Applied Mathematics Commons^™

Undergraduates, The Right Questions, And Cayley Produce Results, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

During the summers of 1989, 1990, and 1991, eighteen undergraduates participated in a National Science Foundation Research Experiences for Undergraduates program at Rose-Hulman for which the author was the principal investigator. This paper provides some examples of the mathematics discovered during these three summers and discusses the philosophy, environment and process which made these discoveries possible.

Computation Of Planar Store Trajectories Using An Adaptive Grid Procedure, William D. Hack

Theses and Dissertations

The objective of this research was to compare a quasi-analytical, potential flow/three-degree-of-freedom model to an implicit-Euler algorithm for the calculation of store trajectories. The implicity algorithm uses a cell- centered, finite-volume, spatial discretization applied to the Euler equations, written in time-dependent, curvilinear-coordinates. A flux-differencing Roe scheme is employed to find the split-fluxes and the Steger/Warming flux-vector method is used to calculate the flux-Jacobians. The potential flow and implicit- Euler algorithm are combined with a three-degree-of-freedom algorithm to evaluate the planar, freefall trajectories of a simple store shape. The research uses two different grid-modification techniques in the implicit algorithm evaluation. Data …

Image Segmentation Using Affine Wavelets, Steven E. Smiley

Theses and Dissertations

This thesis discusses the use of the multiresolution representation and Radial Basis Function (RBF) neural networks to segment both FLIR and SAR imagery. The multiresolution approximation coefficients are used as features into the RBF network which learns to distinguish between different cultural and natural regions or objects. The wavelets used are Mallat's spline wavelet and Daubechies' compactly supported wavelets. Additionally, this thesis provides an explanation of wavelets in a tutorial manner. It introduces wavelet theory and discusses two different approaches to generating the multiresolution or wavelet representation.

An Algorithm For Robust Eigenstructure Assignment Using The Linear Quadratic Regulator, Thomas C. Huckabone

Theses and Dissertations

The Linear Quadratic Regulator (LQR) can guarantee a robust closed loop eigenstructure for full state feedback. The algorithm developed here takes advantage of the stability guarantees of LQR to achieve an eigenstructure close to desired but within the allowable region of LQR. The algorithm selects the LQR weighting matrices, Q and R, that minimize the distance between the elements of the desired and LQR achievable eigenstructures. The minimization is accomplished by using a simplex based optimization routine. Specific weightings placed on the elements of the desired eigenstructure define the relative importance of each element. The algorithm is programmed in FORTRAN …

A Mathematical Model For Outgassing And Contamination, Weifu Fang, Meir Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, E. Zaron

Mathematics and Statistics Faculty Publications

A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the …

An Application Of Interactive Computer Graphics To The Study Of Inferential Statistics And The General Linear Model, Stephen D. Pearce

Theses and Dissertations

This research created a learning environment, known as the Pearce Projection Modeling Environment (PPME) which is used as a tool by a teacher and student. The PPME was developed in an effort to create a new approach to the study of the General Linear Model through a constructive and projective, geometric approach. While the geometric approach to the GLM was developed over the past century, it has not been used extensively because of the inherent complexities associated with visualizing vector spaces. With the PPME, visualization is accomplished effortlessly. The PPME is a computer program that allows the student to enter …

Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Analysis And Finite-Element Approximation Of Optimal-Control Problems For The Stationary Navier-Stokes Equations With Distributed And Neumann Controls, Max D. Gunzburger, L. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes equations. The controls considered may be of either the distributed or Neumann type; the functionals minimized are either the viscous dissipation or the L⁴-distance of candidate flows to some desired flow. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider the approximation, by finite element methods, of solutions of the …

Transformations Of Graphs And Digraphs, Elzbieta B. Jarrett

Dissertations

Some distances defined on graphs depend on transforming one graph into another. Two of these transformations are edge rotation and edge slide. In this dissertation, extensions and generalizations of these transformations are investigated.

Chapter I begins with some preliminary definitions and known results. Then two types of digraph transformations are introduced and their properties are studied.

