2001 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, 大学院・工学研究科, 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, 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)
Keywords	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
Research Abstract	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.

Research Products

(30 results)

All Other

All Publications (30 results)

[Publications] M.Ito: "Nonlinearity of energy of Rankine flows"Nonlinear Analysis, Theory, Methods & Applications. 47. 5467-5477 (2001)
[Publications] 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)
[Publications] 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)
[Publications] 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)
[Publications] X-H.Zhu: "Kuroshio stream path variation and its associated velocity structures south of Shikoku"Japan. Geophys. Res. Lett.. 28・24. 4615-4618 (2001)
[Publications] 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)
[Publications] Y-M.Chung: "Topological entropy for differential maps of intervals"Osaka J. Math.. 38. 1-12 (2001)
[Publications] F.Maitani: "Ahlfors-Rauch type variational formulas on complex manifolds"Mem. Fac. Eng. And Design Kyoto Inst. Tech.. 49. 19-36 (2001)
[Publications] H.Ishida: "Conformal imbeddings of Denjoy domains"Acta Human. Sci. Univ. Sangio Kyotiensis. 30. 1-7 (2001)
[Publications] 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)
[Publications] M.Masumoto: "Extremal lengths of homology classes on compact Riemann surfaces"Nonlinear Analysis, Theory, Methods and Applications. 47. 5491-5500 (2001)
[Publications] T.Futamura: "A generalization of the Liouville theorem to polyharmonic functions"J. Math. Soc. Japan. 53. 113-118 (2001)
[Publications] T.Futamura: "A generalization of Boche's theorem for polyharmonic functions"Hiroshima Math. J.. 31. 59-70 (2001)
[Publications] T.Futamura: "Existence of functions in weighted Sobolev spaces"Nagoya Math. J.. 164. 75-88 (2001)
[Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math. Pures Appl.. 46. 67-75 (2001)
[Publications] S.Nagamachi: "Hyperfunction quantum field theory : Analytic structure, modular aspects, and local observable algebras"J. Math. Phys.. 42・1. 99-129 (2001)
[Publications] T.Nishimura: "Support and Kernel theorem for Fourier hyperfunctions"Osaka J. Math.. 38・3. 667-680 (2001)
[Publications] E.Bruening: "Kernel Theorem for Fourier hyperfunctions"J. Math., The Univ. Tokushima. 35. 57-64 (2001)
[Publications] 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)
[Publications] A.Ramani: "A geometrical description of the discrete Painleve VI and V equations"Comm. Math. Phys.. 217・2. 315-329 (2001)
[Publications] A.Ramani: "The q-Painleve V equation and its geometrical description"J. Phys. A : Math. Gen.. 34・11. 2505-2513 (2001)
[Publications] Y.Ohta: "A bilinear approach to a Pfaffian self-dual Yang-Mills equation"Glasgow Math. J.. 43A. 99-108 (2001)
[Publications] S.Lafortune: "Blending two discrete integrability criteria : Singularity confinement and algebraic entropy"CRM Proceedings and Lecture Notes. 29. 299-311 (2001)
[Publications] Y.Ohta: "An affine Weyl group approach to the eight-parameter discrete Painleve equation"J. Phys. A : Math. Gen.. 34・48. 10523-10532 (2001)
[Publications] S.Kakei: "A differential-difference system related to toroidal Lie algebra"J. Phys. A : Math. Gen.. 34・48. 10585-10592 (2001)
[Publications] K.Kajiwara: "Determinant formulas for the Toda and discrete Toda equations"Funkcial. Ekvac.. 44・2. 291-307 (2001)
[Publications] S.Seto: "Source identification of rural precipitation chemistry in Japan"Water, Air, and Soil Pollution : Int. J. Environmental Pollution. 130. 493-498 (2001)
[Publications] 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)
[Publications] 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)
[Publications] M.Sato: "Source Apportionment in "The Encyclopedia of Environmetrics""Wiley(分担執筆). 2033-2036 (2002)

2001 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, 大学院・工学研究科, 教授 (70025469)

Research Products

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

[Publications] 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)

[Publications] 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)

[Publications] 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)

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

[Publications] 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)

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

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

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

[Publications] 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)

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

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

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

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

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

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

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

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

[Publications] 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)

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

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

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

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

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

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

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

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

[Publications] 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)

[Publications] 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)

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

柴雅和広島大学, 大学院・工学研究科, 教授 (70025469)