Mathematics Commons^™

Understanding Women, Infant And Children Feeding Decisions In Emergencies: The Case Of Covid-19 And The Formula Shortage, Davida Mensah, Edmund F. Agyemang, Constance Gewa

School of Mathematical & Statistical Sciences Faculty Publications

Background: The advantages of breastfeeding and its role in emergencies are undeniable. Studies show that many women in developed countries choose formula over breastmilk, even in emergencies. Nevertheless, no one knows if postpartum women under the Women, Infants and Children (WIC) program turned out to breastfeed or re-lactate their infants during these crises. This study aims to better understand WIC participants' perceptions about breastfeeding their babies in emergencies.

Methods: A chi-square test of independence was used to assess the association between breastfeeding choice and demographic characteristics and potential covariates of respondents. A post hoc analysis using Dunn's multiple comparisons test …

Effects Of Missing Data Imputation Methods On Univariate Blood Pressure Time Series Data Analysis And Forecasting With Arima And Lstm, Nicholas Niako, Jesus D. Melgarejo, Gladys E. Maestre, Kristina Vatcheva

School of Mathematical & Statistical Sciences Faculty Publications

Background

Missing observations within the univariate time series are common in real-life and cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in every incomplete univariate time series. Most of the existing studies focus on comparing the distributions of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series affect the forecasting performance of time series models. We evaluated the prediction performance of autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) network models on imputed time series data using ten different imputation techniques. …

On The Power Series Method For Solitons And Peakons Of Nonlinear Pde, Erika Olivares, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we discuss the power series method to obtain traveling wave solutions of nonlinear PDE in one space variable. The method, including a recursive procedure for the coefficients and error estimate for the partial sums, is presented for the Camassa-Holm equation. Numerical examples of approximate single soliton and single peakon solutions are included.

A Supervised Machine Learning Statistical Design Of Experiment Approach To Modeling The Barriers To Effective Snakebite Treatment In Ghana, Eric Nyarko, Edmund F. Agyemang, Ebenezer Kwesi Ameho, Louis Agyekum, José María Gutiérrez, Eduardo Alberto Fernandez

School of Mathematical & Statistical Sciences Faculty Publications

Background

Snakebite envenoming is a serious condition that affects 2.5 million people and causes 81,000–138,000 deaths every year, particularly in tropical and subtropical regions. The World Health Organization has set a goal to halve the deaths and disabilities related to snakebite envenoming by 2030. However, significant challenges in achieving this goal include a lack of robust research evidence related to snakebite incidence and treatment, particularly in sub-Saharan Africa. This study aimed to combine established methodologies with the latest tools in Artificial Intelligence to assess the barriers to effective snakebite treatment in Ghana.

Method

We used a MaxDiff statistical experiment design …

On The Lagrange And Hermite Quadrature Formula, Shuxia Li, Yonghong Chen

School of Mathematical & Statistical Sciences Faculty Publications

This paper builds on the error analysis method for Newton-Cotes quadrature formulas developed by D. R. Hayes and L. Rubin in 1970, which utilizes Lagrange interpolation polynomials. By adopting and extending their approach, this work derives the error estimate for Hermite interpolation quadrature. Specifically, we construct a polynomial P(x) analogous to the scaling function A(x) used by Hayes and Rubin, and prove its non-negativity over the interval. This allows us to establish a precise error formula for Hermite interpolation quadrature. The results provide a novel application of Hayes and Rubin's methodology, offering new insights …

Teachers’ Perceptions On The Impact And Effectiveness Of Certification Programs In Preparing And Retaining Educators, Teresa De Jesus Padilla

Theses and Dissertations

Mathematics is integral to STEM fields, making math critically important for the stability and development of the nation. As a result, mathematics teachers have a crucial role in our society. A role whose importance needs the necessary support to accomplish its numerous responsibilities. However, research indicates that certification routes—traditional and alternative—often fail to adequately prepare math teachers for the challenges they face, leading to high turnover rates. This study explores the impact of these certification routes on teachers’ abilities to support student achievement, address diverse learning needs, and manage additional duties. Surveying secondary math teachers in the Rio Grande Valley, …

On Representations Of The Super-Yangian Of The Queer Lie Superalgebra, Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

Let Q(n) be the queer Lie superalgebra. We determine conditions under which two 1-dimensional modules over the super-Yangian of Q(n) can be extended nontrivially. We describe the dual modules of the simple finite-dimensional modules over YQ(1) . We use these results to describe blocks in the subcategory of finite-dimensional YQ(1) -modules admitting the zero generalized central character.

