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Journal of Mathematical Chemistry

, Volume 49, Issue 8, pp 1700–1712 | Cite as

Proof of the Fukui conjecture via resolution of singularities and related methods. V

  • Shigeru ArimotoEmail author
  • Mark Spivakovsky
  • Eiji Yoshida
  • Keith F. Taylor
  • Paul G. Mezey
Original Paper

Abstract

The present article is a direct continuation of part IV of this series. The Local Analyticity Proposition (LAP1), which admits a proof via resolution of singularities is a major key to proving the Fukui conjecture via resolution of singularities and related methods. By LAP1, the essential part of the mechanism of the “asymptotic linearity phenomena” is extracted and is elucidated by using tools from the theory of algebraic and analytic curves. Here in the present article, we complete the proof of the LAP1 by using fundamental tools developed in parts III and IV of this series, thus completing the proof of the Fukui conjecture via resolution of singularities and related methods. This series of articles I-V establishes, for the first time, a new linkage between (i) the mathematical field of resolution of singularities and (ii) the chemical field of additivity problems tackled and solved in a unifying manner via the repeat space theory (RST), which is the central theory in the First and Second Generation Fukui Project. A new development called the Matrix Art Program in the Second Generation Fukui Project has also been expounded with a graphical representation of energy band curves of a carbon nanotube.

Keywords

Fukui conjecture Repeat space theory (RST) Asymptotic linearity theorem (ALT) Resolution of singularities Matrix art Asymptotic linearity theorem extension conjecture (ALTEC) 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Shigeru Arimoto
    • 1
    Email author
  • Mark Spivakovsky
    • 2
  • Eiji Yoshida
    • 1
  • Keith F. Taylor
    • 3
  • Paul G. Mezey
    • 4
  1. 1.Division of General Education and ResearchTsuyama National College of TechnologyTsuyama, OkayamaJapan
  2. 2.Institut de Mathematiques de Toulouse, Unité Mixte de Recherche CNRS (UMR 5219) UFR MIGUniversité Paul SabatierToulouse Cedex 9France
  3. 3.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada
  4. 4.Canada Research Chair in Scientific Modeling and Simulation, Chemistry DepartmentMemorial UniversitySt. John’sCanada

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