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Articles 91 - 96 of 96
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Aspects Of The Jones Polynomial, Alvin Mendoza Sacdalan
Aspects Of The Jones Polynomial, Alvin Mendoza Sacdalan
Theses Digitization Project
A knot invariant called the Jones polynomial will be defined in two ways, as the Kauffman Bracket polynomial and the Tutte polynomial. Three properties of the Jones polynomial are discussed. We also see how mutant knots share the same Jones polynomial.
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Theses Digitization Project
The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.
Gauss-Bonnet Formula, Heather Ann Broersma
Gauss-Bonnet Formula, Heather Ann Broersma
Theses Digitization Project
From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Theses Digitization Project
A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs.
Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George
Symmetric Representation Of Elements Of Finite Groups, Timothy Edward George
Theses Digitization Project
The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.
Countable Short Recursively Saturated Models Of Arithmetic, Erez Shochat
Countable Short Recursively Saturated Models Of Arithmetic, Erez Shochat
Dissertations, Theses, and Capstone Projects
Short recursively saturated models of arithmetic are exactly the elementary initial segments of recursively saturated models of arithmetic. Since any countable recursively saturated model of arithmetic has continuum many elementary initial segments which are already recursively saturated, we turn our attention to the (countably many) initial segments which are not recursively saturated. We first look at properties of countable short recursively saturated models of arithmetic and show that although these models cannot be cofinally resplendent (an expandability property slightly weaker than resplendency), these models have non-definable expansions which are still short recursively saturated.