Now showing items 21-40 of 79

    • Estimating Norms of Matrix Functions using Numerical Ranges 

      Choi, Daeshik (2013-11-14)
      We study Crouzeix's conjecture: for any polynomial p and any square matrix A, the spectral norm of the matrix p(A) is at most double of the supremum norm of the polynomial p on the numerical range of the matrix A.
    • Finite-Difference Methods for Second-Order Wave Equations with Reduced Dispersion Errors 

      An, Yajun
      Finite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate ...
    • Finite-Difference Methods for the Wave Equation with Reduced Dispersion Errors 

      An, Yajun (2013-04-17)
      A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finite-difference (FD) schemes in the joint time-space domain to reduce dispersion error. The key idea is that the true dispersion relation ...
    • Four Problems in Probability and Optimization 

      Pfeiffer, James (2014-02-24)
      This thesis studies bootstrap percolation, a problem in probability, as well as several topics in the application of sums of squares to combinatorial optimization. In the chapter on percolation, we bound the critical ...
    • A Geometric Perspective on First-Passage Competition 

      Blair-Stahn, Nathaniel Deveroux (2013-04-17)
      We study the macroscopic geometry of first-passage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ...
    • Graded group schemes 

      Aponte Roman, Camil Ivette
      We define graded group schemes and graded group varieties and develop their theory. We give a generalization of the result that connected graded bialgebras are graded Hopf algebra. Our result is given for a broader class ...
    • The Grothendieck Groups of Module Categories over Coherent Algebras 

      Sisodia, Gautam
      Let <italic>k</italic> be a field and <italic>B</italic> either a finitely generated free <italic>k</italic>-algebra, or a regular <italic>k</italic>-algebra of global dimension two with at least three generators, generated ...
    • Hopf algebras of finite Gelfand-Kirillov dimension 

      Zhuang, Guangbin (2013-11-14)
      We study Hopf algebras of finite Gelfand-Kirillov dimension. By analyzing the free pointed Hopf algebra F(t), we show the existence of certain Hopf subalgebras of pointed Hopf domains H whose GK-dimension are finite and ...
    • Hybrid inverse problems 

      Chen, Jie (2013-11-14)
      Inverse problems arise in different disciplines including exploration geophysics, medical imaging and nondestructive evaluation. In some settings, a single modality displays either high contrast or high resolution but not ...
    • Hybrid Inverse Problems Arising from Acousto-Electric Coupling 

      Kocyigit, Ilker (2013-11-14)
      We study hybrid imaging techniques that aim to overcome the ill-posedness of the Electric Impedance Tomography using the acousto-electric coupling. For the isotropic case, we consider the problem of reconstructing the ...
    • 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. ...