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Articles 31 - 34 of 34
Full-Text Articles in Physical Sciences and Mathematics
Pointwise Schauder Estimates Of Parabolic Equations In Carnot Groups, Heather Arielle Griffin
Pointwise Schauder Estimates Of Parabolic Equations In Carnot Groups, Heather Arielle Griffin
Graduate Theses and Dissertations
Schauder estimates were a historical stepping stone for establishing uniqueness and smoothness of solutions for certain classes of partial differential equations. Since that time, they have remained an essential tool in the field. Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its derivatives. This document establishes pointwise Schauder estimates for second order parabolic equations where the traditional role of derivatives are played by vector fields generated by the first layer of the Lie algebra stratification for a Carnot group. The Schauder estimates are shown …
Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez
Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez
Graduate Theses and Dissertations
In this work we study different dynamic processes for filling tori and n×∞ bands with edge-to-edge black and white squares at random. First we present a simulation for the Random Sequential Adsorption (RSA) with nearest-neighbor rejection on n×n tori. We are interested in the ratio of black to total tiles once the domain is saturated for large domains. Next we study the annealing process. Given a random excited tiling of an n×n torus, we show that as t→∞ the system reaches a stable state in which no tile is excited. This stable state can either be a tiling whose tiles …
A Restarted Homotopy Method For The Nonsymmetric Eigenvalue Problem, Brandon Hutchison
A Restarted Homotopy Method For The Nonsymmetric Eigenvalue Problem, Brandon Hutchison
Graduate Theses and Dissertations
The eigenvalues and eigenvectors of a Hessenberg matrix, H, are computed with a combination of homotopy increments and the Arnoldi method. Given a set, Ω, of approximate eigenvalues of H, there exists a unique vector f = f(H,Ω) in Rn where λ(H-e1ft)=Ω. A diagonalization of the homotopy H(t)=H−(1−t)e1ft at $t=0$ provides a prediction of the eigenvalues of H(t) at later times. These predictions define a new Ω that defines a new homotopy. The correction for each eigenvalue has an O(t2) error estimate, enabling variable step size and efficient convergence tests. Computations are done primarily in real arithmetic, and …
Holomorphic Hardy Space Representations For Convex Domains In Cn, Jennifer West Paulk
Holomorphic Hardy Space Representations For Convex Domains In Cn, Jennifer West Paulk
Graduate Theses and Dissertations
This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to 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 non-tangential limits of a function in Hardy space (p between 1 and infinity, inclusive) of domain D …