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Fall 2013

Feng, Han

One of the main aims in this thesis is to establish analogues of the classical Hardy-Littlewood-Sobolev (HLS) inequality for weighted orthogonal polynomial expansions (WOPEs) on the unit sphere, the unit ball and the simplex. An optimal condition for which this inequality holds is obtained....

Spring 2016

Wang, Xingpu

In this thesis, we first introduce two basic problems of filter, the nonlinear filtering and model selection problem. We show that both of them can be solved by the unnormalized filter approach. Then several web based particle filter algorithms will be discussed. We extend the resampled and...

2004

Liu, Songtao

Fall 2010

Pivovarov, Peter

This thesis is based on three papers on selected topics in Asymptotic Geometric Analysis. The first paper is about the volume of high-dimensional random polytopes; in particular, on polytopes generated by Gaussian random vectors. We consider the question of how many random vertices (or ...

Fall 2021

Farkhutdinov, Tagir

In this thesis, I developed the ideas of applying the variational method in geometric mechanics to the porous media described as solid elastic materials with embedded ideal (incompressible) fluid, also known as Eulerian fluid. The work includes four chapters and a conclusion. In the Introduction,...

Fall 2014

Shi, Qian

This thesis develops an efficient quantile-adaptive framework for linear and nonlinear variable screening with high-dimensional heterogeneous data. Inspired by the success of various variable screening methods, especially in the quantile-adaptive framework, we develop a more efficient variable...

Fall 2014

Wang,Xiaozhou

Two types of robust designs, robust design against a misspecified response function and robust design against autocorrelation, are reviewed in the first chapter of this dissertation. Among robust designs against autocorrelation, this dissertation focuses on V-robust designs. Chapter 2 reviews and...

Spring 2013

Deng, Jian

It has been known that for some physical problems, a small change in the system parameters or in the initial/boundary conditions could leas to a significant change in the system response. Hence, it is of importance to investigate the impact of uncertainty on dynamical system in order to fully...

Fall 2016

O'Brien, Michael J

In this thesis we describe basic properties of unbounded norm convergence (un-convergence) and investigate its relationship with other convergences in Banach lattices. In particular, we show that in order continuous Banach lattices with a weak unit, un-convergence can be viewed as a...

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...