Mathematics Commons^™

Graph Connectivity, Partial Words, And A Theorem Of Fine And Wilf, F. Blanchet-Sadri, Deepak Bal, Gautam Sisodia

Department of Mathematics Faculty Scholarship and Creative Works

The problem of computing periods in words, or finite sequences of symbols from a finite alphabet, has important applications in several areas including data compression, string searching and pattern matching algorithms. The notion of period of a word is central in combinatorics on words. There are many fundamental results on periods of words. Among them is the well known and basic periodicity result of Fine and Wilf which intuitively determines how far two periodic events have to match in order to guarantee a common period. More precisely, any word with length at least p + q - gcd (p, q) …

Polarization Of The Sri Lankan Polity: An Analysis Of Presidential Elections (1982 – 2005), Yajni Warnapala, Zufni Yehiya

Arts & Sciences Faculty Publications

Sri Lanka is a multi-ethnic, multi-religious developing country that has enjoyed continuous universal adult franchise since 1931. Under a new constitution enacted in 1978, Sri Lanka moved to a presidential system of government. Since 1982 five presidential elections were conducted. This paper analyzes voter behavior by looking at all the five presidential elections. This study shows that all the winners of the presidential elections (except in 2005) won them by appealing across racial and religious boundaries with a popular mandate. In 2005, there was a shift; the winner was able to secure victory by promoting a hard-line pro-Sinhala nationalistic platform. …

An Improved Multi-Set Algorithm For The Dense Subset Sum Problem, Andrew Shallue

Scholarship

No abstract provided.

Hands-On Activities And Activities Involving Technology To Help Students Construct Concepts And Gain A Deeper Understanding And Appreciation For Mathematical Concepts Based On The Utah Core Curriculum For Algebra Ii, Brookeann Watterson

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

Research shows there are several methods that expand students' understanding, appreciation for, and interest in mathematics by following teaching strategies. These strategies include incorporating hands-on activities, technology, discovery learning, cooperative learning, and having activities be applicable to real world contexts. This project focuses specifically on activities based on objectives from the Utah State Core for Algebra II that incorporate such strategies in five units: (I) absolute value, (2) exponential growth /decay and logarithms, (3) trigonometric functions, (4) probability, permutations and combinations, and (5) statistics.

Cultural Advantage For Cities: An Alternative For Developing Countries, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. …

New Retarded Integral Inequalities With Applications, Youngho Kim, Ravi P. Agarwal, Syamal K. Sen

Mathematics and System Engineering Faculty Publications

Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan (2003) and Pachpatte (2004). These inequalities can be used as basic tools in the study of certain classes of functional differential equations as well as integral equations. A existence and a uniqueness on the solution of the functional differential equation involving several retarded arguments with the initial condition are also indicated. Copyright © 2008 Ravi P. Agarwal et al.

Pebble Game Algorithms And Sparse Graphs, Audrey Lee, Ileana Streinu

Computer Science: Faculty Publications

A multi-graph G on n vertices is (k,ℓ)-sparse if every subset of n^′⩽n vertices spans at most kn^′-ℓ edges. G is tight if, in addition, it has exactly kn-ℓ edges. For integer valuesk and ℓ∈[0,2k), we characterize the (k,ℓ)-sparse graphs via a family of simple, elegant and efficient algorithms called the (k,ℓ)-pebble games. [A. Lee, I. Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (8) (2008) 1425–1437] from graphs to hypergraphs.

A Brief Study Of Some Aspects Of Babylonian Mathematics, Tom Zara

Senior Honors Theses

Beginning over 4000 years ago, the Babylonians were discovering how to use mathematics to perform functions of daily life and to evolve as a dominant civilization. Since the beginning of the 1800s, about half a million Babylonian tablets have been discovered, fewer than five hundred of which are mathematical in nature. Scholars translated these texts by the end of the 19th century. It is from these tablets that we gain an appreciation for the Babylonians’ apparent understanding of mathematics and the manner in which they used some key mathematical concepts. Through this thesis, the author will provide background information about …

Examining The Validity Of The Spring 2007 Math 1050 Common Final, Angela K. Brock

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

I began this study wanting to know more about the Math 1050 Common Final. I've heard so many negative things about the class from students, I wondered if the common final, which has so much influence on students' grades, is actually valid. A measurement is valid to the degree that it is both reliable and relevant, so I needed to address both relevance and reliability. To do this, I began by finding a reliability coefficient for the multiple choice section. I then analyzed each item with respect to difficulty, discrimination and efficiency. To determine content and learning level relevance, I …

2008 Sonia Kovalevsky Math For Girls Day Report, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

The report for the third annual Lincoln University Sonia Kovalevsky (LUSK) Math for Girls Day held on April 18th, 2008 from 8:30am to 2:00pm on the campus of Lincoln University in Jefferson City, MO.

Cauchy’S Arm Lemma On A Growing Sphere, Zachary Abel, David Charlton, Sébastien Collette, Erik D. Demaine, Martin L. Demaine, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Godfried Toussaint

Computer Science: Faculty Publications

We propose a variant of Cauchy's Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its endpoints increases. The main focus of this work is a comparison of three alternate proofs, to show the links between Toponogov's Comparison Theorem, Legendre's Theorem and Cauchy's Arm Lemma.

