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...
The demand for novel molecularly targeted drugs will continue to rise as we make progress toward personalizing cancer treatments to the molecular signatures of individual tumors. While the collection and analysis of genomic data has become routine,...
We begin with a result on the refocussing of null geodesics in space-times. We show that all oriented refocussing 2-dimensional Lorentz manifolds are also strongly refocussing. We also introduce a theory of virtual Legendrian knots. We show that...
Breast cancer is the most common cancer in women. The discovery of breast tumor subtypes and the subsequent development of treatments aimed at them has allowed a reduction in the mortality of breast cancer. However, tumors with similar...
Epilepsy is associated with cognitive impairments which often manifest as a higher prevalence of memory impairments. Memory impairments in patients with epilepsy may persist even with sufficient control of seizures, suggesting other factors may...
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 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 consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Robustness to genetic perturbations is a fundamental property of all living things. The genetic code is degenerate, RNA secondary structure is robust to sequence changes, and protein structure is robust to amino acid substitutions. Complex systems...
This thesis describes the synthesis of sulfobetaines having the general structure $\rm RN\sp{+}(CH\sb3)\sb2(CH\sb2)\sb{x}SO\sb{3\sp{-}}$ as novel inhibitors of squalene synthase. Squalene synthase reductively couples two molecules of farnesyl...
A series of conformationally restricted bis(9-amino-acridine) derivatives were designed, synthesized, and then evaluated for their chemical and biological behavior. The novel compounds were prepared by treating selected diamines with a...
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...
Electric generators -- Windings. Electric inductors -- Design and construction -- Mathematical models. Electric current converters -- Design and construction -- Mathematical models. Energy dissipation -- Mathematical models.
Magnetic components for high-frequency power conversion applications can have significant losses that compromise the performance of the converter. In particular, winding losses can be large due to high-frequency effects that are difficult to model...
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...
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....
Core Binding Factors (CBFs) are members of a small family of transcription factors that play critical roles in a number of mammalian developmental processes. CBFs are heterodimers consisting of a CBFÎ± subunit, which contacts and binds DNA at the...
Regulatory linkage between epibiotic organisms and their host zooplankton populations is one of the least understood topics in zooplankton biology, despite the likely importance of epibionts to pelagic communities. These laboratory studies with...
Operating systems and low-level applications are usually written in languages like C and assembly, which provide access to low-level abstractions. These languages have unsafe type systems that allow many bugs to slip by programmers. For example, in...
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...