Physical Sciences and Mathematics Commons^™

Estimation And The Stress-Strength Model, Naomi Brownstein

HIM 1990-2015

The paper considers statistical inference for R = P(X < Y) in the case when both X and Y have generalized gamma distributions. The maximum likelihood estimators for R are developed in the case when either all three parameters of the generalized gamma distributions are unknown or when the shape parameters are known. In addition, objective Bayes estimators based on non informative priors are constructed when the shape parameters are known. Finally, the uniform minimum variance unbiased estimators (UMVUE) are derived in the case when only the scale parameters are unknown.

A Mathematical Study Of Two Retroviruses, Hiv And Htlv-I, Dana Ali Baxley

Electronic Theses and Dissertations

In this thesis, we examine epidemiological models of two different retroviruses, which infect the human body. The two viruses under study are HIV or the human immunodefiency virus and HTLV-I, which is the human T lymphotropic virus type I. A retrovirus is a virus, which injects its RNA into the host, rather than it's DNA. We will study each of the different mathematical models for each of the viruses separately. Then we use MATLAB-SIMULINK to analyze the models by studying the reproductive numbers in each case and the disease progression by examining the graphs. In Chapter 1, we mention basic …

Effect Of Inner Scale Atmospheric Spectrum Models On Scintillation In All Optical Turbulence Regimes, Kenneth Mayer

Electronic Theses and Dissertations

Experimental studies have shown that a "bump" occurs in the atmospheric spectrum just prior to turbulence cell dissipation.1,3,4 In weak optical turbulence, this bump affects calculated scintillation. The purpose of this thesis was to determine if a "non-bump" atmospheric power spectrum can be used to model scintillation for plane waves and spherical waves in moderate to strong optical turbulence regimes. Scintillation expressions were developed from an "effective" von Karman spectrum using an approach similar to that used by Andrews et al.8,14,15 in developing expressions from an "effective" modified (bump) spectrum. The effective spectrum extends the Rytov approximation into all optical …

Soliton Solutions Of Nonlinear Partial Differential Equations Using Variational Approximations And Inverse Scattering Techniques, Thomas Vogel

Electronic Theses and Dissertations

Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the error of a variational approximation is established. Note that the material …

An Examination Of The Effectiveness Of The Adomian Decomposition Method In Fluid Dynamic Applications, Sonia Holmquist

Electronic Theses and Dissertations

Since its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This …

Efficient Inversion Of The Cone Beam Transform For A General Class Of Curves, Mikhail Kapralov

Electronic Theses and Dissertations

We extend an efficient cone beam transform inversion formula, proposed earlier for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much in a certain sense, and do not admit lines which are tangent to C at one point and intersect C at another point. A domain U is found where reconstruction is possible with a filtered backprojection type algorithm. Results of numerical experiments demonstrate very good image quality. The algorithm developed is useful for image reconstruction in …

Pade Approximants And One Of Its Applications, Tame-Kouontcho Fowe

Electronic Theses and Dissertations

This thesis is concerned with a brief summary of the theory of Pade approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Pade approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Pade approximants and some of the results that will be related to the work on the second part of the …

Stability And Preservation Properties Of Multisymplectic Integrators, Tomasz Wlodarczyk

Electronic Theses and Dissertations

This dissertation presents results of the study on symplectic and multisymplectic numerical methods for solving linear and nonlinear Hamiltonian wave equations. The emphasis is put on the second order space and time discretizations of the linear wave, the Klein-Gordon and the sine-Gordon equations. For those equations we develop two multisymplectic (MS) integrators and compare their performance to other popular symplectic and non-symplectic numerical methods. Tools used in the linear analysis are related to the Fourier transform and consist of the dispersion relationship and the power spectrum of the numerical solution. Nonlinear analysis, in turn, is closely connected to the temporal …

Positive Solutions Of A Nonlinear Higher Order Boundary-Value Problem, John R. Graef, Johnny Henderson, Bo Yang

Faculty Articles

The authors consider the higher order boundary-value problem u (n)(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i-1)(0) = u (n-2)(p) = u(n-1)(1) = 0, 1 ≤ i ≤ n -2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

Estimates Of Positive Solutions To A Boundary Value Problem For The Beam Equation, Bo Yang

Faculty Articles

We consider a two-point boundary value problem for the fourth order beam equation. New upper and lower estimates of positive solutions of the problem are obtained.

Portfolio Selection In Gaussian And Non-Gaussian Worlds, Jing Wang

Theses and Dissertations (Comprehensive)

In the case of minimizing risk with a given level of expected return, we discuss the portfolio selection problem with the asset returns are characterized by a Gaussian distribution and heavy tailed distribution.

