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Fall 2015

Zhao, Zhenpeng

This thesis concentrates on the construction of directional tensor product complex tight framelets. It uses a complex tight framelet filter bank in one dimension and the tensor product of the one-dimensional filter bank to obtain high-dimensional filter bank. It has a number of advantages over...

Fall 2013

Ma, Junfeng

This thesis develops three major essays on the topic of horizon-dependence for optimal portfolio. The first essay contributes extensively to the newest concept of forward utilities. In this essay, we describe explicitly three classes of forward utilities--that we call HARA forward utilities--as...

Fall 2010

Zhuang, Xiaosheng

In Chapters 1 and 2, we introduce the definition of interpolating refinable function vectors in dimension one and high dimensions, characterize such interpolating refinable function vectors in terms of their masks, and derive their sum rule structure explicitly. We study biorthogonal refinable...

Fall 2009

Tan, Xiaobai

Let $A1$ denote the first Weyl algebra over a field $K$ of characteristic 0; that is, $A1$ is generated over $K$ by elements $p$, $q$ that satisfy the relation $pq-qp=1$. One can view $A1$ as an algebra of differential operators by setting $q=X$, $p=d/dX$. The basic questions which are addressed...

Fall 2021

Niu, Yeli

This thesis includes 2 parts. Part 1 is: Discretization on High Dimensional Compact Domains. Part 2 is: Polynomial Approximation on High Dimensional Spheres. A special example for part 1 is the result on the unit sphere of high-dimensional Euclidean spaces. In chapter 2, we obtained general...

Fall 2015

Omanovic, Jasmin

In this thesis we extend the work of Fabien Morel on Milnor-Witt K-theory over fields of characteristic not 2 to fields of characteristic 2.

Fall 2014

Petrov, Pavel

Persistent Homology broadly refers to tracking the topological features of a geometric object. This study aims to use persistent homology to explore the effect of Human Biotherapy on patients suffering from Clotridium Difficile Infection. The data is presented in the form of several distance...

Fall 2019

Liu,Zhengjun

Prostate cancer is one of the most common cancers among men in the world (excluding non-melanoma skin cancers). According to the statistics from the Canadian Cancer Society, it is the third leading cause of death from cancer in men in Canada. In general, prostate cancer is treatable with 5-year...

Spring 2015

Goswami, Souvik

For a smooth projective variety defined over a number field, Beilinson (and independently Bloch) constructed a `height' pairing under very reasonable assumptions and with a number of conjectural properties. A folklore conjecture related to this pairing states that the rational Griffiths...

Fall 2011

Wilkes, Jason

In the last three decades, the Ricci flow has proved to be an extremely useful tool in mathematics and physics. We explore numerically the long time existence of the Ricci-DeTurck flow and the List flow for a one-parameter family of Riemannian manifolds with non-essential minimal surfaces. This...