Some measures of distance between graphs and distance between digraphs are defined in Chapter II. Also distance graphs and digraphs associated with these measures are introduced. Several known results concerning this topic are generalized and new results are presented.

Chapter III is devoted to …

Surgical Techniques For Constructing Minimal Orientable Imbeddings Of Joins And Compositions Of Graphs, David L. Craft

Dissertations

The various cases within the proof of the Heawood Map-Coloring Theorem, which established the genus of the complete graphs, utilized various techniques--some for the first time. This activity spurred interest in determining the genus of various other classes of graphs. However, very few generally applicable techniques have been developed, beyond those used in the proof of this famous theorem. Finding genera of arbitrary graphs remains a very difficult problem.

In this dissertation, we describe two surgical techniques for imbedding graphs. The first construction, called a graphical surface,views an orientable surface as a fattened graph, i.e., vertices become spheres and edges …

Miscellaneous Publication 17/91 - Mudas - Model Of An Uncertain Dryland Agricultural System: A Description, R. S. Kingwell, A. D. Bathgate

Farm Systems and Economics research reports

In the early 1980s, the Department of Agriculture developed a mixed integer whole-farm mathematical programming model of the dryland farming system in the eastern wheatbelt of Western Australia (Morrison et al. 1986). The model named MIDAS (Model of an Integrated Dryland Agricultural System) was constructed, tested and scrutinised by a multi-disciplinary team of researchers, advisers, farm management consultants and farmers (Kingwell 1987a). The model described in some detail the biology and finances of the dryland farming system in an average season and calculated profit-maximising farm plans.

MIDAS remains an often used tool in research and extension, being applied to many …

A Representation Of Chemical Reactions By Labeled Graphs, Héctor Hevia

Dissertations

Graphs can be used to represent the atomic structure of chemical compounds where the vertices of the graph represent the individual atoms and the edges of the graph represent the valence bonds between a pair of atoms. M. A. Johnson (1991) introduced a graph-theoretic way to represent structural changes in chemical compounds. Thus, certain labelings of graphs called transitional labelings can be thought as representing chemical equations. Associated with these labelings, we introduce a new invariant of a graph G called the transitional value of G. The transitional value of a graph G gives an indication of how dramatic a …

A Tale Of Two Mathematicians, Robert Brabenec

ACMS Conference Proceedings 1991

The goal of this paper is to identify some of the discoveries in mathematics during the period from 1820 to 1875 that have profoundly changed the nature of mathematics. To provide a context for this, the author compares some results of mathematics before the year 1820 with those present after 1875. And to humanize this, the author discusses the details of the life and times of two mathematicians, one who was active before 1820 and one who was active after 1875.

Cantor's Concept Of Infinity: Implications Of Infinity For Contingence, Bruce A. Hedman

ACMS Conference Proceedings 1991

Georg Cantor (1845-1918) was a devout Lutheran whose explicit Christian beliefs shaped his philosophy of science. Joseph Dauben has traced the impact Cantor's Christian convictions had on the development of transfinite set theory. In this paper I propose to examine how Cantor's transfinite set theory has contributed to an increasingly contingent world view in modern science. The contingence of scientific theories is not just a cautious tentativeness, but arises out of the actual state of the universe itself. The mathematical entities Cantor studied, transfinite numbers, he admitted were fraught with paradoxes. But he believed that they were grounded in a …

Using Mathematica To Teach Calculus, Russell W. Howell

ACMS Conference Proceedings 1991

For the past two years Westmont College has been one of the beta test sites for the calculus reform experiment being conducted at the University of Illinois under the direction of Jerry Uhl. Brown, Porta, and Uhl have created text which is integrated with Mathematica, a very powerful symbol manipulation, graphics, and number crunching software package produced by Wolfram Research, Inc. A preliminary version of this text has just been released [2]. We have used the Illinois materials for an honors course of incoming Freshmen with prior calculus experience. The purpose of this paper is to evaluate the curriculum and …

Reviving The Argument From Design: Detecting Design Through Small Probabilities, William A. Dembski

