Applied Mathematics Commons^™

Using Data To Develop Mathematical Methods, Philip R. Carlson

ACMS Conference Proceedings 1995

An analysis of ordered pairs and their scatter plots leads to interesting questions related to mathematical modeling. Some statistical methods suggest ways to approach this analysis of the ordered pairs. Both high school and college methods are illustrated in this paper.

The 25 Greatest Mathematicians, Robert Brabenec

ACMS Conference Proceedings 1995

Many have tried to determine the greatest mathematicians in history. The purpose of this paper is to consider making such a list, along with some criteria to consider in making a rank order of these mathematicians.

Mathematical And Theological Beliefs: A Cognitive Science Perspective, Ron Benbow

ACMS Conference Proceedings 1995

In recent years, research studies have shown that control decisions and processes, beliefs about the nature of mathematics, attitudes, and other affective variables have enormous impact on the mathematical performance of students. This paper gives an overview of the research on mathematical beliefs and reviews some work done in Christian education relating to theological beliefs. It then compares the two.

Parallel Processing In The Undergraduate Curriculum, William E. Toll

ACMS Conference Proceedings 1995

No abstract provided.

Drawing The Boundaries: Mathematical Statistics In Twentieth-Century America, Patti W. Hunter

ACMS Conference Proceedings 1995

No abstract provided.

A Course In Mathematical Recreations, Richard Laatsch

ACMS Conference Proceedings 1995

No abstract provided.

The Intermediate Value Theorem, Dale Varberg

ACMS Conference Proceedings 1995

The Intermediate Value Theorem (a continuous function on an interval assumes all values between any two of its values) is one of the big theorems of calculus. Yet the theorem is absent or briefly mentioned in most calculus textbooks. The theorem deserves better as we intend to show by listing ten picturesque consequences that we think could enliven any calculus course.

Constructivism, Mathematics Education And Christianity, Ted Watanabe

ACMS Conference Proceedings 1995

In this paper, I briefly describe what constructivism is and its implications in the field of mathematics education. I will then discuss what this epistemology may mean to Christians who are in the field of mathematics education

Statistics, Mathematics, And Teaching, David S. Moore

ACMS Conference Proceedings 1995

In discussing our teaching, we may focus on content, what we want our students to learn, or on pedagogy, what we do to help them learn. These two topics are of course related. In particular, changes in pedagogy are often driven in part by changing priorities for what kinds of things we want students to learn. It is nonetheless convenient to address content and pedagogy separately. Pedagogy, certainly the less specific of the two, is the topic of my second paper. This paper concerns content, and in particular contains one side of a conversation between a statistician and mathematicians …

The 25 Greatest Mathematicians, Robert L. Brabenec

ACMS Conference Proceedings 1995

No abstract provided.

Introduction (1995), David L. Neuhouser

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

The Mathematics Of Measuring Capabilities Of Artificial Neural Networks, Martha A. Carter

Theses and Dissertations

Researchers rely on the mathematics of Vapnik and Chervonenkis to capture quantitatively the capabilities of specific artificial neural network (ANN) architectures. The quantifier is known as the V-C dimension, and is defined on functions or sets. Its value is the largest cardinality 1 of a set of vectors in Rd such that there is at least one set of vectors of cardinality 1 such that all dichotomies of that set into two sets can be implemented by the function or set. Stated another way, the V-C dimension of a set of functions is the largest cardinality of a set, such …

Probability Polynomials For Cubic Graphs In The Framework Of Random Topological Graph Theory, Esther Joy Tesar

Dissertations

Topological graph theorists study the imbeddings of graphs on surfaces (spheres with handles). Some interesting questions in the field are on w hat surfaces can a graph be 2 -cell imbedded and how m any such imbeddings are there on each surface. The study of these and related questions is called Enumerative Topological Graph Theory. Random Topological Graph Theory uses probability models to study the 2-cell imbeddings. It generalizes the results from Enumerative Topological Graph Theory (which is the uniform case, p= 1/2) to an arbitrary probability p.

We study the model where the sample space consists of all labeled, …

Asymptotic Diagonalizations Of A Linear Ordinary Differential System, Feipeng Xie

Dissertations

No abstract provided.

Step Domination In Graphs, Kelly Lynne Schultz

Dissertations

One of the major areas in Graph Theory is domination in graphs. It is this area with which this dissertation deals, with the primary emphasis on step domination in graphs.

