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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
Item Type: Refine your search to only Thesis or Dissertation
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On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers

Description: In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of … more
Date: August 2012
Creator: Xuan, Mingzhi
Item Type: Refine your search to only Thesis or Dissertation
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Real Analyticity of Hausdorff Dimension of Disconnected Julia Sets of Cubic Parabolic Polynomials

Description: Consider a family of cubic parabolic polynomials given by for non-zero complex parameters such that for each the polynomial is a parabolic polynomial, that is, the polynomial has a parabolic fixed point and the Julia set of , denoted by , does not contain any critical points of . We also assumed that for each , one finite critical point of the polynomial escapes to the super-attracting fixed point infinity. So, the Julia sets are disconnected. The concern about the family is that the… more
Date: August 2012
Creator: Akter, Hasina
Item Type: Refine your search to only Thesis or Dissertation
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Random Iteration of Rational Functions

Description: It is a theorem of Denker and Urbański that if T:ℂ→ℂ is a rational map of degree at least two and if ϕ:ℂ→ℝ is Hölder continuous and satisfies the “thermodynamic expanding” condition P(T,ϕ) > sup(ϕ), then there exists exactly one equilibrium state μ for T and ϕ, and furthermore (ℂ,T,μ) is metrically exact. We extend these results to the case of a holomorphic random dynamical system on ℂ, using the concepts of relative pressure and relative entropy of such a system, and the variational principle … more
Date: May 2012
Creator: Simmons, David
Item Type: Refine your search to only Thesis or Dissertation
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Mycielski-Regular Measures

Description: Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence a… more
Date: August 2011
Creator: Bass, Jeremiah Joseph
Item Type: Refine your search to only Thesis or Dissertation
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Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

Description: In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapp… more
Date: August 2011
Creator: Farmer, Matthew Ray
Item Type: Refine your search to only Thesis or Dissertation
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Uniformly σ-Finite Disintegrations of Measures

Description: A disintegration of measure is a common tool used in ergodic theory, probability, and descriptive set theory. The primary interest in this paper is in disintegrating σ-finite measures on standard Borel spaces into families of σ-finite measures. In 1984, Dorothy Maharam asked whether every such disintegration is uniformly σ-finite meaning that there exists a countable collection of Borel sets which simultaneously witnesses that every measure in the disintegration is σ-finite. Assuming Gödel’s… more
Date: August 2011
Creator: Backs, Karl
Item Type: Refine your search to only Thesis or Dissertation
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Algebraically Determined Semidirect Products

Description: Let G be a Polish group. We say that G is an algebraically determined Polish group if given any Polish group L and any algebraic isomorphism from L to G, then the algebraic isomorphism is a topological isomorphism. We will prove a general theorem that gives useful sufficient conditions for a semidirect product of two Polish groups to be algebraically determined. This will smooth the way for the proofs for some special groups. For example, let H be a separable Hilbert space and let G be a subset… more
Date: May 2011
Creator: Jasim, We'am Muhammad
Item Type: Refine your search to only Thesis or Dissertation
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Gibbs/Equilibrium Measures for Functions of Multidimensional Shifts with Countable Alphabets

Description: Consider a multidimensional shift space with a countably infinite alphabet, which serves in mathematical physics as a classical lattice gas or lattice spin system. A new definition of a Gibbs measure is introduced for suitable real-valued functions of the configuration space, which play the physical role of specific internal energy. The variational principle is proved for a large class of functions, and then a more restrictive modulus of continuity condition is provided that guarantees a functi… more
Date: May 2011
Creator: Muir, Stephen R.
Item Type: Refine your search to only Thesis or Dissertation
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Algebraically Determined Rings of Functions

Description: Let R be any of the following rings: the smooth functions on R^2n with the Poisson bracket, the Hamiltonian vector fields on a symplectic manifold, the Lie algebra of smooth complex vector fields on C, or a variety of rings of functions (real or complex valued) over 2nd countable spaces. Then if H is any other Polish ring and φ:H →R is an algebraic isomorphism, then it is also a topological isomorphism (i.e. a homeomorphism). Moreover, many such isomorphisms between function rings … more
Date: August 2010
Creator: McLinden, Alexander Patrick
Item Type: Refine your search to only Thesis or Dissertation
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Three Topics in Descriptive Set Theory

Description: This dissertation deals with three topics in descriptive set theory. First, the order topology is a natural topology on ordinals. In Chapter 2, a complete classification of order topologies on ordinals up to Borel isomorphism is given, answering a question of Benedikt Löwe. Second, a map between separable metrizable spaces X and Y preserves complete metrizability if Y is completely metrizable whenever X is; the map is resolvable if the image of every open (closed) set in X is resolvable in Y. I… more
Date: May 2010
Creator: Kieftenbeld, Vincent
Item Type: Refine your search to only Thesis or Dissertation
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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
Item Type: Refine your search to only Thesis or Dissertation
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On the density of minimal free subflows of general symbolic flows.

