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 Resource Type: Thesis or Dissertation
 Degree Discipline: Mathematics
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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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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Compact Operators and the Schrödinger Equation

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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Compact Topological Spaces

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