# School of Mathematical and Statistical Sciences Faculty Publications and Presentations

### Submissions from 2014

On cubic multisections of Eisenstein series, Andrew Alaniz and Timothy Huber

Solution of Fractional Harmonic Oscillator in a Fractional B-poly Basis, Muhammad I. Bhatti

Lessons Learned in Establishing STEM Student Cohorts at a Border University and the Effect on Student Retention and Success, Mikhail M. Bouniaev, Immanuel Edinbarough, and Bill W. Elliott

Connections of zero curvature and applications to nonlinear partial differential equations, Paul Bracken

Limit distributions of random walks on stochastic matrices, Santanu Chakraborty and Arunava Mukherjea

Ill-posedness of the two-dimensional Keller-Segel model in Triebel-Lizorkin spaces, Chao Deng and John Villavert

Energy and potential enstrophy flux constraints in quasi-geostrophic models, Eleftherios Gkioulekas

A theory of theta functions to the quintic base, Timothy Huber

Differential equations for septic theta functions, Timothy Huber and Danny Lara

Reconstruction of Structured Quadratic Pencils from Eigenvalues on Ellipses and Parabolas, R. Ibragimov and Vesselin Vatchev

Quantization dimension for Gibbs-like measures on cookie-cutter sets, Mrinal Kanti Roychowdhury

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, and Susan P. Fisher-Hoch

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, and George Yanev

Gradient-based compressive sensing for noise image and video reconstruction, Huihuang Zhao, Yaonan Wang, Xiaojiang Peng, and Zhijun Qiao

### Submissions from 2013

On Characterizations of Exponential Distribution through Order Statistics and Record Values with Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, and George Yanev

Hydro-thermal convective solutions for an aquifer system heated from below, Dambaru Bhatta

Analytic matrix elements of the Schrödinger equation, Muhammad I. Bhatti

A Note on the Fundamental Solution of the Heat Operator on Forms, Paul Bracken

The Schwinger Action Principle and Its Applications to Quantum Mechanics, Paul Bracken

Optimal Control in the Treatment of Retinitis Pigmentosa, Erika T. Camacho, Luis A. Melara, Cristina Villalobos, and Stephen Wirkus

Parameterizations for quintic Eisenstein series, Richard Charles, Timothy Huber, and Andoni Mendoza

The Two-Phase Arterial Blood Flow with or without a Catheter and in the Presence of a Single or Multi Stenosis, Ani E. Garcia and Daniel N. Riahi

Generalized local test for local extrema in single-variable functions, Eleftherios Gkioulekas

On equivalent characterizations of convexity of functions, Eleftherios Gkioulekas

Zero-bounded limits as a special case of the squeeze theorem for evaluating single-variable and multivariable limits, Eleftherios Gkioulekas

Algebro-geometric Solutions for the Degasperis--Procesi Hierarchy, Yu Hou, Peng Zhao, Engui Fan, and Zhijun Qiao

Peakon, pseudo-peakon, and cuspon solutions for two generalized Camassa- Holm equations, Jibin Li and Zhijun Qiao

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, and Marcia G. Ory

Quantization Dimension Estimate for Condensation Systems of Conformal Mappings, Mrinal Kanti Roychowdhury

Ethnic differences in 25-hydroxyvitamin D levels and response to treatment in CKD, Iris Sanchez, Roberto Mangoo-Karim, Jason R. Stubbs, George Yanev, and James B. Wetmore

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

### Submissions from 2012

Characterizations of Logistic Distribution Through Order Statistics with Independent Exponential Shifts, M. Ahsanullah, George Yanev, and Constantin Onica

Geometry of Partial Differential Equations, Paul Bracken

Quantum Mechanics Entropy and a Quantum Version of the H-Theorem, Paul Bracken

Missed opportunities for diagnosis and treatment of diabetes, hypertension, and hypercholesterolemia in a Mexican American population, Cameron County Hispanic Cohort, 2003-2008, Susan P. Fisher-Hoch, Kristina Vatcheva, Susan T. Laing, Monir Hossain, M Hossein Rahbar, Craig Hanis, H Shelton Brown, Anne R. Rentfro, Belinda M. Reininger, and Joseph B. Mccormick

The effect of asymmetric large-scale dissipation on energy and potential enstrophy injection in two-layer quasi-geostrophic turbulence, Eleftherios Gkioulekas

On quintic Eisenstein series and points of order five of the Weierstrass elliptic functions, Timothy Huber

High prevalence of subclinical atherosclerosis by carotid ultrasound among Mexican Americans: discordance with 10-year risk assessment using the Framingham risk score, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Anne R. Rentfro, David D. McPherson, Susan P. Fisher-Hoch, and Joseph B. McCormick

The Strong Thirteen Spheres Problem, Oleg R. Musin and Alexey S. Tarasov

Minimal Time Functions and the Smallest Intersecting Ball Problem with Unbounded Dynamics, Nguyen Mau Nam, M. Cristina Villalobos, and Nguyen Thai An

Negative-order Korteweg–de Vries equations, Zhijun Qiao and Engui Fan

Electrocardiographic abnormalities among Mexican Americans: Correlations with diabetes, obesity, and the metabolic syndrome, Saulette R. Queen, Beverly Smulevitz, Anne R. Rentfro, Kristina Vatcheva, David D. McPherson, Susan P. Fisher-Hoch, Joseph B. McCormick, and Susan T. Laing

Existence Theory for an Arbitrary Order Fractional Differential Equation with Deviating Argument, Youhui Su and Zhaosheng Feng

