Physical Sciences and Mathematics Commons^™

Evaluation And Enhancement Of Clean Energy Systems: Analytical, Computational And Experimental Study Of Solar And Nuclear Cycles, Nima Fathi

Mechanical Engineering ETDs

Clean (and specifically renewable) energy is steadily improving its global share. However, finite availability of fossil fuels and the growing effects of climate change make it an urgent priority to convince the industry and governments to incentivize investment in the renewable energy field and to make it more attractive by decreasing the capital cost. Until recently, uncertainties in funding limited renewable energy development, especially in the US. That limitation has been one of the barriers to progress. Another limitation of many renewable energy systems is the variability in their output, which makes them unsuitable for baseline power production. Therefore, fossil …

High Order Hermite And Sobolev Discontinuous Galerkin Methods For Hyperbolic Partial Differential Equations, Adeline Kornelus

Mathematics & Statistics ETDs

Many real-world problems involving dynamics of solid or fluid bodies can be modeled by hyperbolic partial differential equations (PDEs). Up to this point, only solutions to selected PDEs are available. Many PDEs are physically or geometrically complex, resulting in difficulties computing the analytical solutions. In this thesis, we focus on numerical methods for approximating solutions to hyperbolic PDEs. Long-term simulation for the motion of the body described by the PDE requires a method that is not only robust and efficient, but also produces small error because the error will be propagated and accumulated over the course of the simulation. Therefore, …

Comparison Of Two Methods In Estimating Standard Error Of Simulated Moments Estimators For Generalized Linear Mixed Models, Danielle K. Duran

Mathematics & Statistics ETDs

We consider standard error of the method of simulated moment (MSM) estimator for generalized linear mixed models (GLMM). Parametric bootstrap (PB) has been used to estimate the covariance matrix, in which we use the estimates to generate the simulated moments. To avoid the bias introduced by estimating the parameters and to deal with the correlated observations, (Lu, 2012) proposed a multi-stage block nonparametric bootstrap to estimate the standard errors. In this research, we compare PB and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, …

Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace

Numeracy

The importance of mathematics to biology is illustrated by search data from Google Scholar. I argue that a pedagogical approach based on student research projects is likely to improve retention and foster critical thinking about mathematical modeling, as well as reinforce quantitative reasoning and the appreciation of calculus as a tool. The usual features of a course (e.g., the instructor, assessment, text, etc.) are shown to have very different purposes in a research-based course.

Adoption Of Switchgrass Cultivation For Biofuel Under Uncertainty: A Discrete-Time Modeling Approach, Pralhad Burli, Eric Forgoston, Pankaj Lal, Lora Billings, Bernabas Wolde

Lora Billings

Adoption Of Switchgrass Cultivation For Biofuel Under Uncertainty: A Discrete-Time Modeling Approach, Pralhad Burli, Eric Forgoston, Pankaj Lal, Lora Billings, Bernabas Wolde

Eric Forgoston

Adoption Of Switchgrass Cultivation For Biofuel Under Uncertainty: A Discrete-Time Modeling Approach, Pralhad Burli, Eric Forgoston, Pankaj Lal, Lora Billings, Bernabas Wolde

Pankaj Lal

Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, Paul J. Weinberg

Journal of Pre-College Engineering Education Research (J-PEER)

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews …

Data Insertion In Bitcoin's Blockchain, Andrew Sward, Vecna Op_0, Forrest Stonedahl

Computer Science: Faculty Scholarship & Creative Works

This paper provides the first comprehensive survey of methods for inserting arbitrary data into Bitcoin's blockchain. Historical methods of data insertion are described, along with lesser-known techniques that are optimized for efficiency. Insertion methods are compared on the basis of efficiency, cost, convenience of data reconstruction, permanence, and potentially negative impact on the Bitcoin ecosystem.

Color-Blind Index In Graphs Of Very Low Degree, Jennifer Diemunsch, Nathan Graber, Lucas Kramer, Victor Larsen, Lauren M. Nelsen, Luke L. Nelsen, Devon Sigler, Derrick Stolee, Charlie Suer

Faculty Articles

Let c : E(G) → [k] be an edge-coloring of a graph G, not necessarily proper. For each vertex v, let c¯(v) = (a1, . . . , ak), where ai is the number of edges incident to v with color i. Reorder ¯c(v) for every v in G in nonincreasing order to obtain c ∗ (v), the color-blind partition of v. When c ∗ induces a proper vertex coloring, that is, c ∗ (u) 6= c ∗ (v) for every edge uv in G, we say that c is color-blind distinguishing. The minimum k for which there exists a …

Tri-Ponderal Mass Index Vs Body Mass Index In Estimating Body Fat During Adolescence, Courtney M. Peterson, Haiyan Su, Diana Thomas, Moonseong Heo, Amir Golnabi, Angelo Pietrobelli, Steven B. Heymsfield

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Importance Body mass index (BMI) is used to diagnose obesity in adolescents worldwide, despite evidence that weight does not scale with height squared in adolescents. To account for this, health care providers diagnose obesity using BMI percentiles for each age (BMI z scores), but this does not ensure that BMI is accurate in adolescents.

