Mathematics Commons^™

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.

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.

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.

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 …

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 …

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.

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 …