Physical Sciences and Mathematics Commons^™

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.

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.

Numerical Solutions For Weakly Singular Hammerstein Equations And Their Superconvergence, Hideaki Kaneko, Richard D. Noren, Yuesheng Xu

Mathematics & Statistics Faculty Publications

In the recent paper [7], it was shown that the solutions of weakly singular Hammerstein equations satisfy certain regularity properties. Using this result, the optimal convergence rate of a standard piecewise polynomial collocation method and that of the recently proposed collocationtype method of Kumar and Sloan [10] are obtained. Superconvergence of both of these methods are also presented. In the final section, we discuss briefly a standard productintegration method for weakly singular Hammerstein equations and indicate its superconvergence property. © 1992 Rocky Mountain Mathematics Consortium.

Solution Uniqueness And Stability Criteria For A Model Of Growth Factor Production, J. A. Adam

Mathematics & Statistics Faculty Publications

Uniqueness and stability criteria are established for the steady states of a nonlinear model of growth factor production. A specific expression for the nonlinearity is chosen, containing three parameters which can be adjusted to fit a specific biological context, but much of the analysis applies to a general class of source terms that exhibit the same qualitative behavior.

Automorphisms Of The Lattice Of Recursively Enumerable Sets: Orbits, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

No abstract provided.

Sliding-Mode Observers Based On Equivalent Control Method, Sergey V. Drakunov

Sergey V. Drakunov

No abstract provided.

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 …

Stochastic Demand, Inventory Management, And Chamberlinian Excess Capacity, Hans Haller, Daniel Orr

About Harlan D. Mills

No abstract provided.

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

Yi Li

No abstract provided.

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 …

An Introduction To The Research Queueing Package For Modeling Computer Systems And Communication Networks, Robert F. Gordon Ph.D., Edward A. Macnair

Faculty Works: MCS (1984-2023)

A queueing network is an important tool for modeling systems where performance is principally affected by contention for resources. Such systems include computer systems, communication networks and manufacturing lines. In order to effectively use queuing networks as performance models, appropriate software is necessary for definition ofthe networks to be solved, for solution ofthe networks and for examination of the performance measures obtained. The RESearch Queueing Package (RESQ) and the RESearch Queueing Package Modeling Environment (RESQME) form a system for constructing, solving and analyzing extended queueing network models. We refer to the class of RESQ networks as "extended" because of characteristics …

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 …

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 …

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 …

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.

Using Mathematics 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 …

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 …

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.

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.

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.

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, …

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.