Physical Sciences and Mathematics Commons^™

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 …

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 …

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 …

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 …

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.

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.

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. …

Elections With Three Candidates Four Candidates And Beyond: Counting Ties In The Borda Count With Permutahedra And Ehrhart Quasi-Polynomials, Adam Margulies

Honors Theses

In voting theory, the Borda count’s tendency to produce a tie in an election varies as a function of n, the number of voters, and m, the number of candidates. To better understand this tendency, we embed all possible rankings of candidates in a hyperplane sitting in m-dimensional space, to form an (m - 1)-dimensional polytope: the m-permutahedron. The number of possible ties may then be determined computationally using a special class of polynomials with modular coefficients. However, due to the growing complexity of the system, this method has not yet been extended past the case of m = 3. …

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 …

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 …

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 …

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 …

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 …

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 …

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.

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.

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.

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

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

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

19th Conference Of The Associations Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Association of Christians in the Mathematical Sciences 19th Biennial Conference Proceedings, May 29 - June 1, 2011, Bethel University.

Local Fractional Series Expansion Method For Solving Wave And Diffusion Equations On Cantor Sets, Yang Xiaojun

Xiao-Jun Yang

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

The Neural Ring: An Algebraic Tool For Analyzing The Intrinsic Structure Of Neural Codes, Carina Curto, Vladimir Itskov, Alan Veliz-Cuba, Nora Youngs

Department of Mathematics: Faculty Publications

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, …

Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi

Scripps Senior Theses

Malaria is a preventable and treatable blood-borne disease whose complications can be fatal. Although many interventions exist in order to reduce the impacts of malaria, the optimal method of distributing these interventions in a geographical area with limited resources must be determined. This thesis refines a model that uses an integer linear program and a compartmental model of epidemiology called an SIR model of ordinary differential equations. The objective of the model is to find an intervention strategy over multiple time steps and multiple geographic regions that minimizes the number of days people spend infected with malaria. In this paper, …

Stress Analysis Of Ramberg-Osgood And Hollomon 1-D Axial Rods, Ronald J. Giardina Jr

University of New Orleans Theses and Dissertations

In this paper we present novel analytic and finite element solutions to 1-D straight rods made of Ramberg-Osgood and Hollomon type materials. These material models are studied because they are a more accurate representation of the material properties of certain metals used often in manufacturing than the simpler composite linear types of stress/strain models. Here, various types of loads are considered and solutions are compared against some linear models. It is shown that the nonlinear models do have manageable solutions, which produce important differences in the results - attributes which suggest that these models should take a more prominent place …

Approximate Solutions For Diffusion Equations On Cantor Space-Time, Xiao-Jun Yang

Xiao-Jun Yang

In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.