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Articles 6931 - 6960 of 7991

Full-Text Articles in Physical Sciences and Mathematics

A Greater Tantalizer, Andrew Simoson May 2003

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.

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What Is A Random Event? A Project For Finite Math Or Statistics, Jeremy Case May 2003

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.

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Sos Checks And Career Management, Russell W. Howell May 2003

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.

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Mathematical Models And Reality, John Byl May 2003

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 …

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Integrating Laptops Into A Mathematics Curriculum, Mary Wagner-Krankel May 2003

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.

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Linear Regression As A 1-Variable Optimization Exercise, Ken Constantine May 2003

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.

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Exploiting The Confidence Interval-Hypothesis Test Equivalence In Basic Statistics Classes, Ken Constantine May 2003

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.

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A Christian Appraisal Of Stephan Wolfram's A New Kind Of Science, Gene B. Chase May 2003

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.

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Creationism - A Viable Philosophy Of Mathematics, Jonathan Zderad May 2003

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, …

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Making Connections: Using Analogies To Enrich Understanding Of Mathematical Ideas And Biblical Truths, Ron Benbow May 2003

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.

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Mathematics, Science, And George Macdonald, David L. Neuhouser May 2003

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 …

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Men Are From The Server Side, Women Are From The Client Side: A Biblical Perspective On Men, Women And Computer Science, Kim Potter Kihlstrom May 2003

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 …

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

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

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

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

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

ACMS Conference Proceedings 2003

Fourteenth Conference of the Association of Christians in the Mathematical Sciences

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

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

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A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou May 2003

A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In the analysis of observational studies, propensity score subclassification has been shown to be a powerful method for adjusting unbalanced covariates for the purpose of causal inferences. One practical difficulty in carrying out such an analysis is to obtain a correct variance estimate for such inferences, while reducing bias in the estimate of the treatment effect due to an imbalance in the measured covariates. In this paper, we propose a bootstrap procedure for the inferences concerning the average treatment effect; our bootstrap method is based on an extension of Efron’s bias-corrected accelerated (BCa) bootstrap confidence interval to a two-sample problem. …

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Reply To "Comment On ‘Atomic Spectral Line Free-Parameter Deconvolution Procedure’”, Vladimir Milosavljevic, Goran Poparic May 2003

Reply To "Comment On ‘Atomic Spectral Line Free-Parameter Deconvolution Procedure’”, Vladimir Milosavljevic, Goran Poparic

Articles

We do not agree with the authors of the preceding Comment [X. Nikolic, X. Ojurovic, and X. Mijatovic, Phys. Rev. E, 67, 058401, 2003]. Our numerical procedure for the deconvolution of the theoretical asymmetric convolution integral of a Gaussian and a plasma broadened spectral line profile jA,R(λ) for spectral lines enables the determination of all broadening parameters. All broadening parameters can be determined directly from the recorded line profile of a single line, with minimal assumptions or prior knowledge. Additional experimental diagnostics are not required.

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The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi May 2003

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 u1,t = u1,xx − uα1 uβ2, u2,t = du2,xx+ uα1 uβ2 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.

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The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi May 2003

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 u1,t = u1,xx − uα1 uβ2, u2,t = du2,xx+ uα1 uβ2 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.

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Applications Of List Decoding To Tracing Traitors, Alice Silverberg, Jessica Staddon, Judy L. Walker May 2003

Applications Of List Decoding To Tracing Traitors, Alice Silverberg, Jessica Staddon, Judy L. Walker

Department of Mathematics: Faculty Publications

We apply results from algebraic coding theory to solve problems in cryptography, by using recent results on list decoding of error-correcting codes to efficiently find traitors who collude to create pirates. We produce schemes for which the TA (traceability) traitor tracing algorithm is very fast. We compare the TA and IPP (identifiable parent property) traitor tracing algorithms, and give evidence that when using an algebraic structure, the ability to trace traitors with the IPP algorithm implies the ability to trace with the TA algorithm. We also demonstrate that list decoding techniques can be used to find all possible pirate coalitions. …

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The Numerical Design Of A Parallel Plate Flow Chamber For Investigation Of Endothelial Cell Response To Shear Stress, Bong Jae Chung, A. M. Robertson, D. G. Peters May 2003

The Numerical Design Of A Parallel Plate Flow Chamber For Investigation Of Endothelial Cell Response To Shear Stress, Bong Jae Chung, A. M. Robertson, D. G. Peters

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Parallel plate chambers are frequently used to examine the response of biological cells to a constant wall shear stress. However, the stress can vary more than 80% across the chamber due to end effects. Earlier estimates of the magnitude of this inhomogeneity used boundary layer theory and experiments. Here, the full equations for steady, three-dimensional flow in a novel parallel plate device were solved numerically and used to identify an active test region where the shear stress is within 5% of a constant value. Endothelial cells can be confined to this region to assure a nearly uniform shear stress exposure.

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Subdifferential And Superdifferential Optimality Conditions In Nonsmooth Minimization, Boris S. Mordukhovich Apr 2003

Subdifferential And Superdifferential Optimality Conditions In Nonsmooth Minimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns first-order necessary optimality conditions for problems of minimizing nonsmooth functions under various constraints in infinite-dimensional spaces. Based on advanced tools of variational analysis and generalized differential calculus, we derive general results of two independent types called subdifferential and superdifferential optimality conditions. The former ones involve basic/limiting subgradients of cost functions, while the latter conditions are expressed via Frechet superdifferentials provided that they are not empty. All the superdifferential and major subdifferential optimality conditions obtained in the paper are new even in finite dimensions. We give applications of general optimality conditions to mathematical programs with equilibrium constraints.