Objective To compare the accuracy of BMI vs other body fat indices of the form body mass divided by heightⁿ in estimating body fat levels in adolescents.

Design, Setting, and Participants Cross-sectional data from the 1999 to 2006 US National Health and Nutrition Examination Survey …

A Partitioned Approach For Computing Fluid-Structure Interaction, With Application To Tumor Modeling And Simulation, Asim Timalsina

Mathematics & Statistics Theses & Dissertations

Modeling and Simulation plays a critical role in understanding complex physical and biological phenomena as it provides an efficient and controlled test environment, without the risk of costly experiments and clinical trials. In this dissertation, we present an extensive study of two such systems with integrated application: Fluid structure interaction (FSI) and virotherapy on tumor. Moreover, we substantiate a few preliminary results of FSI application on tumor.

The FSI problem comprises of fluid forces exerted on the solid body and the motion of the structure affecting the fluid flow. FSI problems are of great interest to applied industries, however they …

Structural Analysis Of Poloidal And Toroidal Plasmons And Fields Of Multilayer Nanorings, Kumar Vijay Garapati

USF Tampa Graduate Theses and Dissertations

Multilayered metallo-dielectric nanoparticles are increasingly considered in various applications to control the spatial and temporal behavior of electromagnetic fields. In particular, the surface mode excitation by photons or electrons in metal nanorings finds significant applications because of the implied field distribution and electromagnetic energy confinement. However, most solid nanorings that are multilayered and/or embedded in a medium have non-simply connected geometry resulting in surface modes which are not linearly independent. That is, unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We investigate the surface modes of such …

Solving Poisson’S Equations With Fractional Order Using Haar Wavelet, The British University In Egypt, Ain Shams University

Basic Science Engineering

The algebraic structure of the linear system appears in solving fractional order Poisson’s equation by Haar wavelet collocation approach is considered. The fractional derivative is described in the Caputo sense. Comparison with the classical integer case as a limiting process is illustrated. Numerical comparison is made between the solution using the Haar wavelet method and the finite difference method. The results confirms the accuracy for the Haar wavelet method.

Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker

Mahurin Honors College Capstone Experience/Thesis Projects

Chronic wounds such as diabetic foot ulcers are the leading cause of non-traumatic amputations in developed countries. For researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can be used to help predict healing responses. The model utilizes equations that are modified from work by Guffey (2015) that consists of four variables – oxygen, bacteria, neutrophils, and chemoattractant within a system of partial differential equations. Our research focuses on numerically solving these partial differential equations using a finite volume approach. This numerical solver will be important for future research in …

An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto

Mahurin Honors College Capstone Experience/Thesis Projects

Exploratory factor analysis is an analytic technique used to determine the number of factors in a set of data (usually items on a questionnaire) for which the factor structure has not been previously analyzed. Parallel analysis (PA) is a technique used to determine the number of factors in a factor analysis. There are a number of factors that affect the results of a PA: the choice of the eigenvalue percentile, the strength of the factor loadings, the number of variables, and the sample size of the study. Although PA is the most accurate method to date to determine which factors …

Conference Program, University Of Dayton

Summer Conference on Topology and Its Applications

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications.

Nontrivial Solutions Of Inclusions Involving Perturbed Maximal Monotone Operators, Dhruba Adhikari

Dhruba Adhikari

No abstract provided.

Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.

Weak Synchronization In Excitatory – Inhibitory Neuronal Networks, Joel Eliason, Benjamin Webb

Journal of Undergraduate Research

One ubiquitously observed dynamic phenomenon in the nervous system is that of weak synchronization or clustering, a behavior in which a large group of neurons in a population will all fire synchronously and then fall out of synchronization. When isolated to neurons that only form short-range connections, this behavior is typically referred to as “neuronal avalanches”, and is thought to be particularly important for robustness of information transmission as well as sensitivity to inputs. Given these potential computational benefits, avalanches have been a focus of theoretical biologists for the past 20 years. In particular, my project focused on the conditions, …

A Management Maturity Model (Mmm) For Project-Based Organisational Performance Assessment, Craig Langston, Amir Ghanbaripour

Amir Ghanbaripour

Common sense suggests that organisations are more likely to deliver successful projects if they have systems in place that reflect a mature project environment based on a culture of continuous improvement. This paper develops and discusses a Management Maturity Model (MMM) to assess the maturity of project management organisations through a customisable, systematic, strategic and practical methodology inspired from the seminal work of Darwin, Deming, Drucker and Daniel. The model presented is relevant to organisations, such as construction and engineering companies, that prefer to use the Project Management Body of Knowledge (PMBOK™ Guide) published by the Project Management Institute (PMI), …

Traveling Wave Solutions To Kawahara And Related Equations, S.C. Mancas

Publications

Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the tanh-method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave …

The Resolved And Unresolved Conjectures Of R.D. Carmichael, Brian D. Beasley

ACMS Conference Proceedings 2017

Even before heading to Princeton University to work on his doctoral degree, Robert Daniel Carmichael started influencing the path of number theory in the 20th century. From his study of Euler's totient function to his discovery of the first absolute pseudoprime, he set the stage for years of productive research. This talk will present a brief overview of Carmichael's life, including his breadth of mathematical interests and his service on behalf of the Mathematical Association of America. It will focus mainly on his two most famous conjectures- which one has been settled, and which one remains open to this day?

