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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 ...
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 ...
Classification, Cobordism, and Curvature of Four-Dimensional Infra-Solvmanifolds
(2014)
Crystallographic groups of solvable Lie groups generalize the crystallographic groups of Euclidean space. The quotient of a solvable Lie group G by the action of a torsion-free crystallographic group of G is an infra-solvmanifold ...
Representations of the marked Brauer algebra
(2017-05-12)
The marked Brauer algebra is a generalization of the diagrammatic Brauer algebra which diagrammatizes Moon's centralizer algebra for the type \mathfrak{p} Lie superalgebra. We prove that the marked Brauer algebra is a ...
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 ...
Intersection Numbers in a Hyperbolic Surface
(2013)
For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus $\mathfrak g\geq2$, we show that the tails of the distribution of $i(\alpha,\beta)/l(\alpha)l(\beta)$ (where $i(\alpha,\beta)$ ...