The Department of Mathematics at the University of Hawaii will purchase computer equipment and software which will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular: Differentiation and the Distribution of Zeros of Functions; Lattice Theory; Learning, Generalization and Model Construction in First-Order Logic; and Symbolic and Numerical Analysis of Ordinary and Partial Differential Equations. The first project is concerned with the effect of differentiation of the distribution of zeros of polynomials and certain other functions. New techniques involving geometric mapping properties will be employed to study several well-- known conjectures. The second project will use recent advances in free and finitely presented lattices to study unsolved problems in lattice theory, including solving equations in free lattices and finding the covers of finitely generated lattice varieties. The third project will study various aspects of mechanical theorem proving. The fourth project will search for normal forms and natural geometric structures associated with control systems.
