Now showing items 33-52 of 82

    • Interacting particle systems with partial annihilation through membranes 

      Fan, Wai Tong
      This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive ...
    • Inverse Boundary-Value Problems on an Infinite Slab 

      Marinov, Kaloyan
      In this work, we study the stability aspect of two inverse boundary-value problems (IBVPs) on an infinite slab with partial data. The uniqueness aspects of these IBVPs were considered and studied by Li and Uhlmann for the ...
    • Inverse Problems for Scalar Elliptic Equations and Systems 

      Lai, Ru-Yu
      In this thesis, we discuss inverse boundary value problems for scalar equations and for systems. First we introduce the famous Calder\'on problem and its recent developments. We focus on deriving the stability estimate of ...
    • An Inverse Source Problem in Radiative Transfer 

      Hubenthal, John Mark (2013-02-25)
      We consider the inverse source problem for the radiative transfer equation, under various assumptions on the scattering and absorption parameters, as well as on the accessible data. In such a setup, we measure the outgoing ...
    • Inverse transport with angularly averaged measurements 

      Langmore, Ian (2008)
      The inverse problem in radiative transfer is considered. The measurement setup involves controlling incoming radiation at the boundary of a convex domain in Rn and measuring the outgoing radiation in an attempt to ...
    • Isolated Curves for Hyperelliptic Curve Cryptography 

      Wang, Wenhan (2013-02-25)
      We introduce the notion of isolated genus two curves. There is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap. Thus there is no known way of transporting ...
    • Lam-Williams Markov chains on symmetric groups 

      Huynh, Anh Trung (2014-02-24)
      This paper reviews the current state of the Lam-Williams conjectures on a multivariate Markov chain on the symmetric group S_n. We start with Lam's work on random core partitions which led to a remarkable Markov chain on ...
    • Local cohomology at generic singularities of Schubert varieties in cominuscule flag varieties 

      Suryanarayan, Sweta (2012-09-13)
      We study the local cohomology of a Schubert variety in a co-minuscule flag variety at a generic singularity. Let $G$ be a reductive complex algebraic group with a Borel subgroup $B$, let $W$ be the Weyl group of $G$ with ...
    • Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications 

      Lewis, Stephen
      In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space ...
    • Markov chain mixting time, card shuffling and spin systems dynamics 

      Ning, Weiyang (2013-07-25)
      The mixing time of a Markov chain describes how fast the Markov chain converges to its stationary distribution. In this thesis, we survey some of the knowledge and main tools available in this field by looking at examples. ...
    • Markov partitions for hyperbolic toral automorphisms 

      Praggastis, Brenda L. (Brenda Lien), 1961- (1992)
      The study of the dynamical properties of hyperbolic toral automorphisms is simplified when the automorphisms are represented as shifts of finite type. The conventional method used to represent such an automorphism symbolically ...
    • Mathematical Aspects of Gerrymandering 

      Solbrig, Mary Katherine (2013-11-14)
      Every 10 years the United States performs a census, and this census determines how many members of congress will represent each state. Then begins an unfortunate battle, as cartographers manipulate the boundaries for ...
    • Matrix free methods for large scale optimization 

      Wang, Jiashan
      Sequential quadratic optimization (SQP) methods are widely used to solve large-scale nonlinear optimization problems. We build two matrix-free methods for approximately solving exact penalty subproblems that arise when ...
    • Non-interior path-following methods for complementarity problems 

      Xu, Song, 1963- (1998)
      Because of its excellent numerical performance, non-interior path following methods (also called smoothing methods) have become an important class of methods for solving complementarity problems. However, no rate of ...
    • The nonexistence of certain free pro-p extensions and capitulation in a family of dihedral extensions of Q 

      Hubbard, David, 1955- (1996)
      $\doubz\sbsp{p}{d}$-extensions are a natural way to extend Iwasawa's theory of $\doubz\sb{p}$-extensions. A further extension would be to look at free pro-p extensions which though nonabelian, can be studied by looking at ...
    • Nonholonomic Euler-Poincaré equations and stability in Chaplygin's sphere 

      Schneider, David, 1970- (2000)
      A method of reducing several classes of nonholonomic mechanical systems that are defined on semidirect products of Lie groups is developed. The method reduces the Lagrange-d'Alembert principle to obtain a reduced constrained ...
    • On numerics and inverse problems 

      Caday, Peter Anthony
      In this thesis, two projects in inverse problems are described. The first concerns a simple mathematical model of synthetic aperture radar with undirected beam, modeled as a 2D circular Radon transform with centers restricted ...
    • On Particle Interaction Models 

      Banerjee, Sayan (2014-02-24)
      This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ...
    • On singularities of generic projection hypersurfaces 

      Doherty, Davis C (2006)
      The present work studies singularities of hypersurfaces arising from generic projections of smooth projective varieties, in the context of Du Bois and semi log canonical singularities. It is demonstrated that Du Bois ...
    • On special Lagrangian equations 

      Wang, Dake (2014-02-24)
      In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ...