Physical Sciences and Mathematics Commons^™

Three Population Models Applied To Competition, Disease And Invasion, Erika Asano

Doctoral Dissertations

In this work, we present three diffrent types of population models. The first two models are examined in the context of optimal control problems. The third involves the construction of an invasion model using a significant amount of data.

The first model describes the interaction of three populations, motivated by a combat scenario. One of the three populations can switch the mode of alliance with the other two populations between cooperation and competition. The other two populations always compete with each other. In this system of parabolic partial differential equations, the control is the function which measures the strength of …

Two Biological Applications Of Optimal Control To Hybrid Differential Equations And Elliptic Partial Differential Equations, Wandi Ding

Doctoral Dissertations

In this dissertation, we investigate optimal control of hybrid differential equations and elliptic partial differential equations with two biological applications. We prove the existence of an optimal control for which the objective functional is maximized. The goal is to characterize the optimal control in terms of the solution of the opti- mality system. The optimality system consists of the state equations coupled with the adjoint equations. To obtain the optimality system we differentiate the objective functional with respect to the control. This process is applied to studying two prob- lems: one is a type of hybrid system involving ordinary differential …

Coarse Structures And Higson Compactification, Christian Stuart Hoffland

Masters Theses

FOLLOWING John Roe in his Lectures on Coarse Geometry, we begin by describing the large-scale structure of metric spaces by means of coarse maps between them, those being maps which preserve distances at large scales. Using these techniques, we demonstrate that the real numbers and the integers have the same large scale structure--or are coarsely equivalent--but that the real line is coarsely equivalent to neither the Euclidean plane nor the set of positive real numbers. Following a generalization of these concepts for general topological spaces with the introduction of an abstract coarse structure on the space, we show, among …

Nikolski's Approach To The Theorems Of Beurling And Nyman Regarding Zeros Of The Riemann Ζ-Function, Jared R. Bunn

Masters Theses

In this thesis we present the proof of a theorem by Nikolai Nikolski. This theorem leads to a more general theorem by Nikolski regarding zero free regions of the Riemann ζ-function. This theorem is an improvement on the theorems that Nyman and Beurling proved in the nineteen fifties. Nikolski’s approach uses, in addition to step function approximations introduced by Nyman, distance functions to give more flexibility, including possible numerical experiments. The introduction discusses the Riemann Hypothesis, which always surrounds any study of the Riemann ζ-function.

The background material discussed in this thesis gives all the necessary prerequi- sites …

On Some Aspects Of The Differential Operator, Panakkal Jesu Mathew

Mathematics Theses

The Differential Operator D is a linear operator from C1[0,1] onto C[0,1]. Its domain C1[0,1] is thoroughly studied as a meager subspace of C[0,1]. This is analogous to the status of the set of all rational numbers Q in the set of the real numbers R. On the polynomial vector space Pn the Differential Operator D is a nilpotent operator. Using the invariant subspace and reducing subspace technique an appropriate basis for the underlying vector space can be found so that the nilpotent operator admits its Jordan Canonical form. The study of D on Pn is completely carried out. Finally, …

Uncertainty Principles On Nilpotent Lie Groups., Sanjay Parui Dr.

Doctoral Theses

No abstract provided.

Markov Chain Monte Carlo Methods For Regression Splines With A Penalized Acceptance Ratio, David Keith Stamps

Dissertations

An increasingly popular method for fitting complex models, particularly with a hierchical structure involvese the use of Markov Chain Monte Carlo simulation. Within a Bayesian framework, two major strategies are Gibbs sampling and Metropolis-Hastings methods. Recent research in the area of MCMC methods has witnessed the emergence of modeling efforts which permit the movement of the chain across models of varying dimensions. When properly constructed, such Markov chains converge to the joint posterior distribution of the parameters to be estimated, making Bayesian averaging an attractive option after convergence has occurred. With this transdimensional methodology, the Bayesian averaging process takes place …

Image Segmentation By Energy And Related Functional Minimization Methods, Eric Hudson Mason

Dissertations

Effective and efficient methods for partitioning a digital image into image segments, called ¿image segmentation,¿ have a wide range of applications that include pattern recognition, classification, editing, rendering, and compressed data for image search. In general, image segments are described by their geometry and similarity measures that identify them. For example, the well-known optimization model proposed and studied in depth by David Mumford and Jayant Shah is based on an L₂ total energy functional that consists of three terms that govern the geometry of the image segments, the image fidelity (or closeness to the observed image), and the prior …

