UNT Theses and Dissertations - 171 Matching Results

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The Global Structure of Iterated Function Systems

Description: I study sets of attractors and non-attractors of finite iterated function systems. I provide examples of compact sets which are attractors of iterated function systems as well as compact sets which are not attractors of any iterated function system. I show that the set of all attractors is a dense Fs set and the space of all non-attractors is a dense Gd set it the space of all non-empty compact subsets of a space X. I also investigate the small trans-finite inductive dimension of the space of… more
Date: May 2009
Creator: Snyder, Jason Edward
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Graded Hecke Algebras for the Symmetric Group in Positive Characteristic

Description: Graded Hecke algebras are deformations of skew group algebras which arise from a group acting on a polynomial ring. Over fields of characteristic zero, these deformations have been studied in depth and include both symplectic reflection algebras and rational Cherednik algebras as examples. In Lusztig's graded affine Hecke algebras, the action of the group is deformed, but not the commutativity of the vectors. In Drinfeld's Hecke algebras, the commutativity of the vectors is deformed, but not … more
Date: August 2020
Creator: Krawzik, Naomi
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Graev Metrics and Isometry Groups of Polish Ultrametric Spaces

Description: This dissertation presents results about computations of Graev metrics on free groups and characterizes isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. In Chapter 2, computations of Graev metrics are performed on free groups. One of the related results answers an open question of Van Den Dries and Gao. In Chapter 3, isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces are characterized. The notion of generalized tree is defined and a corre… more
Date: May 2013
Creator: Shi, Xiaohui
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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
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Hausdorff Dimension of Shrinking-Target Sets Under Non-Autonomous Systems

Description: For a dynamical system on a metric space a shrinking-target set consists of those points whose orbit hit a given ball of shrinking radius infinitely often. Historically such sets originate in Diophantine approximation, in which case they describe the set of well-approximable numbers. One aspect of such sets that is often studied is their Hausdorff dimension. We will show that an analogue of Bowen's dimension formula holds for such sets when they are generated by conformal non-autonomous iterate… more
Date: August 2018
Creator: Lopez, Marco Antonio
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Hausdorff, Packing and Capacity Dimensions

Description: In this thesis, Hausdorff, packing and capacity dimensions are studied by evaluating sets in the Euclidean space R^. Also the lower entropy dimension is calculated for some Cantor sets. By incorporating technics of Munroe and of Saint Raymond and Tricot, outer measures are created. A Vitali covering theorem for packings is proved. Methods (by Taylor and Tricot, Kahane and Salem, and Schweiger) for determining the Hausdorff and capacity dimensions of sets using probability measures are discussed… more
Date: August 1989
Creator: Spear, Donald W.
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Hermitian Jacobi Forms and Congruences

Description: In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.
Date: August 2014
Creator: Senadheera, Jayantha
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Hochschild Cohomology and Complex Reflection Groups

Description: A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the se… more
Date: August 2012
Creator: Foster-Greenwood, Briana A.
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Hochschild Cohomology of Finite Cyclic Groups Acting on Polynomial Rings

Description: The Hochschild cohomology of an associative algebra records information about the deformations of that algebra, and hence the first step toward understanding its deformations is an examination of the Hochschild cohomology. In this dissertation, we use techniques from homological algebra, invariant theory, and combinatorics to analyze the Hochschild cohomology of skew group algebras arising from finite cyclic groups acting on polynomial rings over fields of arbitrary characteristic. These algebr… more
Date: May 2023
Creator: Lawson, Colin M.
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Hyperbolic Monge-Ampère Equation

Description: In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prov… more
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Date: August 2006
Creator: Howard, Tamani M.
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Infinitary Combinatorics and the Spreading Models of Banach Spaces

Description: Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks… more
Date: May 2019
Creator: Krause, Cory A.
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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
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Infinitely Many Solutions of Semilinear Equations on Exterior Domains

Description: We prove the existence and nonexistence of solutions for the semilinear problem ∆u + K(r)f(u) = 0 with various boundary conditions on the exterior of the ball in R^N such that lim r→∞u(r) = 0. Here f : R → R is an odd locally lipschitz non-linear function such that there exists a β > 0 with f < 0 on (0, β), f > 0 on (β, ∞), and K(r) \equiv r^−α for some α > 0.
Date: August 2018
Creator: Joshi, Janak R
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Invariant Differential Derivations for Modular Reflection Groups

