Mathematics Commons^™

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 …

A Hyperbolic Two-Step Model Based Finite Difference Method For Studying Thermal Deformation In Three-Dimensional Micro Spheres Exposed To Ultrashort-Pulsed Lasers, Pan Wang

Doctoral Dissertations

Ultrashort-pulsed lasers with pulse durations of the order of sub-picoseconds to femtoseconds possess the capabilities in limiting the undesirable spread of the thermal process zone in a heated sample. Because of this, ultrashort-pulsed lasers have been attracting worldwide interest in science and engineering. The success of ultrashort-pulsed lasers in real application relies on: (1) well characterized pulse width, intensity and experimental techniques; (2) reliable microscale heat transfer models; and (3) prevention of thermal damage. Laser damage induced by ultrashort-pulsed lasers occurs after the heating pulse is over, since the pulse duration time is extremely short and the heat flux is …

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.

Estimating Bounds For Nonidentifiale Parameters Using Potential Outcomes, Thidaporn Supapakorn

Doctoral Dissertations

"Conclusions from studies vary regarding the association of weight loss among obese people and measures of health and/or mortality. Total weight loss for individuals in a population may be a combination of intentional weight loss (IWL) and unintentional weight loss (UWL). Among people who have no intention to lose weight, the total weight loss observed is UWL. Among people who have intention to lose weight, the total weight loss is assumed to be UWL and IWL. Note that total weight loss among subjects intending to lose weight is observable but IWL itself is not and, therefore, the latent variable that …

Inverse Limits Of Permutation Maps, Robbie A. Beane

Doctoral Dissertations

"In this paper we study the topological properties of continua which arise as inverse limits on [0; 1] with bonding maps chosen from the permutation family of Markov maps. For such inverse limits, we examine the occurrence of indecomposability, the number of end points in the continuum, and the types of subcontinua present in the continuum. We provide a process for determining the topological structure of the inverse limit generated by a single permutation map, or by the composition of several such maps. Additionally, we show that all such inverse limits are Kelley continua. We will apply these results to …