open Riemann surfaces"京都大学数理解析研究所講究録. 1223. 10-18 (2001)
[文献書誌] M.Masumoto: "Extremal lengths of homology classes on compact Riemann surfaces"Nonlinear Analysis, Theory, Methods and Applications. 47. 5491-5500 (2001)
[文献書誌] T.Futamura: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)
[文献書誌] T.Futamura: "A generalization of Boche's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)
[文献書誌] T.Futamura: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)
[文献書誌] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math. Pures Appl.. 46. 67-75 (2001)
[文献書誌] S.Nagamachi: "Hyperfunction quantum field theory : Analytic structure, modular aspects, and local observable algebras"J. Math. Phys.. 42・1. 99-129 (2001)
[文献書誌] T.Nishimura: "Support and Kernel theorem for Fourier hyperfunctions"Osaka J. Math.. 38・3. 667-680 (2001)
[文献書誌] E.Bruening: "Kernel Theorem for Fourier hyperfunctions"J. Math., The Univ. Tokushima. 35. 57-64 (2001)
[文献書誌] F.W.Nijhoff: "On discrete Painleve equations associated with the lattice KdV systems and the Painleve VI equation"Stud. Appl. Math.. 106・3. 261-314 (2001)
[文献書誌] A.Ramani: "A geometrical description of the discrete Painleve VI and V equations"Comm. Math. Phys.. 217・2. 315-329 (2001)
[文献書誌] A.Ramani: "The q-Painleve V equation and its geometrical description"J. Phys. A : Math. Gen.. 34・11. 2505-2513 (2001)
[文献書誌] Y.Ohta: "A bilinear approach to a Pfaffian self-dual Yang-Mills equation"Glasgow Math. J.. 43A. 99-108 (2001)
[文献書誌] S.Lafortune: "Blending two discrete integrability criteria : Singularity confinement and algebraic entropy"CRM Proceedings and Lecture Notes. 29. 299-311 (2001)
[文献書誌] Y.Ohta: "An affine Weyl group approach to the eight-parameter discrete Painleve equation"J. Phys. A : Math. Gen.. 34・48. 10523-10532 (2001)
[文献書誌] S.Kakei: "A differential-difference system related to toroidal Lie algebra"J. Phys. A : Math. Gen.. 34・48. 10585-10592 (2001)
[文献書誌] K.Kajiwara: "Determinant formulas for the Toda and discrete Toda equations"Funkcial. Ekvac.. 44・2. 291-307 (2001)
[文献書誌] S.Seto: "Source identification of rural precipitation chemistry in Japan"Water, Air, and Soil Pollution : Int. J. Environmental Pollution. 130. 493-498 (2001)
[文献書誌] K.Iwase: "Estimation of the fifth percentile using a subset of order statistics"Measurement and Multivariate Analysis. ed. by S.Nishisato, Y.Baba, H.Bozdogan and K.Kanefuji. 217-226 (2001)
[文献書誌] M.Shiba: "Analytic continuation beyond the ideal boundary in "Analytic Extension Formulas and their Applications""Kluwer Academic Publishers(分担執筆). 233-250 (2001)
[文献書誌] M.Sato: "Source Apportionment in "The Encyclopedia of Environmetrics""Wiley(分担執筆). 2033-2036 (2002)

2001 年度 実績報告書

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

研究代表者

柴 雅和 広島大学, 大学院・工学研究科, 教授 (70025469)

研究成果

[文献書誌] M.Ito: "Nonlinearity of energy of Rankine flows"Nonlinear Analysis, Theory, Methods & Applications. 47. 5467-5477 (2001)

[文献書誌] G.Schmieder: "On the size of the ideal boundary of a finite Riemann surface"Ann. Univ. Marie Curie-Sklodwske, Sekt. A. 55. 175-180 (2001)

[文献書誌] 伊藤雅明: "トーラス上のランキン流れとそのエネルギー"京都大学数理解析研究所講究録. 1223. 1-9 (2001)

[文献書誌] M.Ito: "Superpositions of a uniform flow on a torus and the flow described by the Weierstrass ξ function"Real and Complex Analysis. Proc. 5^<th> Japan-Korea Workshop held at Hiroshima Univ. (ed. by M. Furushima et al.). (2002)

