This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of the...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...
Large-scale (12,000 liter) and small-scale (3.78 liter) field enclosure experiments were conducted to evaluate the intensity and nature of competition among the planktonic cladoceran grazers of a mesotrophic Vermont lake: Bosmina longirostris,...
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....