Mathematics Commons^™

Latinx Students’ Mathematics Anxiety And Their Study Habits: Exploring Their Relationship At The Postsecondary Level, Luis M. Fernandez, Xiaohui Wang, Olga Ramirez, Cristina Villalobos

School of Mathematical & Statistical Sciences Faculty Publications

Increasing Latinx students’ success in college-level mathematics calls for exploration on their mathematics anxiety as it relates to study habits. Using a sample of Latinx students in a Hispanic Serving Institution and their levels of mathematics anxiety, pairwise analyses revealed significant differences among subgroups. Moreover, regression analyses showed Latinx students’ study habits being predictive of mathematics anxiety. As a result, recommendations are provided that could alleviate mathematics anxiety and its effects on Latinx college students.

Stability Of Peakons And Periodic Peakons For A Nonlinear Quartic Camassa-Holm Equation, Aiyong Chen, Tongjie Deng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the orbital stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation (QCHE).We first verify that the QCHE has global peakon and periodic peakon solutions. Then by the invariants of the equation and controlling the extrema of the solution, we prove that the shapes of the peakons and periodic peakons are stable under small perturbations in the energy space.

Domes Over Curves, Alexey Glazyrin, Igor Pak

School of Mathematical & Statistical Sciences Faculty Publications

A closed piecewise linear curve is called integral if it is comprised of unit intervals. Kenyon's problem asks whether for every integral curve γ in ℝ3, there is a dome over γ, i.e. whether γ is a boundary of a polyhedral surface whose faces are equilateral triangles with unit edge lengths. First, we give an algebraic necessary condition when γ is a quadrilateral, thus giving a negative solution to Kenyon's problem in full generality. We then prove that domes exist over a dense set of integral curves. Finally, we give an explicit construction of domes over all regular n-gons.

Quantization Coefficients For Uniform Distributions On The Boundaries Of Regular Polygons, Joel Hansen, Itzamar Marquez, Mrinal Kanti Roychowdhury, Eduardo Torres

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular m-sided polygons inscribed in a circle. The result shows that the quantization coefficient for the uniform distribution on the boundary of a regular m-sided polygon inscribed in a circle is an increasing function of m, and approaches to the quantization coefficient for the uniform distribution on the circle as m tends to infinity.

Energy On Spheres And Discreteness Of Minimizing Measures, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In particular, we prove that the support of any minimizer of the p-frame energy has empty interior whenever p is not an even integer. A similar effect is also demonstrated for energies with analytic potentials which are not positive definite. In addition, we establish the existence of discrete minimizers for a large class of energies, which includes energies with polynomial potentials.

Hexagon Tilings Of The Plane That Are Not Edge-To-Edge, Dirk Frettlöh, Alexey Glazyrin, Z. Lángi

School of Mathematical & Statistical Sciences Faculty Publications

An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer k≥3, there exists a normal tiling of the Euclidean plane by convex hexagons of unit area with exactly k irregular vertices. Using the same approach we show that there are normal edge-to-edge tilings of the plane by hexagons of unit area and exactly k many n-gons (n>6) of unit area. A result of Akopyan yields an upper bound for k depending on the maximal diameter …

Local Zeta Functions And Koba–Nielsen String Amplitudes, Miriam Bocardo-Gaspar, Hugo García-Compeán, Edgar Y. López, Wilson A. Zúñiga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

This article is a survey of our recent work on the connections between Koba–Nielsen amplitudes and local zeta functions (in the sense of Gel’fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the fact that the p-adic strings seem to be related in some interesting ways with ordinary strings. p-Adic string amplitudes share desired characteristics with their Archimedean counterparts, such as crossing symmetry and invariance under Möbius transformations. A direct connection between p-adic amplitudes and the Archimedean ones is through the limit p→1. Gerasimov and Shatashvili studied the limit p→1 of the p-adic effective action …

Optimal Partial Boundary Condition For Degenerate Parabolic Equations, Huashui Zhan, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

For the stability of the non-Newtonian fluid equation∂u∂t−div(a(x)|∇u|p−2∇u)−N∑i=1bi(x)Diu+c(x,t)u=f(x,t),where a(x)|x∈Ω>0, a(x)|x∈∂Ω=0 and bi(x)∈C1(¯¯¯Ω), we know that the degeneracy of a(x) may make the usual Dirichlet boundary value condition overdetermined and only a partial boundary value condition is expected. How to depict the geometric characteristic of the partial boundary value condition has been a long-time standing open problem. In this study, an optimal partial boundary value condition has been proposed, and the stability of weak solutions based on this partial boundary value condition is established. When the rate of the diffusion coefficient decays to zero, we explore how it affects the …

Factors That Influence Teachers' Utilization Of Siop Learning Strategies When Teaching English Language Learners, Courtney R. Stuart

Theses and Dissertations

Despite standardized certification tests and popular English Language Learner trainings, the strategies and methods used in two educators’ classes would not be identical. In this case-study we look to see what variables cause teachers to utilize certain strategies and how these variables affect the number of strategies used consistently when teaching ELLs. We study the effect of teachers’ language experiences, certifications, participation in SIOP trainings, education levels, perceived preparedness, and years spent in the classroom.

