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**Partner:**UNT Libraries

**Department:**Department of Mathematics

**Collection:**UNT Theses and Dissertations

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130613/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc330906/

### Axiom of Choice Equivalences and Some Applications

**Date:**August 1983

**Creator:**Race, Denise T. (Denise Tatsch)

**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 encountering several applications of the axiom of choice. In particular, we show that every vector space must have a Hamel basis and that any two Hamel bases for the same space must have the same cardinality. We establish that the Tychonoff product theorem implies the axiom of choice and see the use of the axiom of choice in the proof of the Hahn- Banach theorem.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc504170/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130482/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc3061/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc163964/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc332375/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc83479/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc70344/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc283833/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc107821/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc5331/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc5367/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc277894/

### Chebyshev Subsets in Smooth Normed Linear Spaces

**Date:**December 1974

**Creator:**Svrcek, Frank J.

**Description:**This paper is a study of the relation between smoothness of the norm on a normed linear space and the property that every Chebyshev subset is convex. Every normed linear space of finite dimension, having a smooth norm, has the property that every Chebyshev subset is convex. In the second chapter two properties of the norm, uniform Gateaux differentiability and uniform Frechet differentiability where the latter implies the former, are given and are shown to be equivalent to smoothness of the norm in spaces of finite dimension. In the third chapter it is shown that every reflexive normed linear space having a uniformly Gateaux differentiable norm has the property that every weakly closed Chebyshev subset, with non-empty weak interior that is norm-wise dense in the subset, is convex.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc663499/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc164029/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc2789/

### 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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130516/

### Compact Operators and the Schrödinger Equation

**Date:**December 2006

**Creator:**Kazemi, Parimah

**Description:**In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The paper finishes with a discussion of examples of Schrödinger equations and the solutions.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc5453/

### Compact Topological Spaces

**Date:**June 1964

**Creator:**Conway, Thomas M.

**Description:**The purpose of this paper is to investigate some properties of compact topological spaces and to relate these concepts to the separation properties.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130506/

### Compactness and Equivalent Notions

**Date:**August 1967

**Creator:**Bell, Wayne Charles

**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 equivalent or combinations of two or more properties which will guarantee a third.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130821/

### The Comparability of Cardinals

**Date:**May 1964

**Creator:**Owen, Aubrey P.

**Description:**The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130514/

### A Comparative Study of Non Linear Conjugate Gradient Methods

**Date:**August 2013

**Creator:**Pathak, Subrat

**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 is basically a variant of FR and primarily differs from it in the choice of the parameter βk. On applying the nonlinear Rosenbrock function to the MATLAB code for the FR and the PR algorithms we observe that the performance of PR method (k=29) is far better than the FR method (k=42). But, we observe that when the MATLAB codes are applied to general nonlinear functions, specifically functions whose minimum is a large negative number not close to zero and the iterates too are large values far off from zero the PR algorithm does not perform well. This problem with the PR method persists even if we run the PR algorithm for more iterations or with an initial guess closer to the ...

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### Comparison of Some Mappings in Topology

**Date:**January 1964

**Creator:**Aslan, Farhad

**Description:**The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108253/