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  • A thin codimension-one decomposition of the Hilbert Cube

    Creator:
    Phon-On, Aniruth
    Abstract:
    For cell-like upper semicontinuous(usc) decompositions G of finite dimensional manifolds M, the decomposition space M/G turns out to be an ANR provided M/G is finite dimensional ([Dav07], page 129 ). Furthermore, if M/G is finite dimensional and has the Disjoint Disks Property (DDP), then M/G is homeomorphic to M ([Dav07],...
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    Dissertation
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    X are separable metric spaces and the word map refers to a continuous function. For the readers who

  • An inner product on adelic measures

    Creator:
    Oberly, Peter J.
    Abstract:
    We define an inner product on a vector space of adelic measures over a number field $K$. We find that the norm induced by this inner product governs weak convergence at each place of $K$. The canonical adelic measure associated to a rational map is in this vector space, and...
    Resource Type:
    Dissertation
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    for non-exceptional rational maps. (A rational map f is exceptional if f is conjugate to a power map

  • Arithmetic dynamical questions with local rationality conditions

    Creator:
    Noytaptim, Chatchai
    Abstract:
    We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
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    Dissertation
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    -critically finite polynomials One way for a map to be post-critically bounded (PCB) is to be post-critically

  • Canonical states in quantum statistical mechanics

    Creator:
    Kvarda, Robert Edward
    Abstract:
    This report presents a characterization of the quantum mechanical analog of the Gibbs canonical density. The approach is based on a method developed by D.S. Carter for the case of classical statistical mechanics, which considers composite mechanical systems composed of mechanically and statistically independent components. After a brief introductory chapter,...
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    Dissertation
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    transformation Tt, being continuous, maps into itself, in the sense that for each Lc .t the set Tt[L = { Tt(z

  • Critically Separable Rational Maps in Families

    Creator:
    Petsche, Clayton
    Abstract:
    Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
    Resource Type:
    Article

  • Existence and Representation Theorems for a Semilinear Sobolev Equation in Banach Space

    Creator:
    Showalter, R. E.
    Abstract:
    An existence theory is developed for a semilinear evolution equation in Banach space which is modeled on boundary value problems for partial differential equations of Sobolev type. The operators are assumed to be measurable and to satisfy coercive estimates which are not necessarily uniform in their time dependence, and to...
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    Article
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    maps from X to C. If x e X, the map tk d?(x)’X’ C is continuous and conjugate-linear and hence

  • Mathematics Graduate Student Instructors as a Complex System

    Creator:
    Gibbons, Claire J.
    Abstract:
    Mathematics Graduate Student Instructors (GSIs) have a significant impact on the teaching and learning of mathematics in post-secondary contexts through their work as instructors of record, tutors, graders, and recitation, laboratory, or discussion leaders for mathematics courses. Perhaps more importantly, GSIs are future teachers of mathematics: more than 60 percent...
    Resource Type:
    Dissertation
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    , “Vertical Asymptotes of Rational Functions.” I had no idea what a rational function was. I thought I maybe

  • Numerical Analysis of a System of Parabolic Variational Inequalities with Application to Biofilm Growth

    Creator:
    Alhammali, Azhar S. A.
    Abstract:
    In this work we consider a mathematical and computational model for biofilm growth and nutrient utilization. In particular, we are interested in a model appropriate at a scale of interface. The model is a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs). One of these PDEs is subject...
    Resource Type:
    Dissertation
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    space K. Definition 2.1.13. A metric space X is separable if there exists a subset D ⊂ X that is

  • On Small Heights of Totally p-adic Numbers

    Creator:
    Stacy, Emerald T.
    Abstract:
    The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height...
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    Dissertation
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    Overview The height (or more formally, the logarithmic Weil height) of a rational number a b is h (ab

  • Optimization under Uncertainty of a Magnetohydrodynamics Generator

    Creator:
    Rajbhandari, Evan
    Abstract:
    Within this dissertation, we develop tools and techniques to demonstrate the feasibility of real-time optimization of a magnetohydrodynamics generator. To ease computational complexity, we work on the kinematic magnetohydrodynamic system, prescribing the fluid-flow and model the material response of the system through an updated Generalized Ohm’s law. We focus on...
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    Dissertation
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    recovered from mean and standard deviation, and then translation maps from [0,1] to the bounded space. Uni