Modelling Tinnitus Functional Index Reduction Using Supervised Machine Learning Algorithms, Edmund F. Agyemang

School of Mathematical & Statistical Sciences Faculty Publications

This study aims to model the reduction in the Tinnitus Functional Index (TFI) utilizing supervised machine learning algorithms, focusing primarily on Ordinary Least Squares (OLS), K-Nearest Neighbor (KNN), Ridge, and Lasso regressions. Our analysis highlighted Group, ISI, and SWLS as significant predictors of TFI reduction, identified through the best subset selection and confirmed by both forward and backward selection criteria in the OLS regression. Notably, the shrinkage methods, Ridge and Lasso regressions, demonstrated superior performance compared to OLS and KNN, with the Ridge regression presenting the smallest test mean square error (MSE) of 318.30. This finding establishes the Ridge regression …

Bioconvection Dynamics In Rotating And Stationary Cone-Disk Systems, Puneet Rana, Mahanthesh Basavarajappa

School of Mathematical & Statistical Sciences Faculty Publications

This work focuses on the study of bioconvection in a conical region of rotating and stationary cone-disk systems utilizing nanofluids involving gyrotactic micro-organisms. The flow geometry encompasses two different configurations, namely, rotating cone-disk system (RCDS) and stationary cone-disk system (SCDS). For RCDS, four unique configurations are considered: rotating cone static disk (Model-I), static cone rotating disk (Model-II), co-rotating cone-disk (Model-III), and counter-rotating cone-disk (Model-IV), while SCDS includes both swirling and non-swirling flow scenarios. A total of six different physical configurations that differ in boundary conditions are investigated. The mathematical model comprises Navier–Stokes, energy, nanoparticle volume fraction (NVF), and micro-organism density …

On The Total Perimeter Of Pairwise Disjoint Convex Bodies, Arseniy Akopyan, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

In this note we introduce a pseudometric on closed convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a shorter proof of the theorem by Pinchasi that the sum of perimeters of 𝑘 convex planar bodies with disjoint interiors contained in a convex body of perimeter 𝑝 and diameter 𝑑 is not greater than 𝑝 + 2(𝑘 − 1)𝑑.

Quantization Dimensions For The Bi-Lipschitz Recurrent Iterated Function Systems, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong open set condition in terms of the spectral radius have been estimated.

Non-Vanishing Modulo P Of Hecke L-Values Over Imaginary Quadratic Fields, Debanjana Kundu, Antonio Lei

School of Mathematical & Statistical Sciences Faculty Publications

Let p and q be two distinct odd primes. Let K be an imaginary quadratic field over which p and q are both split. Let Ψ be a Hecke character over K of infinity type (k, j) with 0 ≤ − j < k. Under certain technical hypotheses, we show that for a Zariski dense set of finite-order characters κ over K which factor through the Z2q -extension of K, the p-adic valuation of the algebraic part of the L-value L(κΨ¯¯¯¯¯¯¯,k+j) is a constant independent of κ. In addition, when j = 0 and certain technical hypothesis holds, this constant is zero.

Algebraic Structures On Parallelizable Manifolds, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold L , there exists a global trivialization of the tangent bundle, which defines a map ρ p : l ⟶ T p L for each point p ∈ L , where l is some vector space. This allows us to define a particular class of vector fields, known as fundamental vector fields, that correspond to each element of l . Furthermore, flows of these vector fields give rise to a product between elements of l and L , which in turn induces …

Topology And The Quantum Hall Effects, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The quantum Hall effects are an excellent example of physical systems where topology plays a major role in accounting for the physical observations. It is shown that the conductivity that appears in the quantum Hall effect is a topological invariant. It is illustrated how a fiber bundle over a torus can be constructed producing a geometry in which the system can be referred. The fractional effect can be studied by introducing homotopy and associated braid groups. Filling fractions can be obtained as a consequence of commensurability relations.

Substitution Tilings With Transcendental Inflation Factor, Dirk Frettlöh, Alexey Garber, Neil Mañibo

School of Mathematical & Statistical Sciences Faculty Publications

For any λ>2, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor λ. In particular, we obtain the first class of examples of substitutive systems with transcendental inflation factors. We also show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator.

