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On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
Theses and Dissertations - UTB/UTPA
The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …
Fully Coupled Fluid And Electrodynamic Modeling Of Plasmas: A Two-Fluid Isomorphism And A Strong Conservative Flux-Coupled Finite Volume Framework, Richard Joel Thompson
Fully Coupled Fluid And Electrodynamic Modeling Of Plasmas: A Two-Fluid Isomorphism And A Strong Conservative Flux-Coupled Finite Volume Framework, Richard Joel Thompson
Doctoral Dissertations
Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models …
The Machete Number, David Freund
The Machete Number, David Freund
Senior Independent Study Theses
Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Let's Get In The Mood: An Exploration Of Data Mining Techniques To Predict Mood Based On Musical Properties Of Songs, Sarah Smith-Polderman
Senior Independent Study Theses
This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: …
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour
Senior Independent Study Theses
Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …