Mathematics Commons^™

Comparative Investigation Of Cognitive And Pragmatic Thinking Modes Linear Algebra, Enayatollah Kalantarian

Open Access Theses & Dissertations

The analysis focused on the presence of different thinking modes found on the interview and responses to questions related to linear independence, span, and spanning sets of two students taking their first linear algebra course at the college level. The findings provide insight on how first year linear algebra students move from one thinking mode to another. The focal point of this research was to document and discern the similarities and differences between student thinking modes displayed on their interviews and class assignments.

Based on the analysis, it was concluded that the level of exposure of the two students to …

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 …

Dihedral Cayley Directed Strongly Regular Graphs, Jose Jonathan Gamez

Open Access Theses & Dissertations

A graph is a directed strongly regular graph (DSRG) if and only if the number of paths of length 2 from x to y is: λ, if there is an edge from x to y; μ, if there is not an edge from x to y (with x not equal to y); and t, if x = y. For every vertex in G, the in-degree and out-degree is k. The number of vertices in G is denoted by v. If G is a group and S a subset of G, then the …

High-Order Central Finite-Volume Schemes For Atmospheric Modeling, Kiran Kumar Katta

Open Access Theses & Dissertations

Atmospheric numerical modeling has been going through drastic changes over the past decade, mainly to utilize the massive computing capability of the petascale systems. This obliges the modelers to develop grid systems and numerical algorithms that facilitate exceptional level of scalability on these systems. The numerical algorithms that can address these challenges should have the local properties such as the high on-processor operation count and minimum parallel communication i.e., high parallel efficiency. They should also satisfy the following properties such as inherent local and global conservation, high-order accuracy, geometric flexibility, non-oscillatory advection and positivity preservation properties. The goal of this …

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 …

Partial Orders For Representing Uncertainty, Causality And Decision Making: General Properties, Operations, And Algorithms, Francisco Adolfo Zapata

Open Access Theses & Dissertations

One of the main objectives of science and engineering is to help people select the most beneficial decisions. To make these decisions, we must know people's preferences, we must have the information about different possible consequences of different decisions. Since information is never absolutely accurate and precise, we must also have information about the degree of certainty of different parts on information. All these types of information naturally lead to partial orders:

- For preferences, a <= b means that b is preferable to a. This relation is used in decision theory.

- For events, a <= b means that a can influence b. This causality relation is one of the fundamental notions of physics, especially of physics of space-time.

* For uncertain statements, a <= b means that a is less certain than b. This relation is used in logics describing uncertainty, such as fuzzy logic.

In each of these areas, there is abundant research about studying the corresponding partial orders. …

Optimal Control Applied To A Discrete Time Influenza Model, Paula Andrea Gonzalez Parra

Open Access Theses & Dissertations

For the last decades, mathematical epidemiological models have been used to understand the dynamics of infectious diseases and guide public health policy.

In particular, several continuous models have been considered to study influenza outbreaks and their controls policies. However, most epidemiological data is discrete; therefore, a discrete formulation is more convenient to compare collected data with the output of the model. We introduce a discrete time model in order to study optimal control strategies for influenza transmission.

In our model, we divide the population into four classes: susceptible, infectious, treated, and recovered individuals.

In particular, we evaluate the potential effect …

Estimating Statistical Characteristics Under Interval Uncertainty And Constraints: Mean, Variance, Covariance, And Correlation, Ali Jalal-Kamali

Open Access Theses & Dissertations

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, …

A Characterization Of Directly Ordered Subspaces Of R^N, Jennifer Del Valle

Open Access Theses & Dissertations

In the finite dimensional ordered vector space Rⁿ, we consider the standard positive cone to be the set Rⁿ₊ = {x : x ≥ 0} for an element x in Rⁿ. Given a subspace V of Rⁿ, we define the positive cone of V to be the intersection of V with Rⁿ₊. The cone V₊ is said to be generating if V = V₊ − V₊, that is, if any vector v in V can be expressed as the difference of two vectors, v = …

A Reduced Order Parameter Estimation Technique Using Orthonormal Wavelets, Miguel Hernandez Iv

Open Access Theses & Dissertations

In this work we introduce methods for model order reduction using orthonormal wavelets. Specifically, we propose techniques and algorithms for wavelet-based reduced order parameter estimation using orthonormal wavelets for solving nonlinear least squares problems. Approaches for parameter reduction using the one dimensional and two dimensional wavelet transforms are presented using multiple levels of decomposition.

