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 is divided into 2 parts. In the first part of the thesis, we describe a software based approach to speeding up the Magnetic Resonance Imaging modality. In the second part of the thesis, we describe Significance Tree Quantization, which...
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...
I consider the problem of extending certain invariants of subsets of natural numbers to their equivalents for subsets of larger cardinals. The two specific questions I will address are the extension of the off-branch number [Special characters...
Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles Ï‰ = {Ï‰[subscript t]}[subscript tâˆŠ[0,1]] on a locally compact Hausdorff groupoid Æ“ induces an isomorphism of the...
The Euler '-function and Carmichael -function are extremely important in modern number theory, and much work has been devoted to studying the distribution and arithmetic properties of the values of each function. One interesting unresolved question...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Î‘ is an order of level M in H , we define theta series for each ideal I of Î‘ using the reduced norm on H. Using harmonic analysis...
Plant genetic engineering. ; Plants -- Effect of cadmium on. ; Cadmium -- Physiological transport.
Iron plays a central role in key biological processes in both plants and animals. Lack of available iron commonly limits plant growth and nutritional value. Worldwide, dietary iron is primarily obtained from plant sources and, despite our best...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...