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Fall 2009

Deng, Jian

Computation methods based on the Wiener chaos expansion have been developed to study the behaviors of the aeroelastic system with randomparameters. It is proven that the discrete wavelet transformation is one ofthe most accurate and efficient numerical schemes for this uncertainty...

Spring 2016

Zhang,Zecheng

A cell centered finite difference scheme for 2D parabolic problems on grids with a local refinement is presented. Peaceman and Rachford directional splitting is used in the discretization of time. The scheme is unconditionally stable and proven to be of second order convergence in time. Numerical...

Fall 2016

Roda, Weston C

Understanding human immunodeficiency-1 (HIV-1) replication and latency in different reservoirs is an ongoing challenge in the care of patients with HIV/AIDS. A mathematical model was created that predicted HIV-1 and simian immunodeficiency virus (SIV) infection dynamics within the brain during...

Fall 2016

Che, Menglu

BACKGROUND: Healthy dietary intake and appropriate weight gain are two key components of an ideal pregnancy. The objective of this thesis was to investigate the weight gain pattern of a large cohort of pregnant women and its association with dietary intakes, which may provide valuable information...

Spring 2019

Bernstein, Tobias

Atkin and Swinnerton-Dyer conjectured a simple characterization of those Fuchsian groups whose modular forms have integral Fourier coefficient. It has a natural and far-reaching generalization, which we will call the vASD conjecture, to vector-valued modular forms. We confirm vASD conjecture for...

Fall 2018

Vyachkileva, Daria

The main purpose of this thesis is to explore different risk-adjusted ratios, add correlation into account and see which one of them accommodates for risk the best way. In finance it is well-known that investors can not rely on pure return. Some fund managers can produce high return but at the...

Fall 2009

Bogowicz, Paul Joseph

This thesis explores the application of fully sequential methods for the analysis of longitudinal clinical trial data. A new nonparametric approach will be developed, using sequential ranks, for the comparison of several treatment groups. Sequential ranking is an alternative to ranking by the...

Spring 2014

Miao, Lingyu

This thesis deals with the Trotter-Kato approximation in utility maximization. The Trotter-Kato approximation is a method to split a differential equation into two parts, which are then solved iteratively over small time intervals. In the context of utility maximization, this procedure was...

Fall 2011

Bouffard, Nicolas

Left amenability, in it's modern form, was introduced by M. M. Day, in the 1940s. Amenability of groups and semigroups turned out to be quite common, and many interesting results are known, which motivated the introduction of extreme left amenability by Granirer in the 1960s. Extreme amenability...

Spring 2015

Adeeb, Samer

Piecewise affine functions as defined by Aliprantis and Tourky and denoted by the set S are those functions in C(R^m) that agree with a finite number of affine functions. In this thesis, we extend their study by introducing the set of locally piecewise affine functions denoted by S_lp. Unlike...