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Studies on Dynamical systems

Research Project

Project/Area Number 03640099
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionNihon University

Principal Investigator

SUZUKI Osamu  The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (10096844)

Co-Investigator(Kenkyū-buntansha) MOTEGI Kimihiko  The College of Humanities and Sciences, Nihon Univ., Department of Math., Lect.,, 文理学部, 講師 (40219978)
YAGUCHI Teruo  The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (50059987)
NISHIOKA Kumiko  The College of Humanities and Sciences, Nihon Univ., Department of Math., Asso., 文理学部, 助教授 (80144632)
SAKAI Shoichiro  The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (30130503)
SUZUKI Masahiko  The College of Humanities and Sciences, Nihon Univ., Department of Math., Asso., 文理学部, 助教授 (00171249)
黒田 耕嗣  日本大学, 文理学部, 助教授 (50153416)
橘 貞雄  日本大学, 文理学部, 助教授 (70060035)
武笠 敏夫  日本大学, 文理学部, 教授 (00059750)
釜江 慶子  日本大学, 文理学部, 助教授 (60059566)
Project Period (FY) 1991 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1991: ¥600,000 (Direct Cost: ¥600,000)
Keywordsgauge thery / flat extension therem / devergence in quantum field theory / Symmetry structure / algebroid / anomaly / 相転移 / K.M.S状態 / ゲージ接続 / 平坦拡張定理 / 非可変微分幾何 / 量子場の発散 / algebroid / 指数定理 / Gauss-Bonnet定理 / Singular pertuvbation / flat connection / Diff.eq.of Fuchsian Type / dynamical system / singular pertubation / constrained sysytem / quantum field theory / gauge connection / renormalization / anomaly / B.R.S.transformation
Research Abstract

A new formalism for gauge connections is given and monlinear gauge eauations are solved and the divergence of quantu field theory is discussed. The following results are obtained.
(1) A gauge theory is formulated in termas of a certain kind of a decomposition of a linear space, whitch is called a "gauge decomposition." Then every gauge connection connection can be extended to a flat connection, when it admits a representation in some algebra (flat extension theorem).
(2) By use of the result (1), nonlinear gauge equations can be solved by use of a decomposition of a solution of a linear equation. Symmetry structures and special class of silutions can be discussed as a "Galois thery for differntial equations". When it has a representation in "algebroids", divergece appears and anomaly and renormalization can discussed in this case.

Report

(4 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • 1991 Annual Research Report
  • Research Products

    (41 results)

All Other

All Publications (41 results)

  • [Publications] 鈴木理: "Supercomplex structures,surface soliton equations,and quasiconformal mappings" Ann.Polo.Math.55. 245-268 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 鈴木理: "Hermitian Hurwitz pairs" Deformations of Mathematical Structures II Kluwer Academic Publ.135-154 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 鈴木正彦: "Stability of Newton boundaries of real analytic singularities" Trans.Amer.Math.Soc.323-1. 133-150 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 西岡久美子: "Algebraic independence mesures of values of Mahler functions" J.reine angew.Math.420. 203-214 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 谷口彰男: "On the radii of starlikeness o d convexity for certain multivalent functions" Pro.Inst.Nat.Scie.Nihon Univ.26. 87-94 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 茂手木公彦: "Knotting trivial knots and resulting knot types" Pacific.J.Math.161-2. 371-383 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 鈴木理(編著): "Deformations of Mathematical Structures,Hurwitz type structures and applications to surface Physics" Kluwer Academic Publ., 461 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 境正一郎: "Operator algebras in dynamical systems" Cambridge Univ.Press, (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUK,O: "Supercomplex structures, surface soliton equations, and quasiconformal mappings" Ann.Polo.Math. 55. 245-268 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUKI,O: "A geometric approach to the Kadomtsev-Petviasvili systems(II)" Proc. Inst.Nat.Scie. Nihon Univ. 26. 51-68 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUKI,O: "(III), i.b.i.d" Ann.Polo.Math. 26. 85-105 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUKI,M: "Stability of Newton boundaries of real analy6tic singularities" Trans.Ame. Math. Soc. 323.1. 133-150 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] NISHIOKA,K: "New approach in Mahler's method" J.reine.angew.Math. 407. 202-219 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] NISHIOKA,K: "Algebraic independence measures of values of Mahler functions" J.reine. angew.Math. 420. 203-214 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] YAGUCHI,T: "On the Radii of starlikeness and convexity for certain multivalent functions" Pro.Inst.Nat.Scie., Nihon Univ. 26. 87-94 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] MOTEGI,K: "Are Knots obtained from a plain pattern always prime?" Kobe.Math.9. 39-42 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] MOTEGI,K: "Twisting and knot types" J.Math.Soc.Japan. 44. 199-216 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] MOTEGI,K: "Behavior of knots under twisting" Adv.Studies.in pure Math. 20. 113-124 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] MOTEGI,K: "Primeness of twisted knots" Proc.Amer.Math.Soc. 119,3. 979-983 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] MOTEGI,K: "Knotting trivial knots and resulting knot types" Pacific J.Math. 161,2. 371-383 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUKI,O: Hermition Hurwitz pairs, Deformations of Mathematical structure II. Kluwer Academic Publ, 135-154 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUKI.O: The duality theorem for the Hurwitz pairs of bidimension (8,5) and the Penrose theory. Kluwer Academic Publ, 209-212 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] SUZUKI,O: Stochastical mechanics of particle systems in Clifford-analytical formulation related to Hurwitz pairs of bidimension(8,5). Kluwer Academic Publ,

