Structural Analysis on Certain Linear Operators Representing Chemical Network Systems via the Existence and Uniqueness Theorems of Spectral Resolution VII

摘要

The present Part VII of this series of articles is a direct extension of Part VI,where (1) fundamental methodology in the repeat space theory (RST) and (2) Frontier electron theory of reactivity indices were theoretically linked.This part presents an estimate of the size of the regular index set,which was a central notion in Part VI,and two new theorems that are simpler and more powerful than the main theorem in Part VI.The main theorem in this part enables one to globally contextualize the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in Part V) and the mu~(io,jo) Existence Theorem (derived from the main theorem in Part VI) into the star algebra structure of the generalized repeat space &,(q.d).