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Research on Equilibrium Vector Potentials

Research Project

Project/Area Number 09640181
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionShiga University

Principal Investigator

OOKUBO Katsumi (1999)  Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (80024933)

山口 博史 (1997-1998)  滋賀大学, 教育学部, 教授 (20025406)

Co-Investigator(Kenkyū-buntansha) MURAKAMI Ichirou  Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (70210002)
YAMAZOE Shirou  Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (10075137)
NIWA Masahiko  Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (00024969)
YAMAGUCHI Hiroshi  Nara Women Univ., Faculty of Science, Prof., 理学部, 教授 (20025406)
SUGIE Touru  Shiga Univ., Faculty of Education, Ass. Prof., 教育学部, 助教授 (90135509)
大久保 克己  滋賀大学, 教育学部, 教授 (80024933)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥600,000 (Direct Cost: ¥600,000)
KeywordsElectro-magnetic fields / Solenoid / Equilibrium vector potential / Surface current density / Bochnar-Martinelli / Bergman metric / ベクトルポテンシャル / Stein manifald / Robin constant / group completions / モノイド圏 / 2階変分公式
Research Abstract

The mathematical research of the electric condenser at the beginning of 20 century introduced the notion "equilibrium scalar potential". In the previous work we introduced the new notion "equilibrium vector potential" from the study of the electric solenoid. Namely, for the given closed surface Σ in the Eulidean space RィイD13ィエD1, we can construct the surface current density T on Σsuch that T induces the magnetic fields B only inside the domain D bounded by Σ, that is, B is identically zero outside D. We call such T and B the equilibrium surface current density and equilibrium vector field for Σ. We also call its generating vector field A such that rot A = B the equilibrium vector potential for Σ. In this research we construct the algorithm (the alternating method with significant meaning from the electromagnetisms) along which we can obtain such current density T on Σ from the arbitrarily given surface current density TィイD20ィエD2 on Σ with trivial conditions. This algorithm suggests the possibility of obtaining the equilibrium surface current density T for Σ by the computational method.
In another research we try to extend the above phenomena in the case RィイD13ィエD1 to the case of the complex Euclidean space CィイD1nィエD1, and showed that, in the special case, this corresponds to the famous Bochnar-Martinelli theorem. This suggest the existence of the equilibrium vector potentials in the case of CィイD1nィエD1.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] 大久保克巳: "Three dimensional geometry"Proc. 32^<nd> Symposym of Finsler Geometry. 64-67 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 山口博史: "複素及びベクトルポテンシャル論"数学「論説」日本数学会. 50. 225-247 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 丹羽雅彦: "Group Conpletier I"滋賀大学教育学部紀要. 48. 67-74 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 杉江徹: "Siugular fibers of honwlogy planes with pencils"滋賀大学教育学部紀要. 50(予定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] U. Cegrell, 山口博史: "Construction of Equilibrium Magneticvecter Potentials"Potential Analysis (Kluwer社). (予定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 山口博史、米谷文男: "Behavior of Bergman Metric undergran-conformal maps"Proc. 6th international coll. of finite cr infiniteclim. of complex analysis. 167-175 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Levenberg、山口博史: "Translation 「Function Theory of several complex vaiables」"「西野利雄著 多変数函数論」の英訳、アメリカ数学会. 450 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katumi Ookubo: "Three dimensional hyperbolic geometry"Proc. 32ィイD1thィエD1 symp. of Finsler geometry. 64-67 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshi Yamaguchi: "Theory of Complex and vector potentials"Ronsetsu (Suugaku), JMS. Vol.50. 225-247 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masahiko Niwa: "Group completion I"J. of Faculty of Education of Shiga Univ.. Vol.48. 67-74 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Touru Sugie: "Singular fibers of homology planes with pencils"J. of Faculty of Education of Shiga Univ. (to appear). Vol.50 (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Urban Cegrell and Hiroshi Yamaguchi: "Construction of equilibrium magnetic vector potentials"Potential Analysis (Kluwer pub). (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Norman Levenberg and Hiroshi Yamaguchi: "Translation of the book "Function theory in several complex variables" (in Japanese)"written by Toshio Nishino, AMS (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 大久保克巳: "Three dimensional hyperbolic Geometry"Proc.32nd symposium of Fiusler geometry. 64-67 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] 山口博史: "複素およびベクトルポテンシャル論"数学「論説」 日本数学会. 50. 225-247 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 丹羽雅彦: "Group completion I : Observation of Category theory view point"滋賀大学 教育学部 紀要. 48. 67-74 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 杉江 徹: "Singular fibers of homology planes with pencils"滋賀大学 教育学部 紀要. 50(予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] U.Cepell - 山口博史: "Construction of Equilibrium magnetic vector potentials"Potential Analysis (Kluwer社). (予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 山口博史-米谷: "Behavior of Bergman metric under quasi-conformal maps"Proc.6th international coll.of finite or infinite dim of complex analysis. 167-175 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] N,Levenberg-山口による: "Function Theory of several comlex variables"「西野利雄著 多変数函数論」の英訳、アメリカ数学会. 450 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 山口博史: "複素及びベクトルポテンシャル論" 数学(日本数学会). 50. 225-247 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.eveuberg,山口博史: "Robin functions for complex manifald and applications" (京大)数理科学論究録. 1037. 138-142 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 山口博史,米谷文男: "Behavior of Bergman metric under quariconfornal leformation" Proceeding of the 6th international cell an finito and infnite dimensional complex analysis(Audon,Korea). 6. 167-175 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 丹羽雅彦: "Group Conpletion I : An obsevation from Category-Theoutical pt of view on the ordinary group conpletions of amns" 滋賀大学 教育学部紀要. 48. 67-74 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 佐野圭太-大久保克己: "Fundimensional indefinito metric geomaty" Proceedings of the 33rd Symposium on Fiusler geonty. 33. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Levenberg-H.Yamaguchi: "Robin functions for complex manifolds and application" 数理解析研究所講究録 edited by T.Akahori. 予定. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 山口 博史: "領域の変動に関する2階変分公式" 総合講演・企図特別講演アブストラクト(日本数学会). 72-81 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 村上 一三: "図形教育における形式的証明のあり方についての一考察" 第30回論文発表会論文集(日本数学教育学会). 409-414 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 村上 一三: "図形教育のあり方をめぐって-小中高一貫の立場から" 「テーマ別研究部会」発表集録(日本数学教育学会). 111-118 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 山添 史郎: "ロジスティックモデルにおける信頼領域" 滋賀大学教育学部紀要III:自然科学. 47. 41-46 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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