Applied Mathematics Commons^™

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo

Open Access Dissertations

Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …

Why In Mayan Mathematics, Zero And Infinity Are The Same: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In Mayan mathematics, zero is supposed to be, in some sense, equal to infinity. At first glance, while this statement may have a deep philosophical meaning, it does not seem to make much mathematical sense. In this paper, we show, that this statement may be made mathematically reasonable. Specifically, on a real line, it is often useful to consider both −∞ and +∞ as a single infinity. When we deal with very small and very large numbers, it makes sense to use floating point representation, i.e., in effect, consider logarithms of the original values. In terms of logarithms, the original …

On The Performance Of A Hybrid Genetic Algorithm In Dynamic Environments, Quan Yuan, Zhixin Yang

Mathematics Faculty Research Publications

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for different functional dimensions, update frequencies, and displacement strengths in different types of dynamic environments. Experimental results are reported by using the HGA and some other existing evolutionary algorithms in the literature. The results show that the HGA has better capability to track the dynamic optimum than some other existing algorithms.

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mathematics Faculty Publications

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Characterization Of The Drilling Via The Vibration Augmenter Of Rotary-Drills And Sound Signal Processing Of Impacted Pipe As A Potential Water Height Assessment Tool, Nicholas Morris

STAR Program Research Presentations

The focus of the internship has been on two topics: a) Characterize the drilling performance of a novel percussive augmenter – this drill was developed by the JPL’s Advanced Technologies Group and its performance was characterized; and b) Examine the feasibility of striking a pipe as a means of assessing the water height inside the pipe. The purpose of this investigation is to examine the possibility of using a simple method of applying impacts to a pipe wall and determining the water height from the sonic characteristic differences including damping, resonance frequencies, etc. Due to multiple variables that are relevant …

Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp

Mathematics Faculty Publications

We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense G_δ-subsets of Cantor cubes are subcompact.

Investigating Graph Clustering For The Power Grid, Gabriela Radu, Emilie Hogan

STAR Program Research Presentations

Given time series data from multiple power generators containing measurements of phase angle taken at many points in time. The goal is to cluster together generators which have similar phase angle behavior.

In order to achieve this goal, Fast Fourier Transforms and Euclidean distances were used to quantify similarities between generators. A graph was created in which two generators were connected if they were sufficiently similar (known as a nearest neighbor graph). Using different nearest neighbor values, matrices were generated based on similarities between generators. Specific time intervals were taken from the large data set to assess the time dependency …

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …

On Fuzzy Soft Matrix Based On Reference Function, Florentin Smarandache, Said Broumi, Mamoni Dhar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study fuzzy soft matrix based on reference function. Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function. Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.

Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia

Electronic Theses and Dissertations

In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K_v, (2) complete bipartite graphs K_m,n, and (3) complete graphs with a hole K(v,w).

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: …

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, …

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 …

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 …

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.