The rst part of this paper classi es all purely cubic function elds over a nite eld of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function eld of unit rank 1 and characteristic at least 5. The technique is based on Voronoi's algorithm for generating a chain of successive minima in a multipli...

Reverse osmosis (RO). has become a standard unit operation in Chemical Engineering. This separation process can be used for a wide variety of applications including: desalination of sea water, treatment of industrial wastes, concentration of food products, and recovery of value materials from solution mixtures. In order to best utilize RO it is necessary to have a fundamental understanding of t...

The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1 and characteristic at least 5. The technique is based on Voronoi’s algorithm for generating a chain of successive minima in...