Physical Sciences and Mathematics Commons^™

Fluorescence Prediction Through Computational Chemistry, Daniel Craig Lathey

Theses, Dissertations and Capstones

With the growing demand for diverse fluorescent dyes, it is imperative to find a more efficient methodology by which to synthesize dyes. Our research group has found a computational method that can efficiently predict the optical properties of a molecule before it is synthesized. By evaluating different semi-empirical methods, we have found a way to predict the fluorescence maxima. With the new ability of Hyperchem 7.5 to geometrically optimize a molecule in an excited state, we can predict not only the absorption maxima, but we can also predict the fluorescence maxima within 25 nm of the actual fluorescence.

With this …

Reduction Of The Gibbs Phenomenon Via Interpolation Using Chebyshev Polynomials, Filtering And Chebyshev-Pade' Approximations, Rob-Roy L. Mace

Theses, Dissertations and Capstones

In this manuscript, we will examine several methods of interpolation, with an emphasis on Chebyshev polynomials and the removal of the Gibbs Phenomenon. Included as an appendix are the author’s Mat- Lab implementations of Lagrange, Chebyshev, and rational interpolation methods.

Convergence Analysis Of Mcmc Method In The Study Of Genetic Linkage With Missing Data, Diana Fisher

Theses, Dissertations and Capstones

Computational infeasibility of exact methods for solving genetic linkage analysis problems has led to the development of a new collection of stochastic methods, all of which require the use of Markov chains. The purpose of this work is to investigate the complexities of missing data in pedigree analysis using the Monte Carlo Markov Chain (MCMC) method as compared to the exact results. Also, we attempt to determine an association between missing data in a familial pedigree and the convergence to stationarity of a descent graph Markov chain implemented in the stochastic method for parametric linkage analysis.

In particular, we will …

Temperature And Ph Dependence Of The Cyclization Of Creatine: A Study Via Mass Spectrometry, Brian J. Diamond

Theses, Dissertations and Capstones

The creatine to creatinine cyclization is of significant biological importance, providing energy for muscle cells and indicating proper renal function. From a chemical perspective, the rate at which creatine cyclizes to form creatinine has interested researchers since the late 1920s, but the cyclization is poorly understood both energetically and mechanistically. Mass spectroscopy was used to determine the rate of creatine cyclization as a function of temperature and pH. Using these values, the energetic parameters, activation energy and Arrhenius factor, were determined as a function of pH to better understand this reaction and ultimately determine the mechanistic process for this reaction. …

Dynamic Equations On Changing Time Scales: Dynamics Of Given Logistic Problems, Parameterization, And Convergence Of Solutions, Kelli J. Hall

Theses, Dissertations and Capstones

In this thesis we use the theory of dynamic equations on time scales to understand the changes in dynamics between difference and differen- tial equations by parameterizing the underlying domains. To illustrate where and how these changes occur, we then construct a bifurcation diagram for a simple family of dynamic equations. However, these results are only true if we can move continuously through our domains, i.e, the time scales. In the last part of this thesis, we define what it means to have a convergent sequence of time scales. Then we use this definition to prove that the limit …