Mathematics Commons^™

Browder-Krasnoselskii-Type Fixed Point Theorems In Banach Spaces, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

We present some fixed point theorems for the sum A+B of a weakly-strongly continuous map and a nonexpansive map on a Banach space X. Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.

Determining The Success Of Ncaa Basketball Teams Through Team Characteristics, Raymond Witkos

Honors Projects in Mathematics

Every year much of the nation becomes engulfed in the NCAA basketball postseason tournament more affectionately known as “March Madness.” The tournament has received the name because of the ability for any team to win a single game and advance to the next round. The purpose of this study is to determine whether concrete statistical measures can be used to predict the final outcome of the tournament. The data collected in the study include 13 independent variables ranging from the 2003-2004 season up until the current 2009-2010 season. Different tests were run in an attempt to achieve the most accurate …

Bytes Of Π, Spring 2010, Department Of Mathematics And Computer Science, Bridgewater State College

Department of Mathematics Newsletter

No abstract provided.

Regressive Functions On Pairs, Andrés Eduardo Caicedo

Mathematics Faculty Publications and Presentations

We compute an explicit upper bound for the regressive Ramsey numbers by a combinatorial argument, the corresponding function being of Ackermannian growth. For this, we look at the more general problem of bounding g(n, m), the least l such that any regressive function ƒ: [m, l]^[2]→ℕ admits a min-homogeneous set of size n. Analysis of this function also leads to the simplest known proof that the regressive Ramsey numbers have rate of growth at least Ackermannian. Together, these results give a purely combinatorial proof that, for each m, g …

Least Squares Problems With Inequality Constraints As Quadratic Constraints, Jodi Mead, Rosemary A. Renaut

Mathematics Faculty Publications and Presentations

Linear least squares problems with box constraints are commonly solved to find model parameters within bounds based on physical considerations. Common algorithms include Bounded Variable Least Squares (BVLS) and the Matlab function lsqlin. Here, the goal is to find solutions to ill-posed inverse problems that lie within box constraints. To do this, we formulate the box constraints as quadratic constraints, and solve the corresponding unconstrained regularized least squares problem. Using box constraints as quadratic constraints is an efficient approach because the optimization problem has a closed form solution.

The effectiveness of the proposed algorithm is investigated through solving three …

Signal Recovery From Inaccurate And Incomplete Measurements Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin

CMC Faculty Publications and Research

We demonstrate a simple greedy algorithm that can reliably recover a vector v ?? ??d from incomplete and inaccurate measurements x = ??v + e. Here, ?? is a N x d measurement matrix with Nv with O(n) nonzeros from its inaccurate measurements x in at most n iterations, where each iteration amounts to solving a least squares problem. The noise level of the recovery is proportional to ??{logn} ||e||2. In particular, if the error term e vanishes the reconstruction is exact.

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Detecting Malicious Javascript, Matthew F. Der

Honors Theses

The increased use of the World Wide Web and JavaScript as a scripting language for Web pages have made JavaScript a popular attack vector for infecting users' machines with malware. Additionally, attackers often obfuscate their code to avoid detection, which heightens the challenge and complexity of automated defense systems. We present two analyses of malicious scripts and suggest how they could be extended into intrusion detection systems. For our analyses we use a sample of deobfuscated malicious and benign scripts collected from actual Web sites. First, using our malicious sample, we perform a manual analysis of attack signatures, identifying four …

On Calculating Residuated Approximations And The Structure Of Finite Lattices Of Small Width, Wu Feng

Doctoral Dissertations

The concept of a residuated mapping relates to the concept of Galois connections; both arise in the theory of partially ordered sets. They have been applied in mathematical theories (e.g., category theory and formal concept analysis) and in theoretical computer science. The computation of residuated approximations between two lattices is influenced by lattice properties, e.g. distributivity.

In previous work, it has been proven that, for any mapping f : L → [special characters omitted] between two complete lattices L and [special characters omitted], there exists a largest residuated mapping ρf dominated by f, and the notion of "the shadow …

Section Abstracts: Astronomy, Mathematics, And Physics & Materials Science

Virginia Journal of Science

Abstracts of papers of the Astronomy, Mathematics, and Physics (Including Materials Science) Section for the 88th Annual Meeting of the Virginia Academy of Science, May 20-21, 2010, James Madison University, Harrisonburg, VA.

