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Multifractal Measures

Description: The purpose of this dissertation is to introduce a natural and unifying multifractal formalism which contains the above mentioned multifractal parameters, and gives interesting results for a large class of natural measures. In Part 2 we introduce the proposed multifractal formalism and study it properties. We also show that this multifractal formalism gives natural and interesting results when applied to (nonrandom) graph directed self-similar measures in Rd and "cookie-cutter" measures in R. I… more
Date: May 1994
Creator: Olsen, Lars
Item Type: Refine your search to only Thesis or Dissertation
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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
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A Numerical Method for Solving Singular Differential Equations Utilizing Steepest Descent in Weighted Sobolev Spaces

Description: We develop a numerical method for solving singular differential equations and demonstrate the method on a variety of singular problems including first order ordinary differential equations, second order ordinary differential equations which have variational principles, and one partial differential equation.
Date: August 1995
Creator: Mahavier, William Ted
Item Type: Refine your search to only Thesis or Dissertation
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On Groups of Positive Type

Description: We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.
Date: August 1995
Creator: Moore, Monty L.
Item Type: Refine your search to only Thesis or Dissertation
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Overrings of an Integral Domain

Description: This dissertation focuses on the properties of a domain which has the property that each ideal is a finite intersection of a π-ideal, the properties of a domain which have the property that each ideal is a finite product of π-ideal, and the containment relations of the resulting classes of ideals. Chapter 1 states definitions which are needed in later chapters. Chapters 2 and 3 focuses on domains which have the property that each ideal in D is a finite intersection of π-ideals while Chapter 4 f… more
Date: August 1992
Creator: Emerson, Sharon Sue
Item Type: Refine your search to only Thesis or Dissertation
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Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Description: We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
Date: August 1995
Creator: Thompson, Jeremy R. (Jeremy Ray)
Item Type: Refine your search to only Thesis or Dissertation
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Plane Curves, Convex Curves, and Their Deformation Via the Heat Equation

Description: We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is … more
Date: August 1998
Creator: Debrecht, Johanna M.
Item Type: Refine your search to only Thesis or Dissertation
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Polish Spaces and Analytic Sets

Description: A Polish space is a separable topological space that can be metrized by means of a complete metric. A subset A of a Polish space X is analytic if there is a Polish space Z and a continuous function f : Z —> X such that f(Z)= A. After proving that each uncountable Polish space contains a non-Borel analytic subset we conclude that there exists a universally measurable non-Borel set.
Date: August 1997
Creator: Muller, Kimberly (Kimberly Orisja)
Item Type: Refine your search to only Thesis or Dissertation
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Primitive Substitutive Numbers are Closed under Rational Multiplication

Description: Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is … more
Date: August 1998
Creator: Ketkar, Pallavi S. (Pallavi Subhash)
Item Type: Refine your search to only Thesis or Dissertation
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Properties of Power Series Rings

Description: This thesis investigates some of the properties of power series rings. The material is divided into three chapters. In Chapter I, some of the basic concepts of rings which are a prerequisite to an understanding of the definitions and theorems which follow are stated. Simple properties of power series rings are developed in Chapter II. Many properties of a ring R are preserved when we attach the indeterminant x to form the power series ring R[[x]]. Further results of power series rings are exami… more
Date: August 1990
Creator: O'Brien, Rita Marie
Item Type: Refine your search to only Thesis or Dissertation
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Property (H*) and Differentiability in Banach Spaces

Description: A continuous convex function on an open interval of the real line is differentiable everywhere except on a countable subset of its domain. There has been interest in the problem of characterizing those Banach spaces where the continuous functions exhibit similar differentiability properties. In this paper we show that if a Banach space E has property (H*) and B_E• is weak* sequentially compact, then E is an Asplund space. In the case where the space is weakly compactly generated, it is shown th… more
Date: August 1993
Creator: Obeid, Ossama A.
Item Type: Refine your search to only Thesis or Dissertation
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Steepest Descent for Partial Differential Equations of Mixed Type

Description: The method of steepest descent is used to solve partial differential equations of mixed type. In the main hypothesis for this paper, H, L, and S are Hilbert spaces, T: H -> L and B: H -> S are functions with locally Lipshitz Fréchet derivatives where T represents a differential equation and B represents a boundary condition. Define ∅(u) = 1/2 II T(u) II^2. Steepest descent is applied to the functional ∅. A new smoothing technique is developed and applied to Tricomi type equations (which are of … more
Date: August 1992
Creator: Kim, Keehwan
Item Type: Refine your search to only Thesis or Dissertation
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Steepest Sescent on a Uniformly Convex Space

Description: This paper contains four main ideas. First, it shows global existence for the steepest descent in the uniformly convex setting. Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces. Thirdly, it shows an isomorphism between the dual space of H^{1,p}[0,1] and the space H^{1,q}[0,1] where p > 2 and {1/p} + {1/q} = 1. Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H^{1,p}[0,1] to L_{p}[1,0] where p … more
Date: August 1995
Creator: Zahran, Mohamad M.
Item Type: Refine your search to only Thesis or Dissertation
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Sufficient Conditions for Uniqueness of Positive Solutions and Non Existence of Sign Changing Solutions for Elliptic Dirichlet Problems

Description: In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $… more
Date: August 1995
Creator: Hassanpour, Mehran
Item Type: Refine your search to only Thesis or Dissertation
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Tensor Products of Banach Spaces

Description: Tensor products of Banach Spaces are studied. An introduction to tensor products is given. Some results concerning the reciprocal Dunford-Pettis Property due to Emmanuele are presented. Pelczyriski's property (V) and (V)-sets are studied. It will be shown that if X and Y are Banach spaces with property (V) and every integral operator from X into Y* is compact, then the (V)-subsets of (X⊗F)* are weak* sequentially compact. This in turn will be used to prove some stronger convergence results for … more
Date: August 1996
Creator: Ochoa, James Philip
Item Type: Refine your search to only Thesis or Dissertation
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A Topological Uniqueness Result for the Special Linear Groups

Description: The goal of this paper is to establish the dependency of the topology of a simple Lie group, specifically any of the special linear groups, on its underlying group structure. The intimate relationship between a Lie group's topology and its algebraic structure dictates some necessary topological properties, such as second countability. However, the extent to which a Lie group's topology is an "algebraic phenomenon" is, to date, still not known.
Date: August 1997
Creator: Opalecky, Robert Vincent
Item Type: Refine your search to only Thesis or Dissertation
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The Torus Does Not Have a Hyperbolic Structure

Description: Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of… more
Date: August 1992
Creator: Butler, Joe R.
Item Type: Refine your search to only Thesis or Dissertation
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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 - Δ u(x)= g(λ,u(x)) in B, u(x) = 0 on ϑB, where A is the Laplace operator, B is the unit ball in RˆN, and A>0. We show that if g(λ,u)=uˆ(N+2)/(N-2) + λ, that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(λ,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
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Universal Branched Coverings

Description: In this paper, the study of k-fold branched coverings for which the branch set is a stratified set is considered. First of all, the existence of universal k-fold branched coverings over CW-complexes with stratified branch set is proved using Brown's Representability Theorem. Next, an explicit construction of universal k-fold branched coverings over manifolds is given. Finally, some homotopy and homology groups are computed for some specific examples of Universal k-fold branched coverings.
Date: May 1993
Creator: Tejada, Débora
Item Type: Refine your search to only Thesis or Dissertation
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