Physical Sciences and Mathematics Commons^™

Tree-Like Spaces With The Fixed-Point Property, Realized As Inverse Limits Of Special Finite Trees, Jennifer Katherine Aust

Masters Theses

In this paper, we explore some properties of inverse limit sequences on sub-spaces of Euclidean n-space. We address some well-known examples, in particular the example by David Bellamy of the "tree-like" continuum that does not have the fixed-point property. We highlight some spaces with the fixed-point property that are between snake-like continua and Bellamy's example in their level of complexity. Specifically, we prove the fixed-point property for inverse limits of limit sequences on the unit interval and on the n-ad (in two configurations), and for inverse limits that can be mapped via a continuous function with small point pre-images to …

A Note On Hamel Bases, Jeremy S. Higdon

Masters Theses

The purpose of this paper is to discuss certain properties of Hamel bases. In particular, we reprove and generalize a theorem of R. Mabry (Aequations Mathematicae 71 (2006) p. 294-299) on the non-existence of nontrivial Hamel bases closed under multiplication.

Biochemical Reactions Instigating Vision – Parameter Sensitivity Analysis, Sophonie Ketcha Tchoua

Masters Theses

The purpose of this work is to investigate the sensitivity of parameters involved in a cascade of biochemical reactions occurring in photoreceptor cells in the retina of the eye. This cascade constitutes the first stage of the elaborate process of vision, by which light captured in a photoreceptor generates an electrical signal. It is this signal that travels to the brain enabling vision.

Sensitivity on parameters was performed on an ODE model of the biochemical cascade using two methods. One method used SimLab, a statistical sensitivity analysis program. We found that there are at most five important parameters out of …

Optimal Control Of Epidemic Models Involving Rabies And West Nile Viruses, Timothy Joseph Clayton

Doctoral Dissertations

This research considers the application of Optimal Control theory to minimize the spread of viral infections in disease models. The population models under consideration are systems of ordinary differential equations and represent epidemics arising due to either rabies or West Nile virus. Optimal control strategies are analyzed using Pontryagin’s Maximum Principle and illustrated based upon computer simulations.

The first model describes a population of raccoons and its interaction with the rabies virus, thus dividing the animals into four classes: susceptible, exposed, immune, and recovered (SEIR). The model includes a birth pulse during the spring of the year and …

Parallel Simulation Of Individual-Based, Physiologically-Structured Population And Predator-Prey Ecology Models, Jeffrey A. Nichols

Doctoral Dissertations

Utilizing as testbeds physiologically-structured, individual-based models for fish and Daphnia populations, techniques for the parallelization of the simulation are developed and analyzed. The techniques developed are generally applicable to individual-based models. For rapidly reproducing populations like Daphnia which are load balanced, then global birth combining is required. Super-scalar speedup was observed in simulations on multi-core desktop computers.

The two populations are combined via a size-structured predation module into a predator-prey system with sharing of resource weighted by relative mass. The individual-based structure requires multiple stages to complete predation.

Two different styles of parallelization are presented. The first distributes both populations. …

Zero-Divisor Graphs, Commutative Rings Of Quotients, And Boolean Algebras, John D. Lagrange

Doctoral Dissertations

The zero-divisor graph of a commutative ring is the graph whose vertices are the nonzero zero-divisors of the ring such that distinct vertices are adjacent if and only if their product is zero. We use this construction to study the interplay between ring-theoretic and graph-theoretic properties. Of particular interest are Boolean rings and commutative rings of quotients.