We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
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 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....
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
Siegel domains. Modular groups. Hecke algebras. Forms
In the 1960s Satake proved the existence of an isomorphism between the local Hecke algebra and the ring of polynomials invariant under the action of the signed permutation group W n (the Weyl group associated to Sp n over a local field)....
Cancer Control Program (National Cancer Institute) -- Evaluation. Cancer -- Treatment -- United States -- Evaluation. Cancer -- Patients -- Care -- Evaluation.
Background. Disparities in access to cancer care and cancer-related outcomes have been demonstrated in the U.S. Patterns of access to National Cancer Institute-designated Cancer Centers (NCI-CCs), the most specialized cancer care settings, have not...
Primary care (Medicine) -- United States -- Evaluation. ; Medicine -- Specialties and specialists. ; Physicians -- Supply and demand -- United States.
Background. Strengthening the role of primary care is considered a key element in improving the outcomes and efficiency of health care delivery. Previous studies of the benefits of primary care have primarily examined the association of primary...
Problem Statement: Increasing physical activity is a priority for decreasing obesity rates, but we have a limited understanding of which factors are most influential in promoting physical activity among adolescents. We also do not know what forms...
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...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
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...
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector...
Nursing services -- United States -- Evaluation. Nursing services -- United States -- Personnel management. Hospitals -- United States -- Administration. Outcome assessment (Medical care). Nursing Service.
Primary care (Medicine) -- United States -- Evaluation.
Medicine -- Specialties and specialists.
Physicians -- Supply and demand -- United States.
Background: Strengthening the role of primary care is considered a key element in improving the outcomes and efficiency of health care delivery. Previous studies of the benefits of primary care have primarily examined the association of primary...
This thesis focuses on the emergence of universal dynamical scaling in quantum critical spin systems driven out of equilibrium, with emphasis on quench dynamics which involves isolated standard critical points, multi-critical points, and...