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A Continuous, Nowhere-Differentiable Function with a Dense Set of Proper Local Extrema

Description: In this paper, we use the following scheme to construct a continuous, nowhere-differentiable function 𝑓 which is the uniform limit of a sequence of sawtooth functions 𝑓ₙ : [0, 1] β†’ [0, 1] with increasingly sharp teeth. Let 𝑋 = [0, 1] x [0, 1] and 𝐹(𝑋) be the Hausdorff metric space determined by 𝑋. We define contraction maps 𝑀₁ , 𝑀₂ , 𝑀₃ on 𝑋. These maps define a contraction map 𝑀 on 𝐹(𝑋) via 𝑀(𝐴) = 𝑀₁(𝐴) ⋃ 𝑀₂(𝐴) ⋃ 𝑀₃(𝐴). The iteration under 𝑀 of the diagonal in 𝑋 defines a sequence of graphs of… more
Date: December 1993
Creator: Huggins, Mark C. (Mark Christopher)
Item Type: Refine your search to only Thesis or Dissertation
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Continuous, Nowhere-Differentiable Functions with no Finite or Infinite One-Sided Derivative Anywhere

Description: In this paper, we study continuous functions with no finite or infinite one-sided derivative anywhere. In 1925, A. S. Beskovitch published an example of such a function. Since then we call them Beskovitch functions. This construction is presented in chapter 2, The example was simple enough to clear the doubts about the existence of Besicovitch functions. In 1932, S. Saks showed that the set of Besicovitch functions is only a meager set in C[0,1]. Thus the Baire category method for showing the e… more
Date: December 1994
Creator: Lee, Jae S. (Jae Seung)
Item Type: Refine your search to only Thesis or Dissertation
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Continuous Solutions of Laplace's Equation in Two Variables

Description: In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.
Date: May 1968
Creator: Johnson, Wiley A.
Item Type: Refine your search to only Thesis or Dissertation
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The Continuous Wavelet Transform and the Wave Front Set

Description: In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.
Date: December 1993
Creator: Navarro, Jaime
Item Type: Refine your search to only Thesis or Dissertation
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Contributions to Descriptive Set Theory

Description: In this dissertation we study closure properties of pointclasses, scales on sets of reals and the models L[T2n], which are very natural canonical inner models of ZFC. We first characterize projective-like hierarchies by their associated ordinals. This solves a conjecture of Steel and a conjecture of Kechris, Solovay, and Steel. The solution to the first conjecture allows us in particular to reprove a strong partition property result on the ordinal of a Steel pointclass and derive a new boundedn… more
Date: August 2015
Creator: Atmai, Rachid
Item Type: Refine your search to only Thesis or Dissertation
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Contributions to Descriptive Set Theory

Description: Assume AD+V=L(R). In the first chapter, let W^1_1 denote the club measure on \omega_1. We analyze the embedding j_{W^1_1}\restr HOD from the point of view of inner model theory. We use our analysis to answer a question of Jackson-Ketchersid about codes for ordinals less than \omega_\omega. In the second chapter, we provide an indiscernibles analysis for models of the form L[T_n,x]. We use our analysis to provide new proofs of the strong partition property on \delta^1_{2n+1}
Date: December 2016
Creator: Dance, Cody
Item Type: Refine your search to only Thesis or Dissertation
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Contributions to Geometry and Graph Theory

Description: In geometry we will consider n-dimensional generalizations of the Power of a Point Theorem and of Pascal's Hexagon Theorem. In generalizing the Power of a Point Theorem, we will consider collections of cones determined by the intersections of an (n-1)-sphere and a pair of hyperplanes. We will then use these constructions to produce an n-dimensional generalization of Pascal's Hexagon Theorem, a classical plane geometry result which states that "Given a hexagon inscribed in a conic section, the… more
Date: August 2020
Creator: Schuerger, Houston S
Item Type: Refine your search to only Thesis or Dissertation
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Convergence of Conditional Expectation Operators and the Compact Range Property

Description: The interplay between generalizations of Riezs' famous representation theorem and Radon-NikodΓ½m type theorems has a long history. This paper will explore certain aspects of the theory of bounded linear operators on continuous function spaces, Radon-NikodΓ½m type properties, and their connections.
Date: August 1992
Creator: Dawson, C. Bryan (Charles Bryan)
Item Type: Refine your search to only Thesis or Dissertation
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Convergence of Infinite Series

