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Fall 2017

Morrill, Ryan W

In this thesis, we formulate and prove the theorem of quadratic reciprocity for an arbitrary number field. We follow Hecke and base our argument on analytic techniques and especially on an identity of theta functions called theta inversion. From this inversion formula and a limiting argument, we...

Spring 2018

Bandyopadhyay, Choiti

The concepts of semihypergroups and hypergroups were first introduced by C. Dunkl, I. Jewett and R. Spector independently around the year 1972. Till then, a variety of research has been carried out on different areas of hypergroups. However, no extensive study is found so far on the more general...

Fall 2017

Yu, Dengdeng

In this thesis, we study the partial quantile regression methods in functional data analysis. In the first part, we propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression...

Spring 2018

Gervais, Alain

As internal gravity wavepackets propagate upward in the atmosphere, their amplitude experiences exponential growth so that nonlinear effects influence their evolution. This thesis examines the weakly and fully nonlinear evolution, stability, and overturning of horizontally and vertically...

Fall 2017

Hanratty, Chantelle

We give an explicit criterion for when a toric GIT quotient is a stacky vector bundle over a projective base. That is given a charge matrix satisfying a certain property, we construct a projective base such that the semi-stable locus of the original GIT quotient is a G-equivariant vector bundle...

2008

Eftimie, Raluca A

In this thesis, we investigate the formation and movement of self-organizing collectives of animals in homogeneous environments. For this, we propose a general modeling framework that incorporates how individuals perceive information from neighbors, and the amount of information perceived. In...

Fall 2021

Budinski, Paul Garrett

The majority of known examples of fusion categories come directly from classical structures -- vector spaces, groups, representations, and the like. In recent years the technique of constructing fusion categories as endomorphisms on Cuntz algebras was developed and has already lead to completely...

Fall 2017

Kong, Jude D

This thesis focuses on formulating and analyzing non linear models for microbial dynamics vis-a-vis human and environmental health. Firstly, we develop and investigate a stoichiometric organic matter decomposition model in a chemostat culture that incorporates the dynamics of grazers. This...

Fall 2017

Akinwumi, Segun M

Epstein-Barr virus (EBV) is a “kissing disease virus” that has infected more than 95% of the adult human population. It has been associated with diseases such as Acute Infectious Mononucleosis (AIM) and post-transplant lymphoproliferative disorder (PTLD). The kinetics of primary EBV infection has...

Spring 2018

Zong, Fei

In this thesis, we study a mathematical model for the survival of a cells’ population exposed to various chemical compounds with different concentrations. For experimental planning, it is important to find the threshold value for the initial concentrations at which the cells become extinct....