Physical Sciences and Mathematics Commons^™

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 …

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 …

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 = …

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 …

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 …