Applied Mathematics Commons^™

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Mathematics and Statistics Faculty Publications

In this paper, we study the following Duffing-type equation:

x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

Optimization And Equilibrium Problems With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns optimization and equilibrium problems with the so-called equilibrium constraints (MPEC and EPEC), which frequently appear in applications to operations research. These classes of problems can be naturally unified in the framework of multiobjective optimization with constraints governed by parametric variational systems (generalized equations, variational inequalities, complementarity problems, etc.). We focus on necessary conditions for optimal solutions to MPECs and EPECs under general assumptions in finite-dimensional spaces. Since such problems are intrinsically nonsmooth, we use advanced tools of generalized differentiation to study optimal solutions by methods of modern variational analysis. The general results obtained are concretized for special …

When Abelian Groups Split, Rachel M. Thomas, Robert C. Rhoades

Mathematical Sciences Technical Reports (MSTR)

Let S be a hyperbolic surface tiled by kaleidoscopic triangles. Let R_e denote the set of fixed points by the reflection in an edge, e, of a triangle. We say that R_e is separating if S-R_e has two components. Once we have a tiling, we can define a group of orientation preserving transformations, G. We develop a method for determining when a reflection is separating using the group algebra of G. Using this method we give necessary and sufficient conditions for a mirror to be separating when G is abelian. We also conjecture, that …

Optimal Control Of Differential-Algebraic Inclusions, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

No abstract provided.

On Adaptive Estimation In Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss

Mathematics and Statistics Faculty Publications

A simple method is provided to construct a general class of individual and simultaneous confidence intervals for the effects in orthogonal saturated designs. These intervals use the data adaptively, maintain the confidence levels sharply at 1 - α at the least favorable parameter configuration, work effectively under effect sparsity, and include the intervals by Wang and Voss (2001) as a special case.

A Forward-Backward Fluence Model For The Low-Energy Neutron Boltzmann Equation, Gary Alan Feldman

Mathematics & Statistics Theses & Dissertations

In this research work, the neutron Boltzmann equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary differential equations (O.D.E.'s). Difference approximations were then used to recast the O.D.E.'s into a coupled system of linear equations that were solved for forward and backward neutron fluences. Adding forward and backward fluences gave the total fluence at selected energies and depths in the material. Neutron fluences were computed in single material shields and in a shield followed by a target …

Natural Superconvergent Points Of Triangular Finite Elements, Zhimin Zhang, Runchang Lin

Mathematics Research Reports

In this work, we analytically identify natural superconvergent points of function values and gradients for triangular elements. Both the Poisson equation and the Laplace equation are discussed for polynomial finite element spaces (with degrees up to 8) under four different mesh patterns. Our results verify computer findings of [2], especially, we confirm that the computed data have 9 digits of accuracy with an exception of one pair (which has 8-7 digits of accuracy). In addition, we demonstrate that the function value superconvergent points predicted by the symmetry theory [14] are the only superconvergent points for the Poisson equation. Finally, we …

On The Stability Of The Positive Radial Steady States For A Semilinear Cauchy Problem, Yinbin Deng, Yi Li, Yi Liu

Mathematics and Statistics Faculty Publications

No abstract provided.

Orthogonal Macroelement Scaling Vectors And Wavelets In 1-D, Douglas P. Hardin, Bruce Kessler

Mathematics Faculty Publications

We develop a {\em macroelement} based technique for constructing orthogonal univariate multiwavelets. We illustrate the technique with two examples. In the first example we provide a new construction of the symmetric, orthogonal, continuous scaling vector given in \cite{GHM}. In the second example, we construct a continuous orthogonal scaling vector with three components. The components of this scaling vector are symmetric or antisymmetric and provide approximation order 3, (equivalently, the components of $\Psi$ are orthogonal to polynomials of degree 2 or less.) We believe this second example to be new.

New Graphical Approach On The Analysis Of Experimental Data, Suha Sari

Dissertations

This study presents a new graphical method to identify significant effects in factorial experiments. The proposed methods are obtained for the different cases in which the design can be of full factorial or fractional factorial and the factor levels can be pure or mixed.

