Physical Sciences and Mathematics Commons^™

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 and Statistical Sciences Faculty Publications and Presentations

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 …

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 and Statistical Sciences Faculty Publications and Presentations

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 and Statistical Sciences Faculty Publications and Presentations

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 …

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 and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 and Statistical Sciences Faculty Publications and Presentations

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 …