Using quantitative and qualitative data we conclude that dual-language fluency and professional advancements can lead to teachers using more ELL learning strategies in their classrooms, …

Blood Flow Through An Artery In The Presence Of A Stenosis, Martin Carrillo

Theses and Dissertations

We consider blood flow through an artery in the form of a cylindrical pipe in the presence of a stenosis. Here blood is treated as an incompressible, viscous and non-Newtonian Bingham plastic fluid. We derive the equation of continuity and the momentum equation which are obtained using mass conservation law and momentum conservation law, respectively. Assuming that the flow is due to the pressure drop and wall shear stress, we derive the expressions for the velocity component in the axial direction and the volumetric flow rate in an artery. Computational results for the axial velocity and flow rate are obtained …

Optimal Quantization For Mixtures Of Two Uniform Distributions, Eduardo Orozco

Theses and Dissertations

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this thesis, for a mixed distribution we determine the optimal sets of n-means and the nth quantization errors for all positive integers n.

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical & Statistical Sciences Faculty Publications

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

Gupta, Ramanujan, Dyson And Ehrhart: Formulas For Partition Functions, Congruences, Cranks, And Polyhedral Geometry, Joselyne Rodriguez

Theses and Dissertations

We will revisit Gupta's result regarding properties of a formula for restricted partitions and generalize this. We will then use this result to prove an infinite family of congruences for a certain restricted partition function. We find and prove combinatorial witnesses, also known as cranks, for the congruences using polyhedral geometry.

Ramanujan Type Congruences For Quotients Of Level 7 Klein Forms, Timothy Huber, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dissection formulas for the series imply Ramanujan type congruences modulo powers of 7 for a family of generating functions that subsume the counting function for 7-core partitions. The broad class of arithmetic functions considered here enumerate colored partitions by weights determined by parts modulo 7. The method is a prototype for similar analysis of modular forms of level 7 and at other prime levels. As an example of the utility of the dissection method, the paper concludes with a derivation of novel congruences …

Visualization Of Exact Invariant Solutions Associated With Atmospheric Waves In A Thin Circular Layer, Ranis N. Ibragimov, Lauren D. Mongrain, Benjamin Stimmel, Olga Trozkaya, Guang Lin, Sheng Zhang, Vesselin Vatchev, Daniel Stankiewicz

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).

Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid-19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose E. Campo Maldonado, Timothy Huber, Cristina Villalobos

School of Mathematical & Statistical Sciences Faculty Publications

At the beginning of August 2020, the Rio Grande Valley (RGV) of Texas experienced a rapid increase of coronavirus disease 2019 (abbreviated as COVID-19) cases and deaths. This study aims to determine the optimal levels of effective social distancing and testing to slow the virus spread at the outset of the pandemic. We use an age-stratified eight compartment epidemiological model to depict COVID-19 transmission in the community and within households. With a simulated 120-day outbreak period data we obtain a post 180-days period optimal control strategy solution. Our results show that easing social distancing between adults by the end of …

A High-Precision Sar Echo Simulation Method Based On Fdtd, Bin Zou, Yanqiu Jia, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Synthetic aperture radar (SAR) echo simulation offers a low-cost and convenient way to obtain high-resolution images of targets, and plays an important role in system design and algorithm validation. Although high frequency approximation simulation is widely used, it is considered to be imprecise when calculating scattering field of fine structures, such as exhaust pipes and groove structures, especially in low frequency band. In this paper, a finite-difference time-domain (FDTD) based method is proposed for high-precision SAR echo simulation. In this method, scattering process of electromagnetic wave is accurately simulated to obtain equivalent electric and magnetic current on the surface of …

Road Network Detection Based On Improved Flicm-Mrf Method Using High Resolution Sar Images, Lamei Zhang, Chenwei Jiang, Bin Zou, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The automatic detection of road network from satellite and aerial images is highly significant in many actual applications, for instance, urban traffic measurement, military emergency response, and vehicle target tracking. Compared with other high-resolution satellite remote sensing images, high-resolution synthetic aperture radar (SAR) has become a popular research perspective for road detection owing to its insensitivity to the atmosphere and sun-illumination. However, the method of road network detection is still lagging due to the strong multiplicative speckle noise and complex background interference, causing the loss and break in the road segment extraction results. Aiming to solve this problem, a three-step …

On Problems With Weighted Elliptic Operator And General Growth Nonlinearities, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

This article establishes existence, non-existence and Liouville-type theorems for nonlinear equations of the form −div(|x| aDu) = f(x, u), u > 0, in Ω, where N ≥ 3, Ω is an open domain in R N containing the origin, N−2+a > 0 and f satisfies structural conditions, including certain growth properties. The first main result is a non-existence theorem for boundary-value problems in bounded domains star-shaped with respect to the origin, provided f exhibits supercritical growth. A consequence of this is the existence of positive entire solutions to the equation for f exhibiting the same growth. A Liouville-type theorem is then established, …

Lions-Type Theorem Of The P-Laplacian And Applications, Yu Su, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this article, our aim is to establish a generalized version of Lions-type theorem for the p-Laplacian. As an application of this theorem, we consider the existence of ground state solution for the quasilinear elliptic equation with the critical growth.

