UNT Theses and Dissertations - 8 Matching Results

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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
Partner: UNT Libraries

A Global Spatial Model for Loop Pattern Fingerprints and Its Spectral Analysis

Description: The use of fingerprints for personal identification has been around for thousands of years (first established in ancient China and India). Fingerprint identification is based on two basic premises that the fingerprint is unique to an individual and the basic characteristics such as ridge pattern do not change over time. Despite extensive research, there are still mathematical challenges in characterization of fingerprints, matching and compression. We develop a new mathematical model in the spa… more
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Date: August 2019
Creator: Wu, Di
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries

A Novel Two-Stage Adaptive Method for Estimating Large Covariance and Precision Matrices

Description: Estimating large covariance and precision (inverse covariance) matrices has become increasingly important in high dimensional statistics because of its wide applications. The estimation problem is challenging not only theoretically due to the constraint of its positive definiteness, but also computationally because of the curse of dimensionality. Many types of estimators have been proposed such as thresholding under the sparsity assumption of the target matrix, banding and tapering the sample c… more
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Date: August 2019
Creator: Rajendran, Rajanikanth
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Prophet Inequalities for Multivariate Random Variables with Cost for Observations

Description: In prophet problems, two players with different levels of information make decisions to optimize their return from an underlying optimal stopping problem. The player with more information is called the "prophet" while the player with less information is known as the "gambler." In this thesis, as in the majority of the literature on such problems, we assume that the prophet is omniscient, and the gambler does not know future outcomes when making his decisions. Certainly, the prophet will get a b… more
Date: August 2019
Creator: Brophy, Edmond M.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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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
Partner: UNT Libraries
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Annihilators of Bounded Indecomposable Modules of Vec(R)

Description: The Lie algebra Vec(ℝ) of polynomial vector fields on the line acts naturally on ℂ[]. This action has a one-parameter family of deformations called the tensor density modules F_λ. The bounded indecomposable modules of Vec(ℝ) of length 2 composed of tensor density modules have been classified by Feigin and Fuchs. We present progress towards describing the annihilators of the unique indecomposable extension of F_λ by F_(λ+2) in the non-resonant case λ ≠ -½. We give the intersection of the annihil… more
Date: May 2019
Creator: Kenefake, Tyler Christian
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Equivalence of the Rothberger and k-Rothberger Games for Hausdorff Spaces

Description: First, we show that the Rothberger and 2-Rothberger games are equivalent. Then we adjust the former proof and introduce another game, the restricted Menger game, in order to obtain a broader result. This provides an answer in the context of Hausdorff spaces for an open question posed by Aurichi, Bella, and Dias.
Date: May 2019
Creator: Hiers, Nathaniel Christopher
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
open access

Infinitary Combinatorics and the Spreading Models of Banach Spaces

Description: Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks… more
Date: May 2019
Creator: Krause, Cory A.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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