In Chapter 1 we present some preliminary definitions and examples. In addition, a background of the area of domination is presented. We then introduce the concepts that lead to step domination.

In Chapter II we formally define the concept of step domination and give several examples. We determine the minimum number of vertices needed in a step domination set for many classes of graphs. We then explore step domination for …

Table Of Contents (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Schedule (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez

Mathematical Sciences Technical Reports (MSTR)

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …

A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order pre­dictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.

Distortion And Evolution Of A Localized Vortex In An Irrotational Flow, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

This paper examines the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational flow. At leading order, the monopole is advected with the background flow velocity at the center of vorticity. However, inhomogeneities of the flow will cause the monopole to distort. It is shown that a shear‐diffusion mechanism, familiar from the study of mixing of passive scalars, plays an important role in the evolution of the vorticity distribution. Through this mechanism, nonaxisymmetric vorticity perturbations which do not shift the center of vorticity are homogenized along streamlines on a Re1/3 time scale, much faster …

Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny

Mathematics and Statistics Faculty Publications

A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.

Descartes And Problem-Solving, Judith V. Grabiner

Pitzer Faculty Publications and Research

What can Descartes' Geometry teach us about problem solving?

Semi-Strongly Regular Graphs And Generalized Cages, Cong Fan

Dissertations

Two well-known classes of graphs, strongly regular graphs and cages, have been studied extensively by many researchers for a long period of time. In this dissertation, we mainly deal with semi-strongly regular graphs, a class of graphs including all strongly regular graphs, and (r, g, t)-cages, a generalization of the usual cage concept.

Chapter I introduces the two new concepts: semi-strongly regular graphs and generalized (r, g, t)-cages, gives necessary conditions for the existence of semi-strongly regular graphs and some interesting properties regarding common neighbors of pairs of vertices, and shows connections between these two new concepts and the old …

Mathematical Models Of Chemotherapy, John Carl Panetta

Mathematics & Statistics Theses & Dissertations

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens.

The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling …

Wing-Section Optimization For Supersonic Viscous Flow, Cem Cihan Item

Mechanical & Aerospace Engineering Theses & Dissertations

The recent interest in the High Speed Civil Transport (HSCT) has resulted in renewed research studies of optimized supersonic cruise transport configurations. Incorporation of flow viscosity effects in the design process of such a supersonic wing is currently under investigation. This may lead to more accurate problem formulations and, in tum, greater aerodynamic efficiency than can be obtained by the traditional, inviscid, linear theories. In this context, for a design code to be a candidate for a complex optimization problem, such as three-dimensional viscous supersonic wing design, it should be validated using simpler building-block shapes.

To optimize the shape of …

Nonlinear Time Series Analysis, James A. Stewart

Theses and Dissertations

This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency …

An Improved Solution Methodology For The Arsenal Exchange Model (Aem), Jeffery D. Weir

Theses and Dissertations

The purpose of this research was to design a solution methodology for the Arsenal Exchange Model (AEM) that is faster and contains less precision error than the current one. The current solution methodology modifies some of the original constraints and uses a computationally slow matrix inverter. The improved methodology uses a revised simplex algorithm to first solve a subproblem having only the weapon constraints generated by the AEM. Given this optimal allocation, hedge constraints and target constraints that are violated by the current solution are added to the original subproblem. A dual simplex algorithm is used to find the optimal …

Multipoint Quadratic Approximation For Numerical Optimization, Michael A. Blaylock

Theses and Dissertations

A quadratic approximation for nonlinear functions is developed in order to realize computational savings in solving numerical optimization problems. Function and gradient information accumulated from multiple design points during the iteration history is used in estimating the Hessian matrix. The approximate Hessian matrix is the available for a second order Taylor series approximation to the functions of interest. Several truss and frame models will be used to demonstrate the effectiveness of the new Multipoint Quadratic Approximation (MQA) in solving structural optimization problems.

An Elementary Proof That Finite Groups Lack Unique Product Structures, Matthew Cushman

Mathematical Sciences Technical Reports (MSTR)

We provide an elementary proof that no nontrivial finite group has a unique m-element product structure for any m greater than or equal to 2.

Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury

Mathematics and Statistics Faculty Publications

In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.