Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 12 of 12 for “"Convex domains"”.
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Hardy type inequalities for non-convex domains
… study of certain Hardy-type inequalities for non-convex domains \(\Omega\) \(\subset\)R\(^n\). Please see the thesis for a fuller abstract.
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Lattice points in disks and strongly convex domains
… a lattice point discrepancy result for strongly convex domains.
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Holomorphic Hardy Space Representations for Convex Domains in Cn
… well known theorems in one complex variable. The domains we are concerned with are strongly convex with real boundary of class C^2. We obtain integral representations utilizing the Leray kernel for Hardy space (p=1) functions on such domains D. Next we define an operator to prove the …
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Weakly q-Convex Domains and Bounded q-Subharmonic Exhaustion Functions
… the Diederich-Fornaess index to bounded weakly q-convex domains with bounded q-subharmonic exhaustion functions. Sufficient conditions for this generalized Diederich-Fornæss index to have a given lower bound are proved. We show this generalized index is positive on bounded weakly q-convex domains …
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Boundary Value Problems for the Laplace Equation on Convex Domains with Analytic Boundary
… applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the …
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Numerical analysis of the Fokas method in two and three dimensions
… to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the two-dimensional problem in a polygon, and the three dimensional problem in a polyhedron. The nature of elliptic equations means that, knowing the values of a solution on the boundary, one can reconstruct …
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Regularity of Neumann solutions to an elliptic free boundary problem
… which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , in a weak sense. We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. …
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Essays on Algorithmic Learning and Uncertainty Quantification
… three essays. The first, titled “Localization, Convexity, and Star Aggregation,” develops new analytical tools based upon the offset Rademacher complexity for studying stochastic optimization in non-convex domains, including statistical prediction and model aggregation problems. Using these …
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Flows, Submodularity, Sparsity, and Beyond: Continuous Optimization Insights for Discrete Problems
… of the thesis we propose faster second-order convex optimization algorithms for classical graph algorithmic problems. Our main contribution is to show that the runtime of interior point methods is closely connected to spectral connectivity notions in the underlying graph, such as electrical …
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Generalized Characteristics Of A Generic Polytope
… curves of XH. When S is the boundary of a smooth convex domain K˜ ⊂ R 2n, then the least action among closed characteristics of LS is equal to the Ekeland-Hofer-Zehnder capacity, a symplectic invariant. From a result due to Artstein-Avidan and Ostrover, there exists a continuous extension of this …
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The power of random information for numerical approximation and integration
… on the radius of random information both in a convex and a quasi-normed setting, which extend and, in some cases, improve existing results. We conjecture and partially establish that the power of random information is subject to a dichotomy determined by the decay of the length of the semiaxes …
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Procedural generation of vascular networks for tissue engineering
… a complete package for vascularizing arbitrary domains with an arbitrary number of distinct networks is developed, which can generate networks from a single starting point and radius (the typical engineering case) as well as being able to take existing networks and develop them further to ensure …