Mathematics Commons^™

Evaluation Of Control Strategies For The Spread Of Citrus Greening, Vicente Valle Martinez

Theses and Dissertations - UTB/UTPA

Huanglongbing, also known as citrus greening, is a vector-based disease in citrus (with no cure known to date) that has drastically affected the citrus production in Florida in less than a decade and has been recently detected in Texas and California. In this paper, an epidemic model of the spatial spread of the disease is implemented among commercial and residential groves by taking into consideration the diffusion patterns of the psyllid vectors. A system of differential equations resembling one for malaria infection in humans is derived to evaluate different control methods such as quarantine, treatment, removal, foliar treatment, and pest …

Bounded Rationality Alters The Dynamics Of Paediatric Immunization Acceptance, Tamer Oraby, Chris T. Bauch

School of Mathematical & Statistical Sciences Faculty Publications

Interactions between disease dynamics and vaccinating behavior have been explored in many coupled behavior-disease models. Cognitive effects such as risk perception, framing, and subjective probabilities of adverse events can be important determinants of the vaccinating behaviour, and represent departures from the pure “rational” decision model that are often described as “bounded rationality”. However, the impact of such cognitive effects in the context of paediatric infectious disease vaccines has received relatively little attention. Here, we develop a disease-behavior model that accounts for bounded rationality through prospect theory. We analyze the model and compare its predictions to a reduced model that lacks …

Non-Communicable Diseases And Preventive Health Behaviors: A Comparison Of Hispanics Nationally And Those Living Along The Us-Mexico Border, Belinda M. Reininger, Jing Wang, Susan P. Fisher-Hoch, Alycia Boutte, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Background: Non-communicable diseases (NCDs) are rising among US Hispanics, but few studies have examined the preventive health behaviors for these NCDs among Hispanics. This study compared the preventive health behaviors of smoke-free living, physical activity, fruit and vegetable consumption, and avoidance of heavy alcohol use in Hispanics in the United States and Hispanics living along the US-Mexico border.

Methods: Two weighted data sets with information on Hispanic populations were analyzed: 1) the national Behavioral Risk Factor Surveillance Survey (n = 29,942) from 2009; and 2) the Cameron County Hispanic Cohort (n = 1,439) recruited from the US-Mexico border between 2008–2011. …

Complex Short Pulse Equation And Its Integrable Discretizations, Raul M. Guajardo

Theses and Dissertations - UTB/UTPA

In this thesis, we are mainly concerned with the complex short pulse (CSP) equation which was proposed in Physica D [1]. We present the Lax pair of the CSP equation and show the compatibility condition gives the CSP equation. Therefore, the integrability is confirmed. Then, a set of bilinear equations is proposed which yields the CSP equation through the hodograph transformation. Based on the bilinear form, general N-soliton solution is given in determinant form. Regarding two-soliton solution, a bound state can be formed if the velocities of two solitons are equal. Furthermore, a semi- and fully discrete analogues are constructed …

Subclinical Atherosclerosis And Obesity Phenotypes Among Mexican Americans, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Mohammad H. Rahbar, Belinda M. Reininger, David D. Mcpherson, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

Background

Data on the influence of obesity on atherosclerosis in Hispanics are inconsistent, possibly related to varying cardiometabolic risk among obese individuals. We aimed to determine the association of obesity and cardiometabolic risk with subclinical atherosclerosis in Mexican‐Americans.

Methods and Results

Participants (n=503) were drawn from the Cameron County Hispanic Cohort. Metabolic health was defined as <2 of the following: blood pressure ≥130/85; triglyceride ≥150 mg/dL; high‐density lipoprotein cholesterol <40 mg/dL (men) or <50 mg/dL (women); fasting glucose ≥100 mg/dL; homeostasis model assessment of insulin resistance value >5.13; or high‐sensitivity C‐reactive protein >3 mg/L. Carotid intima media thickness (cIMT) was measured. A high proportion of participants (77.8%) were metabolically unhealthy; they were more likely to be male, older, with fewer years of education, and less likely to meet daily recommendations regarding …

Some Results For The Hodge Decomposition Theorem In Euclidean Three-Space, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The Hodge Decomposition Theorem plays a significant role in the study of partial differential equations. Several interrelated propositions which are required for the proof of the Hodge theorem in Euclidean three-space are introduced and proved in a novel way.

