Applied Mathematics Commons^™

Delaware, Dickeson, Assessment And How You Can Help, Greg Crow, Maria Zack

ACMS Conference Proceedings 2013

How much release time should a chair receive? What is the cost per unit for a particular academic program? What is a student credit hour (SCH) anyway and why would anyone care? Why are so many boards enamored of Delaware, Dickeson and Assessment? The answer to these and many related questions will be presented in this talk. Analytics and various“efficiency measures” are becoming increasingly important in higher education and mathematicians and computer scientists are being regularly recruited to help university administrators make meaning from large volumes of data. Come and learn about this trend and how you can be of …

Explore Global Opportunities For Mathematics Scholarship, Teaching, And Service, Ron Benbow

ACMS Conference Proceedings 2013

There are numerous overseas opportunities in which to apply your knowledge and interest in mathematics. These international experiences allow you to expand your scholarship, to extend your teaching skills, to offer professional services to K-12 teachers or other university instructors, and to provide much personal enrichment as well. Examples from recent professional experiences in Liberia, Haiti, Guatemala, and Ecuador will be shared to illustrate the connections to teaching, scholarship, and service. Information regarding MAA Study Tours, Fulbright Specialist grants, and other relevant organizations will be provided.

Euler And The Ongoing Search For Odd Perfect Numbers, Brian D. Beasley

ACMS Conference Proceedings 2013

Leonhard Euler, after proving that every even perfect number has the form given by Euclid, turned his attention to finding odd perfect numbers. Euler established a basic factorization pattern that every odd perfect number must have, and mathematicians have expanded upon this Eulerian form ever since. This paper will present a brief summary of Euler’s result and some recent generalizations. It will also note connections between odd perfect numbers and the abundancy index (the abundancy index of a positive integer is the ratio of the sum of its positive divisors to itself). In particular, finding a positive integer with an …

Computing Foundations For The Scientist, Catherine Bareiss, Larry Vail

ACMS Conference Proceedings 2013

There is a need for a new style of supporting a computer course. Although it is widely recognized that computer technology provides essential tools for all current scientific work, few university curricula adequately ground science majors in the fundamentals that underlie this technology. Introducing science students to computational thinking in the areas of algorithms and data structures, data representation and accuracy, abstraction, performance issues, and database concepts can enable future scientists to become intelligent, creative and effective users of this technology. The intent of this course is not to turn scientists into computer scientists, but rather to enhance their ability …

A Different Approach, Catherine Crockett

ACMS Conference Proceedings 2013

This paper discusses an approach used to encourage science majors to rethink their attitudes and study habits in a first semester calculus course. Two activities were used to enhance study habits. They are outlining concepts and in-class quizzes designed for self-evaluation of skills. After using both methods in two sections of the calculus course, the students were surveyed to determine if these activities were successful. A majority of the students felt the activities were helpful and wanted to continue them.

Reading Assignments And Assessments: Are Your Students Reading Math Texts Before Class, After Class, Both, Or Neither?, David Klanderman, Mandi Maxwell, Sharon Robbert, Bill Boerman-Cornell

ACMS Conference Proceedings 2013

In his recent book What the Best College Students Do [Bain, 2012], Ken Bain defines a number of different types of students including “surface learners,” “strategic learners,” “routine experts,” and finally, “deep learners.” In our mathematics courses at Trinity, we have found examples of all of these student types. A major determinant of their preferred approach to learning appears to be the ways and degrees to which mathematical texts and other written materials are read prior to class sessions. Each full-time member of the department both assigns and assesses the reading of mathematical materials prior to class sessions. Assessment methods, …

Philosophy Of “Spinning Wheels”, Loredana Ciurariu

ACMS Conference Proceedings 2013

In this material I will speak about some well-known mechanisms studied by students and engineers emphasizing the impact which “spinning wheels” had and have in development of the society, on Christians and the church. Also the discovery of the machineries determines major changes in the people’s outlook and leads to new trends in philosophy and Christianity. Then, I will give some examples from the Bible where “spinning wheels” it seems to appear: Judges 16:21, Ezekiel 1 and Revelation. It is also interesting to see 2 Kings 2:9-12, 2 Kings 6:13-18 and maybe Daniel 7:9.

In addition, an avi file where …

An Investigation Of Hi Ho! Cherry-O Using Markov Chains, Nicholas C. Zoller

ACMS Conference Proceedings 2013

In the children’s board game Hi Ho! Cherry-O, players attempt to move 10 cherries from their trees to a bucket in the center of the game board. A spinner determines whether a turn includes moving cherries from tree to bucket or bucket to tree. The winner of the game is the first player to move all of her cherries from her tree to the bucket. We model the gameplay using a Markov chain and calculate the expected number of turns needed to complete one game. Then we investigate what happens when the rules are changed. We discover that rules …

The Structures Of The Actual World, Walter J. Schultz, Lisanne D’ Andrea Winslow

ACMS Conference Proceedings 2013

Scripture teaches that God has a plan for the universe. In this paper we argue that in order for it to function as a plan, it must have a temporal structure, a representational structure, and a proto-causal structure. This paper presents a formal model of the these three structures. As it turns out, the structures of God’s plan are best understood as the structures of a musical composition. We, then very briefly describe its implications. The first is that this model (based ultimately in the doctrine of God) grounds a metaphysics of science. Second, it grounds a structuralist philosophy of …

Perspectives On Chaos: Reflections Of A Mathematical Physicist, Kyle Spyksma

ACMS Conference Proceedings 2013

Chaos Theory, the mathematical media darling of the ’90s, has become less of a societal fad and research interest over the past couple of decades. However, from a mathematical physicists’ perspective, issues surrounding Chaos Theory can be valuable aides in forming views on how mathematics, science and reality relate. In this talk, I will briefly explore how Chaos Theory can shape views of these relationships, with a focus on the language we use and (perhaps unintentionally) abuse when doing science and mathematics.

