Advances in Mathematics Research : Volume 26

The opening chapter aims to show the importance of mathematical means associated with the role of Pythagorean musical tradition in mathematical and architectural contexts up to the Renaissance. The following chapter proposes a formalism which enables us to separate fields of investigation from the epistemological questions in philosophy and to consider models as parts of hierarchical model families. Continuity of the modulus and phase degrees-of-freedom of molecular electronic states is commented upon in the next section, and the resultant entropy/information descriptors of electronic states, combining the probability and current contributions, are applied to classical issues in chemical-reactivity theory. Additionally, the authors study the categorical generalisations of the Möbius function emphasising the geometric meaning of these constructions, and discuss the relations between the various approaches. The final chapter introduces the PWP method as a technique for measuring indirect influences in complex networks.