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Articles 1 - 5 of 5
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Analysis And Implementation Of High-Order Compact Finite Difference Schemes, Jonathan G. Tyler
Analysis And Implementation Of High-Order Compact Finite Difference Schemes, Jonathan G. Tyler
Theses and Dissertations
The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were …
The Minimum Rank Problem Over Finite Fields, Jason Nicholas Grout
The Minimum Rank Problem Over Finite Fields, Jason Nicholas Grout
Theses and Dissertations
We have two main results. Our first main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal forbidden subgraphs for any field. Our second main result is a structural characterization of all graphs having minimum rank at most k for any k over any finite field. This characterization leads to a very strong connection to projective geometry and we apply projective …
Infinite Product Group, Keith G. Penrod
Infinite Product Group, Keith G. Penrod
Theses and Dissertations
The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.
Pipe Diagrams For Thompson's Group F, Aaron L. Peterson
Pipe Diagrams For Thompson's Group F, Aaron L. Peterson
Theses and Dissertations
We review the definition and standard description of Thompson's Group F. We define the set of pipe diagrams and show that this set forms a group isomorphic to F. We use pipe diagrams to prove two theorems about giving a minimal representation for an arbitrary element of F.
On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor
On Connections Between Univalent Harmonic Functions, Symmetry Groups, And Minimal Surfaces, Stephen M. Taylor
Theses and Dissertations
We survey standard topics in elementary differential geometry and complex analysis to build up the necessary theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. Finally, we demand two minimal surfaces M and M' be locally isometric, formulate a system of partial differential equations modeling this constraint, and calculate their symmetry group. The group elements generate transformations that when applied to a prescribed harmonic …