Unified computational approach to nilpotent algebra classification problems

A unified approach to network location problems

In this paper we introduce a new type of single facility location problems on networks which includes as special cases most of the classical criteria in the literature. Structural results as well as a nite dominating set for the optimal locations are developed. Also the extension to the multi-facility case is discussed.

Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing

We use the concept of the algebra eigenstates that provides a unified description of the generalized coherent states (belonging to different sets) and of the intelligent states associated with a dynamical symmetry group. The formalism is applied to the two-photon algebra and the corresponding algebra eigenstates are studied by using the Fock-Bargmann analytic representation. This formalism yiel...

Problems in Computational Algebra and Integer Programming

Problems in Computational Algebra and Integer Programming Tristram Bogart Chair of the Supervisory Committee: Associate Professor Rekha R. Thomas Department of Mathematics This thesis is a compendium of several projects that span the gap between commutative algebra and geometric combinatorics: one in tropical geometry, one in computational algebra, and two in discrete geometry and integer progr...

A Computational Approach to Foreign Accent Classification

A computational approach to stability problems

A polytope in R is said to be stable on a facet if and only if the perpendicular to that facet through the center of gravity meets the facet itself. One may consider the stability of a body with respect to an arbitrary "center of gravity on the interior of the body [1,3,6], or one may take the center of gravity to be determined by the shape of the body itself. Most typically, the center of grav...