"Big Idea" Reflection Assignments For Learning And Valuing Mathematics, Jeremy Case, Mark Colgan

ACMS Conference Proceedings 2017

While participating in a Faculty Learning Community, we explored the "big questions" we wanted our students to take away from our mathematics courses. We called these questions the Big Ideas of the course and developed a Big Ideas Reflection Assignment, which we continue to assign at the end of each of our courses. Students are able to demonstrate understanding and application of their learning as well as their values and appreciation of mathematics. The assignment encourages students to move beyond a focus on technique and symbolic manipulations towards a broader and more holistic approach, including making connections between their learning …

Using Real-World Team Projects: A Pedagogical Framework, Mike Leih

ACMS Conference Proceedings 2017

The use of team projects in a program capstone course for computer science or information systems majors has been a popular method for reinforcing and assessing program learning objectives for students in their final semester. Using real-world group projects as a learning activity is an excellent pedagogical approach in helping students develop critical thinking, team work, real-world problem solving, and communication skills. However, real-world group projects also provide many challenges to both the instructor and students alike. Instructors or students must find real-world projects appropriate for the learning objectives in the course. Instructors must determine how to provide teams with …

Variations On The Calculus Sequence, Christopher Micklewright

ACMS Conference Proceedings 2017

Many institutions have embraced a standard format for the Calculus sequence, comprising three four-credit courses covering a fairly consistent set of topics. While there is much to recommend this approach, it still leaves some fantastic concepts rushed or untouched, and it can be argued that it demands too much of students with weaker backgrounds. As such, some schools have experimented with variations on the standard format. In this talk, I will present the model that my institution currently uses, exploring the strengths and weaknesses of our particular approach. I will also suggest ideas, developed in conversation with other ACMS members …

The Topology Of Harry Potter: Exploring Higher Dimensions In Young Adult Fantasy Literature, Sarah Klanderman, Alexa Schut, Dave Klanderman, William Boerman-Cornell

ACMS Conference Proceedings 2017

As one of the most beloved series in children’s literature today, the Harry Potter books excite students of all ages with the adventures of living in a magical world. Magical objects (e.g., bottom-less handbags, the Knight Bus, time turners, and moving portraits) can inspire generalizations to mathematical concepts that would be relevant in an undergraduate geometry or topology course. Intuitive explanations for some of the magical objects connect to abstract mathematical ideas. We
offer a typology with a total of five categories, including Three Dimensions in Two Dimensions, Higher Dimensions in Three Dimensions, Two and Three Dimensional Movement, Higher Dimensional …

Ten Mathematicians Who Recognized God's Hand In Their Work (Part 2), Dale Mcintyre

ACMS Conference Proceedings 2017

Scottish philosopher David Hume (1711-1776) once observed that "Whoever is moved by faith to assent to [the Christian religion], is conscious of a continued miracle in his own person, which subverts all the principles of his understanding, and gives him a determination to believe what is most contrary to custom and experience." Evidently Hume's cynical pronouncement did not apply to Descartes, Newton, Riemann, and other profound thinkers who believed God had commissioned and equipped them to glorify Him in their pursuit of truth through mathematics - And based on their extraordinary achievements the principles of their understanding do not appear …

The Set Of Zero Divisors Of A Factor Ring, Jesús Jiménez

ACMS Conference Proceedings 2017

Let A be a ring and a an ideal of A. In this paper we show how to construct factor rings A/ a and a finite set of ideals a1, a2, ... , ak, of A/a, such that: each ideal aj is contained in the set of zero divisors of A/a, the factor ring A/a is a direct sum of these ideals, and each ideal aj is a ring with unity when endowed with addition and multiplication modulo a. Explicit examples are given when A is the ring of integers, Gaussian integers or the ring of polynomials over a field.

The Daily Question: Building Student Trust And Interest In Undergraduate Introductory Probability And Statistics Courses, Matthew A. Hawks

ACMS Conference Proceedings 2017

Introducing probability or statistics to disinterested undergraduate students is challenging. Adding faith in such a classroom at a secular institution only increases the complexity. We share an unobtrusive way to build trust with students, creating a medium to both naturally share your faith and have your students look forward to attending each class. The context is the United States Naval Academy, a four-year undergraduate institution with an emphasis on leader development. In addition to a calculus sequence, Humanities majors enroll in Probability with Naval Applications or Introductory Statistics. These sophomores or juniors are split between those who have no intention …