Physical Sciences and Mathematics Commons^™

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. …

Zero-Divisor Graphs, Commutative Rings Of Quotients, And Boolean Algebras, John D. Lagrange

Doctoral Dissertations

The zero-divisor graph of a commutative ring is the graph whose vertices are the nonzero zero-divisors of the ring such that distinct vertices are adjacent if and only if their product is zero. We use this construction to study the interplay between ring-theoretic and graph-theoretic properties. Of particular interest are Boolean rings and commutative rings of quotients.

Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene

Publications and Research

A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …

Calculus Of Variations On Time Scales And Its Applications To Economics, Chris Mcmahon

Masters Theses & Specialist Projects

The goal of time scale research is to progress the development of a harmonized theory that is all encompassing of the more commonly known specialized forms. The main results of this paper is the presentation of the Ramsey model which can be written using both the A and V operators, and solved using the two separate theories of the calculus of variations on time scales. The next presentation will be of the solution of an adjustment model, for a specific form of a time scale, whose functional can only be optimized, using the existing theory, when written with the A …

Generalized Inverse Scattering Transform For The Nonlinear Schrödinger Equation, Theresa Nicole Busse

Mathematics Dissertations

The nonlinear Schrödinger (NLS) equation describes wave propagation in optical fibers, and it is one of the most well-known nonlinear partial differential equations. In 1972 Zakharov and Shabat introduced a powerful method (known as the inverse scattering transform) to solve the initial-value problem for the NLS equation. Due to mathematical and technical difficulties, this method has been available mainly in the case where the multiplicity of each bound state is one. In our research we remove that restriction and generalize the inverse scattering transform for the NLS equation to the case where the multiplicity of each bound state is arbitrarily …

It's All About The Teachers: Bank Street's Math For Teachers As Professional Development, Robin Hummel

Graduate Student Independent Studies

This work describes a professional development initiative that was based on the graduate course, Mathematics for Teachers in Diverse and Inclusive Educational Settings (K-6), taught by Linda Metnetsky at Bank Street College of Education. The author wrote and implemented this professional development initiative for teachers in her former district: a large, middle class, suburban school district outside of Philadelphia. It consisted of six full day sessions, held from October through April during the 2004-05 school year. Eleven teachers from third, fourth, and fifth grades participated, and the impact of this professional development on two participants is the focus of this …

Parallel Simulation Of Individual-Based, Physiologically-Structured Population And Predator-Prey Ecology Models, Jeffrey A. Nichols

Doctoral Dissertations

Utilizing as testbeds physiologically-structured, individual-based models for fish and Daphnia populations, techniques for the parallelization of the simulation are developed and analyzed. The techniques developed are generally applicable to individual-based models. For rapidly reproducing populations like Daphnia which are load balanced, then global birth combining is required. Super-scalar speedup was observed in simulations on multi-core desktop computers.

The two populations are combined via a size-structured predation module into a predator-prey system with sharing of resource weighted by relative mass. The individual-based structure requires multiple stages to complete predation.

Two different styles of parallelization are presented. The first distributes both populations. …

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

Andrew Shallue

No abstract provided.

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 …

Intersections Of Longest Paths And Cycles, Thomas Hippchen

Mathematics Theses

It is a well known fact in graph theory that in a connected graph any two longest paths must have a vertex in common. In this paper we will explore what happens when we look at k - connected graphs, leading us to make a conjecture about the intersection of any two longest paths. We then look at cycles and look at what would be needed to improve on a result by Chen, Faudree and Gould about the intersection of two longest cycles.

"Clustering Categorical Response" Application To Lung Cancer Problems In Living Scales, Ling Guo

Mathematics Theses

The study aims to estimate the ability of different grouping techniques on categorical response. We try to find out how well do they work? Do they really find clusters when clusters exist? We use Cancer Problems in Living Scales from the ACS as our categorical data variables and lung cancer survivors as our studying group. Five methods of cluster analysis are examined for their accuracy in clustering on both real CPILS dataset and simulated data. The methods include hierarchical cluster analysis (Ward's method), model-based clustering of raw data, model-based clustering of the factors scores from a maximum likelihood factor analysis, …

Singular Value Decomposition In Image Noise Filtering And Reconstruction, Tsegaselassie Workalemahu

Mathematics Theses

The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods …

Riccati Equations In Optimal Control Theory, James Bellon

Mathematics Theses

It is often desired to have control over a process or a physical system, to cause it to behave optimally. Optimal control theory deals with analyzing and finding solutions for optimal control for a system that can be represented by a set of differential equations. This thesis examines such a system in the form of a set of matrix differential equations known as a continuous linear time-invariant system. Conditions on the system, such as linearity, allow one to find an explicit closed form finite solution that can be more efficiently computed compared to other known types of solutions. This is …

Algorithms For Toeplitz Matrices With Applications To Image Deblurring, Symon Kipyagwai Kimitei

Mathematics Theses

In this thesis, we present the O(n(log n)^2) superfast linear least squares Schur algorithm (ssschur). The algorithm we will describe illustrates a fast way of solving linear equations or linear least squares problems with low displacement rank. This program is based on the O(n^2) Schur algorithm speeded up via FFT. The algorithm solves a ill-conditioned Toeplitz-like system using Tikhonov regularization. The regularized system is Toeplitz-like of displacement rank 4. We also show the effect of choice of the regularization parameter on the quality of the image reconstructed.

Direct Adjustment Method On Aalen's Additive Hazards Model For Competing Risks Data, Haci Mustafa Akcin

Mathematics Theses

Aalen’s additive hazards model has gained increasing attention in recently years because it model all covariate effects as time-varying. In this thesis, our goal is to explore the application of Aalen’s model in assessing treatment effect at a given time point with varying covariate effects. First, based on Aalen’s model, we utilize the direct adjustment method to obtain the adjusted survival of a treatment and comparing two direct adjusted survivals, with univariate survival data. Second, we focus on application of Aalen’s model in the setting of competing risks data, to assess treatment effect on a particular type of failure. The …

Treatments Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Ken Kun Zhao

Mathematics Theses

Chlamydia Trachomatis and Neisseria Gonorrhoeae rank as the two most commonly reported sexually transmitted diseases (STDs) in the United States. Under limited budget, publicly funded clinics are not able to screen and treat the two diseases for all patients. They have to make a decision as to which group of population shall go through the procedure for screening and treating the two diseases. Therefore, we propose a cubic integer programming model on maximizing the number of units of cured diseases. At the same time, a two-step algorithm is established to solve the cubic integer program. We further develop a web-server, …

Sign Pattern Matrices That Require Almost Unique Rank, Assefa D. Merid

Mathematics Theses

A sign pattern matrix is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrixA, the sign pattern class of A, denoted Q(A), is defined as { B : sgn(B)= A }. The minimum rank mr(A)(maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost …

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.

Generic Continuous Functions And Other Strange Functions In Classical Real Analysis, Douglas Albert Woolley

Mathematics Theses

In this paper we examine continuous functions which on the surface seem to defy well-known mathematical principles. Before describing these functions, we introduce the Baire Category theorem and the Cantor set, which are critical in describing some of the functions and counterexamples. We then describe generic continuous functions, which are nowhere differentiable and monotone on no interval, and we include an example of such a function. We then construct a more conceptually challenging function, one which is everywhere differentiable but monotone on no interval. We also examine the Cantor function, a nonconstant continuous function with a zero derivative almost everywhere. …

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.

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

Communications on Stochastic Analysis

No abstract provided.

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.

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

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.

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

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.