On The N-Body Problem, Zhifu Xie

Theses and Dissertations

In this thesis, central configurations, regularization of Simultaneous binary collision, linear stability of Kepler orbits, and index theory for symplectic path are studied. The history of their study is summarized in section 1. Section 2 deals with the following problem: given a collinear configuration of 4 bodies, under what conditions is it possible to choose positive masses which make it central. It is always possible to choose three positive masses such that the given three positions with the masses form a central configuration. However, for an arbitrary configuration of 4 bodies, it is not always possible to find positive masses …

Knots Not For Naught, Sharleen Adrienne Roberts

Theses and Dissertations

The goal of this paper is to find the Homfly polynomial for each knot in a specific family of knots. This family of knots is generated from placing the Whitehead link into a solid torus, slicing the torus at a spot where the Whitehead has no crossings and then twisting the torus 360 degrees in either direction an integral number of times. Let L(n) denote the knot obtained by twisting the torus 360 degrees, n times. Note that n is an integer. Let the twists be towards the center of the torus for positive n and away from the center …

Conjugacy Classes Of The Piecewise Linear Group, Matthew L. Housley

Theses and Dissertations

The piecewise linear group is the set of all piecewise linear orientation preserving homeomorphisms from the interval to itself under the operation of composition. We present here a complete set of invariants to classify the conjugacy classes of this group. Our approach to this problem relies on the factorization of elements into elements having only a single breakpoint.

Topics On The Spectral Theory Of Automorphic Forms, Dustin David Belt

Theses and Dissertations

We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's Eigenvalue Conjecture to the study of the nonvanishing of the Eisenstein Series $E(z,s)$ for Hecke congruence subgroups $Gamma_0(N)$ at $s=frac {1+i}{2}$.

Proven Cases Of A Generalization Of Serre's Conjecture, Jonathan H. Blackhurst

Theses and Dissertations

In the 1970's Serre conjectured a correspondence between modular forms and two-dimensional Galois representations. Ash, Doud, and Pollack have extended this conjecture to a correspondence between Hecke eigenclasses in arithmetic cohomology and n-dimensional Galois representations. We present some of the first examples of proven cases of this generalized conjecture.

On The Combinatorics Of Certain Garside Semigroups, Christopher R. Cornwell

Theses and Dissertations

In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.

Ricci Curvature Rigidity For Weakly Asymptotically Hyperbolic Manifolds, Vincent Bonini, Pengzi Miao, Jie Qing

Mathematics

A rigidity result for weakly asymptotically hyperbolic manifolds with lower bounds on Ricci curvature is proved without assuming that the manifolds are spin. The argument makes use of a quasilocal mass characterization of Euclidean balls from [9] [14] and eigenfunction compactification ideas from [12].

Charactarizations Of Linear Suboptimality For Mathematical Programs With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization theory and its applications. Based on robust generalized differential calculus, we …

Erratum: The Emergence Of A Large-Scale Coherent Structure Under Small-Scale Random Bombardments (Communications On Pure And Applied Mathematics (2006) 59:4 (467-500)), Andrew Majda, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Large Deviations For Stochastic Systems With Memory, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

We establish a large deviations principle for stochastic delay equations driven by small multiplicative white noise. Both upper and lower large deviations estimates are obtained.

Tme Volume 3, Number 2

The Mathematics Enthusiast

No abstract provided.

Numbers And Polynomials- 50 Years Since The Publication Of Wittgenstein's Bemerkungen Über Die Grundlagen Der Mathematik (1956): Mathematical And Educational Reflections, Giorgio T. Bagni

The Mathematics Enthusiast

According to L. Wittgenstein, the meaning of a mathematical object is to be grounded upon its use. In this paper we consider Robinson theory Q, the subtheory of firstorder Peano Arithmetic PA; some theorems and conjectures can be interpreted over one model of Q given by a universe of polynomials; with respect to nonconstant polynomials some proofs by elementary methods are given and compared with corresponding results in the standard model of PA. We conclude that the creative power of the language can be pointed out in how the language itself is embedded into the rest of human activities, and …

The Effects Of Blended E-Learning On Mathematics And Computer Attitudes In Pre-Calculus Algebra, Balarabe Yushau