Persisting role of healthcare settings in hepatitis C transmission in Pakistan: cause for concern, E Var Hoeve, A J. Codlin, F Jawed, A J. Khan, L Samad, Kristina Vatcheva, M B. Fallon, M Ali, S K. Niaz, J B. Mccormick, and S P. Fisher-Hoch

### Submissions from 2011

The Hodge–de Rham decomposition theorem and an application to a partial differential equation, Paul Bracken

When is hyponormality for 2-variable weighted shifts invariant under powers?, Raul E. Curto and Jasang Yoon

Mathematical Modeling and Computation of Channel Flow over Discrete Structures, Rolando J. Olivares and Daniel N. Riahi

Statistical Changes of Lake Stages in Two Rapidly Urbanizing Watersheds, Shayne Paynter, Mahmood Nachabe, and George Yanev

A new integrable two-component system with cubic nonlinearity, Junfeng Song, Changzheng Qu, and Zhijun Qiao

Characterizations of Exponential Distribution Via Conditional Expectations of Record Values, George Yanev

### Submissions from 2010

Exterior Differential Systems Prolongations and Application to a Study of Two Nonlinear Partial Differential Equations, Paul Bracken

Dissipation scales and anomalous sinks in steady two-dimensional turbulence, Eleftherios Gkioulekas

Zeros of generalized Rogers–Ramanujan series: Asymptotic and combinatorial properties, Timothy Huber

Combinatorics of generalized q-Euler numbers, Timothy Huber and Ae Ja Yee

Bifurcations of traveling wave solutions for an integrable equation, Jibin Li and Zhijun Qiao

### Submissions from 2009

Polyphasic Wake/Sleep Episodes in the Fire Ant, Solenopsis Invicta, Deby L. Cassill, Skye Brown, Devon Swick, and George Yanev

Basic representations for Eisenstein series from their differential equations, Timothy Huber

Spatial Instability of Electrically Driven Jets with Finite Conductivity and Under Constant or Variable Applied Field, Saulo Orizaga and Daniel N. Riahi

Analysis of Rotating Flow Around a Growing Protein Crystal, Daniel N. Riahi and Charles W. Obare

### Submissions from 2008

A fragment on Euler's constant in Ramanujan's lost notebook, Bruce C. Berndt and Timothy Huber

An action for a classical string, the equation of motion and group invariant classical solutions, Paul Bracken

Quantum phases for a generalized harmonic oscillator, Paul Bracken

Some Applications of Dirac's Delta Function in Statistics for More Than One Random Variable, Santanu Chakraborty

Locality and stability of the cascades of two-dimensional turbulence, Eleftherios Gkioulekas

Winterberg’s conjectured breaking of the superluminal quantum correlations over large distances, Eleftherios Gkioulekas

Hadamard products for generalized Rogers–Ramanujan series, Timothy Huber

Changes in coral reef communities among the Florida Keys, 1996–2003, P. J. Somerfield, W. C. Jaap, K. R. Clarke, M. Callahan, K. Hackett, J. Porter, M. Lybolt, C. Tsokos, and George Yanev

### Submissions from 2007

On the elimination of the sweeping interactions from theories of hydrodynamic turbulence, Eleftherios Gkioulekas

A new proof on net upscale energy cascade in two-dimensional and quasi-geostrophic turbulence, Eleftherios Gkioulekas and Ka Kit Tung

Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasi-geostrophic turbulence?, Eleftherios Gkioulekas and Ka Kit Tung

Solving Ramanujan's differential equations for Eisenstein series via a first order Riccati equation, James M. Hill, Bruce C. Berndt, and Timothy Huber

New integrable hierarchy, its parametric solutions, cuspons, one-peak solitons, and M/W-shape peak solitons, Zhijun Qiao

On Mathematical Modeling, Nonlinear Properties and Stability of Secondary Flow in a Dendrite Layer, Daniel N. Riahi

### Submissions from 2006

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum, Eleftherios Gkioulekas and Ka Kit Tung

A New Integrable Equation with Cuspons and W/M-Shape-Peaks Solitons, Zhijun Qiao

### Submissions from 2005

On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence, Eleftherios Gkioulekas and Ka Kit Tung

### Submissions from 2003

Recent applications of fractional calculus to science and engineering, Lokenath Debnath

Category of Nonlinear Evolution Equations, Algebraic Structure, and r-Matrix, Zhijun Qiao, Cewen Cao, and Walter Strampp

### Submissions from 1999

The Weierstrass–Enneper System for Constant Mean Curvature Surfaces and the Completely Integrable Sigma Model, Paul Bracken, A. M. Grundland, and L. Martina

### Submissions from 1998

On Different Integrable Systems Sharing the Same Nondynamical R-Matrix, Zhijun Qiao and Walter Strampp

### Submissions from 1996

Effective characteristic polynomials and two-point Pade approximants as summation techniques for the strongly divergent perturbation expansions of the ground state energies of anharmonic oscillators, Jiri Cizek, Ernst Joachim Weniger, Paul Bracken, and Vladimir Spirko

### Submissions from 1995

A completely integrable system and parametric representation of solutions of the Wadati-Konno-Ichikawa hierarchy, Zhijun Qiao

### Submissions from 1994

A hierarchy of nonlinear evolution equations and finite-dimensional involutive systems, Zhijun Qiao

An involutive system and integrable C. Neumann system associated with the modified Korteweg-de Vries hierarchy, Zhijun Qiao

### Submissions from 1993

A new completely integrable Liouville's system produced by the Kaup-Newell elgenvalue problem, Zhijun Qiao