Physical Sciences and Mathematics Commons^™

Integrating Moral And Spiritual Themes In Middle School And High School Mathematics Teaching Units, Dave Klanderman, Sean Bird

ACMS Conference Proceedings 2007

In 2006, the Kuyers Institute published a total of nine math lessons for the middle school and high school which incorporate a Christian perspective. This paper examines the impact of teaching all of these lessons at a the high school level as well as selected lessons at the college level with preservice elementary and secondary mathematics teachers.

Tanzania, Mathematics, And Me: Reflections From My Work With Tanzanian Teachers, Mandi Maxwell

ACMS Conference Proceedings 2007

In June 2006 I had the privilege of participating in a four-day teacher training workshop in Mumba, Tanzania. In this paper I will discuss the challenges and triumphs of working with Tanzanian Secondary Mathematics teachers. We will discuss the educational environment, teaching strategies, and curricular issues that affect mathematics teachers in rural areas of Tanzania and contrast that with the American educational experience. We will also discuss some of the goals of the Teacher Training workshop that my colleagues and I led and look at some of the specific mathematical ideas and applications that I shared with the Mathematics teachers …

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.

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Conference Proceedings 2007

Enlightenment thinkers saw the universe as mechanistic and mathematics as the language in which the universe is written. They viewed mathematics as eternal, as transcending human minds, and as comprehensible by human beings. Thus mathematics, from their perspective, is our best tool for understanding the secrets of nature. This outlook was nicely summarized by Morris Kline: (Kline, 1953) In brief the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine. From a Christian perspective, however, the Enlightenment outlook is flawed. It privileges …

Chaos Theory And Metaphysical (In) Determinism, Tim Rogalsky

ACMS Conference Proceedings 2007

This paper will begin by introducing the issues that arise from chaos theory for the Christian mathematician and scientist: What is at stake in this debate? It will then briefly review chaos theory, by means of two examples. It will then introduce the metaphysical interpretations given to chaos theory by three different scientist-theologians. The paper will conclude with a brief introduction to open theists, and analyze their use of chaos theory to supper their theological claims.

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 …

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 …

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 …

A Large-Scale Rheumatoid Arthritis Genetic Study Identifies Association At Chr 9q33.2, Steven J. Schrodi

Steven J Schrodi

No abstract provided.

Introduction (2007), Angela Hare

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

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

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 …

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.

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.

Mathematical Methods In Composing Melodies, Thomas Brown

Undergraduate Theses and Capstone Projects

This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …

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, …

Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba

Mathematics & Statistics Theses & Dissertations

The solution to the neutron Boltzmann equation is separated into a straightahead component dominating at high energies and an isotropic component dominating at low energies. The high-energy solution is calculated using HZETRN-05, and the low-energy isotropic component is modeled by two non-coupled integro-differential equations describing both forward and backward neutron propagation. Three different solution methods are then used to solve the equations. The collocation method employs linear I3-splines to transform each equation into a system of ODES; the resulting system is then solved exactly and evaluated using numerical integration techniques. Wilson's method uses a perturbational approach in which a fundamental …

Using Math In Cell Biology: A Tale Of Two Channel Types, Borbala Mazzag

Borbala Mazzag

No abstract provided.

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

Gregory S. Spradlin

A Multivariate Magnitude Robust Control Chart For Mean Shift Detection And Change Point Estimation, Ryan M. Harrell

Theses and Dissertations

Statistical control charts are often used to detect a change in an otherwise stable process. This process may contain several variables affecting process stability. The goal of any control chart is to detect an out-of-control state quickly and provide insight on when the process actually changed. This reduces the off-line time the quality engineer spends assigning causality. In this research, a multivariate magnitude robust chart (MMRC) was developed using a change point model and a likelihood-ratio approach. Here the process is considered in-control until one or more normally distributed process variables permanently and suddenly shifts to out-of-control, stable value. Using …

Spacecraft Proximity Operations Used To Estimate The Dynamical & Physical Properties Of A Resident Space Object, Abraham F. Brunner

Theses and Dissertations

When conducting a space proximity operation, developing high-fidelity estimates of the dynamical and physical properties of a Resident Space Object (RSO) based on post-rendezvous observational data acquired, is imperative for the understanding of the RSO itself and the operating environment. This research investigates the estimation of relative motion dynamics, rotational dynamics, and the feasibility of estimating the moments of inertia of a RSO. Using the Hill-Clohessy-Wiltshire equations, rigid-body dynamics, and estimation theory, a nonlinear least squares estimation algorithm is implemented in the processing of range data from tracked observation points on the RSO body. Through simulation, it was determined that …

Variational Analysis In Bilevel Programming, S Dempe, J Dutta, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of advanced tools of modern variational analysis and generalized differentiation to problems of optimistic bilevel programming. In this way, new necessary optimality conditions are derived for two major classes of bilevel programs: those with partially convex and with fully convex lower-level problems. We provide detailed discussions of the results obtained and their relationships with known results in this area.

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.