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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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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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