Pedagogical Moves Related To Analogy That Support A Unified Understanding Of Eigentheory Concepts In A Quantum Mechanics Class, Kaitlyn Stephens Serbin, Megan Wawro

School of Mathematical & Statistical Sciences Faculty Publications

It is beneficial for quantum mechanics students to have a unified understanding of eigentheory concepts, so they can recognize the shared structure of mathematized phenomena from the different quantum mechanical systems of spin, energy, or position and recognize those as instantiations of the same overarching concept. Quantum mechanics instructors should, therefore, provide opportunities for their class community to develop a shared unified understanding of eigentheory concepts. One such opportunity can arise by engaging students in analogizing eigentheory concepts in one context with those from another context. We investigate the pedagogical moves related to analogies that can be used by a …

Integrable Semi-Discretization For A Modified Camassa-Holm Equation With Cubic Nonlinearity, Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin, Guo-Fu Yu

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and appropriate definition of discrete reciprocal transformations. First, we demonstrate that these bilinear equations and their determinant solutions can be derived from the discrete KP equation through Miwa transformation and some reductions. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solutions in the Gram-type determinant form. Finally, we obtain an integrable semi-discrete analog of the mCH equation by …

Stability Of Optimal Spherical Codes, Károly J. Böröczky, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this framework to prove the stability of the two spherical codes formed by minimal vectors of the lattice E8 and of the Leech lattice.

Further Results On Vanishing Coefficients In The Series Expansion Of Lacunary Eta Quotients, Timothy Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

In a previous paper the authors proved the existence of various pairs\break (A(q),B(q)) of lacunary eta quotients with identically vanishing coefficients. Further experiments indicated that the results in this previous paper were just the "tip of the iceberg". We provide a comprehensive description of what experiment suggests and employ a variety of methods to prove experimentally-derived results. The work is a template and atlas for the subsequent study of lacunary eta quotients. A broad range of proof strategies are applied to confirm the vanishing structure. These comprise a representative sample of techniques that may be used to study the remaining …

On Helly Numbers For Crystals And Cut-And-Project Sets, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

We prove existence of Helly numbers for crystals and for cut-and-project sets with convex windows. Also we show that for a two-dimensional crystal consisting of 𝑘 copies of a single lattice the Helly number does not exceed 𝑘 + 6.

The P-Adic Schrödinger Equation And The Two-Slit Experiment In Quantum Mechanics, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space, Q_{p}^{N}. This choice is equivalent to the hypothesis of the discreteness of the space. The time is assumed to be a real variable. p-Adic quantum mechanics is the response to the question: what happens with the standard quantum mechanics if the space has a discrete nature? The time evolution of a quantum state is controlled by a nonlocal Schrödinger equation obtained from a p-adic heat equation by a temporal Wick rotation. This p-adic heat equation describes a particle performing …

Testing The Reliability Of Chatgpt In Providing Spectral Information Of Organic Molecules, Ana Fraiman, Paola Barron, Brooke Dorsey, Sofia A. Delgado, Emanuel Sanchez

School of Mathematical & Statistical Sciences Faculty Publications

ChatGPT has emerged as a tool for predicting Hydrogen-1 Nuclear Magnetic Resonance (1HNMR), Infrared (IR), and Mass Spectrometry (MS) spectra. In order to rely on ChatGPT as a tool, a proof of concept for its application was essential. Having the ChatGPT outputs be validated by experimental data and databases (SDBS) has proven valuable for future uses. By inference, ChatGPT spectra output can be used to design problems without interference of copyright infringement of existing databases.

Predicting Students' Academic Performance Via Machine Learning Algorithms: An Empirical Review And Practical Application, Edmund F. Agyemang, Joseph A. Mensah, Obu-Amoah Ampomah, Louis Agyekum, Justice Akuoko-Frimpong, Amma Quansah, Oluwaferanmi M. Akinlosotu

School of Mathematical & Statistical Sciences Faculty Publications

Predicting academic outcomes is complex and influenced by factors like socioeconomic background, motivation, and learning style. Machine Learning (ML) algorithms have become increasingly important due to their ability to analyze large data volumes and identify prediction patterns. Results show ML’s success in predicting academic performance, though effectiveness varies by dataset, algorithm choice, and training features. There is no consensus on the most effective ML method for predicting student performance with broad applicability. Among the five algorithms evaluated in this study, the Random Forest Classifier emerged as the best model, achieving the highest G-Mean and accuracy of 0.9243 and 85.42% respectively. …

A Garch-Midas Approach To Modelling Stock Returns, Ezekiel N.N. Nortey, Ruben Agbeli, Godwin Debrah, Theophilus Ansah-Narh, Edmund F. Agyemang