The Mathematics Enthusiast

This study examines the influence of blended e-learning on students' attitude towards mathematics and computers. A random sample of 70 students of the preparatory year program of King Fahd University of Petroleum & Minerals (KFUPM), Dhahran served as the sample of this study. Data were collected at the beginning (pre-program) and the end (post-program) of the semester using Aiken Mathematics Attitude Scale and Greessen and Loyd Computer Attitude Scale. The result indicates that the subjects have positive attitude towards mathematics and computer. However, analysis of variance shows no statistically significant change in students’ attitudes towards mathematics and computer except for …

An In-Depth Investigation Of The Divine Ratio, Birch Fett

The Mathematics Enthusiast

The interesting thing about mathematical concepts is that we can trace their development or discoveries throughout history. Most cultures of the ancient world had some form of mathematics, and these basic skills developed into what we now call modern mathematics. The divine ratio is similar in that it was used in many different sections of history. The divine ratio, sometimes called the golden ratio or golden section, has been found in very diverse areas. The mathematical concepts of the golden ration have been found throughout nature, in architecture, music as well as in art. Phi is an astonishing number because …

Frames Of Reference And Achievement In Elementary Arithmetic, Eddie M. Gray, Demetra Pitta-Pantazi

The Mathematics Enthusiast

This paper considers the relationship between 8-11 years old students’ numerical achievement and a possible disposition towards the construction of particular frames of reference. The paper uses the characteristics of a variety of kinds of images to focus upon frames of reference and explores a possible relationship between children’s verbal descriptions of concrete and abstract nouns and the different ways they respond to aspects of elementary arithmetic. It seeks to establish whether or not children towards the extremes of arithmetical achievement (low and high achievement) have a disposition towards different kinds of frames of reference. The analysis suggests that at …

Tme's Worldwide Circulation Statistics

The Mathematics Enthusiast

No abstract provided.

A Classification Of Strategies Employed By High School Students In Isomorphic Combinatorial Problems, Martina Janácková, Jaroslav Janácek

The Mathematics Enthusiast

The aim of the paper is to discuss some aspects of the combinatorial thinking of high school students. We took one student - Jane and gave her 4 isomorphic testing problems. Then we tried to classify the different strategies the students took in their solutions.

Using Manipulatives In Mathematical Problem Solving: A Performance-Based Analysis, Catherine A. Kelly

The Mathematics Enthusiast

This article explores problem solving in elementary classrooms while focusing on how children use (perform tasks) manipulatives and/or tools in problem solving while working on mathematical tasks. Ways for teachers to assess children’s learning through performance-based tool (manipulative) use will also be examined and suggested. Current research reveals that teachers need to teach and assess children’s mathematical knowledge in ways that will allow them to show (perform) what they really understand. And, teachers must be able to see beyond obvious correct or incorrect answers into children’s thinking processes by testing with “tests that allow students the opportunity to show what …

Editorial: A Global Intellectual Collage, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

World-Class High Quality Mathematics Education For All K-12 American Students, Om P. Ahuja

The Mathematics Enthusiast

In September 1989, the United States’ Governors Conference in Charlottesville, Virginia set an ambitious goal by declaring that “By the year 2000, United States students will be first in the world in mathematics and science achievements”. However, recent results of the ‘Programme for International Student Achievement’ and ‘Trends in International Mathematics and Science Study’ indicate that the United States students’ achievements in mathematics are far below world class standards. This paper seeks to discuss issues in an international context related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also …

Sunrise… Sunset…, Alex Friedlander, Tzippora Resnick

The Mathematics Enthusiast

Sunrise and sunset are obviously a part of our everyday life. Our connection to the movement of celestial bodies, including the Sun, has been somewhat diminished by modern life, in contrast to the practical interest, fascination or even awe of earlier civilizations. Mathematics and astronomy have a long history of cooperative work, but due to their complexity and technical difficulty, usually those who participated in this endeavor were at the advanced studies level, or occupied high religious positions.

How Students Conceive Function: A Triarchic Conceptual-Semiotic Model Of The Understanding Of A Complex Concept., Iliada Elia, Panayotis Spyrou

The Mathematics Enthusiast

This study explores conceptions for function amongst 164-second year students of the Department of Education at the University of Cyprus and their relationship with students’ abilities in dealing with tasks involving different modes of representations of function. The test that was administered to the students included recognition tasks given in various representations and questions requesting definition and examples of function’s applications in real life situations. Results have shown that students’ definitions and examples of the notion are closely related to their ability to use different modes of representations of function. These three factors, i.e., definitions given by the students, functions …