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Intuitive Black-Scholes Option Pricing With A Simple Table, Tom Arnold, Terry D. Nixon, Richard L. Shockley Jr. Apr 2003

Intuitive Black-Scholes Option Pricing With A Simple Table, Tom Arnold, Terry D. Nixon, Richard L. Shockley Jr.

Finance Faculty Publications

The Black-Scholes option pricing model (1973) can be intimidating for the novice. By rearranging and combining some of the variables, one can reduce the number of parameters in the valuation problem from five to two: 1) the option's moneyness ratio and 2) its time-adjusted volatility. This allows the computationally complex Black-Scholes formula to be collapsed into an easy-to-use table similar to those in some popular textbooks. The tabular approach provides an excellent tool for building intuition about the comparative statics in the Black-Scholes equation. Further, the pricing table can be used to price options on dividend-paying stocks, commodities, foreign exchange …

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Visualizing The Stochastic Calculus Of Option Pricing With Excel And Vba, Tom Arnold, Stephen C. Henry Apr 2003

Visualizing The Stochastic Calculus Of Option Pricing With Excel And Vba, Tom Arnold, Stephen C. Henry

Finance Faculty Publications

Stochastic calculus, part calculus and part statistics, is an integral part of option pricing that can be intimidating. By developing the statistical nature of stochastic processes and introducing Monte Carlo simulation using Microsoft Excel, this paper develops a visualization of how stochastic processes are evaluated using Ito's lemma and integral calculus. Ultimately, the Black-Scholes (1973) option pricing equation is the natural result.

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Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten Mar 2003

Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten

UW Biostatistics Working Paper Series

PCR-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive" yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity when the target number is 0). However, estimating this "sensitivity curve" is problematic since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle …

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Simple Parallel Statistical Computing In R, Anthony Rossini, Luke Tierney, Na Li Mar 2003

Simple Parallel Statistical Computing In R, Anthony Rossini, Luke Tierney, Na Li

UW Biostatistics Working Paper Series

Theoretically, many modern statistical procedures are trivial to parallelize. However, practical deployment of a parallelized implementation which is robust and reliably runs on different computational cluster configurations and environments is far from trivial. We present a framework for the R statistical computing language that provides a simple yet powerful programming interface to a computational cluster. This interface allows the development of R functions that distribute independent computations across the nodes of the computational cluster. The resulting framework allows statisticians to obtain significant speed-ups for some computations at little additional development cost. The particular implementation can be deployed in heterogeneous computing …

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Literate Statistical Practice, Anthony Rossini, Friedrich Leisch Mar 2003

Literate Statistical Practice, Anthony Rossini, Friedrich Leisch

UW Biostatistics Working Paper Series

Literate Statistical Practice (LSP, Rossini, 2001) describes an approach for creating self-documenting statistical results. It applies literate programming (Knuth, 1992) and related techniques in a natural fashion to the practice of statistics. In particular, documentation, specification, and descriptions of results are written concurrently with writing and evaluation of statistical programs. We discuss how and where LSP can be integrated into practice and illustrate this with an example derived from an actual statistical consulting project. The approach is simplified through the use of a comprehensive, open source toolset incorporating Noweb, Emacs Speaks Statistics (ESS), Sweave (Ramsey, 1994; Rossini, et al, 2002; …

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Pareto Optimal Allocations In Nonconvex Models Of Welfare Economics, Boris S. Mordukhovich Mar 2003

Pareto Optimal Allocations In Nonconvex Models Of Welfare Economics, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern variational analysis to the study of Pareto (as well as weak and strong Pareto) optimal allocations in nonconvex models of welfare economics with infinite-dimensional commodity spaces. Our basic tool is the extremal principle of variational analysis that provides necessary conditions for set extremality and may be viewed as a variational extension of the classical convex separation principle to the case of nonconvex sets. In this way we obtain new versions of the generalized second welfare theorem for nonconvex economies in terms of appropriate concepts of normal cones.

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Shortest Path Problems In A Stochastic And Dynamic Environment, Jae Il Cho Mar 2003

Shortest Path Problems In A Stochastic And Dynamic Environment, Jae Il Cho

Theses and Dissertations

In this research, we consider stochastic and dynamic transportation network problems. Particularly, we develop a variety of algorithms to solve the expected shortest path problem in addition to techniques for computing the total travel time distribution along a path in the network. First, we develop an algorithm for solving an independent expected shortest path problem. Next, we incorporate the inherent dependencies along successive links in two distinct ways to find the expected shortest path. Since the dependent expected shortest path problem cannot be solved with traditional deterministic approaches, we develop a heuristic based on the K-shortest path algorithm for this …

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Redundant Discrete Wavelet Transform Based Super-Resolution Using Sub-Pixel Image Registration, Daniel L. Ward Mar 2003

Redundant Discrete Wavelet Transform Based Super-Resolution Using Sub-Pixel Image Registration, Daniel L. Ward

Theses and Dissertations

The limited resolution of video imagery taken by aircraft, over geographical areas of interest, hinders the accurate extraction of useful information. The frame resolution of the video is determined by the camera that created it. Information exists about the camera which can be used to increase frame resolution beyond the resolution capability of the camera. This is achieved by a process called super-resolution, which uses multiple low-resolution video frames to create one high-resolution image.

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