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Fall 2015

Huang, Qianhong

Let a locally compact semitopological semigroup S have a separately con- tinuous left action on a locally compact Hausdorff X. We define a jointly continuous left action of the measure algebra M(S) on the bounded Borel measure space M(X) which is an analogue of the convolution of measure alge-...

Fall 2021

Niu, Yeli

This thesis includes 2 parts. Part 1 is: Discretization on High Dimensional Compact Do￾mains. 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

Biglands, Adrian J.

The use of ordinary differential equations modelled on networks has become an increasingly important technique in many areas of research. The local behaviour of the system is modelled with differential equations and interactions between members or nodes are described using weighted digraphs....

Fall 2010

Or, Ying Ming

After the scientific problem of interest is defined, collecting data is the first stage of any statistical analyses. The question of how large the sample should be is thus of great interest. In this thesis we demonstrate that in a geostatistical experiment determining the minimum sample size to...

Fall 2013

Taschuk, Steven J.

We present some inequalities in convex geometry falling under the broad theme of quantifying complexity, or deviation from particularly pleasant geometric conditions: we give an upper bound for the Banach--Mazur distance between an origin-symmetric convex body and the $n$-dimensional cube which...

Fall 2013

Che, Menglu

It is well known that most information of an image is contained in its edges. Therefore capturing edges in an image is of fundamental importance in image processing. Tensor product real-valued wavelets only capture edges along the horizontal and vertical direc- tions. Hence they are only...

2002

Choboter, Paul F

2006

Zhou, Quan

Fall 2010

Cheng, Valerie

In this thesis we examine singularities of surfaces and affine Schubert varieties in the affine Grassmannian $\mathcal{G}/\mathcal{P}$ of type $A^{(1)}$, by considering the action of a particular torus $\widehat{T}$ on $\mathcal{G}/\mathcal{P}$. Let $\Sigma$ be an irreducible...

Spring 2014

Ye, Zi

We introduce two kinds of particle filters, one is weighted particle filter and the other is resampling particle filter. We prove the Strong Law of Large Numbers and Central Limit Theorem for both particle filters. Then, we show that the resampling particle filter is better than the weighted one.