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**Degree Discipline:**Mathematics

**Collection:**UNT Theses and Dissertations

### A Comparison of Velocities Computed by Two-Dimensional Potential Theory and Velocities Measured in the Vicinity of an Airfoil

**Date:**June 1947

**Creator:**Copp, George

**Description:**In treating the motion of a fluid mathematically, it is convenient to make some simplifying assumptions. The assumptions which are made will be justifiable if they save long and laborious computations in practical problems, and if the predicted results agree closely enough with experimental results for practical use. In dealing with the flow of air about an airfoil, at subsonic speeds, the fluid will be considered as a homogeneous, incompressible, inviscid fluid.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc699611/

### Complemented Subspaces of Bounded Linear Operators

**Date:**August 2003

**Creator:**Bahreini Esfahani, Manijeh

**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 ) be the space of all compact operators, and W(X, Y ) be the space of all weakly compact operators. We denote space all operator ideals by O.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4349/

### Complete Ordered Fields

**Date:**August 1977

**Creator:**Arnold, Thompson Sharon

**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 least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc504449/

### Completely Simple Semigroups

**Date:**August 1968

**Creator:**Barker, Bruce W.

**Description:**The purpose of this thesis is to explore some of the characteristics of 0-simple semigroups and completely 0-simple semigroups.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130974/

### Completeness Axioms in an Ordered Field

**Date:**December 1971

**Creator:**Carter, Louis Marie

**Description:**The purpose of this paper was to prove the equivalence of the following completeness axioms. This purpose was carried out by first defining an ordered field and developing some basic theorems relative to it, then proving that lim [(u+u)*]^n = z (where u is the multiplicative identity, z is the additive identity, and * indicates the multiplicative inverse of an element), and finally proving the equivalence of the five axioms.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131462/

### Completing the Space of Step Functions

**Date:**August 1972

**Creator:**Massey, Linda K.

**Description:**In this thesis a study is made of the space X of all step functions on [0,1]. This investigation includes determining a completion space, X*, for the incomplete space X, defining integration for X*, and proving some theorems about integration in X*.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc164014/

### A Computation of Partial Isomorphism Rank on Ordinal Structures

**Date:**August 2006

**Creator:**Bryant, Ross

**Description:**We compute the partial isomorphism rank, in the sense Scott and Karp, of a pair of ordinal structures using an Ehrenfeucht-Fraisse game. A complete formula is proven by induction given any two arbitrary ordinals written in Cantor normal form.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc5387/

### The Computation of Ultrapowers by Supercompactness Measures

**Date:**August 1999

**Creator:**Smith, John C.

**Description:**The results from this dissertation are a computation of ultrapowers by supercompactness measures and concepts related to such measures. The second chapter gives an overview of the basic ideas required to carry out the computations. Included are preliminary ideas connected to measures, and the supercompactness measures. Order type results are also considered in this chapter. In chapter III we give an alternate characterization of 2 using the notion of iterated ordinal measures. Basic facts related to this characterization are also considered here. The remaining chapters are devoted to finding bounds fwith arguments taking place both inside and outside the ultrapowers. Conditions related to the upper bound are given in chapter VI.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2201/

### Concerning linear spaces

**Date:**June 1965

**Creator:**Gilbreath, Joe

**Description:**The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130586/

### Concerning Measure Theory

**Date:**August 1972

**Creator:**Glasscock, Robert Ray

**Description:**The purpose of this thesis is to study the concept of measure and associated concepts. The study is general in nature; that is, no particular examples of a measure are given.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131547/