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Abelian Group Actions and Hypersmooth Equivalence Relations

Description: We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian grou… more
Date: May 2019
Creator: Cotton, Michael R.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Results in Algebraic Determinedness and an Extension of the Baire Property

Description: In this work, we concern ourselves with particular topics in Polish space theory. We first consider the space A(U) of complex-analytic functions on an open set U endowed with the usual topology of uniform convergence on compact subsets. With the operations of point-wise addition and point-wise multiplication, A(U) is a Polish ring. Inspired by L. Bers' algebraic characterization of the relation of conformality, we show that the topology on A(U) is the only Polish topology for which A(U) is a Po… more
Date: May 2017
Creator: Caruvana, Christopher
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Fourier Transforms of Functions on a Finite Abelian Group

Description: This paper presents a theory of Fourier transforms of complex-valued functions on a finite abelian group and investigates two applications of this theory. Chapter I is an introduction with remarks on notation. Basic theory, including Pontrvagin duality and the Poisson Summation formula, is the subject of Chapter II. In Chapter III the Fourier transform is viewed as an intertwining operator for certain unitary group representations. The solution of the eigenvalue problem of the Fourier transform… more
Date: August 1982
Creator: Currey, Bradley Norton
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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The Cohomology for the Nil Radical of a Complex Semisimple Lie Algebra

Description: Let g be a complex semisimple Lie algebra, Vλ an irreducible g-module with high weight λ, pI a standard parabolic subalgebra of g with Levi factor £I and nil radical nI, and H*(nI, Vλ) the cohomology group of Λn'I ⊗Vλ. We describe the decomposition of H*(nI, Vλ) into irreducible £1-modules.
Date: May 1994
Creator: Sawyer, Cameron C. (Cameron Cunningham)
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Fundamental Issues in Support Vector Machines

Description: This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be … more
Date: May 2014
Creator: McWhorter, Samuel P.
Item Type: Refine your search to only Thesis or Dissertation
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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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Partner: UNT Libraries
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Measurable Selection Theorems for Partitions of Polish Spaces into Gδ Equivalence Classes

Description: Let X be a Polish space and Q a measurable partition of X into Gδ equivalence classes. In 1978, S. M. Srivastava proved the existence of a Borel cross section for Q. He asked whether more can be concluded in case each equivalence class is uncountable. This question is answered here in the affirmative. The main result of the author is a proof that shows the existence of a Castaing Representation for Q.
Date: May 1980
Creator: Simrin, Harry S.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Polynomial Isomorphisms of Cayley Objects Over a Finite Field

Description: In this dissertation the Bays-Lambossy theorem is generalized to GF(pn). The Bays-Lambossy theorem states that if two Cayley objects each based on GF(p) are isomorphic then they are isomorphic by a multiplier map. We use this characterization to show that under certain conditions two isomorphic Cayley objects over GF(pn) must be isomorphic by a function on GF(pn) of a particular type.
Date: December 1989
Creator: Park, Hong Goo
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Minimality of the Special Linear Groups

Description: Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, q… more
Date: December 1997
Creator: Hayes, Diana Margaret
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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A Topological Uniqueness Result for the Special Linear Groups

Description: The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Date: August 1997
Creator: Opalecky, Robert Vincent
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Using Steepest Descent to Find Energy-Minimizing Maps Satisfying Nonlinear Constraints

Description: The method of steepest descent is applied to a nonlinearly constrained optimization problem which arises in the study of liquid crystals. Let Ω denote the region bounded by two coaxial cylinders of height 1 with the outer cylinder having radius 1 and the inner having radius ρ. The problem is to find a mapping, u, from Ω into R^3 which agrees with a given function v on the surfaces of the cylinders and minimizes the energy function over the set of functions in the Sobolev space H^(1,2)(Ω; R^3) h… more
Date: August 1994
Creator: Garza, Javier, 1965-
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Descriptive Set Theory and Measure Theory in Locally Compact and Non-locally Compact Groups

Description: In this thesis we study descriptive-set-theoretic and measure-theoretic properties of Polish groups, with a thematic emphasis on the contrast between groups which are locally compact and those which are not. The work is divided into three major sections. In the first, working jointly with Robert Kallman, we resolve a conjecture of Gleason regarding the Polish topologization of abstract groups of homeomorphisms. We show that Gleason's conjecture is false, and its conclusion is only true when the… more
Date: May 2013
Creator: Cohen, Michael Patrick
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Partner: UNT Libraries
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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
Partner: UNT Libraries
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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
Partner: UNT Libraries
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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
Partner: UNT Libraries
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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
Partner: UNT Libraries
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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
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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
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Partner: UNT Libraries

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
Partner: UNT Libraries
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