Mathematics Commons^™

The Mean Transform Of Bounded Linear Operators, Sang Hoon Lee, Woo Young Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we introduce the mean transform of bounded linear operators acting on a complex Hilbert space and then explore how the mean transform of weighted shifts behaves, in comparison with the Aluthge transform.

Optimal Control In The Treatment Of Retinitis Pigmentosa, Erika T. Camacho, Luis A. Melara, Cristina Villalobos, Stephen Wirkus

School of Mathematical & Statistical Sciences Faculty Publications

Numerous therapies have been implemented in an effort to minimize the debilitating effects of the degenerative eye disease Retinitis Pigmentosa (RP), yet none have provided satisfactory long-term solution. To date there is no treatment that can halt the degeneration of photoreceptors. The recent discovery of the RdCVF protein has provided researchers with a potential therapy that could slow the secondary wave of cone death. In this work, we build on an existing mathematical model of photoreceptor interactions in the presence of RP and incorporate various treatment regiments via RdCVF. Our results show that an optimal control exists for the administration …

On Cubic Multisections Of Eisenstein Series, Andrew Alaniz, Timothy Huber

School of Mathematical & Statistical Sciences Faculty Publications

A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. We prove that the resulting series are rational functions of η(τ) and η(3τ), where η is the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations. These operators exhibit properties that mirror those of similarly defined quintic operators.

Assessing The Optimal Virulence Of Malaria‐Targeting Mosquito Pathogens: A Mathematical Study Of Engineered Metarhizium Anisopliae, Bernhard Konrad, Michael R. Lindstrom, Anja Gumpinger, Jielin Zhu, Daniel Coombs

School of Mathematical & Statistical Sciences Faculty Publications

Background

Metarhizium anisopliae is a naturally occurring fungal pathogen of mosquitoes. Recently, Metarhizium has been engineered to act against malaria by directly killing the disease agent within mosquito vectors and also effectively blocking onward transmission. It has been proposed that efforts should be made to minimize the virulence of the fungal pathogen, in order to slow the development of resistant mosquitoes following an actual deployment.

Results

Two mathematical models were developed and analysed to examine the efficacy of the fungal pathogen. It was found that, in many plausible scenarios, the best effects are achieved with a reduced or minimal pathogen …

Ill-Posedness Of The Two-Dimensional Keller-Segel Model In Triebel-Lizorkin Spaces, Chao Deng, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

This article proves the ill-posedness of the Cauchy problem for the two-dimensional Keller–Segel model in Triebel–Lizorkin spaces, for . In particular, it is shown that solutions can develop norm inflation under certain settings in that the solution can become arbitrarily large after an arbitrarily short time even for small initial data.

Lessons Learned In Establishing Stem Student Cohorts At A Border University And The Effect On Student Retention And Success, Mikhail M. Bouniaev, Immanuel Edinbarough, Bill W. Elliott

School of Mathematical & Statistical Sciences Faculty Publications

The University of Texas at Brownsville (UTB) serves more than 8,000 students in the Lower Rio Grande Valley area and broader Mexico region. UTB is a Hispanic-serving institution that attracts students from the surrounding areas, including the Mexico border region. The College of Science, Mathematics and Technology (CSMT) established a Science, Technology, Engineering, and Mathematics (STEM) cohort program to help the majority of students to earn a degree in a STEM field in the shortest possible time. The challenges and obstacles encountered during the planning and implementation phase of the STEM cohort program are discussed in this paper, as are …

Peakon, Pseudo-Peakon, And Cuspon Solutions For Two Generalized Camassa- Holm Equations, Jibin Li, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing.

