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Categorizing Students' Difficulties with Mathematical Proofs: Developing a Model of the Structure of Proof Construction
(2015-08-14)
Studies have shown that proof construction is a challenging task for students at all levels. The purposes of my study were to examine students' difficulties with proof construction and to explore a practical method to help ...
A Coupled Chemo-Thermo-Poroelastic System: Well-Posedness and Approximation for Control Applications
(2015)
This dissertation addresses well-posedness and approximation problems for coupled parabolic-elliptic systems with applications to geomechanics. The work is motivated by problems of borehole stability in porous formations ...
EXISTENCE AND STABILITY OF SOLUTIONS TO A MODEL RQUATION FOR DISPERSION-MANAGED SOLITARY WAVES
(2015-05-29)
We study the existence and stability of solutions of the initial-value problem for the dispersion-managed nonlinear Schro ̈dinger (DMNLS) equation, a model equation for optical pulses in a dispersion-managed fiber. One ...
SOME RESULTS ON ELLIPTIC EQUATIONS AND MODELING SEASONAL DYNAMICS OF HUMAN INFLUENZA
(2015-08-14)
This dissertation includes two parts: the theoretical study of an elliptic equation, and the practical study regarding the seasonality of human influenza.
In the first part, we focus on the study of an elliptic equation ...
Controllability of Linear and Nonlinear Control Systems related through Simulation Relations
(2015-12)
For nonlinear input-disturbance systems that are connected by a simulation relation, we examine to what extent they share certain controllability properties. Specifically our main objective is to determine the conditions ...
Dehn Functions of the Stallings-Bieri Groups and Constructions of Non-Unique Product Groups
(2015-05-08)
This thesis will consist of two separate halves in which we will present results concerning two different families of finitely generated torsion-free groups. The themes of each half are quite different and are related to ...
The representations of p-adic fields associated to elliptic curves
(2015)
The goal of this dissertation is to find the irreducible, admissible representation
of GL(2; F) attached to an elliptic curve E over a p-adic field F. Associated
to E is a 2-dimensional complex representation of the ...