Browsing Mathematics by Title
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[20140712] 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 ... 
[20100909] 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 ... 
[20140916] 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 ... 
[20100910] 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 ... 
[20150128] DELAUNAYLAGUERRE GEOMETRY FOR MACROMOLECULAR MODELING AND IMPLICIT SOLVATION
We develop and implement geometric methods to study threedimensional structures of proteins, the knowledge of which is critical to the understanding of the molecules and their interactions. Delaunay and Laguerre methods, ... 
[20150901] Improving the Material Point Method
The material point method (MPM) was designed to solve problems in solid mechanics, and it has been used widely in research and industry. In MPM, the equations of motion are solved on a background grid and Lagrangian material ... 
[20160609] Lifts of Frobenius on Arithmetic Jet Spaces of Schemes
Lifts of Frobenius on formal schemes X over the padic completion of the maximal unramified extension of the padic integers may be viewed as arithmetic analogues of vector fields on manifolds. In particular, vector fields ... 
[20090129] Modeling Arctic sea ice using the materialpoint method and an elasticdecohesive 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. ... 
[20140213] 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 ... 
[20120827] 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 ... 
[20130905] 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 SasakiEinstein metrics have positive Ricci curvature, and since positive Sasakian ... 
[20120201] 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 ... 
[20140214] 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 ... 
[20140915] 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. 
[20090827] 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 ... 
[20150901] Spatial Decay of Rotating Waves and Restrictions on Finite Disks.
In this thesis, we consider the system of reactiondiffusion equations and the behavior of the solution of such a system. The focus is to concentrate on solutions which decay at infinity. Under suitable assumptions, we ... 
[20140712] 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 ... 
[20110831] Steady states, nonsteady evolution, pinchoff and postpinchoff of axisymmetric drops in Stokes flow
A good understanding of drop evolution and breakup is important in many applications. For instance, controlling the liquid droplet size is crucial in atomization processes such as fuel combustion and fertilizer application, ... 
[20150128] Strongly Nonlinear Phenomena and Singularities in Optical, Hydrodynamic and Biological Systems
Singularity formation is an inherent feature of equations in nonlinear physics, in many situations such as in selffocusing of light nonlinearity is essential part of the model and physical events cannot be captured ... 
[20160201] Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method
In this thesis, we present methods for integrating Maxwell's equations in FrenetSerret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines ...