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...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
An interval order is an ordered set whose elements are in correspondence with a collection of intervals in a linearly ordered set, with disjoint intervals ordered by their relative position. The order complex of an ordered set is the simplicial...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
Indole alkaloids -- Synthesis. Ring formation (Chemistry). Radicals (Chemistry).
A novel radical cyclization of 2-bromoindoles was examined, generating a series of hexahydropyrrolo[3,4- b ]indoles in fair yield. This process involved the generation of a variety of indole-3-carboxamides followed by the introduction of bromine at...
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...
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....
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
The oxygen-dependent microbicidal events of neutrophils have been studied with reference to the triggering of the respiratory burst and with particular emphasis on the role of quinone. Ubiquinone as well as a previously described cytochrome b were...