Now showing items 49-68 of 102

    • 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 ...
    • Non-local operators, jump diffusions and Feynman-Kac tranforms 

      Wang, Lidan
      Non-local operators are analytically defined by integrals over the whole space, hence hard to study certain properties. This thesis studies inverse local times at $0$ of one-dimensional reflected diffusions on $[0, ...
    • 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 ...
    • Novel uses of the Mallows model in coloring and matching 

      Levy, Avi William
      A natural model of a highly ordered random ranking is the Mallows model. Disorder is measured by the number of inversions; these are pairs of elements whose order is reversed. The Mallows model assigns to each ranking of ...
    • On f-vectors of polytopes and matroids 

      Samper Casas, Jose Alejandro
      The f-vector of a simplicial complex is a fundamental invariant that counts the number of faces in each dimension. A natural question in the theory of simplicial complexes is to understand the relationship between the ...
    • 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 Selmer groups and factoring p-adic L-functions 

      Palvannan, Bharathwaj
      Samit Dasgupta has proved a formula factoring a certain restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and ...
    • 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 ...
    • On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions 

      Van Huele, Yannick
      For certain Zp-extensions of abelian number fields, we study the Iwasawa module associated to the ideal class groups. We show that generic Zp-extensions of abelian number fields are T-semisimple. We also construct the ...
    • On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities 

      Merhej, Jessica
      A central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$-dimensional subset $M$ of $\mathbb{R}^{n+d}$ is well ...