The performance of wavelet-based reduced order parameter estimation is tested using a suite of orthonormal wavelets on a groundwater hydraulics model provided by the U.S. Army Corps of Engineers. Using the hydraulics model, the goal is to find a least-squares solution of the permeability field given …

Metaphors, Metonymies, Modes And Linear Algebra, Persis Samanta Beaven

Open Access Theses & Dissertations

The analysis focused on the presence of different thinking modes, metonymies, and metaphors found on the interview responses to questions related to linear independence, span, and spanning sets of four students taking their first linear algebra course at the college level. The findings provide insight of how first year linear algebra students move from one thinking mode to another and what kind of metonymies and metaphors are used to construct new knowledge. The main purpose of this research was to document and determine the main characteristics that categorize the four students' reasoning.

The Isomorphisms Between The Upper And Lower Triangular Matrix Algebras, Zahi Fawaz

Open Access Theses & Dissertations

Since matrix equations with triangular matrices are easier to solve, the triangular matrices are very important in mathematics. For instance, the LU decomposition gives an algorithm to decompose any invertible matrix A into two triangular factors: a lower triangle matrix L and an upper triangle matrix U. Moreover, the inverse of a triangular matrix is also triangular. Also the product of two lower triangular matrices produces a lower triangular matrix, the same apply for upper triangular matrices. A lot of important notions, such as the determinant, the eigenvalue problem and many others are easy to handle when we are working …

Cognitive Constructs In Linear Algebra; Metaphors, Metonymies, Modes, Ruben Carrizales

Open Access Theses & Dissertations

Analysis focused on the presence of different thinking modes, metonymies, and metaphors found on the interview responses to questions related to linear independence, span, and spanning sets of three students, A12, A22 and C3, taking their first linear algebra course at the college level. Findings provide insight into how first year linear algebra students move from one thinking mode to another, and the kind of metonymies and metaphors are used to construct new knowledge. The main purpose of this research was to discover and analyze the presence of the different modes of thinking and metonymy/metaphors- in the reasoning of these …

Incidence Functions, Yiyu Liao

Open Access Theses & Dissertations

In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we have …

Use Of Cognitive Constructs In Linear Algebra, Azucena Zamora

Open Access Theses & Dissertations

Thesis analyzed the presence of two cognitive entities-- modes of thinking and metonymies and metaphors- in the reasoning of three students enrolled in a first year matrix algebra course at a southwest university via the responses given to a set of eight questions asked during one-on-one interviews. The findings of our analysis shed light on the cognitive constructs that students employ to form their understanding of linear algebra concepts. Furthermore, our findings provide clues about the ways in which students move from one mode of thinking to another in the context of varying levels of exposure to graphical, algebraic, and …

Signature Matrices: The Eigenvalue Problem, Valeria Aguirre Holguin

Open Access Theses & Dissertations

Dealing with matrices can give us a hard time, especially when their dimension is too big, but we also well know how valuable information a matrix may carry, and that is why we study them. When a matrix has a significant number of zeroes we realize how much easier all calculations are. For instance, the product will be simpler to calculate, the determinant, the inverse and even the eigenvalue problem. This thesis provides the description and behavior of a very special kind of matrices which we call signature matrices. A particular feature of these matrices lies in the fact that …

A Characterization Of Pseudo-Orders In The Ring Zn, Jorge Ivan Vargas

Open Access Theses & Dissertations

Partially ordered sets are widely studied in algebra. The theory of lattice-ordered and partially-ordered rings is an important case. In this paper, we consider a more general relation: pseudo orders, which are relations that are reflexive and antisymmetric, but are not necessarily transitive. Analogously to partially-ordered rings, we study pseudo-ordered rings. We present a general characterization for pseudo-ordered rings, and then we focus on a specific structure: the ring Zn. Having the constraints of this ring, we are able to give the conditions under which Zn can be pseudo-ordered.

Multiplicative Riesz Decomposition On The Ring Of Matrices Over A Totally Ordered Field, Julio Cesar Urenda

Open Access Theses & Dissertations

The Riesz Decomposition Theorem for lattice ordered groups asserts that when G is an l-group and when a nonnegative element a is bounded by a product of nonnegative elements b1,...,bn, then a can be decomposed into a product of nonnegative elements b'1,...,b'n, i.e., a = b'1·...·b' n, with the property that b'i ≤ bi for any i = 1,...,n. In this work we characterize all nonnegative matrices for which this decomposition is possible with respect to matrix multiplication. In addition, we show that this result can be applied to ordered semigroups.