More specifically, under the Gaussian assupmtion, we give the explicit solutions to the problems of minimizing risk variance, CaR and EaR respectively. When a compound Poisson process is assumed, we derive explicit solutions to the variance, CaR and EaR. Furthermore, we give the explicit soultion for the CaR when a Lévy distribution is considered.

For the more realistic process-normal inverse process, we are able to obtain the …

Partial Separability And Partial Additivity For Orderings Of Binary Alternatives, Md. Abul Bashar

Theses and Dissertations (Comprehensive)

In Multiple-Criteria Decision Analysis (MCDA), a good way to find the best alternative is to construct a value function that represents a Decision Maker’s (DM) preferences. For multidimensional alternatives, an additive value function is easiest to work with because it assesses the alternatives in a simple and transparent manner. A DM’s preferences over consequences on a subset of the set of criteria may or may not depend on consequences on the rest of the criteria. Preferences that are free from all such interdependence are said to be separable. The existence of an additive value function implies separability and, when consequences …

Lectures In Computational Fluid Dynamics Of Incompressible Flow: Mathematics, Algorithms And Implementations, James M. Mcdonough

Mechanical Engineering Textbook Gallery

From Prologue:

The present lecture notes are written to emphasize the mathematics of the Navier–Stokes (N.–S.) equations of incompressible flow and the algorithms that have been developed over the past 30 years for solving them.

Relations Among Algebraic Models Of 1-Connected Homotopy 3-Types, Erdal Ulualan

Turkish Journal of Mathematics

In this paper, we explore the relations among reduced cases of algebraic models for homotopy 3-types for groups such as braided crossed and quadratic modules and reduced simplicial groups with Moore complex of length 2.

An Example Of An Indecomposable Module Without Non-Zero Hollow Factor Modules, Christian Lomp

Turkish Journal of Mathematics

A module M is called hollow-lifting if every submodule N of M such that M/N is hollow contains a direct summand D \subseteq N such that N/D is a small submodule of M/D. A module M is called lifting if such a direct summand D exists for every submodule N. We construct an indecomposable module M without non-zero hollow factor modules, showing that there are hollow-lifting modules which are not lifting. The existences of such modules had been left open in a recent work by N. Orhan, D. Keskin-Tütüncü and R. Tribak [2].

A New Lower Bound On Guard Placement For Wireless Localization, Mirela Damian, Robin Flatland, Joseph O'Rourke, Suneeta Ramswami

Computer Science: Faculty Publications

The problem of wireless localization asks to place and orient stations in the plane, each of which broadcasts a unique key within a fixed angular range, so that each point in the plane can determine whether it is inside or outside a given polygonal region. The primary goal is to minimize the number of stations. In this paper we establish a lower bound of ⌊2n/3⌋−1 stations for polygons in general position, for the case in which the placement of stations is restricted to polygon vertices, improving upon the existing ⌈n/2⌉ lower bound.

Categorical Properties Of Lattice-Valued Convergence Spaces, Paul Flores

Electronic Theses and Dissertations

This work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of Lattice-Valued Convergence Spaces given by Jager [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L = f0; 1g:Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of Lattice Valued Fuzzy Convergence Spaces defined and studied by Jager [2001]. Our principal category is shown to be a topological universe …

Mars: An Education-Oriented Mips Assembly Language Simulator, Pete Sanderson, Kenneth Vollmar

Mathematics Faculty Scholarship

We describe the implementation of “MARS,” a GUI, Java-based simulator for the MIPS assembly language. MIPS, the computer architecture underlying the simulated assembly language, is widely used in industry and is the basis of the popular textbook Computer Organization and Design [6], used at over 400 universities. The MARS simulator has been implemented with characteristics that are especially useful to undergraduate computer science students and their instructors.

Extrapolation Of Operators Defined On Domains And Boundary Respecting Ap Weights, Ryan Berndt

Mathematics Faculty Scholarship

No abstract provided.

Generic Subideals Of Graph Ideals And Free Resolutions, Leah Gold

Mathematics and Statistics Faculty Publications

For a graph of an n-cycle Δ with Alexander dual Δ∗, we study the free resolution of a subideal G (n) of the Stanley-Reisner ideal IΔ∗. We prove that if G(n) is generated by 3 generic elements of IΔ∗, then the second syzygy module of G(n) is isomorphic to the second syzygy module of (x1,x2,... ,x n). A result of Bruns shows that there is always a 3-generated ideal with this property. We show that it can be chosen to have a particularly nice form.

