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 Resource Type: Thesis or Dissertation
 Degree Discipline: Mathematics
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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Borel Determinacy and Metamathematics

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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Borel Sets and Baire Functions

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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Bounded, Finitely Additive, but Not Absolutely Continuous Set Functions

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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The Buckling of a Uniformly Compressed Plate with Intermediate Supports

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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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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