Introduction To Pseudo-Ordered Groups, Maria Dolores Cruz

Open Access Theses & Dissertations

We will give a definition, examples and basic properties of pseudo-ordered groups. These generalize partially-ordered groups. The pseudo-ordered groups have a compatible pseudo-order relation that may lack transitivity. Unlike partially-ordered groups, our groups can be finite and still admit a non-trivial pseudo-order. We will show necessary and sufficient conditions for a group to have a compatible pseudo-order. We also consider maximal pseudo-orders. We give a definition of a pseudo chain induced by a pseudo-order and characterize all pseudo chains on the group $\mathbb {Z}_{n}.$ We will calculate the number of non-isomorphic pseudo-orders on $\mathbb {Z}_{n}$ for $ n < 24.$

Survey Research On Communication And Language For English Language Learners And Native English Speakers Enrolled In A College Course On Statistical Literacy, Maria Guadalupe Valenzuela

Open Access Theses & Dissertations

The purpose of this study was to examine in what ways language is a factor that affects the learning process of students in an introductory statistics class. This research used a questionnaire survey instrument called: CLASS, Communication, Language And Statistics Survey that was applied to a total of 137 college students from a large southwestern public university, 83 of these students were self-identified as native English speakers (NOELL) and 53 were self-identified as English learner speakers (ELL) and one was dropped. This research found that in statistical instruction, there are some particular differences in behavior and learning process in the …

Exponential Dichotomy Of Ode's, Nada Farid Al-Hanna

Open Access Theses & Dissertations

I present an elementary Functional Analytic proof of the roughness of Exponential Dichotomy of Ordinary Differential Equations (with exponential growth) on an arbitrary Banach Space.

Asymptotic Approximation Of The Free Boundary For The American Put Near Expiry, Walt E. Bales

Open Access Theses & Dissertations

An introduction to boundary value problems for the heat operator will focus on the Dirichlet and Neumann problems in bounded domains. Following an overview of the basic financial principles of derivative securities, a derivation of the Black-Scholes formulae will be given. Partial differential equations as free boundary problems will then be discussed and applied to modeling the American Put option. A method of solution close to expiry will then be investigated.

Third Grade Students' Challenges And Strategies To Solving Mathematical Word Problems, Elizabeth Bernadette

Open Access Theses & Dissertations

This project explores the difficulties and challenges that third grade students face solving mathematical word problems. Three students were asked to be participants and share their knowledge on this topic as well as their work. After extensive interviews it was concluded that the challenges of mathematical word problems include but are not limited to the level of reading comprehension, conceptual understanding of mathematical concepts, and the belief that math is a compilation of computations and unexplainable procedures. The participants provided insight as to what strategies are helpful to students. These strategies include group discussion on problem solving strategies, self-assessment, incorporating …

Examples Of Hyperbolic Knots With Distance 3 Toroidal Surgeries In The 3-Sphere, Cesar Garza

Open Access Theses & Dissertations

By the work of Thurston, any surgery on a hyperbolic knot in the 3-sphere produces a hyperbolic 3-manifold except in at most finitely many cases. So far, the figure-8 knot seems to be the best candidate for a hyperbolic knot with the most (8) non-trivial exceptional surgeries. In recent years, much progress has been made in the classification of hyperbolic knots admitting more than one exceptional toroidal surgery. In fact, such classification is known for toroidal surgeries with distance at least 4.

We give a classification of hyperbolic knots in $S^3$ admitting two toroidal surgeries at distance 3, whose slopes …

Semi-Automated Frame Transformations Using Fft Analysis On 2-D Images, Francisco Javier Osuna

Open Access Theses & Dissertations

Cassini entered Saturn's orbit on July 1, 2004 beginning a four-year exploration of Saturn. In 2008 the mission was extended, and Cassini continues to collect and transmit images and data collected during its mission. In order to accurately interpret images, it is necessary to know the location and orientation of the camera provided the field of view when the image was collected. While the mission managers provide initial estimates of this orientation, scientific analysis requires better estimates than the initial data provided. Navigation is a process for improving the estimation of the true camera pointing vector as determined by features …

Adaptive Hp-Fem For Elliptic Problems In 3d On Irregular Meshes, David Andrs

Open Access Theses & Dissertations

This work deals with adaptive hp-FEM on irregular meshes. It shows the advantage of completely irregular meshes, using the arbitrary level hanging nodes. The above is demonstrated on a numerical example with distribution of electrical potencial.

On Markov Chain Monte Carlo Methods For Neural Networks, Raul Cruz-Cano

Open Access Theses & Dissertations

Neural Networks (NN) have been used successfully to solve many different problems. It is an area of computer science and statistics that is very useful in real life. The advantages of NN consist of their ability to produce nonlinear input-output mapping, their adaptability, fault tolerance, uniform analysis and design. The search for better ways to train them consists of trying to find the optimal values of their free parameters. Some of these training algorithms are based on Markov Chains. They have some advantages over the traditionally used deterministic methods. In this document the main ideas related to these concepts are …