

 This thesis mainly concerns the dispersive properties of Schrodinger equations with certain potentials, and some of their consequences.
First, we consider the charge transfer models in R^n with n > 2. In this case, the potential is a sum of several individual realvalued potentials, each moving with constant velocities. We get an L^1 to L^infty estimate for the evolutio....
By Kaihua CaiCalifornia Institute of Technology20050519
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 Cardiovascular development and its proper function are essential for the development and survival of animals, while malformation of vasculature leads to a variety of diseases. The significance of vasculature during development and in adulthood has been delineated by investigating the functions of genes expressed in the vasculature. Endothelial cells lining the lumen of ....
By Donghun ShinCalifornia Institute of Technology20050518
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 Cyclindependent kinases (Cdk) direct cell cycle transitions by associating with various cyclins throughout the cell cycle. For cells to exit mitosis, mitotic Cdk activity must be turned off. In Saccharomyces cerevisiae, the mitotic exit network, or MEN, comprises of a group of proteins that form a signaling pathway required for mitotic exit. The MEN regulates the activ....
By Angie Siu Yee MahCalifornia Institute of Technology20050518
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 This dissertation can be divided into two main sections:
I. In previous studies, we have used fluorinated tryptophan derivatives to conclusively identify a cationpi interaction with Trp 149 in the binding of acetylcholine (ACh) to the muscletype nicotinic acetylcholine receptor (nAChR). We have incorporated mimics of ACh, termed tethered agonists, in the binding site ....
By Ernest James PeterssonCalifornia Institute of Technology20050518
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 This thesis introduces a novel geometry processing pipeline based on unconstrained spherical parameterization and normal remeshing. We claim three main contributions:
First we show how to increase the stability of Normal Mesh construction, while speeding it up by decomposing the process into two stages: parameterization and remeshing. We show that the remeshing step can....
By Ilja Heinrich FriedelCalifornia Institute of Technology20050518
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 White dwarfs are ubiquitous in the known Universe. They are frequently found in binary systems with ordinary stars, giants, or compact objects as companions. Depending upon their histories, such systems may have significantly eccentric orbits. Because of gravitational radiation, a white dwarfcompact object binary will shrink and circularize with time. If the system is ....
By Yasser RathoreCalifornia Institute of Technology20050518
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 In this thesis, new results excluding finite time singularities with localized assumptions/conditions are obtained for the 3D incompressible Euler equations.
The 3D incompressible Euler equations are some of the most important nonlinear equations in mathematics. They govern the motion of ideal fluids. After hundreds of years of study, they are still far from being well....
By Xinwei YuCalifornia Institute of Technology20050518
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 GProtein Coupled Receptors (GPCRs) form a major target class of membrane proteins for therapeutic drug design, and the challenge is to design subtype specific drugs. Hence the knowledge of threedimensional structure is critical to drug design for GPCRs. Since GPCRs are membrane bound proteins, there is only one crystal structure for a GPCR, namely bovine rhodopsin. Th....
By Spencer Eugene HallCalifornia Institute of Technology20050518
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 We study the relation between topological sigma models and generalized geometries. The existence conditions for the most general type of topological sigma models obtained from twisting the N=(2,2) supersymmetric sigma model are investigated, and are found to be related to twisted generalized CalabiYau structures. The properties of these topological sigma models are ana....
By Yi LiCalifornia Institute of Technology20050518
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 The conjectured duality between type IIB string theory on AdS5 x S5 and N = 4 SU(Nc) super YangMills theory in four dimensions simplifies in the Penrose limit or, in other words, when the string's angular momentum is large. As the string action in this limit is solvable, it is possible to go beyond the supergravity approximation and compare exact string energies with t....
By Tristan McLoughlinCalifornia Institute of Technology20050518
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 The studies presented herein are on three distinct topics in astrophysics:
I. We solve for the evolution of the vertical extent of the convective region of a neutron star atmosphere during a type I Xray burst. The convective region is wellmixed with ashes of nuclear burning, and its extent determines the burst rise time. We show that the maximum extent of the convecti....
By Nevin Nachum WeinbergCalifornia Institute of Technology20050518
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 Current estimates of the number of species on Earth range from four to forty million total species. Why are there so many species? The answer must include both ecology and evolution. Ecology looks at the interactions between coexisting species, while evolution tracks them through time. Both are required to understand aspects of environments which promote speciation, and....
By Stephanie S. ChowCalifornia Institute of Technology20050518
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