2004•Progress in geophysicsRequires access

Fractal dimension structure of Cosmos and its mathematical foundations

Kun Yan

Abstract

Fractal dimension structure form of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, of fractal dimension calculus and fractal measure are given. As annotation, an equation of the relation between neutrons and protons in nuclei and its periodical solutions as well as atomic number limit are discussed.

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Key concepts: Fractal derivative, Fractal, Fractal dimension, Fractal dimension on networks, Minkowski–Bouligand dimension, Mathematics, Measure (data warehouse), Calculus (dental)