Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...
Chapter 1: Munchnones and mesoionic heterocycles The reactivity, regioselectivity, and synthetic applications of munchnones (1,3-oxazolium-5-olates) is a common theme which runs through Chapters 2-5. The definition, structure, and reactivity of...
Access control is a core component of any information-security strategy. Researchers have spent tremendous energy over the past forty years defining abstract access-control models and proving various properties about them. However, surprisingly...
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 Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
Black-throated blue warbler -- Habitat. Black-throated blue warbler -- Behavior. Black-throated blue warbler -- Food. Black-throated blue warbler -- Nests.
Ice mechanics. Compressibility. Fracture mechanics. Strains and stresses. Brittleness.
This work describes the effect of triaxial compressive confinement on the strength of columnar S2 ice loaded under conditions leading to brittle failure. Cubes of columnar S2 ice were tested at -10 Â°C under triaxial (proportional) loading where...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
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...
Clinical medicine -- Decision making. ; Medical informatics. ; Patient participation. ; Osteoarthritis -- Treatment. ; Knee -- Diseases -- Treatment. ; Decision Making. ; Decision Support Techniques.
Problem Statement. Effective patients' decision aids (PtDAs) help patients understand clinical information and reduce decisional conflict. PtDAs that also explicitly provide guidance through four """"Deliberative Steps"""" may achieve additional...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Many alkaloids of biological importance have the 11H-pyrido (4,3,2-mn) acridine ring structure such as cystodytin and amphimedine. It would be desirable to find an effective way to synthesize a wide variety of these compounds using a single...
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...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...