This award will support collaborative research in applied mathematics between Dr. George Baker, Los Alamos National Laboratory and Professor P.R. Graves-Morris, Bradford University, West Yorkshire, England. The objective of this investigation is to develop the theory and practice of approximation methods, based on Taylor series expansions which go beyond the first Riemann sheet. The proposed work will be based on approximations by the solution of differential equations. The investigators will apply recently developed theoretical techniques, develop new ones and supplement them by numerical investigations. The results of this research are expected to have wide applica- tions. One case in point is the theory of critical phenomena, which has suffered from lack of methods to interpret adequately the complex singular structure at some of the harder critical points. Both Dr. Baker and Dr. Graves Morris are established mathematical physicists, who have made important contributions to the theory of applications of Pade approximants.
