Applied Mathematics Commons^™

The Dynamics Of Growth-Factor-Modified Immune-Response To Cancer Growth: One-Dimensional Models, J. A. Adam

Mathematics & Statistics Faculty Publications

By characterizing the effect of tumor growth factors as deviations from normal logistic-type growth rates, the spatio-temporal dynamics for a one-dimensional model of cancer growth incorporating immune response are studied. The growth rates considered are classified respectively as normal, activated, inhibited and delay activated. The homogeneous steady states are defined by relative extrema of a ''free energy'' function V(x) for each of the above four cases. This function is of particular importance in studying the coexistence of tumoral and cancer-free steady states, and in identifying the nature (progressive or regressive) of travelling wave solutions to the nonlinear partial differential equation …

Optimal Greedy Algorithms For Indifference Graphs, Peter J. Looges, Stephan Olariu

Computer Science Faculty Publications

A fundamental problem in social sciences and management is understanding and predicting decisions made by individuals, various groups, or the society as a whole. In this context, one important concept is the notion of indifference. We characterize the class of indifference graphs, that is, graphs which arise in the process of quantifying indifference relations. In particular, we show that these graphs are characterized by the existence of a special ordering of their vertices. As it turns out, this ordering leads naturally to optimal greedy algorithms for a number of computational problems, including coloring, finding a shortest path between two vertices, …

Interactive Graphics System For The Study Of Variance/Covariance Structures Of Bivariate And Multivariate Normal Populations, Ronald G. Garlicki

Theses and Dissertations

This research created a graphics oriented computer program which was used as part of a Visualization, Verbalization, Algorithization and Mathematization (VVAM) learning protocol. The curriculum for this research was the study of variance/covariance structures of bivariate and multivariate normal populations. The program displays the geometric images corresponding to the various possible covariance structures. These images facilitate and encourage experiment-based self discovery learning. The program encourages the student to take an active role in their own education. The program created is self contained, calculating all the statistical values it requires to create the various geometric images. The students have complete control …

The Morphology Of Convex Polygons, Stephan Olariu

Computer Science Faculty Publications

A simple polygon P is said to be unimodal if for every vertex of P, the Euclidian distance function to the other vertices of P is unimodal. The study of unimodal polygons has emerged as a fruitful area of computational and discrete geometry. We study unimodality properties of a number of special convex polygons from the morphological point of view. In particular, we establish a hierarchy among three classes of convex polygons in terms of their unimodality properties.

On Sources In Comparability Graphs, With Applications, Stephan Olariu

Computer Science Faculty Publications

We characterize sources in comparability graphs and show that our result provides a unifying look at two recent results about interval graphs.

A Tree Representation For P4-Sparse Graphs, B. Jamison, Stephan Olariu

Computer Science Faculty Publications

A graph G is P₄-sparse if no set of five vertices in G induces more than one chordless path of length three. P₄-sparse graphs generalize both the class of cographs and the class of P₄-reducible graphs. We give several characterizations for P₄-sparse graphs and show that they can be constructed from single-vertex graphs by a finite sequence of operations. Our characterization implies that the P₄-sparse graphs admit a tree representation unique up to isomorphism. Furthermore, this tree representation can be obtained in polynomial time.

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 …

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 Boundary Element Method Applied To The Two Dimensional Stefan Moving Boundary Problem, Donald C. Vosika

Theses and Dissertations

This thesis considers problems for which the boundary is not known before the problem is solved and must be determined as part of the solution. We consider a time dependent problem which results in a moving boundary. We look at the heat conduction/diffusion equation in one and two spatial dimensions. We use Green's Theorem to yield a Volterra boundary integral equation which involves an unknown function on the moving boundary. We use the boundary element method to obtain a solution. Graphical results for the two dimensional problem are presented.

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

Some Aspects Of The Semi-Perfect Elimination, Stephan Olariu

Computer Science Faculty Publications

Several efficient algorithms have been proposed to construct a perfect elimination ordering of the vertices of a chordal graph. We study the behaviour of two of these algorithms in relation to a new concept, namely the semi-perfect elimination ordering, which provides a natural generalization of chordal graphs.

On A Unique Tree Representation For P4-Extendible Graphs, B. Jamison, S. Olariu

Computer Science Faculty Publications

Several practical applications in computer science and computational linguistics suggest the study of graphs that are unlikely to have more than a few induced paths of length three. These applications have motivated the notion of a cograph, defined by the very strong restriction that no vertex may belong to an induced path of length three. The class of P₄-extendible graphs that we introduce in this paper relaxes this restriction, and in fact properly contains the class of cographs, while still featuring the remarkable property of admitting a unique tree representation. Just as in the case of cographs, the …

Wings And Perfect Graphs, Stephan Olariu

Computer Science Faculty Publications

An edge uv of a graph G is called a wing if there exists a chordless path with vertices u, v, x, y and edges uv, vx, xy. The wing-graph W(G) of a graph G is a graph having the same vertex set as G; uv is an edge in W(G) if and only if uv is a wing in G. A graph G is saturated if G is isomorphic to W(G). A star-cutset in a graph G is a non-empty set of …

Simulated Annealing On Np-Complete Problems, Russell W. Howell

ACMS Conference Proceedings 1989

The Random House Dictionary defines anneal as " ... to free (glass, metals, etc.) from internal stress by heating and gradually cooling." In the physical world, impurities are annealed out of a substance by heating it to a high temperature. As it is cooled, its molecular structure gradually settles into a stable "low-energy" configuration. It is important to cool the substance slowly, especially at lower temperatures, so that impurities do not get "frozen" into place. With careful cooling, a low-energy state can eventually be reached. This state may not be the one with the lowest potential energy, where the spins …

The Mathematical Intelligencer, Dmitrii Egorov: Mathematics And Theology In Russia, Charles E. Ford

ACMS Conference Proceedings 1989

This paper tells the story of Russian mathematician Dmitri Egorov, recounting his faith and contributions to the field of mathematics.

A Course On Mathematics And The Christian Faith, W. David Laverell, Carl J. Sinke

ACMS Conference Proceedings 1989

The January interim term at Calvin College provides an opportunity for developing and teaching courses outside a normal major program. As a result faculty members are frequently given the interim off to provide time for research and development of new courses. In 1987 we were given such a leave in order to pursue the questions of the relationship between mathematics and the Christian Faith. One result was our presentation at the 1987 Association of Christians in the Mathematical Sciences conference. Immediately thereafter we began to develop a specific interim course based on our studies. We offered the course during the …

The Bisexual Galton-Watson Branching Process, David M. Hull

ACMS Conference Proceedings 1989

I would like to present the bisexual Galton-Watson branching process. The word "bisexual" indicates that we will be considering a population of two sexes--which will be designated as the usual male and female. Here is a brief overview of what I would like to cover.

1. The bisexual process motivated: why is it needed?
2. The standard Galton-Watson branching process.
3. The state of affairs regarding two-sex models.
4. The nuts and bolts of the bisexual Galton-Watson branching process (parameters defined and how it works).
5. A review of published bisexual results to date.
6. What is to come?