Proof of the Fukui conjecture via resolution of singularities and related methods. II $$^{\star}$$
作者: Shigeru ArimotoMark SpivakovskyKeith F. TaylorPaul G. Mezey
作者单位: 1Department of Chemistry, University of Saskatchewan
2Laboratoire de Mathematiques Emile Picard, Unité Mixte de Recherches CNRS (UMR 5580), UFR MIG, Université Paul Sabatier
3Department of Mathematics and Statistics, Dalhousie University
4Canada Research Chair in Scientific Modeling and Simulation, Chemistry Department, Memorial University
刊名: Journal of Mathematical Chemistry, 2005, Vol.37 (2), pp.171-189
来源数据库: Springer Nature Journal
DOI: 10.1007/s10910-004-1449-5
关键词: additivity problemsasymptotic linearity theorem (ALT)Fukui conjecturerepeat space theory (RST)resolution of singularities
英文摘要: Abstract(#br)The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the “asymptotic linearity phenomena” is extracted and is elucidated by using tools from the mathematical theory of...
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影响因子:1.226 (2012)

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