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Infinite Planar Graphs

Description: How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this exte… more
Date: May 2000
Creator: Aurand, Eric William
Item Type: Refine your search to only Thesis or Dissertation
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Maximum-Sized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7

Description: Let M be the class of simple matroids which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find all the maximum-sized matroids for each rank.
Date: May 2000
Creator: Mecay, Stefan Terence
Item Type: Refine your search to only Thesis or Dissertation
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Examples and Applications of Infinite Iterated Function Systems

Description: The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems. We discuss particular examples of infinite iterated function systems derived … more
Date: August 2000
Creator: Hanus, Pawel Grzegorz
Item Type: Refine your search to only Thesis or Dissertation
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A Collapsing Result Using the Axiom of Determinancy and the Theory of Possible Cofinalities

Description: Assuming the axiom of determinacy, we give a new proof of the strong partition relation on ω1. Further, we present a streamlined proof that J<λ+(a) (the ideal of sets which force cof Π α < λ) is generated from J<λ+(a) by adding a singleton. Combining these results with a polarized partition relation on ω1
Date: May 2001
Creator: May, Russell J.
Item Type: Refine your search to only Thesis or Dissertation
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Hyperspace Topologies

Description: In this paper we study properties of metric spaces. We consider the collection of all nonempty closed subsets, Cl(X), of a metric space (X,d) and topologies on C.(X) induced by d. In particular, we investigate the Hausdorff topology and the Wijsman topology. Necessary and sufficient conditions are given for when a particular pseudo-metric is a metric in the Wijsman topology. The metric properties of the two topologies are compared and contrasted to show which also hold in the respective topolog… more
Date: August 2001
Creator: Freeman, Jeannette Broad
Item Type: Refine your search to only Thesis or Dissertation

The Pettis Integral and Operator Theory

Description: Let (Ω, Σ, µ) be a finite measure space and X, a Banach space with continuous dual X*. A scalarly measurable function f: Ω→X is Dunford integrable if for each x* X*, x*f L1(µ). Define the operator Tf. X* → L1(µ) by T(x*) = x*f. Then f is Pettis integrable if and only if this operator is weak*-to-weak continuous. This paper begins with an overview of this function. Work by Robert Huff and Gunnar Stefansson on the operator Tf motivates much of this paper. Conditions that make Tf weak*-to-weak c… more
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Date: August 2001
Creator: Huettenmueller, Rhonda
Item Type: Refine your search to only Thesis or Dissertation
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Borel Determinacy and Metamathematics

Description: Borel determinacy states that if G(T;X) is a game and X is Borel, then G(T;X) is determined. Proved by Martin in 1975, Borel determinacy is a theorem of ZFC set theory, and is, in fact, the best determinacy result in ZFC. However, the proof uses sets of high set theoretic type (N1 many power sets of ω). Friedman proved in 1971 that these sets are necessary by showing that the Axiom of Replacement is necessary for any proof of Borel Determinacy. To prove this, Friedman produces a model of ZC and… more
Date: December 2001
Creator: Bryant, Ross
Item Type: Refine your search to only Thesis or Dissertation

Quantization Dimension for Probability Definitions

Description: The term quantization refers to the process of estimating a given probability by a discrete probability supported on a finite set. The quantization dimension Dr of a probability is related to the asymptotic rate at which the expected distance (raised to the rth power) to the support of the quantized version of the probability goes to zero as the size of the support is allowed to go to infinity. This assumes that the quantized versions are in some sense ``optimal'' in that the expected distances… more
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Date: December 2001
Creator: Lindsay, Larry J.
Item Type: Refine your search to only Thesis or Dissertation

Topological uniqueness results for the special linear and other classical Lie Algebras.

Description: Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to i… more
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Date: December 2001
Creator: Rees, Michael K.
Item Type: Refine your search to only Thesis or Dissertation
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Dimensions in Random Constructions.

Description: We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
Date: May 2002
Creator: Berlinkov, Artemi
Item Type: Refine your search to only Thesis or Dissertation
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Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Description: Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction f… more
Date: August 2002
Creator: Arthur, Christopher
Item Type: Refine your search to only Thesis or Dissertation
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Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions

Description: Hill and Monticino (1998) introduced a constructive method for generating random probability measures with a prescribed mean or distribution on the mean. The method involves sequentially generating an array of barycenters that uniquely defines a probability measure. This work analyzes statistical properties of the measures generated by sequential barycenter array constructions. Specifically, this work addresses how changing the base measures of the construction affects the statististics of m… more
Date: December 2002
Creator: Valdes, LeRoy I.
Item Type: Refine your search to only Thesis or Dissertation
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Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field