The Computation Of Fluid Velocity In A Closed Cavity With A Moving Lid, Daniel A. Montez

Theses and Dissertations - UTB/UTPA

We consider a cavity filled with fluid whose three sides are stationary and the lid at the top is moving at a constant speed. The flow in the cavity is modeled using the conservation of mass and momentum equations with proper boundary conditions. We compute the fluid velocity for the steady state case using the finite element method. We seek the weak formulation and develop a finite element model based on the Galerkin method. Furthermore we use the penalty function method to modify our weak formulation to eliminate the pressure. The Gaussian quadrature method is used to evaluate our integrals …

On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera

Theses and Dissertations - UTB/UTPA

The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …

Mexican-American Children's Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors influencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children through …

Mexican-American Children’S Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, David Irizarry, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors infl uencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children …

Distributed Sparse Matrix Solver And Pivoting Algorithms For Large Linear Equations, Esteban Torres

Theses and Dissertations - UTB/UTPA

This thesis presents a distributed sparse direct solver and pivoting strategies for distributed sparse LU factorization. In Chapter I, we introduce some background concepts in linear algebra. In Chapter II, we discuss parallel hardware architectures and introduce our problem for discussion. In Chapter III, we describe the implementation of our sparse direct solver and our pivoting algorithms. Next, we present our simulation methodology and results in Chapter IV and we show that our pivoting algorithm yields up to 50% more accurate results than a current state-of-the-art solver, SuperLU_DIST. Finally, in Chapter V, we present some ideas to further improve the …

Synthetic Aperture Radar With Compressed Sensing, Yufeng Cao

Theses and Dissertations - UTB/UTPA

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and compressed sensing are introduced to the signal model for SAR image reconstruction. Random Partial Fourier Matrices were applied to prove that compressed sensing can be used to this signal model from the viewpoint of mathematics. In the numerical simulation part, we show that the procedure of basis pursuit can reconstruct SAR image, based on our main results, which is shown efficient in comparison with the matched filter algorithm.

Examine Participant Dropout, Undiagnosed Diabetes And Undiagnosed Prediabetes In A Chronic Disease Prevention Education Program, Yiwen Cao

Theses and Dissertations - UTB/UTPA

There were 2768 participants enrolled in a chronic disease prevention education program. Survey and health measurements were obtained at three time points. We examine potential factors that might contribute to participant dropout, undiagnosed diabetes and undiagnosed prediabetes respectively. Logistic regression was used to examine the association between participant dropout and predictors, and to compare the odds of being undiagnosed with diabetes and prediabetes. We found that the potential predictors for participant dropout included age, employment, insurance, diabetes, self-reported health status, session type, program duration and curriculum. Factors affecting undiagnosed diabetes and prediabetes were age, self-reported health status birth country, limited …

Traveling Wave Solution To Two-Dimensional Burgers-Korteweg-De Vries Equation, Xiaoqian Gong

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analyzing the equivalent Abel equation, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded traveling wave solution. By using the theorem of contractive mapping, a traveling wave solution to the 2D-BKdV equation is expressed explicitly. In the end, the behavior of the proper solution of the 2D-BKdV equation is established by applying the comparison theorem of differential equations.

On Cubic Multisections, Andrew Alaniz

Theses and Dissertations - UTB/UTPA

In this thesis, a systematic procedure is given for generating cubic multi-sections of Eisenstein series. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. The resulting series are shown to be rational functions of the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations.

Lax Pairs For Some Nonlinear Equations, Ana Castillo

Theses and Dissertations - UTB/UTPA

Several methods have been proposed to approach the topic of integrable systems of nonlinear partial differential equations. One of these methods is called the Lax pair. The Lax pair is a pair of matrices or operators, that depend on time and satisfy the Lax equation. Based on the inverse scattering method introduced by Gardner, Greene, Kruskal and Miura (1967), Peter Lax introduced the Lax pair to derive soliton equations from the Lax equation. This thesis provides with a brief background on soliton theory, inverse scattering theory, and Lax pairs. The details missing in the work published by Ablowitz, Kaup, Newell, …

Hydro-Thermal Convective Solutions For An Aquifer System Heated From Below, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

We investigate the effect of hydro-thermal convection in an aquifer system. It is assumed that the aquifer is bounded below and above by impermeable boundaries and it is heated from below. The solution of the governing system is expressed in terms of the basic steady state solution and perturbed solution. We obtain the critical Rayleigh number and critical wavenumber using Runge-Kutta method in combination of shooting method and present the marginal stability curve. The amplitude equation is derived by introducing the adjoint system. After amplitude is obtained, we compute the linear solutions for super-critical and sub-critical cases. Numerical results for …

Algebro-Geometric Solutions For The Degasperis--Procesi Hierarchy, Yu Hou, Peng Zhao, Engui Fan, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Though the completely integrable Camassa--Holm (CH) equation and Degasperis--Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the …

Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical …

Mathematical Modeling Of Two-Phase Arterial Blood Flow, Ani Emire Garcia Escorcia

Theses and Dissertations - UTB/UTPA

Problem of blood flow in an artery with or without catheter and in the presence of single or multi stenosis will be considered. The presence of stenosis locally thickens the artery wall and the use of catheter in the affected area is very important to the diagnostic and treatment of the patient. The blood flow in the arterial tube is represented by a two-phase model composing a suspension of erythrocytes in plasma. The governing equations for both fluid and particles are solved subjected to reasonable modeling and approximations. The important quantities such as blood speed, blood pressure force, impedance (blood …

Compressed Sensing For Multiple Input-Multiple Output Radar Imaging, Juan F. Lopez Jr.

Theses and Dissertations - UTB/UTPA

Multiple input - multiple output (MIMO) radar utilizes the transmission of spatially diverse waveforms from a static antenna array to gather information about the desired scene. We will demonstrate how techniques from compressed sensing can be applied to image formation in MIMO radar when in the presence of undersampling. We analyze the problem under the general theoretical framework of inverse scattering.

A Model For The Micro-Doppler Effect Of The Quadrupedal Body Motion, Noe Pena

Theses and Dissertations - UTB/UTPA

In radar returns from quadrupedal body motion the micro-Doppler effect is present. This effect can be used to identify and distinguish this motion from others. In this work the model for the micro-Doppler effect due to quadrupedal motion is developed from Maxwell’s equations. The common gait for all quadrupedal mammal motion is described and analyzed. The radar crossection of quadrupedal motion backscattering is discussed. Quadrupedal motion is simulated and the radar returns are analyzed. The micro-Doppler signatures are decomposed and kinematic parameters are extracted

The Schwinger Action Principle And Its Applications To Quantum Mechanics, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

Analytic Matrix Elements Of The Schrödinger Equation, Muhammad I. Bhatti

School of Mathematical & Statistical Sciences Faculty Publications

A previously defined analytic technique of constructing matrix elements from the Bernstein-polynomials (B-poly) has been applied to Schr¨odinger equation. This method after solving generalized eigenvalue problem yields very accurate eigenenergies and eigenvectors. The numerical eigenvectors and eigenvalues obtained from this process agree well with exact results of the hydrogen-like systems. Furthermore, accuracy of the numerical spectrum of hydrogen equation depends on the number of B-polys being used to construct the analytical matrix elements. Validity of eigenvalues and quality of the constructed wavefunctions is verified by evaluating the Thomas-Reiche-Kuhn (TRK) sum rules. Excellent numerical agreement is seen with exact results of …

On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

Characterizations Of Exponential Distribution Based On Sample Of Size Three, George Yanev, Santanu Chakraborty

School of Mathematical & Statistical Sciences Faculty Publications

Two characterizations of the exponential distribution based on equalities among order statistics in a random sample of size three are proved. This proves two conjectures stated recently in Arnold and Villasenor [4].

On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

Distributional relations of the form Y d= X +T where X, Y, and T are record values or order statistics and the random translator T is independent from X are considered. Characterizations of the exponential distribution when the ordered random variables are non-neighboring are proved. Corollaries for Pareto and power function distributions are also derived.

Zero-Bounded Limits As A Special Case Of The Squeeze Theorem For Evaluating Single-Variable And Multivariable Limits, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

Many limits, typically taught as examples of applying the ‘squeeze’ theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful for both single-variable limits and multidimensional limits. A comprehensive treatment of multidimensional limits and continuity is also outlined.

The Two-Phase Arterial Blood Flow With Or Without A Catheter And In The Presence Of A Single Or Multi Stenosis, Ani E. Garcia, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

We consider the problem of blood flow in an artery with or without a catheter and in the presence of single or multi stenosis whose shape is based on the available experimental data for the stenosis in a human’s artery. The presence of stenosis in the artery, which locally narrows portion of the artery, can be a result of fatty materials such as cholesterol in the blood. The use of catheter is important as a standard tool for diagnosis and treatment in patience whose blood flow passage in the artery is affected adversely by the presence of the stenosis within …