We focus on the different decomposition methods, for example orthogonal components system and orthogonal contrast method, to make use of the chisquare plot which requires that the sums of squares are of the same degrees of freedom. Examples and simulations illustrating the different cases of the procedure are presented.

Validation Of The A Posteriori Error Estimator Based On Polynomial Preserving Recovery For Linear Elements, Zhimin Zhang, Ahmed Naga

Mathematics Research Reports

In this paper the quality of the error estimator based on the Polynomial Preserving Recovery (PPR) is investigated using the computer-based approach proposed by Babiiska et al. A comparison is made between the error estimator based on the PPR and the one based on the Superconvergence Patch Recovery (SPR). It was found that the PPR is at least as good as the SPR.

Sos Checks And Career Management, Russell W. Howell

ACMS Conference Proceedings 2003

This paper compares the careers of King Saul and King David in the Bible and how they inform the career management methods of a Christian.

A Christian Appraisal Of Stephan Wolfram's A New Kind Of Science, Gene B. Chase

ACMS Conference Proceedings 2003

Wolfram exposes some ideas about informatics that relate to Christian Scholarship: Does Wolfram's definition of free will permit God to have free will? Will human souls resurrected to a new body–as described by St. Paul and Aquinas–by like software that is moved to new hardware? Jesus' incarnation as in-form-ation in the Aristotelian sense.

Linear Regression As A 1-Variable Optimization Exercise, Ken Constantine

ACMS Conference Proceedings 2003

Derivation of the least squares line for a set of bivariate data entails minimizing a function of two variables, say the line's slope and intercept. Imposing the requirement that the line pass through the mean point for the data reduces this problem to a 1-variable problem easily solved as a single-variable Calculus exercise. The solution to this problem is, in fact, the solution to the more general problem. We illustrate with a dataset involving charitable donations.

Exploiting The Confidence Interval-Hypothesis Test Equivalence In Basic Statistics Classes, Ken Constantine

ACMS Conference Proceedings 2003

An emphasis is offered for the inference portion of an elementary Statistics course: the equivalence between confidence intervals and tests of hypotheses. This equivalence is rarely mentioned in basic texts but seems helpful to students. Student reference sheets which employ this equivalence are available on-line.

Making Connections: Using Analogies To Enrich Understanding Of Mathematical Ideas And Biblical Truths, Ron Benbow

ACMS Conference Proceedings 2003

Recent standards and research, published by mathematics education professional organizations, place a great emphasis on “connections” in all grade levels. Through this emphasis on interrelatedness, students begin to see the subject not as a collection of separate strands, but rather as an integrated field of study. When linkages between diverse domains of knowledge are formed (by comparing, contrasting, analyzing, and applying), we have increased the likelihood that we develop deeper understandings within both domains. This paper explores some specific examples of the use of analogies to connect mathematical and Biblical concepts.

What Is A Random Event? A Project For Finite Math Or Statistics, Jeremy Case

ACMS Conference Proceedings 2003

Randomization is an important idea in Finite Mathematics and Statistics. One main idea in these courses is that events that appear to be performed in a random fashion are often not random. Here we present a simple project involving "randomly" opening the Bible. This activity leads to deeper philosophical questions such as how to study the Bible and whether an event can be considered random if God intervenes.

Creationism - A Viable Philosophy Of Mathematics, Jonathan Zderad

ACMS Conference Proceedings 2003

The purpose of this essay is to try to answer the ontological and epistemological question of mathematics. Specifically, "What, if any, of mathematics exists in the objective sense?" And, "How do we as humans know that our knowledge of mathematics is correct?" These questions will be investigated by looking at the applications or mathematics, the practice of mathematicians, and most telling, the content of mathematics. Mathematics, admittedly, can only go so far in answering its own philosophical questions, even when aided by recent developments in the field of logic. The overwhelming evidence, as will be shown, points toward a theistic, …

A Greater Tantalizer, Andrew Simoson

ACMS Conference Proceedings 2003

The children’s puzzle, sometimes called the Great Tantalizer, consists of four blocks each of whose faces have been colored with four colors; a solution consists in stacking the blocks so that on each stack face, all four colors appear. This article renders the puzzle as six octahedral blocks, each of which is colored with six colors, and describes a scheme to successfully stack all six.

