Physical Sciences and Mathematics Commons^™

On The Spherical Symmetry Of Perfect-Fluid Stellar Models In General Relativity, Joshua M Brewer

Masters Theses

It is well known in Newtonian theory that static self-gravitating perfect fluids in a vacuum are necessarily spherically symmetric. The necessity of spherical symmetry of perfect-fluid static spacetimes with constant density in general relativity is shown.

Contractible Theta Complexes Of Graphs, Chelsea Marian Mcamis

Masters Theses

We examine properties of graphs that result in the graph having a contractible theta complex. We classify such properties for tree graphs and graphs with one loop and we introduce examples of graphs with such properties for tree graphs and graphs with one or two loops. For more general graphs, we show that having a contractible theta complex is not an elusive property, and that any skeleton of a graph with at least three loops can be made to have a contractible theta complex by strategically adding vertices to its skeleton.

Alexander And Conway Polynomials Of Torus Knots, Katherine Ellen Louise Agle

Masters Theses

We disprove the conjecture that if K is amphicheiral and K is concordant to K', then C_K'(z)C_K'(iz)C_K\(z²) is a perfect square inside the ring of power series with integer coefficients. The Alexander polynomial of (p,q)-torus knots are found to be of the form A_T(p,q)(t)= (f(t^q))/(f(t)) where f(t)=1+t+t²+...+t^p-1. Also, for (pⁿ,q)-torus knots, the Alexander polynomial factors into the form A_T(pⁿ ,q)=f(t)f(t^p)f(t^p2 )...f(t^pn-2 )f(t^pn-1 ). A new conversion from the Alexander polynomial to the …

Hyperbolic Structures From Link Diagrams, Anastasiia Tsvietkova

Doctoral Dissertations

As a result of Thurston's Hyperbolization Theorem, many 3-manifolds have a hyperbolic metric or can be decomposed into pieces with hyperbolic metric (W. Thurston, 1978). In particular, Thurston demonstrated that every link in a 3-sphere is a torus link, a satellite link or a hyperbolic link and these three categories are mutually exclusive. It also follows from work of Menasco that an alternating link represented by a prime diagram is either hyperbolic or a (2,n)-torus link.

A new method for computing the hyperbolic structure of the complement of a hyperbolic link, based on ideal polygons bounding the regions of a …

Orderly Ε-Homotopies Of Discrete Chains, Alexander Thomas Happ

Chancellor’s Honors Program Projects

No abstract provided.

On The Number Of Tilings Of A Square By Rectangles, Timothy Michaels

Chancellor’s Honors Program Projects

No abstract provided.

Generalized Branching In Circle Packing, James Russell Ashe

Doctoral Dissertations

Circle packings are configurations of circle with prescribed patterns of tangency. They relate to a surprisingly diverse array of topics. Connections to Riemann surfaces, Apollonian packings, random walks, Brownian motion, and many other topics have been discovered. Of these none has garnered more interest than circle packings' relationship to analytical functions. With a high degree of faithfulness, maps between circle packings exhibit essentially the same geometric properties as seen in classical analytical functions. With this as motivation, an entire theory of discrete analytic function theory has been developed. However limitations in this theory due to the discreteness of circle packings …