[文献書誌] X-H.Zhu: "Kuroshio stream path variation and its associated velocity structures south of Shikoku"Japan. Geophys. Res. Lett.. 28・24. 4615-4618 (2001)

[文献書誌] A.Kaneko: "Repeat meridional survey of the western North Pacific subtropical gyre by a VOS ADCP during 1997 to 1998"Japan. Geophys. Res. Lett.. 28・18. 3429-3432 (2001)

[文献書誌] Y-M.Chung: "Topological entropy for differential maps of intervals"Osaka J. Math.. 38. 1-12 (2001)

[文献書誌] F.Maitani: "Ahlfors-Rauch type variational formulas on complex manifolds"Mem. Fac. Eng. And Design Kyoto Inst. Tech.. 49. 19-36 (2001)

[文献書誌] H.Ishida: "Conformal imbeddings of Denjoy domains"Acta Human. Sci. Univ. Sangio Kyotiensis. 30. 1-7 (2001)

[文献書誌] M.Masumoto: "A theorem of Schmieder-Shiba on compact continuations of open Riemann surfaces"京都大学数理解析研究所講究録. 1223. 10-18 (2001)

[文献書誌] M.Masumoto: "Extremal lengths of homology classes on compact Riemann surfaces"Nonlinear Analysis, Theory, Methods and Applications. 47. 5491-5500 (2001)

[文献書誌] T.Futamura: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)

[文献書誌] T.Futamura: "A generalization of Boche's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)

[文献書誌] T.Futamura: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)

[文献書誌] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math. Pures Appl.. 46. 67-75 (2001)

[文献書誌] S.Nagamachi: "Hyperfunction quantum field theory : Analytic structure, modular aspects, and local observable algebras"J. Math. Phys.. 42・1. 99-129 (2001)

[文献書誌] T.Nishimura: "Support and Kernel theorem for Fourier hyperfunctions"Osaka J. Math.. 38・3. 667-680 (2001)

[文献書誌] E.Bruening: "Kernel Theorem for Fourier hyperfunctions"J. Math., The Univ. Tokushima. 35. 57-64 (2001)

[文献書誌] F.W.Nijhoff: "On discrete Painleve equations associated with the lattice KdV systems and the Painleve VI equation"Stud. Appl. Math.. 106・3. 261-314 (2001)

[文献書誌] A.Ramani: "A geometrical description of the discrete Painleve VI and V equations"Comm. Math. Phys.. 217・2. 315-329 (2001)

[文献書誌] A.Ramani: "The q-Painleve V equation and its geometrical description"J. Phys. A : Math. Gen.. 34・11. 2505-2513 (2001)

[文献書誌] Y.Ohta: "A bilinear approach to a Pfaffian self-dual Yang-Mills equation"Glasgow Math. J.. 43A. 99-108 (2001)

[文献書誌] S.Lafortune: "Blending two discrete integrability criteria : Singularity confinement and algebraic entropy"CRM Proceedings and Lecture Notes. 29. 299-311 (2001)

[文献書誌] Y.Ohta: "An affine Weyl group approach to the eight-parameter discrete Painleve equation"J. Phys. A : Math. Gen.. 34・48. 10523-10532 (2001)

[文献書誌] S.Kakei: "A differential-difference system related to toroidal Lie algebra"J. Phys. A : Math. Gen.. 34・48. 10585-10592 (2001)

[文献書誌] K.Kajiwara: "Determinant formulas for the Toda and discrete Toda equations"Funkcial. Ekvac.. 44・2. 291-307 (2001)

[文献書誌] S.Seto: "Source identification of rural precipitation chemistry in Japan"Water, Air, and Soil Pollution : Int. J. Environmental Pollution. 130. 493-498 (2001)

[文献書誌] K.Iwase: "Estimation of the fifth percentile using a subset of order statistics"Measurement and Multivariate Analysis. ed. by S.Nishisato, Y.Baba, H.Bozdogan and K.Kanefuji. 217-226 (2001)

[文献書誌] M.Shiba: "Analytic continuation beyond the ideal boundary in "Analytic Extension Formulas and their Applications""Kluwer Academic Publishers(分担執筆). 233-250 (2001)

[文献書誌] M.Sato: "Source Apportionment in "The Encyclopedia of Environmetrics""Wiley(分担執筆). 2033-2036 (2002)

2001 年度実績報告書

柴雅和広島大学, 大学院・工学研究科, 教授 (70025469)