Light Meals And Morsels From Mathematics Magazine, Paul Zorn

ACMS Conference Proceedings 2003

No abstract provided.

General-Education Mathematics Course From A Christian Perspective, Saburo Matsumoto, Ph.D.

ACMS Conference Proceedings 2003

No abstract provided.

Some Fibonacci Gems, Peter Rothmaler

ACMS Conference Proceedings 2003

No abstract provided.

A Christian Perspective On Mathematics - History Of Mathematics And Study Guides, Johan H. De Klerk

ACMS Conference Proceedings 2003

No abstract provided.

Learning To Construct Proofs In A First Course On Mathematical Proof, Peter R. Atwood, Ph.D.

ACMS Conference Proceedings 2003

No abstract provided.

The Search For The Real Josephus Problem, Eric Gossett

ACMS Conference Proceedings 2003

Many of the problems that mathematicians and computer scientists dearly love have been around for a long time. One such problem is known as the Josephus Problem, named after the first century Jewish historian Flavius Josephus. Josephus did not invent the problem. Instead, an event from his life served as the inspiration for the problem statement. Many current books refer to "Mathematical Recreations and Essays" by W. W. Rouse Ball [originally published in 1892] for the problem statement. The problem is quite interesting (and will be solved here). However, the story, as quoted in Bell, is not completely accurate.

The Inverse Problem: Christianity Through A Mathematical Lens, Sharon K. Robbert

ACMS Conference Proceedings 2003

An inverse problem is a partner problem that reverses some type of direct problem. Usually the inverse problem is more challenging to solve than the direct problem: integration is more challenging than differentiation, factoring large numbers is more challenging than multiplying numbers. In this paper, the author poses that using mathematical thinking to understand the concepts of theological principles is the direct problem to the much more challenging inverse problem of using theological thinking to influence understanding in mathematics. Acknowledging that a problem is difficult allows one to be satisfied with understanding small pieces and progressing slowly to a complete …

Integrating Laptops Into A Mathematics Curriculum, Mary Wagner-Krankel

ACMS Conference Proceedings 2003

In 1999, St. Mary's University in San Antonio received a Title V Grant, providing $2.1 million over five years. The money was used to help finance computers for students, fund faculty training for computer-related curriculum, convert traditional classrooms into technology or "Smart classrooms", and upgrade the school's Internet connections. This article discusses specific software and hardware advancements made at the University through this grant. The article also describes how the Math department specifically integrated the laptops into their courses using software programs such as Mathcad and Blackboard.

Men Are From The Server Side, Women Are From The Client Side: A Biblical Perspective On Men, Women And Computer Science, Kim Potter Kihlstrom

ACMS Conference Proceedings 2003

The percentage of women in computer science is small and has decreased over the last twenty years. Why is this the case, when computer science is a wonderful and growing field with many opportunities? I believe that the situation has its roots in the basic differences between men and women, differences that were present from the beginning of creation and are a part of the way that God made male and female uniquely. In order to ensure that both talented men and women are attracted to computer science, we need to understand the differences between men and women, and how …

Mathematics, Science, And George Macdonald, David L. Neuhouser

ACMS Conference Proceedings 2003

In writing about George MacDonald choosing a college major, biographer William Raeper wrote that he chose “chemistry, a strange choice perhaps for a future novelist and poet and not an easy one for him to make.” He further conjectured that MacDonald’s choice was based on “common sense and sound economics” rather than “his poetic yearnings.” Many would agree with Raeper that science is a strange choice for a future poet and novelist. This paper argues that the role of beauty and imagination is very similar in science, mathematics, and literature, so it might not be so strange that someone could …

Mathematical Models And Reality, John Byl

ACMS Conference Proceedings 2003

This paper examines the nature and function of mathematical models, using illustrations from cosmology, space geometry and atomic physics. Mathematical models enable us to make precise calculations and predictions; they serve as analogies and conceptual frameworks that lead to new discoveries; and they bridge the gap between appearance and reality. Their success implies that the universe had a mathematical structure. However, one must be careful not to confuse models of reality with reality itself. A variety of models can represent the same data; any model can be given different physical interpretations. The choice of a model and its interpretation depends …