Index Catalog // ScholarsArchive@OSU

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:: shown in Figure 8. Figure 8: Points F and G have been moved along line FG to accommodate the

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

Effectiveness in Stallings' Proof of Grushko's Theorem

Creator:: Synhavsky, Paul
Resource Type:: Capstone Project
Full Text:: 8 and then adding the segments from Ai to each diagram. a1 a2 a3 b1 b2 b3 c1 c3 c4 c2 c1 c3

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:: for the in MATHEMATICS Apl 8, 1963 OF MINIMUM BOUNDARY In this paper we consider the behavior of

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:: Author Hannah Barta Advisor Dr. Elaine Cozzi June 8, 2021 To Jim and Kathy, who listened. Contents 1

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

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:: dissertation. 6 Following Bogley and Williams [8], for l, f ≥ 0, Λ(l, f) = x0xf . . . x(l−1)f , and any

The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms

Creator:: Smith, Karen
Abstract:: As indicated by the title The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms, this paper leads us to an understanding of the relationship between these three areas of study. In [4], Zagier gives the results of an intriguing example of the relationship between these areas. However there...
Resource Type:: Capstone Project
Full Text:: discriminant, so we also note that the first ten negative fundamental discriminants are -3, -4, -7, -8, -11

Two finite Tchebichef transformations

Creator:: Normann, Søren Frederick
Resource Type:: Masters Thesis
Full Text:: ), Erdelyi (8, vol. 2, p. 184) and Courant and Hilbert (7,. vol. 1, p. 88). Tn(X) = cos(n cos-1x), u (X

A synthesis of significant developments in the history, calculation, and properties of the number pi

Creator:: Burdg, Donald Eugene
Abstract:: This thesis brings together under one cover a survey of the history of the real number pi along with a study of the present state of its theory, application, and calculation.
Resource Type:: Masters Thesis
Full Text:: . to 1500 A. D. 4 Rise of Modern Analysis: 1500 to 1750 8 Discovery of the Nature of Pi: 1760-1940 13

ScholarsArchive@OSU

Using Euclidean Geometry to Construct Objects in the Elliptic Klein Disk

Persistence of Populations in Environments with an Interface

Effectiveness in Stallings' Proof of Grushko's Theorem

On the structure of minimum surfaces at the boundary

Existence Theory in Sobolev Spaces for an Aggregation Equation

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

Topological and Dynamical Properties of Cyclically Presented Groups

The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms

Two finite Tchebichef transformations

A synthesis of significant developments in the history, calculation, and properties of the number pi

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