School of Mathematical & Statistical Sciences Faculty Publications

Measuring stock market volatility and its determinants is critical for stock market participants, as volatility spillover effects affect corporate performance. This study adopted a novel approach to analysing and implementing GARCH-MIDAS modelling methods. The classical GARCH as a benchmark and the univariate GARCH-MIDAS framework are the GARCH family models whose forecasting outcomes are examined. The outcome of GARCH-MIDAS analyses suggests that inflation, interest rate, exchange rate, and oil price are significant determinants of the volatility of the Johannesburg Stock Market All Share Index. While for Nigeria, the volatility reacts significantly to the exchange rate and oil price. Furthermore, inflation, exchange …

Collaborative Practices In Virtual Group Work On Dynamic Geometry Tasks, Younggon Bae, V. Rani Satyam, Zareen G. Aga

School of Mathematical & Statistical Sciences Faculty Publications

The goal of this study is to explore productive ways to engage students in groupwork using dynamic geometry tasks in online synchronous classroom environments. In particular, we aim to understand the social, mathematical, and technological aspects of student collaboration in virtual spaces. We analyzed how three online groups of students collaboratively worked on dynamic geometry tasks of exploring interactive kaleidoscope applets in Desmos and producing visual representations and written descriptions of geometric transformations used in the applets. The students shared their screens in Zoom as they shared their findings and discussed how to draw and write to represent the kaleidoscopes. …

Hierarchical Neural Networks, P-Adic Pdes, And Applications To Image Processing, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Baboucarr Dibba

School of Mathematical & Statistical Sciences Faculty Publications

The first goal of this article is to introduce a new type of p-adic reaction–diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to provide a quick review of the state of the art of p-adic cellular neural networks and their applications to image processing.

A Correspondence Between Deep Boltzmann Machines And P-Adic Statistical Field Theories, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

There is a strong interest in studying the correspondence between Euclidean quantum fields and neural networks. This correspondence takes different forms depending on the type of networks considered. In this work, we study this correspondence in the case of deep Boltzmann machines (DBMs) having a tree-like topology. We use p-adic numbers to encode this type of topology. A p-adic continuous DBM is a statistical field theory (SFT) defined by an energy functional on the space of square-integrable functions defined on a p-adic N-dimensional ball. The energy functionals are non-local, meaning they depend on the interaction of all the neurons forming …

Numerical Simulations For Fractional Differential Equations Of Higher Order And A Wright-Type Transformation, Mariana Nacianceno, Tamer Oraby, Hansapani Rodrigo, Y. Sepulveda, Josef A. Sifuentes, Erwin Suazo, T. Stuck, J. Williams

School of Mathematical & Statistical Sciences Faculty Publications

In this work, a new relationship is established between the solutions of higher order fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As applications, we solve the fractional beam equation, fractional electric circuits with special functions as external sources, derive d’Alembert’s formula and show the existence of explicit solutions for a general fractional wave equation with variable coefficients. Due to this relationship, we present two methods for simulating solutions of fractional differential equations. The two approaches use the interpretation of the Caputo derivative of a function as …

Learners’ Mathematics Identity And Achievement: Where Does The Teacher Come In?, Luis M. Fernandez, Ursula Nguyen, Rebecca Callahan

School of Mathematical & Statistical Sciences Faculty Publications

In response to recent interest in K-12th students’ mathematics identity formation and its implications for achievement, the present study examines the relationship between learners’ mathematics identity and student achievement while simultaneously accounting for teacher-enacted instructional practices in mathematics. Drawing from HSLS:2009, a nationally representative dataset of 9th–12th students within the United States, we use multiple linear regression analyses to examine how teachers’ mathematical pedagogies and 9th grade students’ perceptions of teacher equity are associated, first, with students’ mathematics identity, and, subsequently, math achievement after accounting for students’ mathematics identity. Ultimately, results from our models reveal a statistically significant relationship between …

Exact Solutions Of Stochastic Burgers–Korteweg De Vries Type Equation With Variable Coefficients, Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo

School of Mathematical & Statistical Sciences Faculty Publications

We will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients. In each variant, white noise exhibits spatial uniformity, and the three categories include additive, multiplicative, and advection noise. Across all cases, the coefficients are time-dependent functions. Our discovery indicates that solving certain deterministic counterparts of KdV–Burgers equations and composing the solution with a solution of stochastic differential equations leads to the exact solution of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equations.