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Results in Algebraic Determinedness and an Extension of the Baire Property

Description: In this work, we concern ourselves with particular topics in Polish space theory. We first consider the space A(U) of complex-analytic functions on an open set U endowed with the usual topology of uniform convergence on compact subsets. With the operations of point-wise addition and point-wise multiplication, A(U) is a Polish ring. Inspired by L. Bers' algebraic characterization of the relation of conformality, we show that the topology on A(U) is the only Polish topology for which A(U) is a Po… more
Date: May 2017
Creator: Caruvana, Christopher
Item Type: Refine your search to only Thesis or Dissertation
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The Use of the Power Method to Find Dominant Eigenvalues of Matrices

Description: This paper is the result of a study of the power method to find dominant eigenvalues of square matrices. It introduces ideas basic to the study and shows the development of the power method for the most well-behaved matrices possible, and it explores exactly which other types of matrices yield to the power method. The paper also discusses a type of matrix typically considered impossible for the power method, along with a modification of the power method which works for this type of matrix. It g… more
Date: July 1992
Creator: Cavender, Terri A.
Item Type: Refine your search to only Thesis or Dissertation
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The Relative Complexity of Various Classification Problems among Compact Metric Spaces

Description: In this thesis, we discuss three main projects which are related to Polish groups and their actions on standard Borel spaces. In the first part, we show that the complexity of the classification problem of continua is Borel bireducible to a universal orbit equivalence relation induce by a Polish group on a standard Borel space. In the second part, we compare the relative complexity of various types of classification problems concerning subspaces of [0,1]^n for all natural number n. In the last … more
Date: May 2016
Creator: Chang, Cheng
Item Type: Refine your search to only Thesis or Dissertation
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Simplicial Homology

Description: The purpose of this thesis is to construct the homology groups of a complex over an R-module. The thesis begins with hyperplanes in Euclidean n-space. Simplexes and complexes are defined, and orientations are given to each simplex of a complex. The chains of a complex are defined, and each chain is assigned a boundary. The function which assigns to each chain a boundary defines the set of r-dimensional cycles and the set of r—dimensional bounding cycles. The quotient of those two submodules is … more
Date: August 1973
Creator: Chang, Chih-Chen
Item Type: Refine your search to only Thesis or Dissertation
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Which Came First : The Measure or the Integral?

Description: This thesis provides a development of integration from two different points of view. In Chapter I, a measure and a measurable function are defined. A theory of integration is then developed in Chapter II based on the measure. In Chapter III, the integral is introduced directly without first going through the process of defining a measure, and a measure is developed from the integral. The concluding chapter shows the equivalence of the two integrals under rather general conditions.
Date: June 1966
Creator: Chapman, John Barnes
Item Type: Refine your search to only Thesis or Dissertation
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Invertible Ideals and the Strong Two-Generator Property in Some Polynomial Subrings

Description: Let K be any field and Q be the rationals. Define K^1[X] = {f(X) e K[X]| the coefficient of X in f(X) is zero} and Q^1β[X] = {f(X) e Q[X]| the coefficent of β1(X) in the binomial expansion of f(X) is zero}, where {β1(X)}^∞ i=0 are the well-known binomial polynomials. In this work, I establish the following results: K^1[X] and Q^1β[X] are one-dimensional, Noetherian, non-Prüfer domains with the two-generator property on ideals. Using the unique factorization structure of the overrings K[X] and Q… more
Date: May 1987
Creator: Chapman, Scott T. (Scott Thomas)
Item Type: Refine your search to only Thesis or Dissertation
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Results on Non-Club Isomorphic Aronszajn Trees

Description: In this dissertation we prove some results about the existence of families of Aronszajn trees on successors of regular cardinals which are pairwise not club isomorphic. The history of this topic begins with a theorem of Gaifman and Specker in the 1960s which asserts the existence from ZFC of many pairwise not isomorphic Aronszajn trees. Since that result was proven, the focus has turned to comparing Aronszajn trees with respect to isomorphisms on a club of levels, instead of on the entire tre… more
Date: August 2020
Creator: Chavez, Jose
Item Type: Refine your search to only Thesis or Dissertation
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Thermodynamical Formalism

Description: Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressu… more
Date: August 2004
Creator: Chousionis, Vasileios
Item Type: Refine your search to only Thesis or Dissertation
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Descriptive Set Theory and Measure Theory in Locally Compact and Non-locally Compact Groups

Description: In this thesis we study descriptive-set-theoretic and measure-theoretic properties of Polish groups, with a thematic emphasis on the contrast between groups which are locally compact and those which are not. The work is divided into three major sections. In the first, working jointly with Robert Kallman, we resolve a conjecture of Gleason regarding the Polish topologization of abstract groups of homeomorphisms. We show that Gleason's conjecture is false, and its conclusion is only true when the… more
Date: May 2013
Creator: Cohen, Michael Patrick
Item Type: Refine your search to only Thesis or Dissertation
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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

Description: In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal mea… more
Date: May 2005
Creator: Coiculescu, Ion
Item Type: Refine your search to only Thesis or Dissertation
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A Comparison of Velocities Computed by Two-Dimensional Potential Theory and Velocities Measured in the Vicinity of an Airfoil

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.
Date: June 1947
Creator: Copp, George
Item Type: Refine your search to only Thesis or Dissertation
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Properties of Limit Functions

Description: The purpose of this paper is to investigate properties of functions which are limits of functions with prescribed properties. Chapter II asks the question "Does a function which is the limit of a sequence of functions each of which is endowed with a certain property necessarily have that property?"
Date: December 1972
Creator: Coppin, Anthony M.
Item Type: Refine your search to only Thesis or Dissertation
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Mechanization of Aircraft Performance

Description: The purpose of this paper is to describe the mechanization of the basic equations of motion for the performance and maneuver characteristics of an airplane with some simplifications which render solutions more practicable. The results of a study made to program these equations for calculation by the IBM MODEL 650 digital computer are presented as well as the steps to be taken in using this method of calculation.
Date: 1956
Creator: Cotten, Frances Patterson
Item Type: Refine your search to only Thesis or Dissertation
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Abelian Group Actions and Hypersmooth Equivalence Relations

Description: We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian grou… more
Date: May 2019
Creator: Cotton, Michael R.
Item Type: Refine your search to only Thesis or Dissertation
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Applications of a Model-Theoretic Approach to Borel Equivalence Relations

Description: The study of Borel equivalence relations on Polish spaces has become a major area of focus within descriptive set theory. Primarily, work in this area has been carried out using the standard methods of descriptive set theory. In this work, however, we develop a model-theoretic framework suitable for the study of Borel equivalence relations, introducing a class of objects we call Borel structurings. We then use these structurings to examine conditions under which marker sets for Borel equival… more
Date: August 2019
Creator: Craft, Colin N.
Item Type: Refine your search to only Thesis or Dissertation
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