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The Element Spectrum Of A Graph, Milisha Hart-Simmons
The Element Spectrum Of A Graph, Milisha Hart-Simmons
Electronic Theses and Dissertations
Characterizations of graphs and matroids that have cycles or circuits of specified cardinality have been given by authors including Edmonds, Junior, Lemos, Murty, Reid, Young, and Wu. In particular, a matroid with circuits of a single cardinality is called a Matroid Design. We consider a generalization of this problem by assigning a weight function to the edges of a graph. We characterize when it is possible to assign a positive integer value weight function to a simple 3-connected graph G such that the graph G contains an edge that is only in cycles of two different weights. For example, as …
Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach, Lynsey Cargile Naugle
Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach, Lynsey Cargile Naugle
Electronic Theses and Dissertations
We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow …
Orthosymmetric Maps And Polynomial Valuations, Stephan Christopher Roberts
Orthosymmetric Maps And Polynomial Valuations, Stephan Christopher Roberts
Electronic Theses and Dissertations
We present a characterization of orthogonally additive polynomials on vector lattices as orthosymmetric multilinear maps. Our proof avoids partitionaly orthosymmetric maps and results that represent orthogonally additive polynomials as linear maps on a power. We also prove band characterizations for order bounded polynomial valuations and for order continuous polynomials of order bounded variation. Finally, we use polynomial valuations to prove that a certain restriction of the Arens extension of a bounded orthosymmetric multilinear map is orthosymmetric.
Asymptotic Properties Of Polynomials Orthogonal Over Multiply Connected Domains, James A. Henegan
Asymptotic Properties Of Polynomials Orthogonal Over Multiply Connected Domains, James A. Henegan
Electronic Theses and Dissertations
We investigate the asymptotic behavior of polynomials orthogonal over certain multiply connected domains. Each domain that we consider has an analytic boundary and is, in a strong sense, conformally equivalent to a canonical type of multiply connected domain called a circular domain. The two most general results involve the construction of a series expansion and an integral representation for these polynomials. We show that the integral representation can be utilized to derive more specific results when the domain of orthogonality is circular. In this case, we shed light on the manner in which the holes in the domain of orthogonality …