| Affiliation: | (1) Department of Chemistry, University of Saskatchewan, 110 Science Place, Saskatoon, SK, Canada, S7N 5C9;(2) Laboratoire de Mathematiques Emile Picard, Unité Mixte de Recherches CNRS (UMR 5580), UFR MIG, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France;(3) Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada, B3H 3J5;(4) Canada Research Chair in Scientific Modeling and Simulation, Chemistry Department, Memorial University, St. John!["rsquo"]("/content/p7152052706207q4/xlarge8217.gif") s, NL, Canada, A1B 3X7 |
| Abstract: | 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 algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism.Dedicated to the memory of Prof. Kenichi Fukui (1918–1998). |
