Note on the Repeat Space Theory

Abstract

This note provides a chronological sketch of the development from the early 1990s of the Repeat Space Theory (RST), which had originated in the study of the zero-point energy additivity problems of hydrocarbons in 1985. Interacting with the theories of dynamical systems, operator algebra, and so forth, the RST has developed into a comprehensive theoretical framework of axiomatic nature, which unites and solves, in particular, what we call globally-pertaining-type problems, or, for short, g-type problems; these constitute physico-chemical problems for whose solutions global mathematical contextualization is essential. In conjunction with the author's communications with Prof. Kenichi Fukui, the genesis of the notion of g-type problems has also been presented in this note. Through the vision the RST provides, it is foreseeable that investigations of the peripheral research domains of g-type problems in chemistry will play a significant role for future investigations, especially for those related to macromolecules, physico-chemical network systems, and biochemical network systems, in the vast uncharted interdisciplinary regions between chemistry and modern mathematics.