Repeat space theory applied to carbon nanotubes and related molecular networks. II

Abstract

The present article is part II of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. In this part II, three new versions of the Asymptotic Linearity Theorems, which are central in the RST and played a key role in part I of this series, have been established in a new theoretical framework of the generalized repeat space ${\fancyscript {X}}_{\rm r}(q,d)$. These new versions of theorems, which prove the Fukui conjecture and solve additivity and molecular network problems in a context broader than before, unite the present series and the seven paper series of structural analysis of chemical network systems published in the International Journal of Quantum Chemistry. Along with the Fukui conjecture, which is the guiding conjecture of the RST, the research target of mathematical and computational modeling called the ‘virtual nanotube tip RST atomic force microscopy’ has been set up in connection with a variety of modern microscopy useful for nanoscience and technology.