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Fall 2014

JIANG, LONG

he main aim of this thesis lies in describing, as explicit as possible, the local-risk minimizing strategy for a change-point model. To this end, we analyze and investigate the mathematical structures of this model. The change-point model is a model that starts with a dynamic and switches to...

Fall 2014

Roshchenko, Andriy

This thesis presents recent developments in direct numerical simulations of fluid-structure interaction occurring in biological systems, with particular interest in the modeling of particle deposition within the human respiratory system. Two numerical techniques are proposed. The first one is...

Fall 2013

Ye, Wenrui

Estimates of the maximal Cesaro means at the "critical index'' are established for the orthogonal polynomial expansions (OPEs) with respect to the weight function on the unit sphere. These estimates allow us to improve several known results in this area, including the almost everywhere (a.e.)...

Fall 2010

Wang, Xupeng

In financial market, risk management is very critical to a company. However, some risks in the market ( market risk) can not be controlled or eliminated through management improvement or appropriate asset allocation. Thus, it is important to accurately measure these kinds of risks. In this...

Fall 2015

Hiripitiyage, Kasun L.H.

The Busemann-Petty problem asks the following: if 𝐾,𝐿 ⊂ ℝⁿ are origin-symmetric convex bodies such that volₙ₋₁(𝐾 ∩ ξ^⊥)) ≤ volₙ₋₁(𝐿 ∩ ξ^⊥) ∀ ξ ∈ Sⁿ⁻¹, is it necessary that volₙ(𝐾) ≤ volₙ(𝐿)? This problem received a lot of attention, and many analogues have been considered. For origin-symmetric...

Spring 2016

Feng, Han

This thesis contains the following three parts: \egin{description} \item[Part 1(Chapters 1-5):] Spherical $h$-harmonic analysis. \item[Part 2:] Reverse H\"{o}lder's inequality for spherical harmonics. \item[Part 3:] Multivariate Lagrange and Hermite approximation and pointwise limits...

Fall 2010

lemzouji, Khalid

The Indiana Bat (Myotis sodalis) population had decreased by 56% between 1967 and 2006. In summer 2006, a mysterious disease called “White Nose Syndrome” was first identified. Since then, the disease killed almost one million bats in North America. Many Biologists believe that both the...

Fall 2010

Emmett, Matthew

When a semi-infinite body of homogeneous fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier the resulting flow over a horizontal or sloping bed is referred to as a dam-break flow. When resistance to the flow is neglected the exact...

Fall 2020

Rupert, Matthew

Recently, numerous connections between the categories of modules $\mathrm{Rep}{\langle s \rangle} \mcM(r)$ for the singlet vertex operator algebra $\mcM(r)$ and $\mathrm{Rep}{wt}\overline{U}q^H(\mathfrak{sl}2)$ for the unrolled restricted quantum group $\overline{U}q^H(\mathfrak{sl}2)$ at $2r$-th...

Fall 2014

Tan, Xiaobai

Given an algebraic group G over a field k and a k-algebra R, the role of maximal abelian k-diagonalizable subalgebras (MAD for short) of G(R) is the same as that the split maximal torus play in G(k). Let G be a reductive group such that the derived subgroup is simply connected and let Spec(R) be...