This award supports the collaboration between Professor J. Hemmeter and Professor V. Ustimenko of the University of Kiev under the USA/USSR program for cooperation in the field of basic scientific research. The research is concerned with the theory of association schemes and cellular rings in algebraic combinatorics. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And, so it is extremely important to modern communications, for example the design of large networks as in telephone systems and the design of algorithms in computer science.