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Thesis

Analytic structures for the index theory of SL(3, C )

Authors: Yuncken, Robert (2006)

If G is a connected Lie group, the Kasparov representation ring KKG(C, C) contains a singularly important element—the 'y-element—which is an idempotent relating the Kasparov representation ring of G with the representation ring of its maximal compact subgroup K. In the proofs of the Baum-Connes conjecture with coefficients for the groups G = SO0(n, 1) ([Kas84]) and G = SU(n, 1) ([JK95]), a key component is an explicit construction of the 'y-element as an element of G-equivariant K-homology for the space G/B, where B is the Borel subgroup of G. In this thesis, we describe some analytical constructions which may be useful for such a construction of -y in the case of the rank-two Lie group G = SL(3, C). The inspiration is the Bernstein-Gel’fand-Gel’fand complex—a natural differential ...

Thesis

Analyzing and modeling large biological networks: Inferring signal transduction pathways

Authors: Bebek, Gurkan (2006)

Large scale two-hybrid screens have generated a wealth of information describing potential protein-protein intereactions (PPIs). When interacting proteins are asso¬ciated with each other to generate networks, a map of the cell, picturing potential signaling pathways and interactive complexes is formed. PPI networks satisfy the small-world property and their degree distribution follow the power-law degree distribution. Recently, duplication based random graph models have been proposed to emulate the evolution of PPI networks and to satisfy these two graph theoretical properties. In this work, we show that the previously proposed model of Pastor-Satorras et al. (2003) does not generate a power-law degree distribution with exponential cutoff as claimed and the more restrictive model ...

Thesis

Anticyclotomic Iwasawa theory for modular forms

Authors: Arnold, Trevor S. (2006)

Thesis

Application of iminium activation technologies to natural product synthesis: Total syntheses of the spiculisporic acids, progress towards the total synthesis of cylindrocyclophane F, and formal synthesis of cylindrocyclophane A

Authors: Goodwin, Nicole Cathleen (2006)

The first enantioselective, catalytic vinylogous Mukaiyama-Michael reaction of siloxyfurans with simple a,(3-unsaturated aldehydes has been reported using chiral imidazolidinones. This methodology provides access to enantioenriched y-butenolides, a privileged motif in organic synthesis. The utility of this organocatalytic Mukaiyama-Michael reaction was highlighted by the total syntheses of (-)-spiculisporic acid and (-)-5-epi-spiculisporic acid. Investigations into the total syntheses of cylindrocyclophanes A and F necessitated the development of a novel B-alkyl Suzuki cross-coupling of trimethylanilinium salts using a nickel(O) catalyst and bulky phosphine ligand. This methodology study revealed a very competitive nickel-catalyzed demethylation pathway, which produced dimethyla...

Thesis

Applications of Computational Quantum Mechanics

Authors: Temel, Burcin (2006)

This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calcula...

Thesis

Applications of high-performance affinity chromatography in the study of drug-protein binding: Examination of interactions between phenytoin and related compounds with human serum albumin

Authors: Ohnmacht, Corey M. (2006)

This dissertation involves the detailed examination of phenytoin and its binding properties to human serum albumin (HSA). This was accomplished by implementing various affinity chromatographic techniques including zonal elution and frontal analysis along with columns containing immobilized HSA to provide estimates of equilibrium binding constants. Affinity chromatography with plate height measurements was also used with theory-derived equations to measure the rate constants for the multisite binding of phenytoin to the chromatographic column. Part one discusses the complexity of phenytoin’s multisite binding and work that has been done previously to unravel the binding properties of phenytoin. In addition an expansion of current chromatographic theory describing multisite binding a...

Thesis

Applications of noncommutative algebraic geometry to representation theory

Authors: Tang, Xin (2006)

In this dissertation, we recall some basic notions and results in non-commutative algebraic geometry, especially in spectral theory of abelian categories as developed in [49], [50], [55], [56] and [57]. We apply them to study D-modules on the flag variety X = G/B and its quantized analogue. Via a locality theorem, we reduce the study of D-modules on the flag variety X to the study of modules over Weyl algebras. Then we present three explicit constructions of different classes of irreducible modules over Weyl algebras. For the quantized enveloping algebra Uq(g), we recover the construction of highest weight irreducible modules, via the Harish-Chandra homomorphism, in the framework of spectral theory. The rest of this work is based on a quantum analogue Xq of the flag variety X and th...

Thesis

Applications of Rauzy Induction on the Generic Ergodic Theory of Interval Exchange Transformations

Authors: Wu, Yue (2006)

Thesis

Applications of symplectic geometry to Hamiltonian mechanics

Authors: Lisi, Samuel Thomas (2006)

In this thesis, we consider three applications of pseudoholomorphic curves to problems in Hamiltonian dynamics. In a first part, we prove an existence result for homoclinic orbits on a contact-type, critical energy level of an autonomous Hamiltonian, provided that the level is Hamiltonian displaceable. To do this, we transform the problem into a problem of Lagrangian intersection Floer theory. This involves a construction due to Mohnke [34] and some ideas from Legendrian surgery. In particular, we prove a generalization of Sere's result [36] on the existence of homoclinic orbits for an autonomous Hamiltonian system. In a second part, we develop a theory of pseudoholomorphic curves into a singular contact manifold, which represents the critical level of an autonomous Hamiltonian. We...

Thesis

Applications of the formal oxa-[3+3] cycloaddition to natural product synthesis

Authors: Kurdyumov, Aleksey Valeryevich (2006)

For several years in our laboratory we have investigated the formal [3 + 3] cycloaddition. This is a condensation reaction that occurs between an unsaturated aldehyde and a 1,3-diketone or equivalent. The reaction results in a new 2H-pyran or 2H-pyridine fused to the diketone. Chapter I of this thesis concentrates on new developments in the area of oxa-[3 + 3] cycloaddition reaction, in particular, Lewis acid catalyzed version of this reaction. Synthetic scope and limitations of this new methodology are discussed. Chapter II describes synthetic approaches towards naturally occurring chromenes and chromanes. Our total syntheses of such compounds, rhododaurichromanic acid A and B, methyl ester of daurichromenic acid and hongoquercin A, are discussed in detail. Unusual, exo-type poly...