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Estimation of Near Surface Tornadic Wind Speeds
(2011)
Modeling studies consistently demonstrate that the most violent winds in a tornadic vortex occur in the lowest tens of meters above the surface. These velocities are unobservable by radar platforms due to line of sight ...
New Simple Representations of Leavitt Path Algebras
(2019-12-13)
This thesis is about representations of Leavitt Path Algebras (LPAs). Specifically, we first generalize a previously known construction of twisted Chen modules over the Leavitt Path Algebra of a directed graph. We then ...
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 ...
Arithmetic in Quaternion Algebras and Quaternionic Modular Forms
(2019-05-10)
This dissertation has two parts. In the first part, we revisit the correspondence between spaces of modular forms and orders in quaternion algebras addressed first by Eichler and completed by Hijikata, Pizer, and Shemanske, ...
Some Classes of Jacobi Matrices and Schrödinger Operators
(2014)
This dissertation addresses two classes of Jacobi matrices and Schrödinger operators. First, we consider Jacobi matrices and Schrödinger operators that are reflectionless on an interval. We give a systematic development ...
NORMAL TORI IN #_n(S2xS1) AND THE DEHN TWIST AUTOMORPHISMS OF THE FREE GROUP
(2013)
The 3-dimensional space which renders a Out(F_n) action is M = #_n(S2x S1). The relation between M and Out(F_n) is that the latter is isomorphic to the mapping class group of M up to rotations about 2-spheres in M.
F-Harmonic Maps in Kahler Geometry
(2017-05-12)
Let u be an F-harmonic map between Kahler manifolds of finite dimensions. When is u holomorphic or anti-holomorphic? In the special case of a harmonic map, Y. T. Siu gave an affirmative answer when the target manifold is ...
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 ...
Comparison Theorems, Geomatric Inequalities, And Applications to p-harmonic Geometry
(2012)
In this dissertation, we consider three aspects: comparison theorems on complete manifold which posses a pole, geometric inequalities on complete manifolds, and the applications of inequalities to p-harmonic geometry. More ...