Now showing items 1-20 of 28

• #### [2014-07-12]ABC THEOREMS IN THE FUNCTIONAL CASE ﻿

In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the ...
• #### [2010-09-09]Analysis of nonlinear Black Scholes models ﻿

The Black Scholes equation is a fundamental model for derivative pricing. Modifying its assumptions will lead to more realistic but mathematically more complicated models. This dissertation consists of analytical and ...
• #### [2011-07-02]Analysis of the organization and dynamics of proteins in cell membranes ﻿

Cells communicate with the outside world through membrane receptors that recognize one of many possible stimuli (hormones, antibodies, peptides) in the extracellular environment and translate this information to intracellular ...
• #### [2013-09-05]Arithmetic Deformation Classes Associated to Curves via p-Jet Spaces ﻿

We show that for certain curves over p-adic rings its first p-jet space admits the structure of a torsor under a line bundle.
• #### [2014-07-12]Arithmetic Differential Subgroups of GL_{n} ﻿

A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the “Fermat quotient ...
• #### [2012-07-05]Arithmetic jet spaces and modular forms ﻿

In this thesis, we would look into the theory of arithmetic jet spaces and its application in modular forms. The arithmetic jet spaces can be thought of as an analogue of jet spaces in differential algebra. In the case of ...
• #### [2014-07-12]Changes in Student Proving Skills and Attitudes Following a Cooperative Learning Seminar ﻿

This dissertation details research studies designed to explore undergraduate math students’ beliefs and attitudes about mathematical proof, ability to compose valid proofs, and ability to read and validate purported proofs ...
• #### [2010-09-09]Commutators and dyadic paraproducts on weighted Lebesgue spaces ﻿

We prove that the operator norm on weighted Lebesgue space L^2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2 characteristic of the weight, as ...
• #### [2014-09-16]Computational Techniques for Optimal Control of Quantum System ﻿

The control of matter and energy at a fundamental level will be a cornerstone of new technologies for years to come. This idea is exemplified in a distilled form by controlling the dynamics of quantum mechanical systems ...
• #### [2010-09-10]Contact homology of toric contact manifolds of Reeb type ﻿

We use contact homology to distinguish contact structures on various manifolds. We are primarily interested in contact manifolds which admit an action of Reeb type of a compact Lie group. In such situations it is well ...
• #### [2015-01-28]DELAUNAY-LAGUERRE GEOMETRY FOR MACROMOLECULAR MODELING AND IMPLICIT SOLVATION ﻿

We develop and implement geometric methods to study three-dimensional structures of proteins, the knowledge of which is critical to the understanding of the molecules and their interactions. Delaunay and Laguerre methods, ...
• #### [2009-01-29]Modeling Arctic sea ice using the material-point method and an elastic-decohesive rheology ﻿

Sea ice has an important effect on global climate by reducing the heat transfer between the atmosphere and ocean and by reflecting incoming solar radiation. Additionally, sea ice can be an important navigational concern. ...
• #### [2014-02-13]Modeling the Mechanical Response of Polycrystalline Thin Films ﻿

Microelectromechanical systems (MEMS) are part of every modern technological advance. Electrodeposited thin nickel (Ni) polycrystalline films in MEMS often show fiber texture resulting in transverse isotropic elastic ...
• #### [2012-08-27]Numerical and Analytical Studies of Electromagnetic Waves: Hermite Methods, Supercontinuum Generation, and Multiple Poles in the SEM ﻿

The dissertation consists of three parts: Hermite methods, scattering from a lossless sphere, and analysis of supercontinuum generation. Hermite methods are a new class of arbitrary order algorithms to solve partial ...
• #### [2013-09-05]Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities ﻿

Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian ...
• #### [2012-02-01]Propagation of intense UV filaments and vortices. ﻿

The goal of this dissertation is to investigate the propagation of ultrashort high intensity UV laser pulses of order of nanoseconds in atmosphere. It is believed that they have a potential for stable and diffractionless ...
• #### [2014-02-14]Quantification of Stability in Systems of Nonlinear Ordinary Differential Equations ﻿

A common process in ODE theory is to linearize an ODE system about an equilibrium point to determine the local stability properties of its orbits. Less common are results that quantify the domain of stability in the original ...
• #### [2014-09-15]Sasakian geometry on lens space bundles over Riemann surfaces ﻿

we compute the cohomology of the join of a 3 manifold with the sphere and we see the dependence of this cohomology on one of the parameters.
• #### [2009-08-27]Shock formation properties of continuum and kinetic models ﻿

Continuum mechanics and kinetic theory are two mathematical theories with fundamentally different approaches to the same physical phenomenon. Continuum mechanics together with thermodynamics treat a substance (a gas or ...
• #### [2014-07-12]Star Operations and Numerical Semigroup Rings ﻿

We aim to classify the star and semistar operations on conductive numerical semigroup rings which are of the form $k + x^n k[[x]]$. By classifying the star and semistar operations on conductive numerical semigroup rings ...

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