Browse Dissertations and Theses - Mathematics by Title

  • Chen, Ao (2011-08-26)
    This thesis is to study the expected difference of the continuous supremum and discrete maximum of a Lévy process that is often used in finance. We will show that the expected difference is a quantity that highly depends ...
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  • Kim, Seongtag (1994)
    Let (M,g) be a noncompact complete Riemannian manifold whose scalar curvature S(x) is positive for all x in M. In this thesis, we study a conformal deformation of the given metric g, which makes the scalar curvature of the ...
    untranslated PDF (1MB)Restricted to U of Illinois
  • DeJarnette, Noel (2014-01-16)
    In [20], Keith and Zhong prove that spaces admitting Poincar e inequalities also admit a priori stronger Poincar e inequalities. We use their technique, with slight adjustments, to obtain a similar result in the case of ...
    untranslated PDF (992KB)
  • Dennison, Melissa A. (2010-08-20)
    In this dissertation we define and study a two-parameter family of recursive sequences which we call the bow sequences. The general bow sequence is defined similarly to the Stern sequence, and many of the properties of the ...
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  • Xiao, Lechao (2014-05-30)
    This dissertation consists of 4 chapters. In Chapter 1, we will briefly introduce some background of the trilinear oscillatory integrals and the motivations for their study. We also outline some key ideas in their proofs, ...
    untranslated PDF (479KB)Restricted to U of Illinois
  • Bradley, David Michael (1995)
    A sieve is a device for estimating the size of a finite set of integers after certain residue classes have been eliminated. In the sieve theories of Rosser-Iwaniec and Diamond-Halberstam-Richert, the upper and lower bound ...
    untranslated PDF (2MB)Restricted to U of Illinois
  • Zhang, Liang-Cheng (1990)
    We provide explicit solutions for three q-difference equations which arise in Ramanujan and Selberg's work on q-continued fractions. From these solutions, we derive criteria for the convergence of three Ramanujan-Selberg ...
    untranslated PDF (2MB)Restricted to U of Illinois
  • Blaylock, Richard Warren (1991)
    In this manuscript we explore two topics in recursion theory and their interaction.
    untranslated PDF (3MB)Restricted to U of Illinois
  • Saran, Maya (2010-08-20)
    For a compact metric space E, Solecki has defined a broad natural class of G-delta ideals of compact sets on E, called G-delta ideals with property (*), and has shown that any ideal I in this class can be represented ...
    untranslated PDF (363KB)
  • Wang, Gang (1989)
    Let f be a conditionally symmetric martingale taking values in a Hilbert space $\rm I\!H$ and let S(f) be its square function. If $\nu\sb{\rm p}$ is the smallest positive zero of the confluent hypergeometric function and ...
    untranslated PDF (2MB)Restricted to U of Illinois
  • Lee, Si-Chang (1995)
    In this thesis we study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\sb{n-3}(R)$ and (b) for a particular ...
    untranslated PDF (905KB)Restricted to U of Illinois
  • Yancey, Matthew (2013-05-24)
    This thesis focuses on extremal problems about coloring graphs and on finding rainbow matchings in edge-colored graphs. A graph $G$ is $k$-{\em critical} if $G$ is not $(k-1)$-colorable, but every proper subgraph of $G$ ...
    untranslated PDF (894KB)
  • Callahan, Patrick James (1994)
    This thesis uses techniques from spectral geometry and builds from the work of Schoen, Culler and Shalen, Meyerhoff, and others to obtain various estimates and inequalities involving geometric data of hyperbolic 3-manifolds. ...
    untranslated PDF (1MB)Restricted to U of Illinois
  • Son, Sarah (2014-05-30)
    In this dissertation we study how the energy levels of the Laplacian depend upon the shape of the domain, and identify the ground state energy level of the magnetic Laplacian on the disk. Although we consider these different ...
    untranslated PDF (827KB)
  • Iovino, Jose Nicolas (1994)
    Model theory is the logical analysis of mathematical structures. The class of structures considered in model theory includes, among others, all structures from algebra, number theory, and finite-dimensional analysis. A ...
    untranslated PDF (5MB)Restricted to U of Illinois
  • Carpenter, Bruce Franklin (1995)
    State transformers, which form the objects in a subequalizing category, are a generalization of the transition functions of automata. The 2-categorical properties of subequalizers are developed and related to adjunctions ...
    untranslated PDF (3MB)Restricted to U of Illinois
  • Vlasic, Andrew (2012-09-18)
    We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the ...
    untranslated PDF (13MB)Restricted to U of Illinois
  • Zheng, Zhi (2013-02-03)
    In this thesis we study the effect of stochastic perturbations on moving boundary value PDE's with Stefan boundary conditions, or Stefan problems, and show the existence and uniqueness of the solutions to a number of ...
    untranslated PDF (491KB)
  • Amir, Abdelmadjid (1990)
    We show the almost sure uniform pathwise convergence of birth and death processes and random walks to Brownian motion with drift and sticky Brownian motion. We thus provide constructive definitions of such diffusions. In ...
    untranslated PDF (2MB)Restricted to U of Illinois
  • LeSaulnier, Timothy (2012-02-06)
    An H-immersion is a model of a graph H in a larger graph G. Vertices of H are represented by distinct "branch" vertices in G, while edges of H are represented by edge-disjoint walks in G joining branch vertices. By the ...
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