Mathematics Commons^™

An Immersed Interface Method For A 1d Poroelasticity Problem With Discontinuous Coefficients, Maranda Lee Bean

Open Access Theses & Dissertations

Poroelastic models deal with the coupling of changes in stress and fluid pressure in some porous medium. For physical reasons, some of the coefficients used in the models may have discontinuities. This project focuses on applying the immersed interface method to the one dimensional Biot model, in order to handle these discontinuities. This method is applied on a staggered grid. Using the immersed interface method allows us to alter only a small number of irregular grid points surrounding a discontinuity. For most of the grid points, a standard finite difference method is used. However at the irregular grid points, the …

Inverse Semigroups And Inverse Categories, Alexandra Macedo

Open Access Theses & Dissertations

The theory of inverse semigroups forms a major part of semigroup theory. This theory has deep connections with important mathematical disciplines, not only classical ones such as geometry, functional analysis, number theory, but also with more recent theories: the theory of algorithms, graph theory, the mathematical theory of automata, etc. The importance of inverse semigroups, first and foremost, is that they form an abstract class of algebraic structures which are isomorphic to semigroups of partial bijections.

This thesis is organized in two parts, inverse semigroups in Part 1, and inverse categories (that arises if we apply a basic property of …

The Topology Of Statistical Convergence, Khdiga Kalifa Tabib

Open Access Theses & Dissertations

A sequence {xn} is said to be statistically convergent to ℓ provided that "almost all" of the values of {xn} are arbitrarily close to ℓ. One can also define what is meant by statistical limit point, statistical limit superior, statistical limit inferior of a sequence and so forth and thus create a theory of convergence that includes ordinary convergence. In this work we investigate all these concepts and prove some new results. We also introduce a topology defined by this new convergence which we call statistical topology. Then we prove that both the statistical topology and the regular topology are …

A Multimodal Freight Collaborative Hub Location And Network Design Problem, Jiri Tylich

Open Access Theses & Dissertations

The study presents an analytical framework to explore the rail-road collaborative paradigm.

New collaborative technologies have been developed in recent years and they offer a potential solutions and opportunities for collaboration among all modes of transportation. The most progressive technologies that could fulfill the gap in rail-road collaborative paradigm are identified and presented in this research.

The research deals with current state and possible development of collaboration of rail and highway modes of transportation, referred to as rail-road collaboration. Multimodal transportation is the shipment of goods in a single transportation unit. The longest part of the route takes place by …

Lifting And Wavelets: A Factorization Method, Adrian Delgado

Open Access Theses & Dissertations

We begin with the concept of a discrete wavelet transformation. We begin with a scaling function satisfying a certain number of properties to be able to implement the wavelet transformation. We will then require translates of the scaling function to obey the same set of properties and this set will form what is called a Multiresolution Analysis. We then switch the ideas to the Fourier transform domain were we get equivalent results. However, instead of choosing a scaling function with coefficients to satisfy a set of properties, we will work backwards and construct a scaling function based on having a …

Number Theory And The Queen Of Mathematics, Megan Wagner

The Mathematics Enthusiast

Geometry is an integral component of secondary mathematics curriculum. From my experience in a mathematics teacher preparation program, I have seen a real push to connect geometry to other areas of mathematics. Secondary geometry can often be presented without clear or any connections to other areas of mathematics. One main purpose of this paper is to explore geometry and its rightful connection to other areas of mathematics, specifically number theory. Such strong emphasis is placed on drawing connections to number theory because of its intrinsic value in enhancing understanding of mathematical concepts. Learning number theory has positive ramifications for students, …

Translating And Adapting The Mathematical Knowledge For Teaching (Mkt) Measures: The Cases Of Indonesia And Norway, Dicky Ng, Reidar Mosvold, Janne Fauskanger

The Mathematics Enthusiast

This paper examines issues of translating and adapting an instrument that aims at measuring mathematical knowledge for teaching in Indonesia and Norway. The instrument was created for use in the U.S., and we discuss problematic and challenging issues of translation and adaptation. Two items from the released items pool were translated using a common framework modified from a previous study to exemplify critical issues that need to be resolved prior to using such instrument in another country. Themes identified in this study include a) minor challenges due to cultural differences; b) the use of technical language in schools; c) incommensurable …

Was Pythagoras Chinese- Revisiting An Old Debate, Ross Gustafson

The Mathematics Enthusiast

Two of the great ancient civilizations were those of the Greeks and the Chinese. Many great works of art, architecture, philosophy and literature have been produced by both of these civilizations. When it comes to mathematics in the Western World, the Greeks have also been credited with many contributions to the field, especially geometry. Anyone who has completed a standard high school mathematical curriculum has been introduced to the names of Pythagoras, Euclid and Archimedes and their methods. Not as widely credited in the Western world are the mathematical contributions of the ancient Chinese civilization. An examination into Chinese mathematics …

Tme Volume 9, Numbers 1 And 2

The Mathematics Enthusiast

No abstract provided.

Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

We review some of the recent developments in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as nonidentically distributed. But most of the time we will be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters as well as the proportional hazard rate model is discussed in detail.

New Symbolic Tools For Differential Geometry, Gravitation, And Field Theory, Ian M. Anderson, Charles G. Torre

Mathematics and Statistics Faculty Publications

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein …

Bi-Integrable And Tri-Integrable Couplings And Their Hamiltonian Structures, Jinghan Meng

USF Tampa Graduate Theses and Dissertations

An investigation into structures of bi-integrable and tri-integrable couplings is undertaken. Our study is based on semi-direct sums of matrix Lie algebras. By introducing new classes of matrix loop Lie algebras, we form new Lax pairs and generate several new bi-integrable and tri-integrable couplings of soliton hierarchies through zero curvature equations. Moreover, we discuss properties of the resulting bi-integrable couplings, including infinitely many commuting symmetries and conserved densities. Their Hamiltonian structures are furnished by applying the variational identities associated with the presented matrix loop Lie algebras.

The goal of this dissertation is to demonstrate the efficiency of our approach and …

On Projection-Invariant Subgroups Of Abelian P-Groups, Brendan Goldsmith

Articles

A subgroup P of an Abelian p-group G is said to be projection-invariant in G if Pf is contained in P for all idempotent endomorphisms f. Clearly fully invariant subgroups are projection invariant, but the converse is not true in general. Hausen and Megibben have shown that in many familiar situations these two concepts coincide. In a different direction, the authors have previously introduced the notions of socle-regular and strongly socle-regular groups by focussing on the socles of fully invariant and characteristic subgroups of p-groups. In the present work the authors examine the socles of projection-invariant subgroups of Abelian p-groups.

The Generalised Zakharov-Shabat System And The Gauge Group Action, Georgi Grahovski

Articles

The generalized Zakharov–Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the example of the multi-component nonlinear Schr¨odinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type …

Using Self Organizing Maps To Analyze Demographics And Swing State Voting In The 2008 U.S. Presidential Election, Paul T. Pearson, Cameron I. Cooper

Faculty Publications

Emergent self-organizing maps (ESOMs) and k-means clustering are used to cluster counties in each of the states of Florida, Pennsylvania, and Ohio by demographic data from the 2010 United States census. The counties in these clusters are then analyzed for how they voted in the 2008 U.S. Presidential election, and political strategies are discussed that target demographically similar geographical regions based on ESOM results. The ESOM and k-means clusterings are compared and found to be dissimilar by the variation of information distance function.

Reducibility, Degree Spectra, And Lowness In Algebraic Structures, Rebecca M. Steiner

Dissertations, Theses, and Capstone Projects

This dissertation addresses questions in computable structure theory, which is a branch of mathematical logic hybridizing computability theory and the study of familiar mathematical structures. We focus on algebraic structures, which are standard topics of discussion among model theorists. The structures examined here are fields, graphs, trees under a predecessor function, and Boolean algebras.

For a computable field F, the splitting set S_F of F is the set of polynomials in F[X] which factor over F, and the root set R_F of F is the set of polynomials in F[X] which have a root in F …

Theoretical Properties Of The Weighted Generalized Rayleigh And Related Distributions, Xueheng Shi, Broderick O. Oluyede, Marvis Pararai

Mathematical Sciences: Faculty Publications

In this paper, a new class of weighted generalization of the Rayleigh distribution is constructed and studied. The statistical properties of these distributions including the behavior of hazard or failure rate and reverse hazard functions, moments, moment generating function, mean, variance, coecient of variation, coecient of skewness, coecient of kurtosis are obtained. Other important properties including entropy (Shannon, beta and generalized) which are measures of the uncertainty in these distributions are also presented.

Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

We investigate the length-biased inverse Weibull (LBIW) distribution, deriving its density function, hazard and reverse hazard functions, and reliability function. The moments, moment-generating function, Fisher information and Shannon entropy are also given. We discuss parameter estimation via the method of moments and maximum likelihood, and hypothesis testing for the LBIW and parent distributions.

On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies

Mathematical Sciences: Faculty Publications

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.

Testing Irreducibility Of Trinomials Over Gf(2), Steven Hayman

Honors Projects

The focus of this paper is testing the irreducibility of polynomials over finite fields. In particular there is an emphasis on testing trinomials over the finite field GF(2). We also prove a the probability of a trinomial satisfying Swan's theorem is asymptotically 5/8 as n goes to infinity.