Applied Mathematics Commons^™

A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi

Doctoral Dissertations

DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …

Exploration Of Aqueous Interfaces And Their Effect On Ion Behavior, Oneka T. Cummings

Doctoral Dissertations

An in-depth understanding of a wide range of physical, chemical, atmospheric and biological processes can only be achieved after the structure and dynamics of interfaces and the interfacial behavior of aqueous species, such as ions, are thoroughly studied and understood. This dissertation describes computational studies conducted to gain a more comprehensive understanding of such interfaces and the behavior of ions in the bulk and interfacial regions of the (1) air/water interface, and (2) alkane/water interfaces.

At the air/water interface the effect of counterion (sodium cations) charge and the influence of ion pairing on anion (chloride) propensity for the air/water interface …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Bimodules Over Cartan Masas In Von Neumann Algebras, Norming Algebras, And Mercer's Theorem, Jan Cameron, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

In a 1991 paper, R. Mercer asserted that a Cartan bimod- ule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal -isomorphism of the von Neumann algebras gener- ated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the literature supporting their Theorem 2.5 contain gaps, and hence Mercer's proof is incomplete.

In this paper, we use the outline in Pitts, 2008, Remark 2.17, to give a proof of Mercer's Theorem under the additional …

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …

Modelling Locally Changing Variance Structured Time Series Data By Using Breakpoints Bootstrap Filtering, Rajan Lamichhane

Mathematics & Statistics Theses & Dissertations

Stochastic processes have applications in many areas such as oceanography and engineering. Special classes of such processes deal with time series of sparse data. Studies in such cases focus in the analysis, construction and prediction in parametric models. Here, we assume several non-linear time series with additive noise components, and the model fitting is proposed in two stages. The first stage identifies the density using all the clusters information, without specifying any prior knowledge of the underlying distribution function of the time series. The effect of covariates is controlled by fitting the linear regression model with serially correlated errors. In …

Multi-Objective Preliminary Design Optimization Of Planing Craft Using Differential Evolution And Artificial Networks, Robert Eugene Weidman

Mechanical & Aerospace Engineering Theses & Dissertations

The differential evolution (DE) algorithm is an evolutionary algorithm that has been utilized as a metaheuristic optimizer in the last few years. A recently developed multi-objective version of DE is utilized in this research in order to optimize the preliminary design of planing craft. The craft performance is evaluated using the planing hull preliminary design software PHAST. The optimization problem objectives are the craft acquisition cost and the overall measure of effectiveness; the latter comprises various performance aspects: ride quality, transportability, payload, and mobility. Static stability and operating constraints are also considered. Each of the aforementioned four measures of effectiveness …

Linear Programming Algorithm With Mixed Real-Integer Variables In Matlab Environments, Gelareh Bakhtyar

Civil & Environmental Engineering Theses & Dissertations

Efficient numerical procedures for solving general Linear Programming (LP) problems with mixed real-integer variables are developed in this work. The proposed algorithms employ the revised dual simplex with Branch and Bound (B&B) algorithms, with special procedures for limited search of subsequent branches. Computational time can be significantly reduced by incorporating the updated inverse formulas into the developed procedures. Both generic LP problems and deterministic pavement maintenance and rehabilitation (M&R) problems are used in this study to vaiidate the developed procedures. Medium to large-scale examples ( 11 pavement M&R) presented in this work have demonstrated that the developed numerical procedures consistently …

Substance Abuse Via Legally Prescribed Drugs: The Case Of Vicodin In The United States, Wendy K. Caldwell, Benjamin Freedman, Luke Settles, Michael M. Thomas, Anarina Murillo, Erika Camacho, Stephen Wirkus

Faculty Articles

Vicodin is the most commonly prescribed pain reliever in the United States. Research indicates that there are two million people who are currently abusing Vicodin, and the majority of those who abuse Vicodin were initially exposed to it via prescription. Our goal is to determine the most effective strategies for reducing the overall population of Vicodin abusers. More specifically, we focus on whether prevention methods aimed at educating doctors and patients on the potential for drug abuse or treatment methods implemented after a person abuses Vicodin will have a greater overall impact. We consider one linear and two non-linear compartmental …

Current Barriers To Successful Implementation Of Fist Principles, Brandon Keller, Joseph R. Wirthlin

Faculty Publications

The Fast, Inexpensive, Simple, and Tiny (FIST) framework proposes a broad set of organizational values, but provides limited guidance on practical implementation. Implementing FIST principles requires clarifying the definitions of “fast,” “inexpensive,” and “simple,” recognizing where FIST does and does not apply. Additionally, a subset of the FIST heuristics was expanded upon to increase their usefulness for practitioners. The primary research findings are that FIST principles are less conducive for highly complex or novel systems, immature technologies, future needs, acquisitions in early development phases, or when performance is the foremost value. FIST principles were also found to be constrained by …

Open Source Kiswahili Spell Checker (Sw-Tz), Hashim Twaakyondo

Tanzania Journal of Engineering and Technology (TJET)

Different English software products are localized into many native languages spoken around the world, the most popular software products localized so far are word processing software and web browsers. The effort has begun to localize these software products in Kiswahili language which is widely spoken in Tanzania, East and Central Africa. Kiswahili is an official language of Tanzania, and is a national language in Uganda and Kenya. To make these software products useful to Kiswahili speaking community particularly in Tanzania a new Kiswahili spell checker has been developed and, it uses most of the Kiswahili words spoken in Tanzania and …

2d Autocad Geometric Data Extraction And Post Processing For Numerical Control, Tito Mwinuka

Tanzania Journal of Engineering and Technology (TJET)

In this paper, a method of extracting 2D geometric data from AutoCAD drawing and post processing for Numerical Control (NC) is presented. Geometric data already available in the Drawing Interchange Files (DXF) can be utilized to accurately and economically prepare part programs for controlling NC/CNC machine tools. AutoCAD, being general purpose software, stores its geometric data in a form that cannot be directly applied for automatic generation of Numerical Control (NC) codes. The way around the discrepancy between the structure of a drawing database (DXF files) and the information requirement for part programming is addressed in this work. NC programming …

Problems And Prospects Of Hydraulic Modelling For Environmental Flows Assessment Studies In East Africa, Preksedis Ndomba

Tanzania Journal of Engineering and Technology (TJET)

The objective of this paper is to document the problems and prospects of hydraulic modelling for Environmental Flows Assessment (EFA) studies based on selected case studies. Most of studies in East Africa use Holistic methodologies. An ideal data set for defining river hydraulics for most of these methods would be six data points of stage measurements over a good distribution of discharges, the stage of zero discharge and some flood-related data. Besides, in East African region EFA studies suffer from data scarcity (i.e., poorly gauged sites) and limited expertise and funding. The hydraulics studies conducted by the authors entailed desktop …

On The Impulse Control Of Jump Diffusions, Erhan Bayraktar, Thomas Emmerling, José-Luis Menaldi

Mathematics Faculty Research Publications

Regularity of the impulse control problem for a nondegenerate n-dimensional jump diffusion with infinite activity and finite variation jumps was recently examined in [M. H. A. Davis, X. Guo, and G. Wu, SIAM J. Control Optim., 48 (2010), pp. 5276–5293]. Here we extend the analysis to include infinite activity and infinite variation jumps. More specifically, we show that the value function u of the impulse control problem satisfies u ∈ W_loc^2,p(Rⁿ).

Insights On The Neyman - Pearson Lemma: Alternative Critical Regions, And Their Power., David E. Wetzell

ACMS Conference Proceedings 2013

The Neyman-Pearson Lemma is a powerful fundamental lemma in the area of hypothesis testing in Statistics. It gives the best test when testing simple vs. simple hypotheses. In this talk we would like to investigate testing a population mean H0 μ = μ0 vs. H1 μ = μ1 > μ0. As a result of the N-P Lemma, the best test is of the form, “Reject H0 if x>c” , where c is chosen so that the Type I error probability is a. Let n be small. What are some alternative decision rules of size a, what …

Service-Learning Panel, Dave Klanderman, Josh Wilkerson, Maria Zack

ACMS Conference Proceedings 2013

Many of us have wanted to incorporate service experiences in courses, or are being asked by our institutions to do so. Service-learning is a way of looking at service as being a partner with and leading to learning for our students. But in math, there are not a lot of resources to use! Our panelists will present classroom-tested ideas from several different levels of course, and we will end with a short time for more brainstorming among all participants.

Pedagogical Enhancements To The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham

ACMS Conference Proceedings 2013

DeSymbol is a program that translates first-order predicate logic expressions into English. It is intended to be a practice tool for students who are learning logic for the first time or who are trying to refresh their memories if they need to use symbolic logic for an upper-level course. Students start with an English sentence and translate it by hand into symbolic logic notation; then they can check their work by using DeSymbol to translate their notation back into English. If the English sentence produced by DeSymbol differs significantly from the original English sentence, this helps the student to see …

Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework, Nathan Gossett, Adam Johnson

ACMS Conference Proceedings 2013

In his writings on Game Theory, an d the Iterated Prisoner’s Dilemma in particular, Robert Axelrod outlined four properties that are predictors of a successful strategy: Niceness, Reciprocity, Forgiveness, and Understandability. On the topic of Reciprocity, Axelrod makes the claim that not only does The Golden Rule lead to a suboptimal strategy, but that one of the most successful strategies (Tit for Tat) shows that a command of “An eye for an eye” leads to a much more optimal strategy. In this paper, we will discuss the details of Axelrod’s four properties, outline Biblical support for all four, and discuss …

Open Source Software: What Is It, And Why Should We Care?, Karl-Dieter Crisman

ACMS Conference Proceedings 2013

This paper examines the distinctions in talking about computer software that has implications for both mathematics and moral thought.

Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics, William M. Kinney

ACMS Conference Proceedings 2013

I taught complex analysis for the first time in my career during the spring of 2013. I decided to do something “radical” and teach it as a lab-type course with a focus on geometric interpretations using the computer program Mathematica. The students and I met in a computer lab and, during most meetings, we spent a large portion of our time experimenting and exploring using Mathematica to visualize key concepts in complex analysis. Because of this, there was a heavy emphasis on viewing analytic functions as conformal mappings as well as considering associated vector fields and flows. Mathematica was used …

Faith Integration Projects For First-Year Students, Doug Phillippy

ACMS Conference Proceedings 2013

This talk will consider the use of projects to motivate students to think deeply about how their faith connects with mathematics. This talk will begin by describing what a faith integration project is, including the goals and objectives of such a project. The talk will briefly describe a number of projects written by the speaker, with a more detailed look at one of those projects. The talk will conclude by discussing how these projects are being used to assess how students are doing at articulating a maturing understanding of the connection between faith and mathematics

Philosophy Motivates Undergraduates In Mathematics, Dustin Wilson

ACMS Conference Proceedings 2013

A talk on how elective seminars on the philosophy of mathematics can inspire undergraduate students to pursue and persist in mathematics.

Forming The Analytical Society At Cambridge University, Richard Stout

ACMS Conference Proceedings 2013

The Analytical Society, an organization begun by students at Cambridge, was founded in 1812. Even though it was entirely student-led, the society was responsible for significant changes in the Cambridge mathematics curriculum and in the way mathematics was perceived in Britain throughout the nineteenth century. Its success was likely due to the outstanding students who formed the group, some of whom went on to become leaders in British science and mathematics for the next fifty years. In this paper we will briefly look at several of those who played important roles in forming and leading the society and we will …

The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne, Matt Delong

ACMS Conference Proceedings 2013

In this paper we will give a brief introduction to Polkinghorne's life and work. We will give an introduction to Polkinghorne's approach to philosophy and theology. We will introduce the two most significant influences on Polkinghorne's development as a theologian and philosopher of science. We will then give a necessarily telegraphic review of some of the topics addressed in Polkinghorne's theology, including his thoughts on science and religion, natural theology, evil, providence, prayer, resurrection, the soul and eschatology. We will then conclude with a few short examples of Polkinghorne's thoughts on mathematics.

Leading A Successful Missions Trip In Your Discipline, Tom Nurkkala, Darci Nurkkala

ACMS Conference Proceedings 2013

The global missions community goes wanting for skilled workers in almost every discipline. However, even students at a Christian institution that emphasizes global engagement remain largely unaware of the impact they can make in missions by leveraging their own academic specialty. In this paper, we draw on our experience leading discipline-specific missions trips as a means to encourage students to reframe their thinking about personal involvement in missions. We discuss the need for students to experience missions firsthand, and the student outcomes we have observed in intercultural awareness and spiritual formation. A key student outcome is an increased willingness to …

Googol-Part Fugue: Another Imagination Of Divine Providence And Game Theory, Gideon Lee

ACMS Conference Proceedings 2013

The problem of evil presents an intellectual hurdle for some to believe in a good and omnipotent God. The emergence of open theism could be seen as an attempt to make a stronger case for the free will defense. However, in denying divine foreknowledge as traditionally understood, open theism contradicts biblical revelation not only in its direct claims, but also when its logical implications for divine providence are worked out. The open theist Alan Rhoda has sought to explain through game theory how some degree of divine providence is possible under open theism. That explanation is astonishing since the open …

Life Lessons From Leibniz, Andrew J. Simoson

ACMS Conference Proceedings 2013

The tri-centennial of Leibniz’s death is nigh (2016). And 2013 is not too early to begin a special celebration of this man of mathematics. Besides being the co-discoverer of calculus and the implementer of binary numbers, formal logic, and formal languages, all of which foreshadowed the computer age, Leibniz is said to be one of the last to know almost everything that was known about almost anything. Professionally, his occupation was librarian in the princely court of Hanover in oldGermany. Serving under three different princes, the last of whom became George I of England, Leibniz had to continual lyre-invent himself—somewhat …

Al-Khwārizmī: Founder Of Classical Algebra, Calvin Jongsma

ACMS Conference Proceedings 2013

Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior toal-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess thehistorical importance of al-Khwarizmi’s contributions for developments in European algebra.

Expanding Jonathan Edwards’ Typology Program: The Bell Curve As A Type Of Christ, Jason Wilson

ACMS Conference Proceedings 2013

Over two hundred years after his death, an unfinished notebook of Jonathan Edwards’ was published for the first time in1993. Edwards was a father of the Evangelical movement, but because his work on typology was not published until recently, it has received almost no attention. In his notebook, Edwards makes an explicit argument for extending biblical typology to nature in a biblically grounded manner. This study is an attempt to extend that research program into mathematics/statistics.We will consider the following proposition, “The normal distribution (the graph of which is the bell curve) is a biblical type of Christ.” The basic …