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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 ...
Specral Theory of Canonical Systems
(2013)
The main purpose of this dissertation is to give an alternate proof of de Branges' theorem on canonical systems and to prove Remling's theorem on canonical systems.
Convergence Rates for Stationary Distributions of Semistochastic Processes
(2017-05)
The primary objects of study in this dissertation are semistochastic processes. The types of semistochastic processes we consider are continuous-time and continuous-state processes consisting of intervals of deterministic ...
Optimization Problem for Klein-Gordon Equation
(2012)
We consider a damped Klein-Gordon equation with a variable diffusion coefficient. The goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function J. First, we show that the ...
MATHEMATICAL THEORY IN CLASSIFICATION AND SEGMENTATION
(2012)
We develop several mathematical approaches to solve a series of questions of interdisciplinary research interests. New distance functions are designed for the verification of meteorological forecasts. Modern active contour ...
Stability of Solitary Waves for Some Schrodinger-KdV Systems
(2013)
This dissertation addresses existence and stability results for a two-parameter family of solitary-wave solutions to systems in which an equation of nonlinear Schrodinger type is coupled to an equation of Korteweg-de Vries ...
Dehn functions of subgroups of right-angled Artin groups
(2018-05)
The question of what is a possible range for the Dehn functions (a.k.a. isoperimetric spectrum) for certain classes of groups is a natural and interesting one. Due to works of many authors starting with Gromov, we know a ...
Geometry of Houghton's Groups
(2012)
Ken Brown showed finiteness properties of Houghton's groups by studying the action of those groups on infinite dimensional cell complex. We modify his proof by construction finite dimensional CAT(0) cubical complexes on ...
Complexity of Modules over Lie Superalgebras
(2014)
In this dissertation, a fair amount of work is dedicated to computing the complexity of modules over a classical Lie superalgebra $\fg=\fg_{\0}\oplus \fg_{\1}$ over the complex numbers $\C$. We will consider the category ...
Snowflake Groups with Super-Exponential 2-dimensional Dehn Functions
(2011)
The objective of this paper is to combine the results of two papers to get a new result. The first paper is called \textit{Super-Exponential 2-Dimensional Dehn Functions} by Josh Barnard, Noel Brady and Pallavi Dani. In ...