The synthesis of macrocyclic tetrapyrroles continues to be an area of vigorous research due to their application to a wide range of fields spanning the physical sciences. Only recently have general syntheses for the reduced systems, such as...
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....
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...
'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...
Sea ice appears to form an impenetrable boundary at the ocean-atmosphere interface in polar regions, yet in fact its porous structure provides critical pathways for the exchange of heat, gases, salts, and other chemical species impacting the global...
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)....
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...
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...
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...
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...
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...
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 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...
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...
Cupredoxins, such as stellacyanin, plastocyanin, amicyanin, rusticyanin, and azurin perform electron transfer (ET) reactions with partner protein(s) in the cell. The role of the redox cofactor in these proteins is played by a copper ion, which...
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...
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...
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...
This thesis describes the synthetic study of two biologically related natural products: porphobilinogen (PBG) and cobyric acid. PBG is the key intermediate in the biosynthesis of all naturally occurring tetrapyrrolic 'pigments of life', including...
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...
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...
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...
The chemistry of indole can be reversed and redirected by the addition of powerful electron-withdrawing groups. Incorporation of a nitro group at C-2 or C-3 renders the adjacent carbon susceptible to nucleophilic attack. Nitro, cyano, and...
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,...
The furanosteroids are an important class of natural products that have been found to effectively inhibit various biologically important enzymes. These enzymes include the phosphoinositide-3-kinase (PI3K) family and the polo-like kinase (PLK1)...
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...
Tetrapyrroles -- Synthesis. Tetrapyrroles -- Mechanism of action. Transition metal catalysts.
Previous studies have shown that the mucosal immune system is present in the female reproductive tract and under hormonal control. With the recognition that underlying stromal cells regulate epithelial cell function and hormonal responsiveness,...