## ASU Electronic Theses and Dissertations

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

Subject
Date Range
2010 2019

## Recent Submissions

Graph coloring is about allocating resources that can be shared except where there are certain pairwise conflicts between recipients. The simplest coloring algorithm that attempts to conserve resources is called first fit. Interval graphs are used in models for scheduling (in computer science and operations research) and in biochemistry for one-dimensional molecules such as genetic material. It is not known precisely how much waste in the worst case is due to the first-fit algorithm for coloring interval graphs. However, after decades of research the range is narrow. Kierstead proved that the performance ratio R is at most 40. Pemmaraju, Raman, …

Contributors
Smith, David A., Kierstead, Henry A., Czygrinow, Andrzej, et al.
Created Date
2010

ABSTRACT This thesis attempts to answer two questions based upon the historical observation that 1^2 +2^2 +· · ·+24^2 = 70^2. The first question considers changing the starting number of the left hand side of the equation from 1 to any perfect square in the range 1 to 10000. On this question, I attempt to determine which perfect square to end the left hand side of the equation with so that the right hand side of the equation is a perfect square. Mathematically, Question #1 can be written as follows: Given a positive integer r with 1 less than or …

Contributors
Roth, Sanford Gary, Bremner, Andrew, Childress, Nancy E, et al.
Created Date
2010

Current trends in the Computer Aided Engineering (CAE) involve the integration of legacy mesh-based finite element software with newer solid-modeling kernels or full CAD systems in order to simplify laborious or highly specialized tasks in engineering analysis. In particular, mesh generation is becoming increasingly automated. In addition, emphasis is increasingly placed on full assembly (multi-part) models, which in turn necessitates an automated approach to contact analysis. This task is challenging due to increases in algebraic system size, as well as increases in the number of distorted elements - both of which necessitate manual intervention to maintain accuracy and conserve computer …

Contributors
Grishin, Alexander, Shah, Jami J., Davidson, Joe, et al.
Created Date
2010

Borda's social choice method and Condorcet's social choice method are shown to satisfy different monotonicities and it is shown that it is impossible for any social choice method to satisfy them both. Results of a Monte Carlo simulation are presented which estimate the probability of each of the following social choice methods being manipulable: plurality (first past the post), Borda count, instant runoff, Kemeny-Young, Schulze, and majority Borda. The Kemeny-Young and Schulze methods exhibit the strongest resistance to random manipulability. Two variations of the majority judgment method, with different tie-breaking rules, are compared for continuity. A new variation is proposed …

Contributors
Jennings, Andrew Blake, Hurlbert, Glenn, Barcelo, Helene, et al.
Created Date
2010

In any instructional situation, the instructor's goal is to maximize the learning attained by students. Drawing on the adage, 'we learn best what we have taught,' this action research project was conducted to examine whether students, in fact, learned college algebra material better if they taught it to their peers. The teaching-to-learn process was conducted in the following way. The instructor-researcher met with individual students and taught a college algebra topic to a student who served as the leader of a group of four students. At the next step, the student who originally learned the material from the instructor met …

Contributors
Nicoloff, Stephen James, Buss, Ray R, Zambo, Ronald, et al.
Created Date
2011

In Iwasawa theory, one studies how an arithmetic or geometric object grows as its field of definition varies over certain sequences of number fields. For example, let $F/\mathbb{Q}$ be a finite extension of fields, and let $E:y^2 = x^3 + Ax + B$ with $A,B \in F$ be an elliptic curve. If $F = F_0 \subseteq F_1 \subseteq F_2 \subseteq \cdots F_\infty = \bigcup_{i=0}^\infty F_i$, one may be interested in properties like the ranks and torsion subgroups of the increasing family of curves $E(F_0) \subseteq E(F_1) \subseteq \cdots \subseteq E(F_\infty)$. The main technique for studying this sequence of curves when …

Contributors
Franks, Chase Leroyce, Childress, Nancy, Barcelo, Helene, et al.
Created Date
2011

The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which …

Contributors
Kamat, Vikram Mahendra, Hurlbert, Glenn, Colbourn, Charles, et al.
Created Date
2011

Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates …

Contributors
Guevara, Cristi Darley, Roudenko, Svetlana, Castillo_Chavez, Carlos, et al.
Created Date
2011

In this thesis, I investigate the C*-algebras and related constructions that arise from combinatorial structures such as directed graphs and their generalizations. I give a complete characterization of the C*-correspondences associated to directed graphs as well as results about obstructions to a similar characterization of these objects for generalizations of directed graphs. Viewing the higher-dimensional analogues of directed graphs through the lens of product systems, I give a rigorous proof that topological k-graphs are essentially product systems over N^k of topological graphs. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with …

Contributors
Patani, Nura, Kaliszewski, Steven, Quigg, John, et al.
Created Date
2011