Problem Solving Based Instruction In The High School Mathematics Classroom, Lawrence Vettleson, Jr.

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of problem solving in classroom instruction. It covers the stages of problems solving as listed by George Polya and how they can be used to enhance mathematics instruction. This research paper will identify that problem solving is a need based on Minnesota state mathematics standards and National mathematics standards. Covered in this paper is the research on the effects of mathematics instruction using problem solving. The research covers some of the benefits to student education if students learn mathematics using a problem solving based approach to classroom instruction.

Volume 03, Cheryl Peck, Charles Hoever, Longwood Theater Department, Brittany Anderson, J. Ervin Sheldon, Richard Hayden, Yuri Calustro, Candice Fleming, Rebecca Franklin, Ashley Yocum, Danielle M. Jagoda, Cristina M. Valdivieso, Jameka Jones, Amy Ellis, Ashley Maser, Erikk Shupp, Jamie Yurasits, Joshua Davis, Alexander Leonhart, Kenny Wolfe, Sally Meadows, J. Haley, Amy Jackson, Morgan Howard, Adrienne Heinbaugh, Melissa Dorton, Ciarra Stalker

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Little Shop of Horrors by Longwood Theater Department

Who Has the Hottest Hotsauce in Farmville: A Quantitative Comparison of Sauces from Local Restaurants by Cheryl Peck and Charles Hoever

Precipitation Effects on the Growth of White Oaks and Virginia Pines on the Mt. Vernon Plantation by Brittany Anderson

Design and Synthesis of Novel Ion Binding Molecules for Self-Assembly and Sensing Applications by J. Ervin Sheldon

A Statistical Analysis of Algorithms for Playing SameGame by Richard Hayden

Intersecting Cylinders at Arbitrary Angles by Yuri Calustro

Putting a Foot in the Revolving Door: Strategies for Reducing …

A Discrete Nonlinear Model Of Resonant Scattering, Katherine Hollister Smith

Honors Capstones

No abstract provided.

Representing Propositional Logic Connectives With Modular Polynomials, Shawn Davis

McNair Scholars Research Journal

This paper explores the relationship between n-valued propositional logic connectives and modular polynomials. Namely the representing of logic connectives using modular polynomials. The case for n = 2 is explored and a method is developed for finding the coefficients of the unique polynomial that represents any given binary logic connective. Examples are then given for using the modular polynomial representations of connectives to determine the validity of propositional arguments. A similar procedure is shown for when n = 3 and an evaluation of the axioms of Łukasiewicz’s 3-valued logic is given using modular polynomials. The general case is explored to …

Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina

Mathematics Research Reports

Abstract. We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in (4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

On The Non-Existence Of A Projective (75, 4,12, 5) Set In Pg(3, 7), Aaron C.S. Chan, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound.

Importance Sampling For Dispersion-Managed Solitons, Elaine T. Spiller, Gino Biondini

Mathematics, Statistics and Computer Science Faculty Research and Publications

The dispersion-managed nonlinear Schrödinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest—large phase or amplitude variations—are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that …

Non Bayesian Conditioning And Deconditioning, Jean Dezert, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present a Non-Bayesian conditioning rule for belief revision. This rule is truly Non-Bayesian in the sense that it doesn’t satisfy the common adopted principle that when a prior belief is Bayesian, after conditioning by X, Bel(X|X) must be equal to one. Our new conditioning rule for belief revision is based on the proportional conflict redistribution rule of combination developed in DSmT (Dezert-Smarandache Theory) which abandons Bayes’ conditioning principle. Such Non-Bayesian conditioning allows to take into account judiciously the level of conflict between the prior belief available and the conditional evidence. We also introduce the deconditioning problem …

Maximal Class Numbers Of Cm Number Fields, Ryan C. Daileda, Raju Krishnamoorthy, Anton Malyshev

Mathematics Faculty Research

Fix a totally real number field F of degree at least 2. Under the assumptions of the generalized Riemann hypothesis and Artin's conjecture on the entirety of Artin L-functions, we derive an upper bound (in terms of the discriminant) on the class number of any CM number field with maximal real subfield F. This bound is a refinement of a bound established by Duke in 2001. Under the same hypotheses, we go on to prove that there exist infinitely many CM-extensions of F whose class numbers essentially meet this improved bound and whose Galois groups are as large …

2010 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2010 Spring Colloquium.