Representations Of Principal W-Algebra For The Superalgebra Q(N) And The Super Yangian Yq(1), Elena Poletaeva, Vera Serganova

School of Mathematical & Statistical Sciences Faculty Publications

We classify irreducible representations of finite W-algebra for the queer Lie superalgebra Q(n) associated with the principal nilpotent coadjoint orbits. We use this classification and our previous results to obtain a classification of irreducible finite-dimensional representations of the super Yangian YQ(1).

Eigenvalues And Eigenfunctions Of A Schrödinger Operator Associated With A Finite Combination Of Dirac-Delta Functions And Ch Peakons, Shouzhong Fu, Zhijun Qiao, Zhong Wang

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we first study the Schrodinger operators with the following weighted function ___________, which is actually a finite linear combination of Dirac-Delta functions, and then discuss the same operator equipped with the same kind of potential function. With the aid of the boundary conditions, all possible eigenvalues and eigenfunctions of the self-adjoint Schrodinger operator are investigated. Furthermore, as a practical application, the spectrum distribution of such a Dirac-Delta type Schrodinger operator either weighted or potential is well applied to the remarkable integrable Camassa-Holm (CH) equation.

Continuous-Time Controlled Branching Processes, Ines Garcia, George Yanev, Manuel Molina, Nikolay Yanev, Miguel Velasco

School of Mathematical & Statistical Sciences Faculty Publications

Controlled branching processes with continuous time are introduced and limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

Correlation Between No-Slip And Slip Boundary Conditions Associated With A Two-Dimensional Navier-Stokes Flows In A Plane Diffuser, Ranis Ibragimov, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro- parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.

Local Well-Posedness And Blow-Up For A Family Of U(1)-Invariant Peakon Equations, Stephen C. Anco, Huijun He, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The Cauchy problem for a unified family of integrable U(1)-invariant peakon equations from the NLS hierarchy is studied. As main results, local well-posedness is proved in Besov spaces, and blow-up is established through use of an L 1 conservation law.

Positive Solutions For A Class Of Elliptic Equations, Xiyou Cheng, Zhaosheng Feng, Lei Wei

School of Mathematical & Statistical Sciences Faculty Publications

This paper is concerned with a class of semilinear elliptic equations with a potential function−Δu=λ|x|−αu−|x|σupinΩ∖{0},where λ,σ∈R, α>0, p>1, and Ω⊂RN (N≥3) is a bounded smooth domain with 0∈Ω. We establish the existence, nonexistence and asymptotic behavior of positive solutions when the potential function |x|−α has strong singularity at the origin. When the potential function |x|−α has weak singularity at the origin, we obtain some qualitative properties of positive solutions.

Modeling The Effect Of Lockdown Timing As A Covid‑19 Control Measure In Countries With Differing Social Contacts, Tamer Oraby, Michael G. Tyshenko, Jose Campo Maldonado, Kristina Vatcheva, Susie Elsaadany, Walid Q. Alali, Joseph C. Longenecker, Mustafa Al‑Zoughool

School of Mathematical & Statistical Sciences Faculty Publications

The application, timing, and duration of lockdown strategies during a pandemic remain poorly quantified with regards to expected public health outcomes. Previous projection models have reached conflicting conclusions about the effect of complete lockdowns on COVID-19 outcomes. We developed a stochastic continuous-time Markov chain (CTMC) model with eight states including the environment (SEAMHQRD-V), and derived a formula for the basic reproduction number, R0, for that model. Applying the R 0 formula as a function in previously-published social contact matrices from 152 countries, we produced the distribution and four categories of possible R 0 for the 152 countries and chose one …

Traveling Wave Phenomena In A Nonlocal Dispersal Predator-Prey System With The Beddington-Deangelis Functional Response And Harvesting, Zhihong Zhao, Yan Li, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant c∗ such that the system possesses a traveling wave solution for any given c>c∗. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for c=c∗ is established by means of Corduneanu's theorem. The nonexistence of traveling wave …

Global-In-Time Solvability And Blow-Up For A Non-Isospectral Two-Component Cubic Camassa-Holm System In A Critical Besov Space, Lei Zhang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space B2,11/2(T). Our results show that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the L1-integrability of the variable coefficients α(t) and γ(t), but nothing to do with the shape of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial estimates of cubic nonlinearities in …

Huygens' Principle For The Generalized Dirac Operator In Curved Spacetime, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

In this article we give sufficient conditions for the generalized Dirac operator to obey the incomplete Huygens principle, as well as necessary and sufficient conditions to obey the Huygens principle by the Dirac operator in the curved spacetime of the Friedmann-Lemaître-Robertson-Walker models of cosmology.