The theme for this work is the development of fast numerical algorithms for sparse optimization as well as their applications in medical imaging and source localization using sensor array processing. Due to the recently proposed theory of Compressive Sensing (CS), the $\ell_1$ minimization problem attracts more attention for its ability to exploit sparsity. Traditional interior point methods encounter difficulties in computation for solving the CS applications. In the first part of this work, a fast algorithm based on the augmented Lagrangian method for solving the large-scale TV-$\ell_1$ regularized inverse problem is proposed. Specifically, by taking advantage of the separable structure, …

Contributors
Shen, Wei, Mittlemann, Hans D, Renaut, Rosemary A, et al.
Created Date
2011

By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a …

Contributors
Manley, Michael, Kadell, Kevin W. J., Kao, Ming-Hung, et al.
Created Date
2011

In a large network (graph) it would be desirable to guarantee the existence of some local property based only on global knowledge of the network. Consider the following classical example: how many connections are necessary to guarantee that the network contains three nodes which are pairwise adjacent? It turns out that more than n^2/4 connections are needed, and no smaller number will suffice in general. Problems of this type fall into the category of extremal graph theory.'' Generally speaking, extremal graph theory is the study of how global parameters of a graph are related to local properties. This dissertation deals …

Contributors
Debiasio, Louis, Kierstead, Henry A, Czygrinow, Andrzej, et al.
Created Date
2011

Let T be a tournament with edges colored with any number of colors. A rainbow triangle is a 3-colored 3-cycle. A monochromatic sink of T is a vertex which can be reached along a monochromatic path by every other vertex of T. In 1982, Sands, Sauer, and Woodrow asked if T has no rainbow triangles, then does T have a monochromatic sink? I answer yes in the following five scenarios: when all 4-cycles are monochromatic, all 4-semi-cycles are near-monochromatic, all 5-semi-cycles are near-monochromatic, all back-paths of an ordering of the vertices are vertex disjoint, and for any vertex in an …

Contributors
Created Date
2011

A fundamental motivation for this study was the underrepresentation of women in Science, Technology, Engineering and Mathematics careers. There is no doubt women and men can achieve at the same level in Mathematics, yet it is not clear why women are opting out. Adding race to the equation makes the underrepresentation more dramatic. Considering the important number of Latinos in the United States, especially in school age, it is relevant to find what reasons could be preventing them from participating in the careers mentioned. This study highlight the experiences young successful Latinas have in school Mathematics and how they shape …

Contributors
Guerra Lombardi, Paula Patricia, Middleton, James, Battey, Daniel, et al.
Created Date
2011

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. …

Contributors
Sanborn, Barbara, Suslov, Sergei K, Suslov, Sergei, et al.
Created Date
2011

Sparse learning is a technique in machine learning for feature selection and dimensionality reduction, to find a sparse set of the most relevant features. In any machine learning problem, there is a considerable amount of irrelevant information, and separating relevant information from the irrelevant information has been a topic of focus. In supervised learning like regression, the data consists of many features and only a subset of the features may be responsible for the result. Also, the features might require special structural requirements, which introduces additional complexity for feature selection. The sparse learning package, provides a set of algorithms for …

Contributors
Thulasiram, Ramesh L., Ye, Jieping, Xue, Guoliang, et al.
Created Date
2011

This study investigated the link between the cognitive clusters from the Woodcock&ndash;Johnson III Tests of Cognitive Ability (WJ III COG) and Broad Math, Math Calculation Skills, and Math Reasoning clusters of the Woodcock&ndash;Johnson III Tests of Achievement (WJ III ACH) using data collected over seven years by a large elementary school district in the Southwest. The students in this study were all diagnosed with math learning disabilities. Multiple regression analyses were used to predict performance on the Broad Math, Math Calculation Skills, and Math Reasoning clusters from the WJ III ACH. Fluid Reasoning (Gf), Comprehension&ndash;Knowledge (Gc), Short&ndash;Term Memory (Gsm), and …

Contributors
Bacal, Emily Beth, Caterino, Linda, Stamm, Jill, et al.
Created Date
2011

The world is grappling with two serious issues related to energy and climate change. The use of solar energy is receiving much attention due to its potential as one of the solutions. Air conditioning is particularly attractive as a solar energy application because of the near coincidence of peak cooling loads with the available solar power. Recently, researchers have started serious discussions of using adsorptive processes for refrigeration and heat pumps. There is some success for the >100 ton adsorption systems but none exists in the <10 ton size range required for residential air conditioning. There are myriad reasons for …

Contributors
Gupta, Yeshpal, Phelan, Patrick E, Bryan, Harvey J, et al.
Created Date
2011

Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with …

Contributors
Han, Zhun, Smith, Hal, Armbruster, Dieter, et al.
Created Date
2012

The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet …

Contributors
Lopez, Raquel, Suslov, Sergei K, Radunskaya, Ami, et al.
Created Date
2012