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Hyperbolicity Equations For Knot Complements, Christopher Martin Jacinto
Hyperbolicity Equations For Knot Complements, Christopher Martin Jacinto
Theses Digitization Project
This study analyzes Carlo Petronio's paper, An Algorithm Producing Hyperbolicity Equations for a Link Complement in S³. Using the figure eight knot as an example, we will explain how Petronio's algorithm was able to decompose the knot complement of an alternating knot into tetrahedra. Then, using the vertex invariants of these tetrahedra, we will explain how Petronio was able to create hyperbolicity equations.
Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan
Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan
Theses Digitization Project
The purpose of this project is to investigate blow-up properties of solutions for specific initial-value problems that involve Bernoulli Ordinary Differential Equations (ODE's). The objective is to find conditions on the coefficients and on the initial-values that lead to unbounded growth of solutions in finite time.
Orthogonal Polynomials, George Gevork Antashyan
Orthogonal Polynomials, George Gevork Antashyan
Theses Digitization Project
This thesis will show work on Orthogonal Polynomials. In mathematics, the type of polynomials that are orthogonal to each other under inner product are called orthogonal polynomials. Jacobi polynomials, Laguerre polynomials, and Hermite polynomials are examples of classical orthogonal polynomials that was invented in the nineteenth century. The theory of rational approximations is one of the most important applications of orthogonal polynomials.
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
Theses Digitization Project
This project demonstrates how an elliptic curve f defined by invariance under two involutions can be represented by the locus of circumcenters of isosceles triangles in the hyperbolic plane, using inversive model.
Geodesics Of Surface Of Revolution, Wenli Chang
Geodesics Of Surface Of Revolution, Wenli Chang
Theses Digitization Project
The purpose of this project was to study the differential geometry of curves and surfaces in three-dimensional Euclidean space. Some important concepts such as, Curvature, Fundamental Form, Christoffel symbols, and Geodesic Curvature and equations are explored.
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
Theses Digitization Project
The purpose of the project is to examine the action of the composition of split inversions on the hyperbolic plane, H². The model that is used is the poincoŕe disk.
Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader
Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader
Theses Digitization Project
The purpose of this project was to define the relationship and show how an important subset of spatial differential equations can be transformed into cellular automata. Contains source code.
A Topological Approach To Nonlinear Analysis, Wendy Ann Peske
A Topological Approach To Nonlinear Analysis, Wendy Ann Peske
Theses Digitization Project
A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.
Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle
Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle
Theses Digitization Project
In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.