ACMS Conference Proceedings 1991

How small do probabilities of events have to get before we refuse to attribute those events to chance? Smallness of probability is itself not enough since events with extremely small probability occur all the time. But when such events are also prespecified, it becomes difficult to attribute their occurrence to chance. Typically we search for a causal account of how chance was offset. Lacking such a causal story, however, are we still justified in asserting that an extremely improbable prespecified event was not the result of chance? This question is relevant to such diverse areas as prophecy, miracles, parapsychology, gambling, …

Real Number Representations And The Distribution Of Following Segments, C.R. Rosentrater

ACMS Conference Proceedings 1991

No abstract provided.

Mathematical And Religious Knowledge In Nineteenth-Century England, Joan Richards

ACMS Conference Proceedings 1991

No abstract provided.

The Rigorous And The Natural In Eighteenth Century Mathematics, Joan Richards

ACMS Conference Proceedings 1991

No abstract provided.

Discrete Mathematics Versus Calculus - A Modern Day Extension Of The Formalist-Intuitionist Controversy, Marvin L. Johnson, Ph.D

ACMS Conference Proceedings 1991

No abstract provided.

Can Mathematical Methods Yield Theological Truth?, Jan De Koning

ACMS Conference Proceedings 1991

This paper discusses the negative impact mathematical methods in theology can have on the church by looking specifically at Arminius and Voetius, Dutch theologians living in the late sixteenth and early seventeenth century. Both Arminius and Voetius used mathematical methodology, although they came to different conclusions. I think their differences were due to their different worldviews, which in turn were fundamentally influenced by their upbringing. Both theologians, however, made the same mistake with their methodology and the church split because of that mistake.

How Has Christian Theology Furthered Mathematics?, Gene B. Chase

ACMS Conference Proceedings 1991

In revising my Bibliography of Christianity and Mathematics to include material prior to the 20th century, it is difficult to know what to include and what to exclude, since Christian presuppositions informed much scholarship in a vague, cultural sort of way. This paper is a first cut at attempting to narrow down candidates for that Bibliography by looking for specific ways in which Christian theology has furthered mathematics.

C. S. Lewis, George Macdonald, And Mathematics, David L. Neuhouser

ACMS Conference Proceedings 1991

This paper examines the influence and role of mathematics and mathematicians in the stories of George MacDonald and C. S. Lewis.

Introduction (1991), Robert Brabenec

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

Table Of Contents (1991), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

Schedule (1991), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

The Hermeneutics Of Mathematical Modeling, David Tudor

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics For Life And Society, Miriam Lipschutz-Yevick

Humanistic Mathematics Network Journal

No abstract provided.

New Modified Anderson-Darling And Cramer-Von Mises Goodness-Of-Fit Tests For A Normal Distribution With Specified Parameters, Goksel Kahya

Theses and Dissertations

This thesis improves the powers of the Anderson-Darling and Cramer-von Mises goodness-of-fit tests using the mean rank and the median rank plotting positions. A Monte Carlo simulation of 5000 repetitions is used to generate the critical values from n =4 through n =80 for certain significance levels. An extensive power study is performed to compare the powers of the modified tests to the known tests for the uniform, the exponential, the double exponential, the lognormal, and the Weibull distributions. The power of the A-D tests modified by the median rank plotting and the mean rank plotting position are approximately 0.01% …

A Goodness-Of-Fit Test For A Family Of Two Parameter Weibulls With Known Shape Using Minimum Distance Estimation Of Parameters, John S. Crown

Theses and Dissertations

This research is to produce a modified Anderson-Darling goodness of fit test for the Weibull distribution when the location parameter is found by minimum distance estimation, the shape parameter is assumed known, and the MLE is used for the scale parameter. The critical values for the Anderson-Darling test are generated via Monte Carlo simulation when both the Anderson-Darling and Cramer-Von Mises distance statistics are minimized. These critical values are then used for a power study. The Monte Carlo simulation used 5000 repetitions for sample sizes of 5,8,12,15,16,20 and 25 with the Weibull shape parameter of . 5(.5)4.0. The power study …