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Skip to Search Results 5Frei, Christoph (Mathematical and Statistical Sciences)
 5Kong, Linglong (Mathematical and Statistical Sciences)
 5Mizera, Ivan (Mathematical and Statistical Sciences)
 4Han, Bin (Mathematical and Statistical Sciences)
 4Karunamuni, Rohana (Mathematical and Statistical Sciences)
 4Lau, Anthony ToMing (Mathematical and Statistical Sciences)

Fall 2013
One of the main aims in this thesis is to establish analogues of the classical HardyLittlewoodSobolev (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
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...

Fall 2010
This thesis is based on three papers on selected topics in Asymptotic Geometric Analysis. The first paper is about the volume of highdimensional random polytopes; in particular, on polytopes generated by Gaussian random vectors. We consider the question of how many random vertices (or ...

Fall 2014
This thesis develops an efficient quantileadaptive framework for linear and nonlinear variable screening with highdimensional heterogeneous data. Inspired by the success of various variable screening methods, especially in the quantileadaptive framework, we develop a more efficient variable...

Fall 2014
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 Vrobust designs. Chapter 2 reviews and...

Spring 2013
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...

Spring 2019
Suppose $X$ is a vector lattice and there is a notion of convergence $x_{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x_{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x_\alphax\rvert \wedge u\xrightarrow{\sigma} 0$ for...

Spring 2019
Atkin and SwinnertonDyer conjectured a simple characterization of those Fuchsian groups whose modular forms have integral Fourier coefficient. It has a natural and farreaching generalization, which we will call the vASD conjecture, to vectorvalued modular forms. We confirm vASD conjecture for...

Fall 2012
Cholera remains epidemic and endemic in the world, causing thousands of deaths annually in locations lacking adequate sanitation and water infrastructure. Yet its dynamics are still not fully understood. An indirectly transmitted infectious disease model, called an iSIR model, was recently...