We consider various infinite series and examine their arithmetic nature. Series of interest are of the form $$\sum_{n =0}^{\infty} \frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n \in \mathbb{Z}}\frac{f(n)A(n)}{B(n)}, \;\;\;\; ...

This thesis proposed two nonparametric statistical tests, based on the Kolmogorov-Smirnov distance and L2 mallows disatnce. To implement the proposed tests, nonparametric bootstrap method is employed to approximate the ...

Data recorded from Voyager 2 in 1979 during closest approach to Jupiter is prepared and analyzed for evidence of Jovian modal forcing. Comparisons are drawn between the data set in question and previously performed ...

Motivated by the longest increasing subsequence problem, we examine sundry topics at the interface of enumerative/algebraic combinatorics and random matrix theory. We begin with an expository account of the increasing ...

It was conjectured in the early 1950¡¯s that the empirical spectral distribution (ESD) of an $n \times n$ matrix whose entries are independent and identically distributed with mean zero and variance one, normalized by ...

For control systems that evolve on Euclidean spaces, Jacobian linearization is a common technique in many control applications, analysis, and controller design methodologies. However, the standard linearization method ...

Joint source-channel coding (JSCC) has been acknowledged to have superior performance over separate source-channel coding in terms of coding efficiency, delay and complexity. In the first part of this thesis, we study ...

An independent set in a graph G is a set of pairwise nonadjacent vertices, and the maximum size, alpha(G), of an independent set in G is called the independence number. Given a graph G and weight matrix A of G with entries ...

The proportional hazards model developed by Cox (1972) is by far the most widely used method for regression analysis of censored survival data. Application of the Cox model to more general event history data has become ...

This thesis represents an attempt to generalize the classical Theory of Optimal Design to popular regression models, based on Rational and Spline approximations. The problem of finding optimal designs for such models can ...