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**Degree Discipline:**Mathematics

**Collection:**UNT Theses and Dissertations

### 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.

**Contributing Partner:**UNT Libraries

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

### 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.

**Contributing Partner:**UNT Libraries

**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.

**Contributing Partner:**UNT Libraries

**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.

**Contributing Partner:**UNT Libraries

**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.

**Contributing Partner:**UNT Libraries

**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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc283864/

### 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/