## 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.

- Quigg, John
- 7 Arizona State University
- 4 Spielberg, John
- 3 Kaliszewski, Steven
- 2 Bremner, Andrew
- 2 Kawski, Matthias
- 1 Bell, Stephanie
- more
- 1 Childress, Nancy
- 1 Eikenberry, Keenan
- 1 Fishel, Susana
- 1 Fishel, Susanna
- 1 Hurlbert, Glenn
- 1 Jin, Wen
- 1 Jones, Donald
- 1 Jones, John
- 1 Kotschwar, Brett
- 1 Menendez, Jose
- 1 Milner, Fabio
- 1 Morgan, Adam
- 1 Nguyen, Tho Xuan
- 1 Patani, Nura
- 1 Sanborn, Barbara
- 1 Smith, Hal
- 1 Spielberg, Jack
- 1 Suslov, Sergei
- 1 Suslov, Sergei K
- 1 Thieme, Horst

- 7 English

- 7 Public

- Mathematics
- 2 C*-algebras
- 1 C*-correspondences
- 1 Condensed Matter Physics
- 1 Crossed products
- 1 Diophantine equations
- 1 Discrete Math
- more
- 1 Dynamical systems
- 1 Graph algebras
- 1 High school
- 1 Hilbert bimodules
- 1 J-holomorphic curves
- 1 Mathematics education
- 1 Quantum physics
- 1 Theoretical mathematics
- 1 adiabatic theorem
- 1 algebraic number theory
- 1 discrete dynamical systems
- 1 elliptic curve
- 1 elliptic curve Chabauty
- 1 functoriality
- 1 geometric quantum mechanics
- 1 higher-rank graph
- 1 mean curvature
- 1 number theory
- 1 p-adic analysis
- 1 persistence
- 1 spectral radius
- 1 symplectic topology
- 1 uncertainty principle

- Microfluidic Models of Tumor-Stroma Interactions to Study the Interplay of Cancer Cells with their Surrounding Microenvironment
- Ain't She Sweet: A Critical Choreographic Study of Identity & Intersectionality
- Suppositions for Desert Modernism: An Architectural Framework Informed by Climate, Natural Light, and Topography
- Concurrent reduction of trichloroethylene and perchlorate in continuous flow-through soil columns
- Design and Fabrication of Fabric ReinforcedTextile Actuators forSoft Robotic Graspers

This thesis focuses on sequencing questions in a way that provides students with manageable steps to understand some of the fundamental concepts in discrete mathematics. The questions are aimed at younger students (middle and high school aged) with the goal of helping young students, who have likely never seen discrete mathematics, to learn through guided discovery. Chapter 2 is the bulk of this thesis as it provides questions, hints, solutions, as well as a brief discussion of each question. In the discussions following the questions, I have attempted to illustrate some relationships between the current question and previous questions, explain ...

- Contributors
- Bell, Stephanie, Fishel, Susana, Hurlbert, Glenn, et al.
- Created Date
- 2014

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

This dissertation contains three main results. First, a generalization of Ionescu's theorem is proven. Ionescu's theorem describes an unexpected connection between graph C*-algebras and fractal geometry. In this work, this theorem is extended from ordinary directed graphs to higher-rank graphs. Second, a characterization is given of the Cuntz-Pimsner algebra associated to a tensor product of C*-correspondences. This is a generalization of a result by Kumjian about graphs algebras. This second result is applied to several important special cases of Cuntz-Pimsner algebras including topological graph algebras, crossed products by the integers and crossed products by completely positive maps. The result has ...

- Contributors
- Morgan, Adam, Kaliszewski, Steven, Quigg, John, et al.
- Created Date
- 2016

Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs, and as with ordinary directed graphs, there are various C*-algebraic objects that can be associated with them. This thesis adopts a functorial approach to study the relationship between k-graphs and their associated C*-algebras. In particular, two functors are given between appropriate categories of higher-rank graphs and the category of C*-algebras, one for Toeplitz algebras and one for Cuntz-Krieger algebras. Additionally, the Cayley graphs of finitely generated groups are used to define a class of k-graphs, and a functor is then given from a category of finitely generated groups to the ...

- Contributors
- Eikenberry, Keenan, Quigg, John, Kaliszewski, Steven, et al.
- Created Date
- 2016

Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations. The map which encapsulates the population development from one year to the next is approximated at the origin (the extinction state) by a linear or homogeneous map. The (cone) spectral radius of this approximating map is the threshold between extinction and persistence. General persistence results are applied to three particular ...

- Contributors
- Jin, Wen, Thieme, Horst, Milner, Fabio, et al.
- Created Date
- 2014

Diophantine arithmetic is one of the oldest branches of mathematics, the search for integer or rational solutions of algebraic equations. Pythagorean triangles are an early instance. Diophantus of Alexandria wrote the first related treatise in the fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat. The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application ...

- Contributors
- Nguyen, Tho Xuan, Bremner, Andrew, Childress, Nancy, et al.
- Created Date
- 2019

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