Description: It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the in&#64258;uence of an externally imposed uniform… more
Date: May 2003
Creator: Hoq, Qazi Enamul
Item Type: Refine your search to only Thesis or Dissertation
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Complemented Subspaces of Bounded Linear Operators

Description: For many years mathematicians have been interested in the problem of whether an operator ideal is complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. Let L(X, Y ) be a Banach space of all bounded linear operator between Banach spaces X and Y , K(X, Y ) b… more
Date: August 2003
Creator: Bahreini Esfahani, Manijeh
Item Type: Refine your search to only Thesis or Dissertation
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The Study of Translation Equivalence on Integer Lattices

Description: This paper is a contribution to the study of countable Borel equivalence relations on standard Borel spaces. We concentrate here on the study of the nature of translation equivalence. We study these known hyperfinite spaces in order to gain insight into the approach necessary to classify certain variables as either being hyperfinite or not. In Chapter 1, we will give the basic definitions and examples of spaces used in this work. The general construction of marker sets is developed in this wor… more
Date: August 2003
Creator: Boykin, Charles Martin
Item Type: Refine your search to only Thesis or Dissertation
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A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions

Description: We follow a research paper that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of our main result.
Date: May 2004
Creator: Vlasic, Andrew
Item Type: Refine your search to only Thesis or Dissertation

Exhaustivity, continuity, and strong additivity in topological Riesz spaces.

Description: In this paper, exhaustivity, continuity, and strong additivity are studied in the setting of topological Riesz spaces. Of particular interest is the link between strong additivity and exhaustive elements of Dedekind s-complete Banach lattices. There is a strong connection between the Diestel-Faires Theorem and the Meyer-Nieberg Lemma in this setting. Also, embedding properties of Banach lattices are linked to the notion of strong additivity. The Meyer-Nieberg Lemma is extended to the setting o… more
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Date: May 2004
Creator: Muller, Kimberly O.
Item Type: Refine your search to only Thesis or Dissertation

Spaces of Compact Operators

Description: In this dissertation we study the structure of spaces of operators, especially the space of all compact operators between two Banach spaces X and Y. Work by Kalton, Emmanuele, Bator and Lewis on the space of compact and weakly compact operators motivates much of this paper. Let L(X,Y) be the Banach space of all bounded linear operators between Banach spaces X and Y, K(X,Y) be the space of all compact operators, and W(X,Y) be the space of all weakly compact operators. We study problems relate… more
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Date: May 2004
Creator: Ghenciu, Ioana
Item Type: Refine your search to only Thesis or Dissertation
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Lyapunov Exponents, Entropy and Dimension

Description: We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; namely that the entropy equals dimension times expansion.
Date: August 2004
Creator: Williams, Jeremy M.
Item Type: Refine your search to only Thesis or Dissertation
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Thermodynamical Formalism

Description: Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressu… more
Date: August 2004
Creator: Chousionis, Vasileios
Item Type: Refine your search to only Thesis or Dissertation

Hamiltonian cycles in subset and subspace graphs.

Description: In this dissertation we study the Hamiltonicity and the uniform-Hamiltonicity of subset graphs, subspace graphs, and their associated bipartite graphs. In 1995 paper "The Subset-Subspace Analogy," Kung states the subspace version of a conjecture. The study of this problem led to a more general class of graphs. Inspired by Clark and Ismail's work in the 1996 paper "Binomial and Q-Binomial Coefficient Inequalities Related to the Hamiltonicity of the Kneser Graphs and their Q-Analogues," we defin… more
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Date: December 2004
Creator: Ghenciu, Petre Ion
Item Type: Refine your search to only Thesis or Dissertation
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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

Description: In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal mea… more
Date: May 2005
Creator: Coiculescu, Ion
Item Type: Refine your search to only Thesis or Dissertation
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Applications in Fixed Point Theory

Description: Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using condi… more
Date: December 2005
Creator: Farmer, Matthew Ray
Item Type: Refine your search to only Thesis or Dissertation

Dimension spectrum and graph directed Markov systems.

Description: In this dissertation we study graph directed Markov systems (GDMS) and limit sets associated with these systems. Given a GDMS S, by the Hausdorff dimension spectrum of S we mean the set of all positive real numbers which are the Hausdorff dimension of the limit set generated by a subsystem of S. We say that S has full Hausdorff dimension spectrum (full HD spectrum), if the dimension spectrum is the interval [0, h], where h is the Hausdorff dimension of the limit set of S. We give necessary cond… more
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Date: May 2006
Creator: Ghenciu, Eugen Andrei
Item Type: Refine your search to only Thesis or Dissertation
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