Description: This paper studies symbolic dynamical systems {0, 1}G, where G is a countably infinite group, {0, 1}G has the product topology, and G acts on {0, 1}G by shifts. It is proven that for every countably infinite group G the union of the minimal free subflows of {0, 1}G is dense. In fact, a stronger result is obtained which states that if G is a countably infinite group and U is an open subset of {0, 1}G, then there is a collection of size continuum consisting of pairwise disjoint minimal free subfl… more
Date: August 2009
Creator: Seward, Brandon Michael
Item Type: Refine your search to only Thesis or Dissertation
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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
Item Type: Refine your search to only Thesis or Dissertation
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A New Algorithm for Finding the Minimum Distance between Two Convex Hulls

Description: The problem of computing the minimum distance between two convex hulls has applications to many areas including robotics, computer graphics and path planning. Moreover, determining the minimum distance between two convex hulls plays a significant role in support vector machines (SVM). In this study, a new algorithm for finding the minimum distance between two convex hulls is proposed and investigated. A convergence of the algorithm is proved and applicability of the algorithm to support vector … more
Date: May 2009
Creator: Kaown, Dougsoo
Item Type: Refine your search to only Thesis or Dissertation
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Urysohn ultrametric spaces and isometry groups.

Description: In this dissertation we study a special sub-collection of Polish metric spaces: complete separable ultrametric spaces. Polish metric spaces have been studied for quite a long while, and a lot of results have been obtained. Motivated by some of earlier research, we work on the following two main parts in this dissertation. In the first part, we show the existence of Urysohn Polish R-ultrametric spaces, for an arbitrary countable set R of non-negative numbers, including 0. Then we give point-by-p… more
Date: May 2009
Creator: Shao, Chuang
Item Type: Refine your search to only Thesis or Dissertation
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A Constructive Method for Finding Critical Point of the Ginzburg-Landau Energy Functional

Description: In this work I present a constructive method for finding critical points of the Ginzburg-Landau energy functional using the method of Sobolev gradients. I give a description of the construction of the Sobolev gradient and obtain convergence results for continuous steepest descent with this gradient. I study the Ginzburg-Landau functional with magnetic field and the Ginzburg-Landau functional without magnetic field. I then present the numerical results I obtained by using steepest descent with t… more
Date: August 2008
Creator: Kazemi, Parimah
Item Type: Refine your search to only Thesis or Dissertation
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Spaces of operators containing co and/or l ∞ with an application of vector measures.

Description: The Banach spaces L(X, Y), K(X, Y), Lw*(X*, Y), and Kw*(X*, Y) are studied to determine when they contain the classical Banach spaces co or l ∞. The complementation of the Banach space K(X, Y) in L(X, Y) is discussed as well as what impact this complementation has on the embedding of co or l∞ in K(X, Y) or L(X, Y). Results concerning the complementation of the Banach space Kw*(X*, Y) in Lw*(X*, Y) are also explored and how that complementation affects the embedding of co or l ∞ in Kw*(X*, Y) … more
Date: August 2008
Creator: Schulle, Polly Jane
Item Type: Refine your search to only Thesis or Dissertation
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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
Item Type: Refine your search to only Thesis or Dissertation
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Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups

Description: Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the pr… more
Date: May 2008
Creator: Atim, Alexandru Gabriel
Item Type: Refine your search to only Thesis or Dissertation
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Around the Fibonacci Numeration System

Description: Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we… more
Date: May 2007
Creator: Edson, Marcia Ruth
Item Type: Refine your search to only Thesis or Dissertation
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Determining Properties of Synaptic Structure in a Neural Network through Spike Train Analysis

Description: A "complex" system typically has a relatively large number of dynamically interacting components and tends to exhibit emergent behavior that cannot be explained by analyzing each component separately. A biological neural network is one example of such a system. A multi-agent model of such a network is developed to study the relationships between a network's structure and its spike train output. Using this model, inferences are made about the synaptic structure of networks through cluster analys… more
Date: May 2007
Creator: Brooks, Evan
Item Type: Refine your search to only Thesis or Dissertation
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Compact Operators and the Schrödinger Equation

Description: In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The pape… more
Date: December 2006
Creator: Kazemi, Parimah
Item Type: Refine your search to only Thesis or Dissertation
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