## 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.

- Spielberg, John
- 9 Arizona State University
- 4 Fishel, Susanna
- 4 Quigg, John
- 3 Czygrinow, Andrzej
- 3 Jones, John
- 2 Bremner, Andrew
- more
- 2 Childress, Nancy
- 2 Kaliszewski, Steven
- 2 Kierstead, Henry
- 2 Milner, Fabio
- 1 AL-SULEIMAN, SULTAN
- 1 Boggess, Albert
- 1 Cochran, Douglas
- 1 Colbourn, Charles
- 1 Eikenberry, Keenan
- 1 Jin, Wen
- 1 Jones, Donald
- 1 Kawski, Matthias
- 1 Menendez, Jose
- 1 Moran, William
- 1 Nelson, Luke Edwin
- 1 Patani, Nura
- 1 Robinson, Benjamin David
- 1 Sanborn, Barbara
- 1 Smith, Hal
- 1 Suslov, Sergei
- 1 Suslov, Sergei K
- 1 Thieme, Horst
- 1 Yie, Jangwon
- 1 Zinzer, Scott

- 9 English

- 9 Public

- Mathematics
- 2 C*-algebras
- 2 Maximal Chains
- 2 Tamari Lattices
- 2 Theoretical mathematics
- 1 $\lambda$-invariant
- 1 C*-correspondences
- more
- 1 Cambrian Lattices
- 1 Condensed Matter Physics
- 1 Crossed products
- 1 Dynamical systems
- 1 Enumeration
- 1 Extremal Graph Theory
- 1 Frames
- 1 G-frames
- 1 Gamma-transform
- 1 Graph algebras
- 1 Hilbert bimodules
- 1 Iwasawa Invariant
- 1 Iwasawa Theory
- 1 J-holomorphic curves
- 1 Lattices
- 1 Operator-valued frames
- 1 Pseudo-polynomial
- 1 Quantum physics
- 1 Radon-Nikodym theorems
- 1 Ramsey Number
- 1 Representation theory
- 1 Sampling
- 1 Turan Number
- 1 adiabatic theorem
- 1 discrete dynamical systems
- 1 functoriality
- 1 geometric quantum mechanics
- 1 higher-rank graph
- 1 m-eralized Cambrian Lattices
- 1 mean curvature
- 1 p-adic Valued Measure
- 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

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

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

In 1984, Sinnott used $p$-adic measures on $\mathbb{Z}_p$ to give a new proof of the Ferrero-Washington Theorem for abelian number fields by realizing $p$-adic $L$-functions as (essentially) the $Gamma$-transform of certain $p$-adic rational function measures. Shortly afterward, Gillard and Schneps independently adapted Sinnott's techniques to the case of $p$-adic $L$-functions associated to elliptic curves with complex multiplication (CM) by realizing these $p$-adic $L$-functions as $Gamma$-transforms of certain $p$-adic rational function measures. The results in the CM case give the vanishing of the Iwasawa $mu$-invariant for certain $mathbb{Z}_p$-extensions of imaginary quadratic fields constructed from torsion points of CM elliptic curves. In ...

- Contributors
- Zinzer, Scott, Childress, Nancy, Bremner, Andrew, et al.
- Created Date
- 2015

Since Duffin and Schaeffer's introduction of frames in 1952, the concept of a frame has received much attention in the mathematical community and has inspired several generalizations. The focus of this thesis is on the concept of an operator-valued frame (OVF) and a more general concept called herein an operator-valued frame associated with a measure space (MS-OVF), which is sometimes called a continuous g-frame. The first of two main topics explored in this thesis is the relationship between MS-OVFs and objects prominent in quantum information theory called positive operator-valued measures (POVMs). It has been observed that every MS-OVF gives rise ...

- Contributors
- Robinson, Benjamin David, Cochran, Douglas, Moran, William, et al.
- Created Date
- 2014

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

Since the seminal work of Tur ́an, the forbidden subgraph problem has been among the central questions in extremal graph theory. Let ex(n;F) be the smallest number m such that any graph on n vertices with m edges contains F as a subgraph. Then the forbidden subgraph problem asks to find ex(n; F ) for various graphs F . The question can be further generalized by asking for the extreme values of other graph parameters like minimum degree, maximum degree, or connectivity. We call this type of question a Tura ́n-type problem. In this thesis, we will study Tura ́n-type ...

- Contributors
- Yie, Jangwon, Czygrinow, Andrzej, Kierstead, Henry, et al.
- Created Date
- 2018

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

The Cambrian lattice corresponding to a Coxeter element c of An, denoted Camb(c), is the subposet of An induced by the c-sortable elements, and the m-eralized Cambrian lattice corresponding to c, denoted Cambm(c), is dened as a subposet of the braid group accompanied with the right weak ordering induced by the c-sortable elements under certain conditions. Both of these families generalize the well-studied Tamari lattice Tn rst introduced by D. Tamari in 1962. S. Fishel and L. Nelson enumerated the chains of maximum length of Tamari lattices. In this dissertation, I study the chains of maximum length of the Cambrian ...

- Contributors
- AL-SULEIMAN, SULTAN, Fishel, Susanna, Childress, Nancy, et al.
- Created Date
- 2017

The Tamari lattices have been intensely studied since they first appeared in Dov Tamari’s thesis around 1952. He defined the n-th Tamari lattice T(n) on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Despite their interesting aspects and the attention they have received, a formula for the number of maximal chains in the Tamari lattices is still unknown. The purpose of this thesis is to convey my results on progress toward the solution of this problem and to discuss future work. A few years ago, Bergeron and Préville-Ratelle generalized ...

- Contributors
- Nelson, Luke Edwin, Fishel, Susanna, Czygrinow, Andrzej, et al.
- Created Date
- 2016