Fiber Bundle Description Of Flow And Nonlinear Hydrodynamics On Circles, Andrei Ludu

Publications

We introduce a differential geometry description of the path lines, stream lines and particles contours in hydrodynamics. We present a generalized form of a Korteweg-de Vries type of equation for the exterior of a circle. Nonlinearities from the boundary conditions, surface tension and the Euler equations are taken into account, but the flow is considered inviscid and irrotational. For the circular case we describe the traveling waves shapes, solitons and the particles trajectories.

Two Classes Of Time-Inhomogeneous Markov Chains: Analysis Of The Periodic Case, Attahiru Sule Alfa, Barbara Haas Margolius

Mathematics and Statistics Faculty Publications

We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions. These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems, insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating to queueing systems to allow us a focus. An example application of the model to a real life problem is …

Traveling Waves And Shocks In A Viscoelastic Generalization Of Burgers' Equation, Victor Camacho '07, Robert D. Guy, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider traveling wave phenomena for a viscoelastic generalization of Burgers' equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth traveling waves, piecewise smooth waves, and piecewise constant (shock) solutions. Each solution type is possible for a given pair of asymptotic limits, and we characterize the dynamics in terms of the relaxation time and viscosity.

Quasigeometric Distributions And Extra Inning Baseball Games, Darren B. Glass, Philip J. Lowry

Math Faculty Publications

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and …

The Shapley Value Of Phylogenetic Trees, Claus-Jochen Haake, Akemi Kashiwada '05, Francis E. Su

All HMC Faculty Publications and Research

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space …

Volume 01, Jessica Fields, Stephanie Neeley, Derek W. Hambright, Mary E. Lehman, Andrew R. Grzankowski, Zachary Johnson, Boone M. Prentice, Ashley M. Swandby, Victoria Morgan, Katie Williamson, Kristine G. Bender, Katelyn N. Romaine, D. Nicole Swann, Jessica Fox, Mike Mcateer, Alex Grabiec, Laura Nodtvedt, Nick Costa, Rachel Wolfe, Zack Dalton

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Three Decades of Digging: Undergraduate Archeology at Longwood by Jessica Fields and Stephanie Neeley

Interactions of Allelopathy and Heat Stress in Plants by Derek W. Hambright and Mary E. Lehman

Inertial Electrostatic Confinement D-D Fusion Device: Construction and Simulation by Andrew R. Grzankowski

Shackled Nim by Zachary Johnson

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Boone M. Prentice

A Comparison of Image Analysis Methods in cDNA Microarrays by Ashley M. Swandby

Perceived Sexual Activity of Short and Long-Term Relationships by Victoria Morgan and Katie Williamson

Elderly …

Leonard Gross's Work In Infinite-Dimensional Analysis And Heat Kernel Analysis, Brian C Hall

Communications on Stochastic Analysis

No abstract provided.

Pricing Functionals And Pricing Measures, Eric Hillebrand, Ambar N Sengupta

Communications on Stochastic Analysis

No abstract provided.

Abstract Wiener Space, Revisited, Daniel W Stroock

Communications on Stochastic Analysis

No abstract provided.

Analysis Of Complex Brownian Motion, Yuh-Jia Lee, Kuang-Ghieh Yen

Communications on Stochastic Analysis

No abstract provided.

An Impregnable Lightweight Device Discovery (Ildd) Model For The Pervasive Computing Environment Of Enterprise Applications, Munirul H. Haque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

The worldwide use of handheld devices (personal digital assistants, cell phones, etc.) with wireless connectivity will reach 2.6 billion units this year and 4 billion by 2010. More specifically, these handheld devices have become an integral part of industrial applications. These devices form pervasive ad hoc wireless networks that aide in industry applications. However, pervasive computing is susceptible and vulnerable to malicious active and passive snoopers. This is due to the unavoidable interdevice dependency, as well as a common shared medium, very transitory connectivity, and the absence of a fixed trust infrastructure. In order to ensure security and privacy in …

Estimating Absolute Transcript Concentration For Microarrays Using Langmuir Adsorption Theory, Min Mo

Mathematics Dissertations - Archive

This paper estimates the Langmuir parameters for probe on microarray then improves estimation of absolute transcript concentration using Langmuir adsorption model. We use the spike-in probes found on commercial microarrays, along with Langmuir adsorption model to estimate Langmuir parameters for spike-in probes, then combine with an assumed log-linear model for those Langmuir parameters in terms of the spike-in probe sequence features, to estimate the assumed-invariant model coefficients. These estimated coefficients are then used, along with the probe sequence features of the target probes, to estimate the Langmuir parameters for each target probe. Finally, these estimated Langmuir parameters are combined with …

Quadratic Wiener Functionals Of Square Norms On Measure Spaces, Setsuo Taniguchi

Communications on Stochastic Analysis

No abstract provided.

Diffeomorphisms Of The Circle And Brownian Motions On An Infinite-Dimensional Symplectic Group, Maria Gordina, Mang Wu

Communications on Stochastic Analysis

No abstract provided.

Complex Hermite Polynomials: From The Semi-Circular Law To The Circular Law, Michel Ledoux

Communications on Stochastic Analysis

No abstract provided.

Log-Sobolev Inequalities With Potential Functions On Pinned Path Groups, Shigeki Aida

Communications on Stochastic Analysis

No abstract provided.

Hedging Claims With Feedback Jumps In The Price Process, Kiseop Lee, Philip Protter

Communications on Stochastic Analysis

No abstract provided.

An Infinite Dimensional Stochastic Analysis Approach To Local Volatility Dynamic Models, R Carmona, S Nadtochiy

Communications on Stochastic Analysis

No abstract provided.