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Fall 2022

Liu, Shuo

This thesis concerns dynamical systems subject to small noise perturbations. Our purpose is to obtain a deep understanding of how small noise perturbations influence the original unperturbed dynamical system, especially over long but finite time intervals. We consider two special systems, the...

Fall 2021

Kosakian, Aslan

Hydrogen fuel cells convert the chemical energy of hydrogen directly into electricity, with the only byproducts being heat and water. The high cost of hydrogen fuel cells due to the expensive platinum catalyst is one of the limiting factors to their global commercialization. Improving fuel-cell...

Fall 2010

Cheng, Yin-Hei

Let $G$ be a locally compact group, $G^$ be the set of all extreme points of the set of normalized continuous positive definite functions of $G$ and $a(G)$ be the closed subalgebra generated by $G^$ in $B(G)$. When $G$ is abelian, $G^$ is the set of dirac measures of the dual group of $G$. The...

Fall 2011

Gong, Jiafen

Cancer is one of the major causes of death in the world. In the field of Oncology, clinical trials form the crux of medical effort to find better treatment schedules. These trials are expensive, time consuming, and carry great risks for the patients involved. Mathematical models provide a...

Fall 2012

Davis, William L

Cholera remains epidemic and endemic in the world, causing thousands of deaths annually in locations lacking adequate sanitation and water infrastructure. Yet its dynamics are still not fully understood. An indirectly transmitted infectious disease model, called an iSIR model, was recently...

Spring 2019

Bernstein, Tobias

Atkin and Swinnerton-Dyer conjectured a simple characterization of those Fuchsian groups whose modular forms have integral Fourier coefficient. It has a natural and far-reaching generalization, which we will call the vASD conjecture, to vector-valued modular forms. We confirm vASD conjecture for...

Fall 2016

O'Brien, Michael J

In this thesis we describe basic properties of unbounded norm convergence (un-convergence) and investigate its relationship with other convergences in Banach lattices. In particular, we show that in order continuous Banach lattices with a weak unit, un-convergence can be viewed as a...

Spring 2019

Taylor, Mitchell A.

Suppose $X$ is a vector lattice and there is a notion of convergence $x{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x\alpha-x\rvert \wedge u\xrightarrow{\sigma} 0$ for every...

Spring 2013

Deng, Jian

It has been known that for some physical problems, a small change in the system parameters or in the initial/boundary conditions could leas to a significant change in the system response. Hence, it is of importance to investigate the impact of uncertainty on dynamical system in order to fully...

Fall 2014

Wang,Xiaozhou

Two types of robust designs, robust design against a misspecified response function and robust design against autocorrelation, are reviewed in the first chapter of this dissertation. Among robust designs against autocorrelation, this dissertation focuses on V-robust designs. Chapter 2 reviews and...