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Model Reduction for Nanoscale Stick-Slip Friction Using Proper Orthogonal Decomposition
(2006-12-14)
Advances in computing hardware and algorithms have led to molecular dynamical models being able to model more realist cases. In this paper, we focus on a special case of molecular dynamics as a starting example. The ...
Generalized Volatility Model And Calculating VaR Using A New Semiparametric Model
(2005-12-05)
The first part of the dissertation concerns financial volatility models. Financial volatility has some stylized facts, such as excess kurtosis, volatility clustering and leverage effects. A good volatility model should be ...
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics: a staggered dissipation-control differencing algorithm.
(2006-08-01)
A new unsplit staggered mesh algorithm (USM) that solves multidimensional magnetohydrodynamics (MHD) on a staggered mesh is introduced and studied. Proper treatments of multidimensional flow problems are required for MHD ...
Local Rigidity of Triangle Groups in Sp(4,R)
(2009)
This paper studies configurations of Lagrangians in a four dimensional real symplectic vector space. We develop a generalized cross ratio as an invariant for quadruples of Lagrangians. This invariant is then used to study ...
MODELING MEDIAN HOUSEHOLD INCOME DISTRIBUTION
(2008)
In this thesis we are going to use U.S. Census data to study median household income distribution for 13 U.S. counties and seven U.S. states. Over the years, researchers have fitted income data with various probability ...
Maximum Likelihood Estimation and Computation in a Random Effect Factor Model
(2004-08-04)
We first briefly review some multivariate statistical models
such as Principal Component Analysis (PCA), Factor Analysis (FA),
and Probabilistic PCA (PPCA). Alternatively, we approach PCA from
the least-squares point ...
Existence and Stability of Vortex Solutions of Certain Nonlinear Schrodinger Equations
(2004-05-04)
The nonlinear Schrodinger equation models a wide variety of different physical phenomena ranging from nonlinear optics, water waves, magnetization of ferromagnets to Bose-Einstein condensates (BEC). The structure of the ...
Sigma Delta Modulation and Correlation Criteria for the Construction of Finite Frames Arising in Communication Theory
(2004-04-29)
In this dissertation we first consider a problem in
analog to digital (A/D) conversion. We compute the power spectra of the error arising from an A/D conversion. We then design various higher dimensional analogs of A/D ...
Infinite-Dimensional Dynamical Systems and Projections
(2004-04-27)
We address three problems arising in the theory of infinite-dimensional dynamical systems. First, we study the extent to which the Hausdorff dimension and the dimension spectrum of a fractal measure supported on a compact ...
Performance Analysis of a Multi-Class, Preemptive Priority Call Center with Time-Varying Arrivals
(2004-06-08)
We model a call center as a an $M_{t}/M/n$, preemptive-resume priority queue with time-varying arrival rates and two priority classes of customers. The low priority customers have a dynamic priority where they become high ...