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  Partner: UNT Libraries
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
The Analytical Development of the Trigonometric Functions

The Analytical Development of the Trigonometric Functions

Date: 1951
Creator: Mackey, Pearl Cherrington
Description: This thesis is a study of the analytical development of the trigonometric functions.
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Applications in Fixed Point Theory

Applications in Fixed Point Theory

Date: December 2005
Creator: Farmer, Matthew Ray
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 conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.
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Applications of Graph Theory and Topology to Combinatorial Designs

Applications of Graph Theory and Topology to Combinatorial Designs

Date: December 1988
Creator: Somporn Sutinuntopas
Description: This dissertation is concerned with the existence and the isomorphism of designs. The first part studies the existence of designs. Chapter I shows how to obtain a design from a difference family. Chapters II to IV study the existence of an affine 3-(p^m,4,λ) design where the v-set is the Galois field GF(p^m). Associated to each prime p, this paper constructs a graph. If the graph has a 1-factor, then a difference family and hence an affine design exists. The question arises of how to determine when the graph has a 1-factor. It is not hard to see that the graph is connected and of even order. Tutte's theorem shows that if the graph is 2-connected and regular of degree three, then the graph has a 1-factor. By using the concept of quadratic reciprocity, this paper shows that if p Ξ 53 or 77 (mod 120), the graph is almost regular of degree three, i.e., every vertex has degree three, except two vertices each have degree tow. Adding an extra edge joining the two vertices with degree tow gives a regular graph of degree three. Also, Tutte proved that if A is an edge of the graph satisfying the above conditions, ...
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Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory

Applications of Rapidly Mixing Markov Chains to Problems in Graph Theory

Date: August 1993
Creator: Simmons, Dayton C. (Dayton Cooper)
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.
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An Approximate Solution to the Dirichlet Problem

An Approximate Solution to the Dirichlet Problem

Date: August 1964
Creator: Redwine, Edward William
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.
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Around the Fibonacci Numeration System

Around the Fibonacci Numeration System

Date: May 2007
Creator: Edson, Marcia Ruth
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 give a formula for R(n) in terms of binomial coefficients modulo two.
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Aspects of Universality in Function Iteration

Aspects of Universality in Function Iteration

Date: December 1991
Creator: Taylor, John (John Allen)
Description: This work deals with some aspects of universal topological and metric dynamic behavior of iterated maps of the interval.
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Atmospheric Gusts and Their Effect on Aircraft

Atmospheric Gusts and Their Effect on Aircraft

Date: August 1958
Creator: Walling, Waunnetta Keene
Description: This thesis investigates atmospheric gusts and their effect on aircraft.
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Automorphism Groups

Automorphism Groups

Date: August 1965
Creator: Edwards, Donald Eugene
Description: This paper will be concerned mainly with automorphisms of groups. The concept of a group endomorphism will be used at various points in this paper.
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Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

Date: August 1986
Creator: Sutherland, David C. (David Craig)
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 dihedral group D_4.
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Basic Fourier Transforms

Basic Fourier Transforms

Date: January 1962
Creator: Cumbie, James Randolph
Description: The purpose of this paper is to develop some of the more basic Fourier transforms which are the outgrowth of the Fourier theorem. Although often approached from the stand-point of the series, this paper will approach the theorem from the standpoint of the integral.
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Borel Determinacy and Metamathematics

Borel Determinacy and Metamathematics

Date: December 2001
Creator: Bryant, Ross
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 a Borel set of Turing degrees that neither contains nor omits a cone; so by another theorem of Martin, Borel Determinacy is not a theorem of ZC. This paper contains three main sections: Martin's proof of Borel Determinacy; a simpler example of Friedman's result, namely, (in ZFC) a coanalytic set of Turing degrees that neither contains nor omits a cone; and finally, the Friedman result.
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Borel Sets and Baire Functions

Borel Sets and Baire Functions

Date: January 1970
Creator: Wemple, Fred W.
Description: This paper examines the relationship between Borel sets and Baire functions.
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Bounded, Finitely Additive, but Not Absolutely Continuous Set Functions

Bounded, Finitely Additive, but Not Absolutely Continuous Set Functions

Date: May 1989
Creator: Gurney, David R. (David Robert)
Description: In leading up to the proof, methods for constructing fields and finitely additive set functions are introduced with an application involving the Tagaki function given as an example. Also, non-absolutely continuous set functions are constructed using Banach limits and maximal filters.
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The Buckling of a Uniformly Compressed Plate with Intermediate Supports

The Buckling of a Uniformly Compressed Plate with Intermediate Supports

Date: 1949
Creator: Dean, Thomas S.
Description: This problem has been selected from the mathematical theory of elasticity. We consider a rectangular plate of thickness h, length a, and width b. The plate is subjected to compressive forces. These forces act in the neutral plane and give the plate a tendency to buckle. However, this problem differs from other plate problems in that it is assumed that there are two intermediate supports located on the edges of the plate parallel to the compressive forces.
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The Cantor Ternary Set and Certain of its Generalizations and Applications

The Cantor Ternary Set and Certain of its Generalizations and Applications

Date: 1942
Creator: Hembree, Gwendolyn
Description: This thesis covers the Cantor Ternary Set and generalizations of the Cantor Set, and gives a complete existential theory for three set properties: denumerability, exhaustibility, and zero measure.
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Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank

Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank

Date: August 2013
Creator: Dahal, Rabin
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 extension of work of Bringmann, Conley, and Richter in the rank 1case.
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Certain Properties of Functions Related to Exhaustibility

Certain Properties of Functions Related to Exhaustibility

Date: 1952
Creator: Bradford, James C.
Description: In this thesis, we shall attempt to present a study of certain properties of real functions related to the set property exhaustible.
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A Characterization of Homeomorphic Bernoulli Trial Measures.

A Characterization of Homeomorphic Bernoulli Trial Measures.

Date: August 2006
Creator: Yingst, Andrew Q.
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.
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Characterizations of Continua of Finite Degree

Characterizations of Continua of Finite Degree

Date: August 2006
Creator: Irwin, Shana
Description: In this thesis, some characterizations of continua of finite degree are given. It turns out that being of finite degree (by formal definition) can be described by saying there exists an equivalent metric in which Hausdorff linear measure of the continuum is finite. I discuss this result in detail.
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Characterizations of Some Combinatorial Geometries

Characterizations of Some Combinatorial Geometries

Date: August 1992
Creator: Yoon, Young-jin
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 characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
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A Classification of Regular Planar Graphs

A Classification of Regular Planar Graphs

Date: December 1972
Creator: McCalla, Linda F.
Description: The purpose of this paper is the investigation and classification of regular planar graphs. The motive behind this investigation was a desire to better understand those properties which allow a graph to be represented in the plane in such a manner that no two edges cross except perhaps at vertices.
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A Collapsing Result Using the Axiom of Determinancy and the Theory of Possible Cofinalities

A Collapsing Result Using the Axiom of Determinancy and the Theory of Possible Cofinalities

Date: May 2001
Creator: May, Russell J.
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
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Compact Convex Sets in Linear Topological Spaces

Compact Convex Sets in Linear Topological Spaces

Date: May 1964
Creator: Read, David R.
Description: The purpose of this paper is to examine properties of convex sets in linear topological spaces with special emphasis on compact convex sets.
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