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Articles 1 - 30 of 112
Full-Text Articles in Mathematics
How To Pick Out The Integers In The Rationals: An Application Of Number Theory To Logic, Daniel Flath, Stan Wagon
How To Pick Out The Integers In The Rationals: An Application Of Number Theory To Logic, Daniel Flath, Stan Wagon
Stan Wagon, Retired
No abstract provided.
Undergraduates, The Right Questions, And Cayley Produce Results, Gary J. Sherman
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.
Convection In The Melt, John Bryant Drake
Convection In The Melt, John Bryant Drake
Doctoral Dissertations
A physical problem involving the melting/freezing of a phase-change material (PCM) is the applied setting of this research. The development of models that couple the partial differential equations for energy transport and fluid motion with phases of differing densities is a primary goal of the research. In Chapter 2, a general framework is developed for the formulation of conservation laws that admit interfaces. A notion of weak solution is developed and its relation with classical and other weak formulations is discussed. Conditions that hold across various kinds of interfaces are also developed. The formulation is examined for the conservation of …
Linear Algebra By Analogy, Scott H. Hochwald
Characterization Of Knot Complements In The 4-Sphere, Vo Thanh Liem, Gerard A. Venema
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.
More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic
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.
How To Pick Out The Integers In The Rationals - An Application Of Number-Theory To Logic, D. Flath, Stan Wagon
How To Pick Out The Integers In The Rationals - An Application Of Number-Theory To Logic, D. Flath, Stan Wagon
Stan Wagon, Retired
No abstract provided.
Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic
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.
Templates And Framed Braids, Paul Melvin, N. B. Tufillaro
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.
Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen
Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen
Scholarship and Professional Work - LAS
No abstract provided.
The Arboricity Of The Random Graph, Paul A. Catlin, Zhi-Hong Chen
The Arboricity Of The Random Graph, Paul A. Catlin, Zhi-Hong Chen
Scholarship and Professional Work - LAS
No abstract provided.
Some Complex Grassmannian Manifolds That Do Not Fibre Nontrivially, John Ferdinands
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.
Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman
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.
Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li
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
Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
On Some Problems In Analysis Of Covariance Structure., Sadhan Samar Maiti Dr.
On Some Problems In Analysis Of Covariance Structure., Sadhan Samar Maiti Dr.
Doctoral Theses
In recent years, the teahniques of struotural analynie of covarianoe and correlation matrioes have frequently be en employed espeed ally in the s ooial and behavioural soieno es for analysing multivariate data. Analysis of covarlance structures (ACOVS) lea; generie tem describing a variety of statistioal procedures for testing and measuring the goodnese-of-fit of certain types of struotures postulated a priori for the cova- riance matrix by plaoing al temative restriotione on the para- neter natrioes of the general model" [Mukherjee, 1976, p. 132].The aoronyn AOOVS' standa for; analyeis of covarianoe atructurea; and waa firat proposed by Book (1960) as a …
A Result On Dillon's Conjecture In Difference Sets, James A. Davis
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.
Difference Sets In Abelian 2-Groups, James A. Davis
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.
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
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 …
Integer Triangles With Rational Medians, Bart Goddard, Dale Mesner
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.
On Shock Capturing For Liquid And Gas Media, Tze Jang Chen
On Shock Capturing For Liquid And Gas Media, Tze Jang Chen
Mathematics & Statistics Theses & Dissertations
The numerical investigation of shock phenomena in gas or liquid media where a specifying relation for internal energy is absent poses special problems. Classically, for gas dynamics the usual procedure is to employ a splitting scheme to remove the source terms from the Euler equations, then up-wind biased shock capturing algorithms are built around the Riemann problem for the system which remains. However, in the case where the Euler equations are formulated in the term of total enthalpy, a technical difficulty associated with equation splitting forces a pressure time derivative to be treated as a source term. This makes it …
The Solution Of A Singular Integral Equation Arising From A Lifting Surface Theory For Rotating Blades, Mark H. Dunn
The Solution Of A Singular Integral Equation Arising From A Lifting Surface Theory For Rotating Blades, Mark H. Dunn
Mathematics & Statistics Theses & Dissertations
A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied …
Corrigendum To "Taxonomies Of Model-Theoretically Defined Topological Properties", Paul Bankston
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.
C. S. Lewis, George Macdonald, And Mathematics, David L. Neuhouser
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
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
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
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
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
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
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, …