Hydro-Thermal Convective Solutions For An Aquifer System Heated From Below, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

We investigate the effect of hydro-thermal convection in an aquifer system. It is assumed that the aquifer is bounded below and above by impermeable boundaries and it is heated from below. The solution of the governing system is expressed in terms of the basic steady state solution and perturbed solution. We obtain the critical Rayleigh number and critical wavenumber using Runge-Kutta method in combination of shooting method and present the marginal stability curve. The amplitude equation is derived by introducing the adjoint system. After amplitude is obtained, we compute the linear solutions for super-critical and sub-critical cases. Numerical results for …

Global Dynamics Of A Water-Borne Disease Model With Multiple Transmission Pathways, Prasanta K. Mondal, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the …

An Exponential Matrix Method For Numerical Solutions Of Hantavirus Infection Model, Şuayip Yüzbaşi, Mehmet Sezer

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new matrix method based on exponential polynomials and collocation points is proposed to obtain approximate solutions of Hantavirus infection model corresponding to a class of systems of nonlinear ordinary differential equations. The method converts the model problem into a system of nonlinear algebraic equations by means of the matrix operations and the collocation points. The reliability and efficiency of the proposed scheme is demonstrated by the numerical applications and all numerical computations have been made by using a computer program written in Maple.

Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the stability of multiwavelet frames with different matrix dilations and matrix translations by means of operator theory and show that these frames remain stable over some kinds of perturbations of the basic generators.

A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam

Applications and Applied Mathematics: An International Journal (AAM)

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.

An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms, T. Valanarasu, R. M. Priyadharshini, N. Ramanujam, A. Tamilselvan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a parameter-uniform numerical method is suggested to solve a system of singularly perturbed convection-diffusion equations with discontinuous convection coefficients and source terms subject to the Dirichlet boundary condition. The second derivative of each equation is multiplied by a distinctly small parameter, which leads to an overlap and interacting interior layer. A numerical method based on a piecewise uniform Shishkin mesh is constructed. Numerical results are presented to support the theoretical results.

Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using …

Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation, P. Y. C. Lee, W. H. Leong

Applications and Applied Mathematics: An International Journal (AAM)

Designing an experimental apparatus requires considerable amount of planning. Despite proper planning, one can easily overlook a design such as the standard uniform temperature boundary condition applied to all or portion of a wall of an experimental apparatus. Although this boundary condition is mathematically simple and precise, achieving it physically may not be that simple. This paper addresses one such three-dimensional natural convection heat transfer apparatus that was designed to measure benchmark Nusselt numbers at various Rayleigh numbers with uniform temperatures specified at two walls of the enclosure. It was found that the effect of thermal spreading/constriction resistance on one …

Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.

Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution, P. Y. C. Lee, W. H. Leong

Applications and Applied Mathematics: An International Journal (AAM)

Temperature measurements along one side of the rectangular plate showed severe temperature non-uniformity along one side of a wall of a cubical experimental apparatus where the uniform temperature was physically desired. Despite proper planning and analyses, this non-uniformity was high enough that a benchmark study could not be carried out to the desired accuracy of about one percent error. This paper presents and extends analyses made previously based on the modifications to the original design of the apparatus to reduce the temperature non-uniformity on the wall by adding an auxiliary heater around a wall where the uniform temperature was desired. …

A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new method based on the generalized Purcell method is proposed to solve the usual least-squares problem arising in the GMRES method. The theoretical aspects and computational results of the method are provided. For the popular iterative method GMRES, the decomposition matrices of the Hessenberg matrix is obtained by using a simple recursive relation instead of Givens rotations. The other advantages of the proposed method are low computational cost and no need for orthogonal decomposition of the Hessenberg matrix or pivoting. The comparisons for ill-conditioned sparse standard matrices are made. They show a good agreement with available …

Numerical Solution Of Some Nonlinear Volterra Integral Equations Of The First Kind, Leila Saeedi, Abolfazl Tari, Sayyed H. Momeni Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the solving of a class of the nonlinear Volterra integral equations (NVIE) of the first kind is investigated. Here, we convert NVIE of the first kind to a linear equation of the second kind. Then we apply the operational Tau method to the problem and prove convergence of the presented method. Finally, some numerical examples are given to show the accuracy of the method.

Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, system of fractional partial differential equation which has numerous applications in many fields of science is considered. Adomian decomposition method, a novel method is used to solve these type of equations. The solutions are derived in convergent series form which shows the effectiveness of the method for solving wide variety of fractional differential equations.

Dispersive Waves In Microstructured Solids, A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets, Mihhail Berezovski

Publications

The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler–Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a one-dimensional case.

Discovering Exoplanets Through Hidden Markov Model Analysis, Jon Drobny

Rose-Hulman Undergraduate Research Publications

The goal for the project is to develop a Hidden Markov Model for the detection and characterization of extrasolar planets through the analysis of light curves.

Introduction (2013), Eric Gossett

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Paper Abstracts (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-Jacobi-Bellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.

Schedule (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences