Applied Mathematics Commons^™

Mathematical Knowledge And Leibniz' Epstemology, Jonathan Zderad

ACMS Conference Proceedings 2007

No abstract provided.

Integrating Ethics Into The Database Course With A Focus On Data Modeling And Normalization, James F. Glasgow, Ph.D

ACMS Conference Proceedings 2007

No abstract provided.

Optimize Your Matth Services Through Networking, Patrice Conrath

ACMS Conference Proceedings 2007

No abstract provided.

Modeling Growth In Christian Evangelism, Marvin Bittinger

ACMS Conference Proceedings 2007

No abstract provided.

Breathing Life Into The Liberal Arts Math Course: Ten Teaching Tips, Mark Colgan

ACMS Conference Proceedings 2007

Teaching the liberal arts math course for general education students presents unique challenges, but the course also offers exciting life applications and opportunities for integrating faith with a variety of creative topics. I try to make the course interesting by actively involving students and relating mathematical topics to their lives. In this paper I will discuss some things I have tried in the liberal arts math course I teach at Taylor University: using students' names, use of undergraduate teaching assistants (T As), group guessing games, handout booklets, hangman, group projects, memory verses, reflection papers, and life lessons.

Six Ways, Yea Seven, That Scripture Is Integral To Our Science And Math Classes, Sean Bird

ACMS Conference Proceedings 2007

This paper looks at the ways the Bible informs mathematics and its role in guiding our stewardship of God’s creation.

Voltaire: A Study In Finding A Needle In A Haystack, Andrew Simoson

ACMS Conference Proceedings 2007

In Euler’s popular notes to a German Princess of 1837, he describes Voltaire as laughing about the idea of a hole going to Earth’s center. Did Voltaire actually write about this idea? Herein we describe the answers to be found upon searching through the huge opus of Voltaire’s written work. The result has links to Newton’s 1687 Principia discoveries and the French Academy’s early eighteenth century international scientific expeditions to Lapland and Peru establishing the veracity of those discoveries.

The Beautiful And Sublime In Mathematics, Paul Zwier

ACMS Conference Proceedings 2007

A précis of Paul Zwier's talk presented at the meetings of the ACMS Conference at Messiah College on June 1, 2007.

Connection-Oriented Computer Science Education, Kim Kihlstrom

ACMS Conference Proceedings 2007

Computers play an important role in every area of our society and are integral in every academic discipline. Today's computer science students need a background that will prepare them for the expanding range of computing opportunities. The opportunities for computer professionals are varied and increasing in diversity. However, undergraduate computer science programs tend to be narrowly focused on programming and related technical skills. Female students in particular tend to be highly interested in exploring connections between computer science and other fields.

How can we leverage these observations at a liberal arts college, where interdisciplinary connections are highly desirable, and where …

Exploring Loci In Geometry, Owen Byer, Deirdre Smeltzer

ACMS Conference Proceedings 2007

No abstract provided.

Measures Of Travers Ability In Graphs, Futaba Okamoto

Dissertations

For a connected graph G of order n ≥ 3 and a cyclic ordering sc : v 1, v2,..., vn, v n+1 = v1 of vertices of G, the number d(sc) is defined by d(sc) = i=1n d(vi, vi +1), where d(vi, vi +1) is the distance between vi and vi+1 in G for 1 ≤ i ≤ n. The Hamiltonian number h(G) and upper Hamiltonian number h +(G) of G are defined as h(G) = min{d(sc)} and h+(G) = max{d(sc)}, respectively, where the minimum and maximum are taken over all cyclic orderings s c of vertices of G. For …

The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui

Dissertations

In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dv_s ), where dv_s ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The …

Parameter Estimation In Nonlinear Coupled Advection-Diffusion Equation, Robert R. Ferdinand

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a coupled system of two nonlinear advection-diffusion equations is presented. Such systems of equations have been used in mathematical literature to describe the dynamics of contaminant present in groundwater flowing through cracks in a porous rock matrix and getting absorbed into it. An inverse method procedure that approximates infinite-dimensional model parameters is described and convergence results for the parameter approximants are proved. This is finally followed by a computational experiment to compare theoretical and numerical results to verify accuracy of the mathematics analysis presented.

An Age-Structured Resource-Consumer Dynamical Model, Jean M. Tchuenche

Applications and Applied Mathematics: An International Journal (AAM)

Many dynamical systems in population biology in which agents compete for resources may exhibit chaotic fluctuations. This short letter develops Gamarra and Solé's previous work. We briefly review a classical model of population with complex dynamics, and proceed to study the dynamics of an age-structured resource-consumer model, in which the fertility coefficients are density independent. Implicit or first integral solutions of the model are obtained, and conditions for which they are stable given. It is observed that resource availability at any time depends on the number of potential consumers present.

Intelligence Through Interaction: Towards A Unified Theory For Learning, Ah-Hwee Tan, Gail A. Carpenter, Stephen Grossberg

Research Collection School Of Computing and Information Systems

Machine learning, a cornerstone of intelligent systems, has typically been studied in the context of specific tasks, including clustering (unsupervised learning), classification (supervised learning), and control (reinforcement learning). This paper presents a learning architecture within which a universal adaptation mechanism unifies a rich set of traditionally distinct learning paradigms, including learning by matching, learning by association, learning by instruction, and learning by reinforcement. In accordance with the notion of embodied intelligence, such a learning theory provides a computational account of how an autonomous agent may acquire the knowledge of its environment in a real-time, incremental, and continuous manner. Through a …

Introduction (2007), Angela Hare

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Utilizing Thermal Testing For Recovering, James Preciado, Thomas Werne

Mathematical Sciences Technical Reports (MSTR)

Given a two-dimensional region that contains one or more circular voids, we develop mathematical methods to locate the center and radius of the voids based on thermal boundary data. These methods can be readily applied in the field of non-destructive evaluation.

Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio

Faculty Articles

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n x n boards that form the cube. The other is to tour within the n stacked copies of the n x n board that form the cube. This paper is concerned with the latter. In this paper …

Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We use the notion of backward integration, with respect to a general Lévy process, to treat, in a simpler and unifying way, various classical topics as: Girsanov theorem, rst order partial differential equations, the Liouville (or Lyapunov) equations and the stochastic characteristic method.

Equitable Efficiency In Multiple Criteria Optimization, Vijay Singh

All Dissertations

Equitable efficiency in multiple criteria optimization was introduced mathematically in the middle of nineteen-nineties. The concept tends to strengthen the notion of Pareto efficiency by imposing additional conditions on the preference
structure defining the Pareto preference. It is especially designed to solve multiple criteria problems having commensurate criteria where different criteria values can be compared directly.

In this dissertation we study some theoretical and practical aspects of equitably efficient solutions. The literature on equitable efficiency is not very extensive and provides very limited number of ways of generating such solutions. After introducing
some relevant notations, we develop some scalarization based …

A Reproducible Research Toolkit For R, Roger Peng

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present a collection of R packages for conducting and distributing reproducible research using R, Sweave, and LaTeX. The collection consists of the cacheSweave, stashR, and SRPM packages which allow for the caching of computations in Sweave documents and the distribution of those cached computations via remotely accessible key-value databases. We describe the caching mechanism used by the cacheSweave package and tools that we have developed for authors and readers for the purposes of creating and interacting with reproducible documents.

Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study set-valued optimization problems with equilibrium constraints (SOPEOs) described by parametric generalized equations in the form 0 is an element of the set G(x) + Q(x) where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the PalaisSmale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.

Random Vectors Over Finite Fields, Shannon Lockard

All Dissertations

The study of random objects is a useful one in many applications and areas of mathematics. The Probabilistic Method, introduced by Paul Erdos and his many collaborators, was first used to study the behavior of random graphs and later to study properties of random objects. It has developed as a powerful tool in combinatorics as well as finding applications in linear algebra, number theory, and many other areas. In this dissertation, we will consider random vectors, in particular, dependency among random vectors. We will randomly choose vectors according to a specified probability distribution. We wish to determine how many vectors …

Large Solutions Of Semilinear Elliptic Equations Under The Keller–Osserman Condition, Alan V. Lair

Faculty Publications

Excerpt: We establish conditions on the function p that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the given equation.

Suboptimal Minimax Design Of Constrained Parabolic Systems With Mixed Boundary Control, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in mixed (Robin) boundary conditions. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We design and justify an easily implemented suboptimal structure of the feedback boundary regulator and compute its optimal parameters ensuring the required state performance and robust stability of the nonlinear closed-loop control system on the infinite horizon.

An Isotropic Metric, Joseph D. Rudmin

Virginia Journal of Science

An isotropic metric for a black hole and a better vacuum condition \nabla^2 V_G =0 are presented which yield distinct terms for the energy densities of ordinary matter and gravitational fields in the Einstein tensor (G^44 =-g^2 (2\nabla^2 V_G +(\nabla V_G)^2)). This model resolves an inconsistency between electromagnetism and gravity in the calculation of field energy. Resolution of this inconsistency suggests a slight modification of the Einstein equation to gG^\mu\nu = 8\pi G T^\mu\nu.

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …

Lanchester's Equations In Three Dimensions, Christina Spradlin, Greg Spradlin

Publications

This paper generalizes Lanchester’s equations of warfare to partial differential equations involving time and two spatial variables. Unlike in Lanchester’s original ordinary differential equations, the distribution of armies over the battlefield must be considered. Four different modes of attack are introduced, generalizing Lanchester’s equations for area fire and for direct fire. The effect of the distribution of forces and their movement on the outcome is considered, and numerical simulations given.