The Haar wavelet was one of the first wavelet bases that was developed by Alfred Haar in 1909. Haar used these functions to give an example of an orthonormal system for the space of square-integrable functions on the unit interval [0;1]. We will furth . . .

The additivity of crossing numbers over a composition of links has been an open problem for over one hundred years. It has been proved that the crossing number over alternating links is additive independently in 1987 by Louis Kauffman, Kunio Murasugi, . . .

We will examine how we can use Caputo’s definition of a fractional derivative to develop a method to numerically evaluate a fractional derivative of a function at a point. A fractional derivative can be thought as an instantaneous fractional average. . . .

In this paper we propose a procedure to obtain an optimal clustering solution for a given set of data. The main idea that runs through this thesis is the clustering of a data set with the consideration of multiple clustering solutions. This is achieve . . .

The effect of time delay on the control of a single and two coupled torsion bar structures is explored using analytical expressions solved numerically and numerical simulations of the response of the systems. The maximum gain for stability is determin . . .

In this paper we will modify the classic Suscptible-Infected-Recovered (S-I-R) model to include a fourth Envirnoment (E) class in order to model the dynamics of the waterborne illness Cholera. In this model we are now able to consider the interactions . . .

Sets of data used for business and research are rapidly increasing in size. The problem of analysis on big data has becoming a pressing concern for the statistician. In this thesis, I compare different methods for performing least squares linear regre . . .

We investigate the shape of color space data for Young Stellar Objects cataloged in the NASA archive MIRES using Computational Topology. Mapper was used to construct graphical summaries of the 6-dimensional and 21-dimensional color space data for all . . .

Factor analysis is a multivariate statistical tool that is used in the development, refinement and evaluation of tests and measures of data that can be used in clinical and educational contexts by an analyst. This thesis will focus on a brief understa . . .

The goal of this discussion is to determine the Schnirelmann density of the deficient numbers, which is not currently known. The Schnirelmann density for deficient numbers is defined as the infimum of the set of densities of deficient numbers up to n. . . .