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Mathematics

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1991

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Undergraduates, The Right Questions, And Cayley Produce Results, Gary J. Sherman Dec 1991

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.

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Characterization Of Knot Complements In The 4-Sphere, Vo Thanh Liem, Gerard A. Venema Nov 1991

Characterization Of Knot Complements In The 4-Sphere, Vo Thanh Liem, Gerard A. Venema

University Faculty Publications and Creative Works

Knot complements in S4 are characterized as follows: A connected open set W ⊂ S4 is homeomorphic to the complement of some locally flat 2-sphere in S4 if and only if H1(W) is infinite cyclic, W has one end, and the fundamental group of that end is infinite cyclic. Applications include a characterization of weakly flat 2-spheres in S4 and a complement theorem for 2-spheres in S4.

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More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic Nov 1991

More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

We find an upper bound on the probability that a randomly selected triple in a group is 3-rewriteable, and a bound for the core set rewriteability.

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Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic Oct 1991

Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

Our goal is to define the cyclicizer, which is analogous to the centralizer and normalizer, and to examine groups in which these subsets have certain special properties.

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Templates And Framed Braids, Paul Melvin, N. B. Tufillaro Sep 1991

Templates And Framed Braids, Paul Melvin, N. B. Tufillaro

Mathematics Faculty Research and Scholarship

We show how a template for a dynamical system can be uniquely specified by a framed braid. This leads to a homological classification of strange attractors in terms of an associated linking matrix.

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Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen Sep 1991

Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

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The Arboricity Of The Random Graph, Paul A. Catlin, Zhi-Hong Chen Sep 1991

The Arboricity Of The Random Graph, Paul A. Catlin, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

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Some Complex Grassmannian Manifolds That Do Not Fibre Nontrivially, John Ferdinands Aug 1991

Some Complex Grassmannian Manifolds That Do Not Fibre Nontrivially, John Ferdinands

University Faculty Publications and Creative Works

A finite CW complex X is said to be prime if, given a Hurewicz fibration F→E→B with E homotopy equivalent to X, and B and F homotopy equivalent to finite CW complexes, either B or F is contractible. We show that certain 3- and 4-plane complex Grassmanian manifolds are prime. © 1991.

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Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman Aug 1991

Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

We discuss various results on the number of commuting pairs and the sizes of the centralizers of a group.

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Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li Aug 1991

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

Mathematics and Statistics Faculty Publications

No abstract provided.

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A Result On Dillon's Conjecture In Difference Sets, James A. Davis Jul 1991

A Result On Dillon's Conjecture In Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

Dillon has conjectured that any group of order 22d+2 with a normal subgroup isomorphic to Z2d+1 will have a difference set. He was able to show that this is true if the subgroup is central: this paper extends that idea to noncentral subgroups.

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Difference Sets In Abelian 2-Groups, James A. Davis Jul 1991

Difference Sets In Abelian 2-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

Examples of difference sets are given for large classes of abelian groups of order 22d + 2. This fills in the gap of knowledge between Turyn's exponent condition and Dillon's rank condition. Specifically, it is shown thatℤ/(2d)×ℤ/(2d+2) andℤ/(2d+1)×Z/(2d+1) both admit difference sets, and these have many implications.

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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 Jul 1991

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 …

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Integer Triangles With Rational Medians, Bart Goddard, Dale Mesner Jul 1991

Integer Triangles With Rational Medians, Bart Goddard, Dale Mesner

Mathematical Sciences Technical Reports (MSTR)

A characterization of all integer-sided triangles with a rational median is given, similar to the categorization of Pythagorean triangles. An infinite family of integer-sided triangles with two rational medians is given, along with several examples of three rational medians. All examples come from solutions to systems of quadratic Diophantine equations.

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Corrigendum To "Taxonomies Of Model-Theoretically Defined Topological Properties", Paul Bankston Jun 1991

Corrigendum To "Taxonomies Of Model-Theoretically Defined Topological Properties", Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

An error has been found in the cited paper; namely, Theorem 3.1 is false.

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C. S. Lewis, George Macdonald, And Mathematics, David L. Neuhouser May 1991

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.

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Using Mathematics To Teach Calculus, Russell W. Howell May 1991

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 …

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Cantor's Concept Of Infinity: Implications Of Infinity For Contingence, Bruce A. Hedman May 1991

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 …

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Can Mathematical Methods Yield Theological Truth?, Jan De Koning May 1991

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.

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A Tale Of Two Mathematicians, Robert Brabenec May 1991

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.

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How Has Christian Theology Furthered Mathematics?, Gene B. Chase May 1991

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.

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Reviving The Argument From Design: Detecting Design Through Small Probabilities, William A. Dembski May 1991

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, …

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Introduction (1991), Robert Brabenec May 1991

Introduction (1991), Robert Brabenec

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

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

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

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

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

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

ACMS Conference Proceedings 1991

An Eighth Conference on Mathematics from a Christian Perspective

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Give Saxon The Ax!, Calvin Jongsma May 1991

Give Saxon The Ax!, Calvin Jongsma

Faculty Work Comprehensive List

No abstract provided.

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The Theorms Of The Alternative, Kathryn L. Balsman '91 May 1991

The Theorms Of The Alternative, Kathryn L. Balsman '91

Honors Projects

In layman's terms, a Theorem of the Alternative is a theorem which states that given two conditions, one of the two conditions is true. It further states that if one of those conditions fails to be true, then the other condition must be true. Mathematically, this does not give a very clear picture of this group of theorems, however. Katta Murty defines a typical Theorem of the Alternative as one which shows that corresponding to any given system of linear constraints, system I, there is another associated system of linear constraints, system II, based on the same data, satisfying the …

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An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg May 1991

An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg

Mathematical Sciences Technical Reports (MSTR)

An ordered triple of group elements (x,y,z) is said to be rewriteable if the product xyz is equal to one of the products xzy, yxz, yzx, zxy, zyx. In the present paper, we shall ask the following question: how rewriteable can a finite group be if its derived group has order greater than 2?

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Σary, Moorhead State University, Mathematics Department May 1991

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

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A Simple Proof Of Zorn's Lemma, Jonathan W. Lewin Apr 1991

A Simple Proof Of Zorn's Lemma, Jonathan W. Lewin

Faculty and Research Publications

No abstract provided.

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