Periodic Solution To The Time-Inhomogeneous Multi-Server Poisson Queue, Barbara Haas Margolius

Mathematics and Statistics Faculty Publications

We derive the periodic family of asymptotic distributions and the periodic moments for number in the queue for the multi-server queue with Poisson arrivals and exponential service for time-varying periodic arrival and departure rates, and time-varying periodic number of servers. The method is a straight-forward application of generating functions.

Lessons Learned From The 1918-1919 Influenza Pandemic In Minneapolis And St. Paul, Minnesota, Miles Q. Ott, Shelly F. Shaw, Richard N. Danila, Ruth Lynfield

Statistical and Data Sciences: Faculty Publications

No abstract provided.

Connecting Polygonizations Via Stretches And Twangs, Mirela Damian, Robin Flatland, Joseph O'Rourke, Suneeta Ramswami

Computer Science: Faculty Publications

We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n² ) “moves” between simple polygons. Each move is composed of a sequence of atomic moves called “stretches” and "twangs". These atomic moves walk between weakly simple "polygonal wraps" of S. These moves show promise to serve as a basis for generating random polygons.

Proceedings Of The First Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 1st Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents
• Abstracts of Papers

Assessing Understanding Of Multiplication Through Words, Pictures, And Numbers, Stephanie Z. Smith

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

The objective of this session is to engage mathematics teacher educators in a discussion of how to assess an understanding of the concept of multiplication as an operation and its relationships to other operations. The session will begin with a presentation of a previously published study assessing children’s understanding of multiplication as grouping and the relationship between multiplication and addition. The assessment asked a series of problems involving words, pictures, and numbers. The results of the study indicate that the types of problems asked were successful in providing evidence of children’s understanding of multiplication. The study also found that a …

Change And Relationships In Elementary Preservice Teachers’ Mathematics Pedagogical Beliefs, Teaching Efficacy Beliefs, And Content Knowledge, Susan L. Swars, Lynn C. Hart , Ed., Stephanie Z. Smith, Marvin E. Smith

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

This study investigated the mathematics beliefs and content knowledge of 103 elementary preservice teachers in a developmental teacher preparation program that included a two course mathematics methods sequence. Preservice teachers’ pedagogical beliefs became more cognitively-oriented during the teacher preparation program with these changes occurring during the two methods courses. Pedagogical beliefs remained stable during student teaching. The preservice teachers also significantly increased their personal efficacy for teaching mathematics throughout the program with these shifts occurring across both methods courses and into student teaching. Pedagogical beliefs and teaching efficacy beliefs were not related at the beginning of the program, but, in …

The Kennesaw State University Mathematics Methods Model, Angela L. Teachey

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Kennesaw State University’s comprehensive, nine-credit-hour, methods course integrates general and mathematics-specific pedagogical training with a structured four-week field experience prior to student teaching. This course blends essential units on conceptual understanding of mathematics, lesson planning, assessment, classroom management, and diversity with mathematics-specific methods. All topics are aligned with National Council of Teachers of Mathematics standards and Georgia Performance Standards. Throughout the course, students complete a variety of assignments that require them to practice the skills highlighted in class readings and discussions, and they adapt and generalize those skills during their field experiences. Students have numerous opportunities in class and in …

The Mathematical Preparation Of Secondary School Teachers, Kelly W. Edenfield

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

In the summer of 2007, a group of doctoral students at the University of Georgia gathered to discuss the mathematical preparation of secondary teachers. The group used Mathematics for High School Teachers: An Advanced Perspective by Usiskin, Peressini, Marchisotto, and Stanley (2003) as the catalyst for the discussion. Participants agreed that future teachers need opportunities to examine high school and college mathematics differently from the way they had as students, with specific emphasis on connections, representations, and history. Features of this text that were highlighted in the discussions were the attention topics with commonly held misconceptions, the historical rationales and …

World Bank -Cpa Conflict: The Struggle To Define Human Rights And Development In The Philippines, Adam B. Robbins

Honors Theses

This thesis analyzes the interactions between the World Bank (hereafter, the Bank) and the Cordillera Peoples Alliance (CPA), an indigenous and environmental advocacy group based in the Cordillera region of Luzon, in the Philippines. Using data gathered through both text-based and participatory research methods, I analyze the discursive relationship and violent confrontations between the two organizations. Conflicting development and human rights values cause the majority of these conflicts. I focus on how each organization enacts development and human rights, and how this leads to conflict. Ultimately, I intend for this thesis to offer practical guidance for the reader involved in …

Elementary Fuzzy Matrix Theory And Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out …