Applied Mathematics Commons^™

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

Rewriteability In Finite Groups, Judy Leavitt Walker, G. J. Sherman, Mark E. Walker

Department of Mathematics: Faculty Publications

What's the probability that two elements in a finite group commute? A formal answer,

Pr₂(G) = {(x, y) [element of] G² |xy = yx}| / |G|²

begs our next question. How many ordered pairs of elements of a finite group commute?

A Note On The Connectedness Problem For Nest Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

It has been conjectured that a certain operator T belonging to the group ff of invertible elements of the algebra Alg Z of doubly infinite uppertriangular bounded matrices lies outside the connected component of the identity in W. In this note we show that T actually lies inside the connected component of the identity of & .

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.

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 …

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 …

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

On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger

All HMC Faculty Publications and Research

A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments.

A Double Chain Of Coupled Circuits In Analogy With Mechanical Lattices, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

A unitary transformation obtained from group theoretical considerations is applied to the problem of finding the resonant frequencies of a system of coupled LC-circuits. This transformation was previously derived to separate the equations of motion for one dimensional mechanical lattices. Computations are performed in matrix notation. The electrical system is an analog of a pair of coupled linear lattices. After the resonant frequencies have been found, comparisons between the electrical and mechanical systems are noted.

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 …

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

Mathematics and Statistics Faculty Publications

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist 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. The n, finite …

Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient …

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh

Mathematics and Statistics Faculty Publications

The Berry-Esseen-type bounds of order N^−1/2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.

Rewriteable Sequencings Of Groups, Jeanne Nielsen

Mathematical Sciences Technical Reports (MSTR)

A finite group is called P_n-sequenceable if its nonidentity elements can be listed x₁ , x₂ , ..., x_k so that the product x _i x _i+i · · · x _i+n-1 can be rewritten in at least one nontrivial way for all i. It is shown that S_n , A_n , D_n are P₃-sequenceable, that every finite simple group is P₄ -sequenceable, and that every finite group is P_s-sequenceable. It is conjectured that every finite group is P₃-sequenceable.

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …