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  • Topological and Dynamical Properties of Cyclically Presented Groups

    Creator:
    McDermott, Kirk M.
    Abstract:
    This dissertation investigates the structure and topological properties of cyclicallypresented groups. First, a family of groups called groups of type Z is considered. Withfew exceptions, the finiteness, asphericity, fixed point, and 3-manifold spine problemsare solved. Most groups of type Z have a central element of infinite order fixed by theshift....
    Resource Type:
    Dissertation
    Full Text:
    including H(9, 4) and H(9, 7). The �rst known examples of in�nite, non-aspherical groups with free shift

  • Using Euclidean Geometry to Construct Objects in the Elliptic Klein Disk

    Creator:
    Connolly, Genevieve
    Abstract:
    Constructions using only a straightedge and compass are basic tools in any geometer's toolbox. We show how to construct an elliptic straightedge and compass in the Klein Disk model of (single) elliptic geometry, using only a Euclidean compass and straightedge.
    Resource Type:
    Research Paper
    Full Text:
    as shown in Figure 7. Connolly 15 Figure 7: Line FG is perpendicular to segment ED, so

  • Persistence of Populations in Environments with an Interface

    Creator:
    Rekow, James A.
    Abstract:
    We model a fish population in a spatial region comprising a marine protected area and a fishing ground separated by an interface. The model assumes conservation of biomass density and takes the form of a reaction diffusion equation with a logistic reaction term. At the interface, in addition to continuity...
    Resource Type:
    Masters Thesis
    Full Text:
    (FG). Here, we identify necessary and sufficient conditions for the persistence of populations in an

  • The enumeration of strings of a given length in an n-ary non-associative non-commutative algebra

    Creator:
    Klosinski, Leonard Frank
    Abstract:
    In his book on abstract algebra, Nathan Jacobson poses and solves the problem of finding the number of ways of inserting parentheses in a string of given length with binary operators. We continue the work of Jacobson and go beyond it in that we no longer consider one binary operator...
    Resource Type:
    Masters Thesis
    Full Text:
    have seen that k can equal 1, 4, 7. And in general, the length of a string with ternary operators is

  • Effectiveness in Stallings' Proof of Grushko's Theorem

    Creator:
    Synhavsky, Paul
    Resource Type:
    Capstone Project
    Full Text:
    in one-to-one corre- spondence with X via x 7−→ x−1. Define the alphabet on X to be X ∪X−1. A word on

  • Sheppard's correction : moment relationships and correction terms

    Creator:
    Jumani, Vishnu Balchand
    Abstract:
    This thesis is concerned with the detailed derivation of Sheppard's Correction Formula relating the true to the raw moments by the use of Euler-MacLaurin formula. Special moment relationships have been derived using different special functions, whose application is made to derive correction formula for the semi-invariants. Special investigation is carried...
    Resource Type:
    Masters Thesis
    Full Text:
    = L x " Ai,i=-m x . + w w i 2 7 A. = ," f ( x ) dx = f f ( x . + y) dy i i w w xi- 2--- -7 2 is

  • On the structure of minimum surfaces at the boundary

    Creator:
    Tjoelker, Cornelius Henry
    Abstract:
    In this paper we consider the behavior of certain surfaces at certain boundary points. The surfaces under consideration satisfy a topological definition and are of 2-dimension in 3-dimensional Euclidean space with the boundary a finite set of straight line segments. It is shown that the surface of minimum area with...
    Resource Type:
    Masters Thesis
    Full Text:
    A THESIS S .0 r '.r6l,¡r.iA;a5..7 1,Li : .. ,.1, 1 o') ; I)' :, :r i5'1 f ,'íy..R1 e

  • Generalized measures of deformation-rates in torsional flows of viscoelastic fluids between two infinite parallel planes

    Creator:
    Park, Moon Up
    Abstract:
    An introduction to the generalized measures of deformation- rates involving not only velocity gradients but also acceleration gradients is given and constitutive equations using these measures have been discussed. These new constitutive equations are then used to study torsional flows of viscoelastic fluids between two infinite parallel planes. In order...
    Resource Type:
    Masters Thesis
    Full Text:
    of the Classical Theory of Continuous Media 7 2.3 Nonlinear Theories of Continuous Media 8 2.4

  • Existence Theory in Sobolev Spaces for an Aggregation Equation

    Creator:
    Barta, Hannah E.
    Abstract:
    Aggregation equations have been used to model phenomena such as insect swarming and chemotaxis. Previous work on aggregation equations in the area of analysis applied to PDE has proven well-posedness of certain classes of aggregation equations in Lebesgue spaces. We will prove local existence of solutions in H^1 to an...
    Resource Type:
    Capstone Project
    Full Text:
    considering this case is from Bodnar [7], who proves local existence and uniqueness of solutions when the

  • New Families of pseudo-Anosov Homeomorphisms with Vanishing Sah-Arnoux-Fathi Invariant

    Creator:
    Do, Hieu Trung
    Abstract:
    Translation surfaces can be viewed as polygons with parallel and equal sides identified. An affine homeomorphism φ from a translation surface to itself is called pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger than 2 in absolute value. In this setting, the eigendirections of...
    Resource Type:
    Dissertation
    Full Text:
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Sah-Arnoux-Fathi invariant