Description: The purpose of this paper is to examine certain questions concerning infinite series. The first chapter introduces several basic definitions and theorems from calculus. In particular, this chapter contains the proofs for various convergence tests for series of real numbers. The second chapter deals primarily with the equivalence of absolute convergence, unconditional convergence, bounded multiplier convergence, and c0 multiplier convergence for series of real numbers. Also included in this chap… more
Date: August 1983
Creator: Abbott, Catherine Ann
Item Type: Refine your search to only Thesis or Dissertation
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Convergence Tests for Infinite Series

Description: The field of infinite series is so large that any investigation into that field must necessarily be limited to a particular phase. An attempt has been made to develop a number of tests having a wide range of applications. Particular emphasis has been placed on tests for series of positive terms.
Date: 1950
Creator: Latimer, Philip W.
Item Type: Refine your search to only Thesis or Dissertation
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Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial

Description: The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots are equivalent, as defined in this investigation, then they receive identical polynomials. Yet, if two knots have identical polynomials, no information about their equivalence may be obtained. To define … more
Date: December 1986
Creator: Woodard, Mary Kay
Item Type: Refine your search to only Thesis or Dissertation
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Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices

Description: The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Ξ£) and operator theory for the classical … more
Date: August 1999
Creator: Huff, Cheryl Rae
Item Type: Refine your search to only Thesis or Dissertation
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Counting Plane Tropical Curves via Lattice Paths in Polygons

Description: A projective plane tropical curve is a proper immersion of a graph into the real Cartesian plane subject to some conditions such as that the images of all the edges must be lines with rational slopes. Two important combinatorial invariants of a projective plane tropical curve are its degree, d, and genus g. First, we explore Gathmann and Markwig's approach to the study of the moduli spaces of such curves and explain their proof that the number of projective plane tropical curves, counting mult… more
Date: December 2021
Creator: Zhang, Yingyu
Item Type: Refine your search to only Thesis or Dissertation
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Crystallographic Complex Reflection Groups and the Braid Conjecture

Description: Crystallographic complex reflection groups are generated by reflections about affine hyperplanes in complex space and stabilize a full rank lattice. These analogs of affine Weyl groups have infinite order and were classified by V.L. Popov in 1982. The classical Braid theorem (first established by E. Artin and E. Brieskorn) asserts that the Artin group of a reflection group (finite or affine Weyl) gives the fundamental group of regular orbits. In other words, the fundamental group of the spac… more
Date: August 2017
Creator: Puente, Philip C
Item Type: Refine your search to only Thesis or Dissertation
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Cycles and Cliques in Steinhaus Graphs

Description: In this dissertation several results in Steinhaus graphs are investigated. First under some further conditions imposed on the induced cycles in steinhaus graphs, the order of induced cycles in Steinhaus graphs is at most [(n+3)/2]. Next the results of maximum clique size in Steinhaus graphs are used to enumerate the Steinhaus graphs having maximal cliques. Finally the concept of jumbled graphs and Posa's Lemma are used to show that almost all Steinhaus graphs are Hamiltonian.
Date: December 1994
Creator: Lim, Daekeun
Item Type: Refine your search to only Thesis or Dissertation

The D-Variant of Transfinite Hausdorff Dimension

Description: In this lecture we introduce a new transfinite dimension function for metric spaces which utilizes Henderson's topological D-dimension and ascribes to any metric space either an ordinal number or the symbol Ξ©. The construction of our function is motivated by that of UrbaΕ„ski's transfinite Hausdorff dimension, tHD. Henderson's dimension is a topological invariant, however, like Hausdorff dimension and tHD the function presented will be invariant under bi-Lipschitz continuous maps and generally n… more
Date: May 2022
Creator: Decker, Bryce
Item Type: Refine your search to only Thesis or Dissertation
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A Decomposition of the Group Algebra of a Hyperoctahedral Group

Description: The descent algebra of a Coxeter group is a subalgebra of the group algebra with interesting representation theoretic properties. For instance, the natural map from the descent algebra of the symmetric group to the character ring is a surjective algebra homomorphism, so the descent algebra implicitly encodes information about the representations of the symmetric group. However, this property does not hold for other Coxeter groups. Moreover, a complete set of primitive idempotents in the descent… more
Date: December 2016
Creator: Tomlin, Drew E
Item Type: Refine your search to only Thesis or Dissertation
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