| Institution: | (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 s, A1B 3X7, NL, Canada |
| Abstract: | The present article is the preliminary part of a series devoted to extending the foundation of the Asymptotic Linearity Theorems (ALTs), which prove the Fukui conjecture concerning the additivity problem of the zero-point vibrational energies of hydrocarbons. In this article, we establish a theorem, referred to as the
 Boundedness Theorem, through which one can easily form a chain of logical implications that reduces a proof of the Fukui conjecture to that of the Piecewise Monotone Lemma (PML). This chain of logical implications serves as a basis throughout this series of articles. The PML, which has been indispensable for demonstrating any version of the ALTs and has required for its proof a mathematical language not generally known to chemists, is directly related to the theory of algebraic curves. Proofs of the original and enhanced versions of the PML are obtainable via resolution of singularities and related methods.Dedicated to the memory of Prof. Kenichi Fukui (1918–1998). |