Critical Controlled Branching Processes And Their Relatives, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed.

Customizing Course Redesign And Flipped Classroom Models To Improve Learning Environment, Taeil Yi, Jerzy Mogilski

School of Mathematical & Statistical Sciences Faculty Publications

This article is about a successful adoption of course redesign model of mathematics courses at the Department of Mathematics in the University of Texas at Brownsville (UTB), a Hispanic serve university in the south Texas. Around 2007 National Center for Academic Transformation (NCAT) recommended six models for using of information technology to redesign courses in mathematics: the supplemental model, the replacement model, the emporium model, the fully online model, the buffet model, and the linked workshop model. Because of the local educational environment and resources none of the six models could be implemented exactly like it was described by NCAT. …

Symmetries Of Monocoronal Tilings, Dirk Frettlöh, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher …

Asymptotic Analysis Of A Magnetized Target Fusion Reactor, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Nonlinear conservation laws with moving boundaries often arise in applications such as gas dynamics and more recently in the context of nuclear fusion reactors. Gaining insight into the nature of solutions to such models and their dependence upon design parameters is often done numerically. We use formal asymptotics to study a model of a magnetized target fusion reactor for producing energy. We will asymptotically solve the compressible Euler equations with two free moving boundaries, with an algebraic coupling of fluid pressure at one of the free boundaries. The model consists of an intense pressure being imparted on the boundary of …

Connections Of Zero Curvature And Bäcklund Transformations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Zero curvature connections in a principal bundle are introduced. It is shown that such connections are very useful in formulating the Bäcklund problem and in constructing transformations. A general technique can be proposed for producing such transformations by defining the relevant connection coefficients appropriately. Finally, several applications of this work to various types of nonlinear partial differential equations will be presented.

Two Dimensional Mathematical Model Of Fluid Flow In A Growing Solid Tumor, Adriana Gracia

Theses and Dissertations - UTB/UTPA

We investigate the problem of steady and unsteady fluid flow in a growing solid tumor. We develop a mathematical model for the two dimensional fluid flow in a spherical tumor where the spatial variations of the interstitial velocity, interstitial pressure and the drug concentration within the tumor are, in general, with respect to the radial distance and the latitudinal angle in the spherical coordinates. The expressions for radial and latitudinal variations of the interstitial velocity, interstitial pressure, and the two investigated drug concentrations were determined analytically. We calculated these quantities in the tumor as well as in a corresponding normal …

Gradient-Based Compressive Sensing For Noise Image And Video Reconstruction, Huihuang Zhao, Yaonan Wang, Xiaojiang Peng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a convex minimisation problem, and propose a new compressive sensing based on gradient-based method for noise image and video. Secondly, to improve the computational efficiency of gradient-based compressive sensing, they formulate the convex optimisation of noise signal reconstruction under Lipschitz …

Connections Of Zero Curvature And Applications To Nonlinear Partial Differential Equations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Bäcklund tranformations can be formulated for such equations that occur as zero curvature terms.

Limit Distributions Of Random Walks On Stochastic Matrices, Santanu Chakraborty, Arunava Mukherjea

School of Mathematical & Statistical Sciences Faculty Publications

Problems similar to Ann. Prob. 22 (1994) 424–430 and J. Appl. Prob. 23 (1986) 1019–1024 are considered here. The limit distribution of the sequence XnXn−1 ··· X1, where (Xn)n≥1 is a sequence of i.i.d. 2 × 2 stochastic matrices with each Xn distributed as μ, is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components Cn and Dn (not necessarily independent), (Cn, Dn) being the first column of Xn, have the same (or different) Bernoulli distributions. Thus (Cn, Dn) is valued in {0, r}2, where r is …

Energy And Potential Enstrophy Flux Constraints In Quasi-Geostrophic Models, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We investigate an inequality constraining the energy and potential enstrophy flux spectra in two-layer and multi-layer quasi-geostrophic models. Its physical significance is that it can diagnose whether any given multi-layer model that allows co-existing downscale cascades of energy and potential enstrophy can allow the downscale energy flux to become large enough to yield a mixed energy spectrum where the dominant k−3 scaling is overtaken by a subdominant k−5/3 contribution beyond a transition wavenumber kt situated in the inertial range. The validity of the flux inequality implies that this scaling transition cannot occur within the inertial range, whereas a violation of …

Dynamics For The Compound Burgers-Kdv Equation, Xiangqian Zheng

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation and Two-Dimensional Compound Burgers-Korteweg-de Vries (2D-Compound BKdV) by analyzing the first integral equation, which indicates that under some particular conditions, the 2D-BKdV equation and 2D-Compound BKdV have exact traveling wave solutions. By using the elliptic integral and some transformations, traveling wave solution to the 2D-BKdV equation and 2DCompound BKdV are expressed explicitly.

