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ABSTRACT:The present Part V of this series of articles is devoted to the initial development of the theory of generalized repeat space for a study of the correlation between the structure and properties in molecules having many identical moieties. An element of generalized repeat space, referred to as a generalized repeat sequence, is a d-dimensional generalization of a complex matrix version of repeat sequence, which we studied in Part IV of this series of articles. The generalized repeat space, which satisfies the axioms of a complex U -algebra, is a far-reaching extension of the original repeat space, and we present here the fundamental theorems as an initial step toward the formation of the theory of the generalized repeat space.

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ABSTRACT:The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows.

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