Now showing items 61-80 of 82

    • The Radiative Transfer Equation in Photoacoustic Imaging 

      Patrolia, Lee (2013-07-25)
      Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, ...
    • The regularity of Loewner curves 

      Tran, Huy Vo
      The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...
    • Self-shrinking Solutions to Mean Curvature Flow 

      Drugan, Gregory
      We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
    • Selmer groups for elliptic curves with isogenies of prime degree 

      Mailhot, James Michael (2003)
      The Mordell-Weil theorem states that the points of an elliptic curve defined over a number field form a finitely generated, abelian group. The rank of this group, generally referred to as the rank of the elliptic curve, ...
    • Sheaves on support varieties and varieties of elementary subalgebras 

      Stark, James
      We present several results about two closely related types of objects: the projectivized scheme $\PG$ of one parameter subgroups of an infinitesimal group scheme $G$ and the variety $\bE(\fg)$ of maximal elementary subalgebras ...
    • Shimura Degrees for Elliptic Curves over Number Fields 

      Deines, Alyson Laurene
      A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
    • Smoothness of Loewner Slits 

      Wong, Chun Wai Carto (2013-02-25)
      In this dissertation, we show that the chordal Loewner differential equation with C^{beta} driving function generates a C^{beta + 1/2} slit for 1/2 < beta <= 2, except when beta = 3/2 the slit is only proved to be weakly C^{1,1}.
    • Some cohomology of finite general linear groups 

      Sprehn, David
      We prove that the degree r(2p − 3) cohomology of any (untwisted) finite group of Lie type over F_(p^r), with coefficients in characteristic p, is nonzero as long as its Coxeter number is at most p. We do this by providing ...
    • Some Linear and Nonlinear Geometric Inverse Problems 

      Zhou, Hanming
      Inverse problems is an area at the interface of several disciplines and has become a prominent research topic due to its potential applications. A wide range of these problems can be formulated under various geometric ...
    • Spectral Theory of Z^d Substitutions 

      Bartlett, Alan
      In this paper, we generalize and develop results of Queffelec allowing us to characterize the spectrum of an aperiodic substitution in Z^d by describing the Fourier coefficients of mutually singular measures of pure type ...
    • Stable processes with opposing drifts 

      Wright, James M., 1960- (1996)
      A strong Markov process, $W\sp0$, is constructed by a natural linking together of two independent stable processes of type ($\alpha,\ \beta\sb1$) and ($\alpha,\ \beta\sb2$). The drift for a stable process X of type ($\alpha,\ ...
    • Stationary distribution for spinning reflecting diffusions 

      Duarte Espinoza, Mauricio Andres (2012-09-13)
      This dissertation studies two different types of interaction of diffusion processes with the boundary of a domain $DsubRR^n$, which is assumed to be bounded, and of class $C^2(RR^n)$. The first process that is studied is ...
    • Strichartz estimates for wave equations with coefficients of Sobolev regularity 

      Blair, Matthew D (2005)
      Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. In this work, such methods are used to show Strichartz inequalities for ...
    • A Tensor-Triangulated Approach to Derived Categories of Non-Noetherian Rings 

      Wolcott, Frank Lucas (2012-09-13)
      We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between ...
    • Thermoacoustic Tomography in Elastic Media 

      Tittelfitz, Justin Jeffrey (2013-11-14)
      We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0, T ] × boundary of Omega, where Omega in R3 ...
    • Three Problems in Discrete Probability 

      Slivken, Erik Dustin
      In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231-avoiding permutation. We use a bijection from Dyck paths to 231-avoiding permutations that ...
    • Time-like graphical models 

      Tadic, Tvrtko
      We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical ...
    • The topology of graph homomorphisms 

      Dochtermann, Anton, 1978- (2007)
      In this thesis we consider topological aspects of graph homomorphisms. Our main object of study is the Hom complex of graphs, a space first introduced by Lovasz to obtain lower bounds on chromatic number, and more recently ...
    • Toward the compactification of the stack of Lie(G)-forms using perfect complexes 

      Zsamboki, Pal
      To establish geometric properties of an algebraic stack, one can find a compactification. This method has been successfully employed to find irreducible components for example of the moduli stack of curves [DM69], vector ...
    • Towards a non-Q-Gorenstein Minimal Model Program 

      Chiecchio, Alberto
      In this thesis we do the first steps towards a non-Q-Gorenstein Minimal Model Program. We extensively study non-Q-factorial singularities, using the techniques introduced by [dFH09]. We introduce a new class of singularities, ...