关键词: simplex, mid-facet, median line, Grassmann algebra, geometric inequality

Abstract: In this paper, we propose a competition-share 3-category principle, on which we unite the problems of natural resources, energy, population and environment and so on into a mutual scheme, and provide a united model for the comprehensive research on these problems. This makes the idea of operation analysis of natural resources clearer and the relationships between each of their parts more obvious. On the basis of the above discussion, we propose mathematical models for the operation analysis of multi-networks and the solution of the above global comprehensive problems. We discuss, especially, Shengke(growth and restraint) relationships between two networks of natural resources and share-competitors and their analysis models, providing mathematical tools for solving the problems of the resource-population and the resource-economy, etc.

Key words: simplex, mid-facet, median line, Grassmann algebra, geometric inequality