Balanced Modular Parameterizations, Esteban J. Melendez

Theses and Dissertations - UTB/UTPA

In this thesis, we show that Classical representations for certain modular forms have symmetric form. These symmetric formulations are interpreted in terms of more general balanced homogeneous polynomial representations resulting from a permutative action of Hecke congruence subgroups on quotients of theta functions. For prime levels between 5 and 19, sets of permuted theta quotients are constructed that generate the corresponding vector spaces of modular forms of weight one.

An Empirical Study Of Some Branching Processes With Upper Barrier, Alejandro Aguilar

Theses and Dissertations - UTB/UTPA

We consider discrete time branching processes with a reflecting upper barrier. The processes differ in their offspring distributions being either binary splitting or binomial one. Two important factors for the behavior of the processes characteristics are studied as follows: time to extinction and total progeny up to the n th generation. More specifically, we investigate the distribution and expected value of the time to extinction as well as the probability mass functions of the total progeny. The tools used are basic results for a finite state Markov chain.

Anxiety, Depression And Smoking Status Among Adults Of Mexican Heritage On The Texas-Mexico Border, Anna V. Wilkinson, Kristina Vatcheva, Adriana Pérez, Belinda M. Reininger, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

The goal of the current analysis is to examine relationships between smoking status and anxiety and depression among adults of Mexican heritage to inform the development of culturally relevant smoking cessations efforts. Mexican heritage residents (N=1,791) of the city of Brownsville, TX, aged 18 years or older, enrolled in the Cameron County Hispanic Cohort, were selected through two stage cluster sampling of randomly selected census tracts from the first and third quartile of SES using Census 2000. Among current smokers, anxiety and depression scores were highest among women who had not completed high school (p<0.05). Former smoking women, but not men, with at least a high school education and former smoking women born in the United States reported higher levels of anxiety and depression than never smoking women. Negative affective states may represent a greater barrier to smoking cessation among women than men.

Reconstruction Of Structured Quadratic Pencils From Eigenvalues On Ellipses And Parabolas, R. Ibragimov, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper we study the reconstruction of a structured quadratic pencil from eigenvalues distributed on ellipses or parabolas. A quadratic pencil is a square matrix polynomial

QP(λ) = M λ²+Cλ +K,

where M, C, and K are real square matrices. The approach developed in the paper is based on the theory of orthogonal polynomials on the real line. The results can be applied to more general distribution of eigenvalues. The problem with added single eigenvector is also briefly discussed. As an illustration of the reconstruction method, the eigenvalue problem …

The Born Approximation, Multiple Scattering, And The Butterfly Algorithm, Alejandro F. Martinez

Theses and Dissertations - UTB/UTPA

Radar works by focusing a beam of light and seeing how long it takes to reflect. To see a large region the beam is pointed in different directions. The focus of the beam depends on the size of the antenna (called an aperture). Synthetic aperture radar (SAR) works by moving the antenna through some region of space. A fundamental assumption in SAR is that waves only bounce once. Several imaging algorithms have been designed using that assumption. The scattering process can be described by iterations of a badly behaving integral. Recently a method for efficiently evaluating these types of integrals …

The Generation Model Of Internal Waves In A Forced Rotation-Modified Ocean, Daqi Xin

Theses and Dissertations - UTB/UTPA

A two-layer model which contains the forcing term due to the barotropic tides which flow over a comparatively large bottom topography in the ocean was derived previously. The model can be used to describe the generation of nonlinear dispersive internal tides and the following disintegration into internal waves. We studied the influence of Coriolis effect. A numerical simulation shows that the Earth’s rotation affects the generation of the internal waves since it hampers the disintegration of internal tides into internal waves.

Using The Differential Fay Identities For Ribbon Graph Enumeration, Indalecio Soto Jr.