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 鈴木理: "Supercomplex structures,surface soliton equations and quasiconformal mappings" Ann.Polo.Math.55. 245-268 (1991)

    • Related Report
      1993 Annual Research Report
  • [Publications] 西岡久美子: "Alge〓〓aic independense mesures of values of Mahler functions" J.reine angew.Math.420. 203-214 (1991)

    • Related Report
      1993 Annual Research Report
  • [Publications] 谷口彰男: "On the radii of starlikeness and convexity for certain multivalent functions" Proc.Inst.N.Scie.,Nihon Univ.26. 87-94 (1991)

    • Related Report
      1993 Annual Research Report
  • [Publications] 鈴木正彦: "Stability of Newton boundavies of real analytic singulanties" Trans.Amev.Math.Soc.323. 133-150 (1991)

    • Related Report
      1993 Annual Research Report
  • [Publications] 茂手木公彦: "Knotting trivial knots and resulting knot types." Pacific.J.Math.161.2. 371-383 (193)

    • Related Report
      1993 Annual Research Report
  • [Publications] 黒田耕嗣: "Limit theorem and large deviation principle for Voronoi Tessellation generated by a Gibbs point process" Adv.Appl.Prob.24. 45-72 (1992)

    • Related Report
      1993 Annual Research Report
  • [Publications] 鈴木理(編著): "Deformations of Mathematical Structuves" Kluwer Academic Pub., 461 (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] 西岡久美子: "Mahler関数と超越数" 慶応大学, (1991)

    • Related Report
      1993 Annual Research Report
  • [Publications] (O.Suzuki) 鈴木 理 (他2名): "Dualities generated by the generalised Hurwitz problem and variation of the Yang-Mills fields" (to appear) in Lecture Note in Math, Springer.

    • Related Report
      1992 Annual Research Report
  • [Publications] (O.Suzuki) 鈴木 理 (他3名): "Stochastical mechanics of particle system in Clifford-analyticul formulation related to Huvwife pair of bidimen sion (8.5)" (to appear) in Kulwer Academic Publisher.

    • Related Report
      1992 Annual Research Report
  • [Publications] (O.Suzuki) 鈴木 理 (他3名): "Hermifian Huruifz pair" (to appear) in Kulwer Academic Publisher).

    • Related Report
      1992 Annual Research Report
  • [Publications] (K. Motegi) 茂手木 公彦: "Knotting trivial Rnots and resulting rnot type" (to appear) in Pacific J. Math.

    • Related Report
      1992 Annual Research Report
  • [Publications] (K.Motegi) 茂手木 公彦: "Primeness of twisted knots" (to appear) in Proc. Amer. Math. Soc.

    • Related Report
      1992 Annual Research Report
  • [Publications] (O.Suzuki) 鈴木 理: "ゲージ接続の平担拡張定理と発散の正則化" 数理研講究録(「非線型可積分系の研究の現状と展望」).

    • Related Report
      1992 Annual Research Report
  • [Publications] O.Suzuki: "Supercomplex structures,surface soliton equations,and quasiconformal mappings" ANNALES POLONICI MATHEMATICI. 55. 245-268 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] M.Suzuki: "Stablility of Newton boudaries of a family of real analytic singularites" Transactions of AMS,. 323. 133-150 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] K.NISHIOKA: "Algebraic independence of functions satisfying a certain type of functional equations" J.reine angew.Math.420. 203-214 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] S.Sakai: "Operator algebras in dynamical systems" Cambridge University Press, 219 (1991)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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