UNT Libraries - 11 Matching Results

Search Results

Results: 1 - 11
open access

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
open access

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
open access

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
open access

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
open access

Homotopies and Deformation Retracts

Description: This paper introduces the background concepts necessary to develop a detailed proof of a theorem by Ralph H. Fox which states that two topological spaces are the same homotopy type if and only if both are deformation retracts of a third space, the mapping cylinder. The concepts of homotopy and deformation are introduced in chapter 2, and retraction and deformation retract are defined in chapter 3. Chapter 4 develops the idea of the mapping cylinder, and the proof is completed. Three special cas… more
Date: December 1990
Creator: Stark, William D. (William David)
Item Type: Refine your search to only Thesis or Dissertation
open access

Minimality of the Special Linear Groups

Description: Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, q… more
Date: December 1997
Creator: Hayes, Diana Margaret
Item Type: Refine your search to only Thesis or Dissertation
open access

Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems

Description: In this paper, we prove, for a certain class of open billiard dynamical systems, the existence of a family of smooth probability measures on the leaves of the dynamical system's unstable manifold. These measures describe the conditional asymptotic behavior of forward trajectories of the system. Furthermore, properties of these families are proven which are germane to the PYC programme for these systems. Strong sufficient conditions for the uniqueness of such families are given which depend upon… more
Date: December 1998
Creator: Richardson, Peter A. (Peter Adolph), 1955-
Item Type: Refine your search to only Thesis or Dissertation
open access

Uniqueness of Positive Solutions for Elliptic Dirichlet Problems

Description: In this paper we consider the question of uniqueness of positive solutions for Dirichlet problems of the form - Ξ” u(x)= g(Ξ»,u(x)) in B, u(x) = 0 on Ο‘B, where A is the Laplace operator, B is the unit ball in RΛ†N, and A>0. We show that if g(Ξ»,u)=uΛ†(N+2)/(N-2) + Ξ», that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(Ξ»,u)=A f(u) with f(0) < 0, f "superlinear" and monotone. We use a number of methods from nonlinear functional … more
Date: December 1990
Creator: Ali, Ismail, 1961-
Item Type: Refine your search to only Thesis or Dissertation
open access

Weak and Norm Convergence of Sequences in Banach Spaces

Description: We study weak convergence of sequences in Banach spaces. In particular, we compare the notions of weak and norm convergence. Although these modes of convergence usually differ, we show that in β„“ΒΉ they coincide. We then show a theorem of Rosenthal's which states that if {𝓍ₙ} is a bounded sequence in a Banach space, then {𝓍ₙ} has a subsequence {𝓍'β‚™} satisfying one of the following two mutually exclusive alternatives; (i) {𝓍'β‚™} is weakly Cauchy, or (ii) {𝓍'β‚™} is equivalent to the unit vector basis… more
Date: December 1993
Creator: Hymel, Arthur J. (Arthur Joseph)
Item Type: Refine your search to only Thesis or Dissertation
Back to Top of Screen