UNT Theses and Dissertations - 213 Matching Results

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Ádám's Conjecture and Its Generalizations

Description: This paper examines idam's conjuecture and some of its generalizations. In terms of Adam's conjecture, we prove Alspach and Parson's results f or Zpq and ZP2. More generally, we prove Babai's characterization of the CI-property, Palfy's characterization of CI-groups, and Brand's result for Zpr for polynomial isomorphism's. We also prove for the first time a characterization of the CI-property for 1 SG, and prove that Zn is a CI-Pn-group where Pn is the group of permutation polynomials on Z,, an… more
Date: August 1990
Creator: Dobson, Edward T. (Edward Tauscher)
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Algebraic Integers

Description: The primary purpose of this thesis is to give a substantial generalization of the set of integers Z, where particular emphasis is given to number theoretic questions such as that of unique factorization. The origin of the thesis came from a study of a special case of generalized integers called the Gaussian Integers, namely the set of all complex numbers in the form n + mi, for m,n in Z. The main generalization involves what are called algebraic integers.
Date: August 1969
Creator: Black, Alvin M.
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Algebraic Number Fields

Description: This thesis investigates various theorems on polynomials over the rationals, algebraic numbers, algebraic integers, and quadratic fields. The material selected in this study is more of a number theoretical aspect than that of an algebraic structural aspect. Therefore, the topics of divisibility, unique factorization, prime numbers, and the roots of certain polynomials have been chosen for primary consideration.
Date: August 1991
Creator: Hartsell, Melanie Lynne
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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
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Algorithms of Schensted and Hillman-Grassl and Operations on Standard Bitableaux

Description: In this thesis, we describe Schensted's algorithm for finding the length of a longest increasing subsequence of a finite sequence. Schensted's algorithm also constructs a bijection between permutations of the first N natural numbers and standard bitableaux of size N. We also describe the Hillman-Grassl algorithm which constructs a bijection between reverse plane partitions and the solutions in natural numbers of a linear equation involving hook lengths. Pascal programs and sample output for bot… more
Date: August 1983
Creator: Sutherland, David C. (David Craig)
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Applications of a Model-Theoretic Approach to Borel Equivalence Relations

Description: The study of Borel equivalence relations on Polish spaces has become a major area of focus within descriptive set theory. Primarily, work in this area has been carried out using the standard methods of descriptive set theory. In this work, however, we develop a model-theoretic framework suitable for the study of Borel equivalence relations, introducing a class of objects we call Borel structurings. We then use these structurings to examine conditions under which marker sets for Borel equival… more
Date: August 2019
Creator: Craft, Colin N.
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Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory

Description: In this dissertation the results of Jerrum and Sinclair on the conductance of Markov chains are used to prove that almost all generalized Steinhaus graphs are rapidly mixing and an algorithm for the uniform generation of 2 - (4k + 1,4,1) cyclic Mendelsohn designs is developed.
Date: August 1993
Creator: Simmons, Dayton C. (Dayton Cooper)
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An Approximate Solution to the Dirichlet Problem

Description: In the category of mathematics called partial differential equations there is a particular type of problem called the Dirichlet problem. Proof is given in many partial differential equation books that every Dirichlet problem has one and only one solution. The explicit solution is very often not easily determined, so that a method for approximating the solution at certain points becomes desirable. The purpose of this paper is to present and investigate one such method.
Date: August 1964
Creator: Redwine, Edward William
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Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

Description: In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedr… more
Date: August 1986
Creator: Sutherland, David C. (David Craig)
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Axiom of Choice Equivalences and Some Applications

Description: In this paper several equivalences of the axiom of choice are examined. In particular, the axiom of choice, Zorn's lemma, Tukey's lemma, the Hausdorff maximal principle, and the well-ordering theorem are shown to be equivalent. Cardinal and ordinal number theory is also studied. The Schroder-Bernstein theorem is proven and used in establishing order results for cardinal numbers. It is also demonstrated that the first uncountable ordinal space is unique up to order isomorphism. We conclude by en… more
Date: August 1983
Creator: Race, Denise T. (Denise Tatsch)
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Banach Spaces and Weak and Weak* Topologies

Description: This paper examines several questions regarding Banach spaces, completeness and compactness of Banach spaces, dual spaces and weak and weak* topologies. Examples of completeness and isometries are given using the c₀ and 𝓁ᴰ spaces. The Hahn-Banach extension theorem is presented, along with some applications. General theory about finite and infinite dimensional normed linear spaces is the bulk of the second chapter. A proof of the uniform boundedness principle is also given. Chapter three talks i… more
Date: August 1989
Creator: Kirk, Andrew F. (Andrew Fitzgerald)
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Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank

Description: Let G be a Lie group acting on a homogeneous space G/K. The center of the universal enveloping algebra of the Lie algebra of G maps homomorphically into the center of the algebra of differential operators on G/K invariant under the action of G. In the case that G is a Jacobi Lie group of rank 2, we prove that this homomorphism is surjective and hence that the center of the invariant differential operator algebra is the image of the center of the universal enveloping algebra. This is an extensio… more
Date: August 2013
Creator: Dahal, Rabin
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A Characterization of Homeomorphic Bernoulli Trial Measures.

Description: We give conditions which, given two Bernoulli trial measures, determine whether there exists a homeomorphism of Cantor space which sends one measure to the other, answering a question of Oxtoby. We then provide examples, relating these results to the notions of good and refinable measures on Cantor space.
Date: August 2006
Creator: Yingst, Andrew Q.
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Characterizations of Some Combinatorial Geometries

Description: We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a ch… more
Date: August 1992
Creator: Yoon, Young-jin
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A Classification of the Homogeneity of Countable Products of Subsets of Real Numbers

Description: Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And f… more
Date: August 2017
Creator: Allen, Cristian Gerardo
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Compactness and Equivalent Notions

Description: One of the classic theorems concerning the real numbers states that every open cover of a closed and bounded subset of the real line contains a finite subcover. Compactness is an abstraction of that notion, and there are several ideas concerning it which are equivalent and many which are similar. The purpose of this paper is to synthesize the more important of these ideas. This synthesis is accomplished by demonstrating either situations in which two ordinarily different conditions are equivale… more
Date: August 1967
Creator: Bell, Wayne Charles
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A Comparative Study of Non Linear Conjugate Gradient Methods

Description: We study the development of nonlinear conjugate gradient methods, Fletcher Reeves (FR) and Polak Ribiere (PR). FR extends the linear conjugate gradient method to nonlinear functions by incorporating two changes, for the step length αk a line search is performed and replacing the residual, rk (rk=b-Axk) by the gradient of the nonlinear objective function. The PR method is equivalent to FR method for exact line searches and when the underlying quadratic function is strongly convex. The PR method … more
Date: August 2013
Creator: Pathak, Subrat
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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
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Complete Ordered Fields

Description: The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a … more
Date: August 1977
Creator: Arnold, Thompson Sharon
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