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...
The furanosteroids are a special class of natural products that feature a furan ring fused to the steroid nucleus at C-4 and C-6. In 1945, viridin, the parent member of this group, was isolated by Grove and coworkers from the fungas Gliocladium...
Microwave spectroscopy. Imaging systems -- Design and construction. Diagnostic imaging -- Digital techniques. Breast -- Cancer -- Diagnosis. Microwave imaging in medicine.
Microwave spectroscopy has been investigated as a possible modality for breast imaging because of the significant contrast in electrical properties between normal and malignant tissue over the microwave spectrum. A liquid-coupled, non-contacting...
Investigations into alternative breast cancer (BC) imaging techniques have become increasingly popular based on the limitations of traditional imaging modalities: X-ray mammography uses ionizing radiation, has limited intrinsic contrast and is...
'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...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
Introduction. This chapter provides a brief overview of the thesis. Chapter 1: tert-butyl-diphosphabutarene - Synthesis and reactivity of a novel phosphacycle. Treatment of 1,2-bis(dichlorophosphino)benzene (12) with tert-butylmagesium chloride...
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....
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
The overall scope of my thesis project is to determine effects of farnesol, a secreted factor produced by C. albicans , on P. aeruginosa virulence. These two organisms are frequently found with one another in mixed infections and our lab has...
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...
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...
Part I. A photoprecursor for difluorocarbene . The goal of this research was to develop a more practical and efficient photoprecursor for difluorocarbene. The first approach was concerned with the synthesis of 4,4-difluoropyrazoline-3,5-dione ( 5...
Earlier in our laboratory, a facile synthesis of the 2- and 3-nitroindoles was realized. These compounds showed promise as powerful intermediates in the synthesis of novel structures and natural products. The reactivity of 2- and 3-nitroindoles...
An efficient synthetic approach to both 2-acyl-1-(substituted)indoles and 2-nitro-1-(substituted)indoles by reaction of 2-lithio-1-(substituted)indoles with appropriate electrophiles is presented. Inverse quenching of 2-lithioindoles 5 and 208 with...
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...
The accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...
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)....
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...
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...
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...
A new synthetic approach to both pyrrolo[2,3- b]indoles and pyrrolo[3,4- b]indoles by the reaction of 3-nitro-1-(substituted)indoles with functionalized isocyanides is presented. The reaction between 3-nitro-1-(phenylsulfonyl)indole (185) and ethyl...
I. (3 + 2) Cycloaddition Reactions of Oxyallyl Cationic Intermediates with Indoles Cyclopenta- and cyclohexa[b]indolines are ubiquitous molecular skeletons in natural products and pharmaceutical agents. We have developed (3 + 2) cycloaddition...
Macrocyclic tetrapyrroles are essential to life. In nature, they play important roles in living organisms, such as oxygen transportation and photosynthesis. Pentynoic acids are versatile precursors for preparing pyrrolines and higher homologues....
The matrix metalloproteinases (MMPs) are family of enzymes with a common domain structure that degrade extracellular matrix proteins; these enzymes are overexpressed in numerous diseases including cancer and arthritis. Collagenase-1, 2, 3 (MMP-1,...
Naturally occurring macrocyclic tetrapyrroles of the chlorin and bacteriochlorin classes play important roles in essential biological processes, including photosynthesis and nitrogen cycling. The chromophores also show promise in various...