Theses and Dissertations - UTB/UTPA

In this paper we are exploiting connections between the Differential Fay Identities and the partition function of Gaussian Unitary Random Matrices. The partition function has a asymptotic expression whose terms give the generating function for the enumeration of ribbon graphs partitioned by genus. These ribbon graphs (k; j), of k vertices of degree j have an orientation in genus g where the edges are represented as ribbons. Furthermore, we will develop connections between the Differential Fay Identities and introduce several theorems between the hierarchies of the identities. Lastly, we will briefly explore the first Differential Fay Identity that contains the …

Quantization Dimension For Gibbs-Like Measures On Cookie-Cutter Sets, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper using the Banach limit we have determined a Gibbs-like measure μ h supported by a cookie-cutter set E which is generated by a single cookie-cutter mapping f . For such a measure μ h and r ∈ ( 0 , + ∞ ) we have shown that there exists a unique κ r ∈ ( 0 , + ∞ ) such that κ r is the quantization dimension function of the probability measure μ h , and we established its functional relationship with the temperature function of the thermodynamic formalism. The temperature function is commonly used to …

Illustrations And Supporting Texts For Sound Standing Waves Of Air Columns In Pipes In Introductory Physics Textbooks, Liang Zeng, Chris Smith, G. Herold Poelzer, Jennifer Rodriguez, Edgar Corpuz, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

In our pilot studies, we found that many introductory physics textbook illustrations with supporting text for sound standing waves of air columns in open-open, open-closed, and closed-closed pipes inhibit student understanding of sound standing wave phenomena due to student misunderstanding of how air molecules move within these pipes. Based on the construct of meaningful learning from cognitive psychology and semiotics, a quasiexperimental study was conducted to investigate the comparative effectiveness of two alternative approaches to student understanding: a traditional textbook illustration approach versus a newly designed air molecule motion illustration approach. Thirty volunteer students from introductory physics classes were randomly …

Radar Image Processing And Its Applications Based On Convolution Back Projection, Qitong Li

Theses and Dissertations - UTB/UTPA

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and a SAR image processing algorithm called Convolution Back Projection (CBP) will be introduced in this thesis, which can be applied to data gathered by a Synthetic Aperture Radar (SAR) system to produce high resolution images. The purpose of this thesis is starting from Maxwell’s equations to study the CBP algorithm as it is applied to SAR image processing. Two different image simulation results will be provided by this method.

Solution Of Fractional Harmonic Oscillator In A Fractional B-Poly Basis, Muhammad I. Bhatti

School of Mathematical & Statistical Sciences Faculty Publications

An algorithm for approximating solutions to fractional-order differential equations in fractional polynomial basis is presented. A finite generalized fractional-order basis set is obtained from the modified Bernstein Polynomials, where α is the fractional-order of the modified Bernstein type polynomials (B-polys). The algorithm determines the desired solution in terms of continuous finite number of generalized fractional polynomials in a closed interval and makes use of Galerkin method to calculate the unknown expansion coefficients for constructing the approximate solution to the fractional differential equations. The Caputo’s definition for a fractional derivative is used to evaluate derivatives of the polynomials. Each term in …

Topological Pressure And Fractal Dimensions For Bi-Lipschitz Mappings, Hugo E. Olvera

Theses and Dissertations - UTB/UTPA

In this thesis, first we have defined the topological pressure P(t) and then using Banach limit we have determined a unique Borel probability measure µh supported by the invariant set E of a system of bi-Lipschitz mappings where h is the unique zero of the pressure function. Using the topological pressure and the measure µh, under certain condition on bi-Lipschitz constants, we have shown that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension of the set E are all equal to h. Moreover, it is shown that the h-dimensional Hausdorff measure and the …

On Toroidal Knots, Chirality, And Molecules, Ramiro Garza

Theses and Dissertations - UTB/UTPA

The inspiration for this thesis came from two sources: the book When topology meets chemistry: a topological look at molecular chirality, by Erica Flapan [7], which discusses topologically interesting molecules; and the paper All toroidal embeddings of polyhedral graphs in 3-space are chiral, by T. Castle et al., which proves that toroidal embeddings of polyhedra are chiral. Their proof is examined in detail. A possible application of this work, as discussed by the team, would be in molecules which have the structure of a toroidal polyhedral embedding. Various methods of seeking such an example are attempted and discussed.