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Proof of the Fukui conjecture via resolution of singularities and related methods. V. (English) Zbl 1262.92073

Summary: The present article is a direct continuation of part IV of this series [J. Math. Chem. 48, No. 3, 776–790 (2010; Zbl 1262.92072)]. 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 elucidated by using tools from the theory of algebraic and analytic curves. Here we complete the proof of the LAP1 by using fundamental tools developed in parts III [ibid. 47, No. 2, 856–870 (2010; Zbl 1262.92071)] and IV of this series, thus completing the proof of the Fukui conjecture via resolution of singularities and related methods. This series of articles 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.

MSC:

92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
58K05 Critical points of functions and mappings on manifolds
65C20 Probabilistic models, generic numerical methods in probability and statistics
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