Loo-Keng Hua

Geometries of matrices. I. Generalizations of von Staudt’s theorem

It was first shown in the authors recent investigations on the theory of automorphic functions of a matrix-variable that there are three types of geometry playing important roles. Besides their applications, the author obtained a great miany results which seem to be interesting in themselves. The main objec t of the paper is to generalize a theorenm due to von Staudt, which is known as the fundamental theorem of the geometry in the complex domain. The statement of the theorem is:

On the Calculation of Mineral Reserves and Hillside Areas on Contour Maps

Our geographers, mineralogists and geologists have presented many practical methods for calculating mineral reserves and hillside areas which enable us to engage in further investigations. In the present paper the authors attempt to compare these methods, to interpret their mutual relations and implicit errors, and to present some suggestions.