Now showing items 72-91 of 188

    • Heat Kernel Estimates for Markov Processes Associated with Time-Dependent Dirichlet Forms 

      Wang, Hanchao
      In this paper, time-inhomogeneous stable-like processes are investigated. We establish the relation between the transition operators and time-dependent parabolic equations, as well as upper heat kernel estimates.
    • Higher direct images of ideal sheaves, correspondences in log Hodge cohomology and globally F-full varieties 

      Godfrey, Charles W
      This document consists of three mathematically independent and more or less thematically independent parts. Chapter 1 concerns invariance of the cohomology groups of divisorial ideal sheaves under (a restricted class of) ...
    • Homological algebra of Stanley-Reisner rings and modules 

      Sawaske, Connor
      Associated to each simplicial complex $\Delta$ and each field $\field$ is the Stanley--Reisner ring $\field[\Delta]$. The answers to a multitude of questions related to simplicial complexes have historically been found ...
    • 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 ...
    • How to weld: Energies, weldings, and driving functions 

      Mesikepp, Tim
      We prove a variant of the welding zipper algorithm converges for curves $\gamma \subset \nH \cup \{0\}$ that have Loewner driving functions $\xi \in C^{3/2+\epsilon}$. Convergence holds whether one ``zips up'' with straight ...
    • 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 ...
    • Intersection Rigidity 

      Meyerson, Reed Campbell
      We consider three inverse problems related to geodesic intersections. First, we consider theproblem of recovering the geometry of a Riemannian manifold with boundary from the knowledge of all pairs of inward pointing ...
    • 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 fractional operators involving a magnetic potential 

      Li, Li
      In this thesis, we study forward and inverse problems for fractional operators involving a magnetic potential. We show that many properties of fractional operators are preserved under the perturbation by a magnetic potential. ...
    • Inverse Problems for Linear and Non-linear Elliptic Equations 

      Iyer, Karthik Venkatraman
      An inverse problem is a mathematical framework that is used to obtain information about a physical object or system from observed measurements. A typical inverse problem is to recover the coefficients of a partial differential ...
    • 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 ...
    • Iteratively Re-weighted Schemes for Non-smooth Optimization 

      He, Daiwei
      Iteratively Re-weighted Least Squares (IRLS) has long been used to solve both convex optimization problems, including l_1 regression and compressed sensing, as well as non-convex optimization problems, including l_p ...
    • 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 and Global Convergence for Convex-Composite Optimization 

      Engle, Abraham
      Convex-composite optimization seeks to minimize f(x):=h(c(x)) over x in R^n, where h is closed, proper, and convex, and c is smooth. Such problems include nonlinear programming, mini-max optimization, estimation of nonlinear ...
    • 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 ...