Physical Sciences and Mathematics Commons^™

Optimization For Source Localization And Geoacoustic Inversion In Underwater Acoustics, Urmi Ghosh-Dastidar

Dissertations

Matched-field inversion techniques are widely used for source localization and geoacoustic parameter estimation. These inversion methods correlate the received data with modeled data and find the model parameters which provide the maximum correlation. However, when a large number of unknown parameters is involved, many modeled data need to be generated and correlated with the observed data and thus, matched-field inversion can be computationally intensive. An optimization process applied to matched-field inversion is often required to accelerate the inversion process.

In this work, tabu is applied to matched-field inversion for source localization and environmental parameter estimation. Tabu is a global optimization …

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 …

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.

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.

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.

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.

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 …

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.

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.

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.

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, …

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.

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 …

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 …

Introduction (2003), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

Aspects Of Financial Dualism In Less Developed Country., Rajalaxmi Mallik Dr.

Doctoral Theses

One significant aspect of the economic dualism that characterises less developed countries (LDCS) is financial dualism. This is manifested through the co-existence of formal-lenders (FLs) and informal-lenders (ILs), in the credit markets of LDCS, which stands in stark contrast to the integrated, organised and efficiently functioning credit markets of the developed countries. FLs refer to the large institutional lenders, like commercial banks and other government owned banks that are subject to various central bank regulations. The ILs on the other hand are a heterogeneous lot and consist of non-institutional lenders like indigenous bankers, moneylenders, traders, landlords etc., who are outside …

Schedule (2003), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2003), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

Combinatorial Techniques For Digital Image Charecterization And Retrieval:Algorithms,Architectures,And Applications., Arijit Bishnu Dr.

Doctoral Theses

Interest in digital images stems mostly from its application to various areas of computer vision [33, 57] and pattern recognition [145). Problems include robotic vision and con- trol, geographic and topographic map matching, target recognition, space applications, character recognition, scene analysis, fingerprint and face recognition, etc. Lately, with the advent of content-based image retrieval (CBIR) and proliferation of the Internet, digital imaging applications are in vogue now than ever before. In almost all the cases, the data size is enormously large, and at the same time, fast on-line as well as real- time computation is needed. For example, in fingerprint …

You Think You’Ve Got Trivials?, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Effect sizes are important for power analysis and meta-analysis. This has led to a debate on reporting effect sizes for studies that are not statistically significant. Contrary and supportive evidence has been offered on the basis of Monte Carlo methods. In this article, clarifications are given regarding what should be simulated to determine the possible effects of piecemeal publishing trivial effect sizes.

Trivials: The Birth, Sale, And Final Production Of Meta-Analysis, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

The structure of the first invited debate in JMASM is to present a target article (Sawilowsky, 2003), provide an opportunity for a response (Roberts & Henson, 2003), and to follow with independent comments from noted scholars in the field (Knapp, 2003; Levin & Robinson, 2003). In this rejoinder, I provide a correction and a clarification in an effort to bring some closure to the debate. The intension, however, is not to rehash previously made points, even where I disagree with the response of Roberts & Henson (2003).

A Different Future For Social And Behavioral Science Research, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

The dissemination of intervention and treatment outcomes as effect sizes bounded by conf idence intervals in order to think meta-analytically was promoted in a recent article in Educational Researcher. I raise concerns with unfettered reporting of effect sizes, point out the con in confidence interval, and caution against thinking meta-analytically. Instead, cataloging effect sizes is recommended for sample size estimation and power analysis to improve social and behavioral science research.

Statistical Pronouncements, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi

Yi Li

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u_1,t = u_1,xx − u^α₁ u^β₂, u_2,t = du_2,xx+ u^α₁ u^β₂ with non-negative initial data, where the exponents α,β satisfy 1<α,β<2, α+β = 3 and the constant d>0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Stability Of Hyperbolic And Nonhyperbolic Fixed Points Of One-Dimensional Maps, Fozi M. Dannan, Saber Elaydi, Vadim Ponomarenko

Mathematics Faculty Research

We present a complete theory for the stability of non-hyperbolic fixed points of one-dimensional continuous maps. As well as we give simple criteria for the global stability of general maps without using derivatives.

The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi

Mathematics and Statistics Faculty Publications

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u_1,t = u_1,xx − u^α₁ u^β₂, u_2,t = du_2,xx+ u^α₁ u^β₂ with non-negative initial data, where the exponents α,β satisfy 1<α,βd>0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.

Finite Element Studies In Metal Cutting, Suhail Ahmed

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

AdvantEdge is a finite element software package that integrates advanced dynamics, thermo-mechanically coupled finite element numerics and material modelling appropriate for machining processes. AdvantEdge allows users to specify the workpiece material, tool geometry and cutting conditions. It then provides accurate estimates of thermo-mechanical properties of machining processes such as cutting forces, chip morphology, machined surface residual stresses and temperature behavior of the tool and the workpiece. We will use AdvantEclge to investigate two areas of interest in metal cutting: process clamping via crushing of workpiece material and drilling of metal stacks.

Test Suite For Multiobjective Optimization And Results Using Normal Boundary Intersection (Nbi) In Design Explorer, Siva Kumar Natarajan

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Several methods have been developed to solve multiobjective optimization problems (MOP's). One of these, Normal Boundary Intersection (NBI), is a method developed by John Dennis and Indraneel Das. NBI is used at The Boeing Company as a tool to solve MOP's. This report presents a test suite of MOP's that I developed for Boeing during me internship in summer 2003.

The problems in the test suite were chosen to represent the different types of multiobjective optimization problems that could arise in practice and the complexities involved in solving them. These problems range from those that have nice convex Pareto surfaces …