Description: The invariant theory of finite reflection groups has rich connections to geometry, topology, representation theory, and combinatorics. We consider finite reflection groups acting on vector spaces over fields of arbitrary characteristic, where many arguments of classical invariant theory break down. When the characteristic of the underlying field is positive, reflections may be nondiagonalizable. A group containing these so-called transvections has order which is divisible by the characteristic … more
Date: May 2023
Creator: Hanson, Dillon James
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Invariants of Polynomials Modulo Frobenius Powers

Description: Rational Catalan combinatorics connects various Catalan numbers to the representation theory of rational Cherednik algebras for Coxeter and complex reflection groups. Lewis, Reiner, and Stanton seek a theory of rational Catalan combinatorics for the general linear group over a finite field. The finite general linear group is a modular reflection group that behaves like a finite Coxeter group. They conjecture a Hilbert series for a space of invariants under the action of this group using (q,t)-… more
Date: May 2020
Creator: Drescher, Chelsea
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Invertible Ideals and the Strong Two-Generator Property in Some Polynomial Subrings

Description: Let K be any field and Q be the rationals. Define K^1[X] = {f(X) e K[X]| the coefficient of X in f(X) is zero} and Q^1β[X] = {f(X) e Q[X]| the coefficent of β1(X) in the binomial expansion of f(X) is zero}, where {β1(X)}^∞ i=0 are the well-known binomial polynomials. In this work, I establish the following results: K^1[X] and Q^1β[X] are one-dimensional, Noetherian, non-Prüfer domains with the two-generator property on ideals. Using the unique factorization structure of the overrings K[X] and Q… more
Date: May 1987
Creator: Chapman, Scott T. (Scott Thomas)
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Irreducible Modules for Yokonuma-Type Hecke Algebras

Description: Yokonuma-type Hecke algebras are a class of Hecke algebras built from a Type A construction. In this thesis, I construct the irreducible representations for a class of generic Yokonuma-type Hecke algebras which specialize to group algebras of the complex reflection groups and to endomorphism rings of certain permutation characters of finite general linear groups.
Date: August 2016
Creator: Dave, Ojas
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Iterative Solution of Linear Boundary Value Problems

Description: The investigation is initially a continuation of Neuberger's work on linear boundary value problems. A very general iterative procedure for solution of these problems is described. The alternating-projection theorem of von Neumann is the mathematical starting point for this study. Later theorems demonstrate the validity of numerical approximation for Neuberger's method under certain conditions. A sampling of differential equations within the scope of our iterative method is given. The numerical… more
Date: August 1983
Creator: Walsh, John Breslin
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Kleinian Groups in Hilbert Spaces

Description: The theory of discrete groups acting on finite dimensional Euclidean open balls by hyperbolic isometries was borne around the end of 19th century within the works of Fuchs, Klein and Poincaré. We develop the theory of discrete groups acting by hyperbolic isometries on the open unit ball of an infinite dimensional separable Hilbert space. We present our investigations on the geometry of limit sets at the sphere at infinity with an attempt to highlight the differences between the finite and infin… more
Date: August 2012
Creator: Das, Tushar
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Level Curves of the Angle Function of a Positive Definite Symmetric Matrix

Description: Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following quest… more
Date: December 2009
Creator: Bajracharya, Neeraj
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Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN

Description: We establish the existence of radial solutions to the p-Laplacian equation ∆p u + f(u)=0 in RN, where f behaves like |u|q-1 u when u is large and f(u) < 0 for small positive u. We show that for each nonnegative integer n, there is a localized solution u which has exactly n zeros. Also, we look for radial solutions of a superlinear Dirichlet problem in a ball. We show that for each nonnegative integer n, there is a solution u which has exactly n zeros. Here we give an alternate proof to tha… more
Date: May 2008
Creator: Pudipeddi, Sridevi
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Maximum Likelihood Estimation of Logistic Sinusoidal Regression Models

Description: We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample perform… more
Date: December 2013
Creator: Weng, Yu
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The Maximum Size of Combinatorial Geometries Excluding Wheels and Whirls as Minors

Description: We show that the maximum size of a geometry of rank n excluding the (q + 2)-point line, the 3-wheel W_3, and the 3-whirl W^3 as minor is (n - 1)q + 1, and geometries of maximum size are parallel connections of (q + 1)-point lines. We show that the maximum size of a geometry of rank n excluding the 5-point line, the 4-wheel W_4, and the 4-whirl W^4 as minors is 6n - 5, for n ≥ 3. Examples of geometries having rank n and size 6n - 5 include parallel connections of the geometries V_19 and PG(2,3).
Date: August 1989
Creator: Hipp, James W. (James William), 1956-
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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
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