Mathematics Commons^™

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, …

Mathematical And Statistical Methods To Harness Limited Data In Models For Ecological Space Use Under Global Change, Sarah C. Bogen

All Graduate Theses and Dissertations, Fall 2023 to Present

The dynamics of how plants and animals use space in their habitats has important implications for the fields of ecology and conservation. However, understanding and responding to these spatial and temporal dynamics is often limited by data availability, financial resources and biases. As average global temperatures increase, suitable habitats shift poleward and require local populations to move with suitable habitat, adapt to the changing environment, or risk extinction. Capacity to persist without movement may be estimated by considering changes to a combination of habitat characteristics. Capacity to track suitable habitat may be modeled through synthesizing information on species demographic mechanisms …

A Novel Phenotype Imputation Method With Copula Model, Jianjun Zhang, Jane Zizhen Zhao, Samantha Gonzales, Xuexia Wang, Qiuying Sha

Michigan Tech Publications

BACKGROUND: Jointly analyzing multiple phenotype/traits may increase power in genetic association studies by aggregating weak genetic effects. The chance that at least one phenotype is missing increases exponentially as the number of phenotype increases especially for a real dataset. It is a common practice to discard individuals with missing phenotype or phenotype with a large proportion of missing values. Such a discarding method may lead to a loss of power or even an insufficient sample size for analysis. To our knowledge, many existing phenotype imputing methods are built on multivariate normal assumptions for analysis. Violation of these assumptions may lead …

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.

Quantum Markov Chains Related To Certain Lattice Models, Ali Alalaai

Thesis/ Dissertation Defenses

A central open problem in quantum field theory is the construction of a general theory of quantum field, this thesis introduces quantum probability and applies it via the construction of quantum Markov chains on different hierarchical lattices (Cayley trees). Furthermore, these trees correspond to the Ising-XY-Model which then the existence of a unique Markov chain can be utilized to detect phase transitions.

A Dynamical Systems Approach For Modeling Malware Propagating Through A Network And Potential Solutions Towards Mitigating Spread, James Johnson

Cybersecurity Undergraduate Research Showcase

Many people draw close parallels between malware propagating through a network and an epidemic spreading through a population. Epidemics are often modeled by a Susceptible-Infected-Recovered (SIR) model, in which a similar system of equations can model the spread of a virus through a computer network, and can be simplified when making assumptions about the network itself and its fixed number of nodes and edges. In this instance, malware propagating in a network also should reflect the network it is propagating through, in which the dynamical system will factor in the nodes of the network and their properties. The system itself …

Implementing Bernstein Operational Matrices To Solve A Fractional‐Order Smoking Epidemic Model, Jalal Al Hallak, Mohammed Alshbool, Ishak Hashim

All Works

This paper leverages the Bernstein operational matrices method for the first time in order to resolve the nonlinear fractional smoking epidemic model presented in terms of Caputo’s fractional derivative. An approximate solution is derived using Bernstein’s operational matrices and strategically chosen collocation points. This is followed by the validation of the proposed method’s accuracy and reliability against the established Runge–Kutta fourth‐order method. Furthermore, a comprehensive comparative analysis is conducted against two prominent techniques: the fractional differential transform method (FDTM) and the q‐homotopy analysis transform method (q‐HATM). The results show a superior and significant performance regarding accuracy as well as approximation. …

Newton's Electromagnetic Bucket, Angelina Georg

Mathematics Colloquium Series

We examine Newton’s thought experiment: Newton’s Bucket. We replace the bucket with a charged infinite cylindrical shell in order to extend the analysis to an electromagnetic one. We show that Newton’s mechanical conclusions are equally valid electromagnetically.

Exclusion Tests For Approximating All Solutions Of Nonlinear Equations, Yasmeen Omar Hamida

Thesis/ Dissertation Defenses

The exclusion test is a mathematical technique used to isolate and approximate solutions of nonlinear equations within a defined interval. This thesis introduces a new exclusion test-based approach that aims to accelerate convergence to the zeros of nonlinear equations within a compact domain. By selecting Taylor, series, and Lipschitz test and solving nonlinear equations, the proposed method substantially reduces the number of subintervals necessary for accurate approximation. The primary contribution of this research is the development of a more efficient algorithm, which significantly improves the speed of convergence. These findings have meaningful implications for the field of numerical analysis, presenting …

On Fractional Dunkl-Type Laplacian, Saba Ibrahim Aldan

Thesis/ Dissertation Defenses

This thesis provides a comprehensive study of the fractional Dunkl-type Laplacian operator (—llxllΔ_k) ^σ for 0 < σ < 1, focusing on four key equivalent characterizations: the heat semigroup approach, the pointwise formulation, the spherical mean representation, and through an extension theorem. A significant part of the thesis is devoted to the extension theorem, where, following the approach of Caffarelli and Silvestre for the Euclidean Laplacian, we prove that (—llxllΔ_k) ^σ can be characterized as an operator that maps a Dirichlet boundary condition to a Neumann-type condition via an extension PDE problem. Further, a Poisson formula for the extension was established. These four characterizations provide distinct perspectives on the operator llxllΔ_k, extending Euclidean Laplacian results to include reflection symmetries and revealing connections between the fractional operator (—llxllΔ_k) ^σ, harmonic analysis, and applications in mathematical physics and PDEs.

Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, Martin H. Weissman

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Opioid Addiction In Hand Surgery Patients, Eli Goldwyn, Grace Bowman, Kathryn Montovan, Julie Blackwood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identifiability And Convergence Behavior For Markov Chain Monte Carlo Using Multivariate Probit Models, Xiao Zhang

Michigan Tech Publications

Multivariate probit models have been popularly utilized to analysis multivariate ordinal data. However, the identifiable multivariate probit models entail the covariance matrix for the underlying multivariate normal variables to be a correlation matrix, which brings a rigorous task to conduct efficient statistical analysis. Parameter expansion to make the identifiable model to be non-identifiable has been inevitably explored. However, the effect of the expanded parameters on the convergence of Markov chain Monte Carlo (MCMC) is seldomly investigated; in addition, the comparison of MCMC developed based on the identifiable model and that based on the non-identifiable model is hardly ever explored, especially …

Telu Activation Function For Fast And Stable Deep Learning, Alfredo Fernandez

USF Tampa Graduate Theses and Dissertations

We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as $TeLU(x)=x \cdot tanh(e^x)$. TeLU’s design is grounded in the core principles of key activation functions, achieving strong convergence by closely approximating the identity function in its active region while effectively mitigating the vanishing gradient problem in its saturating region. Its simple formulation enhances computational efficiency, leading to improvements in scalability and convergence speed. Unlike many modern activation functions, TeLU seamlessly combines the simplicity and effectiveness of ReLU with the smoothness and analytic properties essential for learning stability in deep neural networks. TeLU’s ability …

Preservative Splitting Numerical Schemes For Solving A Variable Coefficient Quenching Problem, Julienne Kabre

Mathematics Colloquium Series

Physical processes are modelled mathematically using Partial Differential Equations(PDEs). An insight into these processes requires solving those PDEs. Since these equations most of the time do not have analytical solutions, delicate numerical methods are required. In this talk, we will explore the numerical solution of the two-dimensional quenching type nonlinear reaction-diffusion problem via dimensional splitting. The differential equation possesses a variable diffusion coefficient and a nonlinear forcing term that leads to a strong quenching singularity. Our current investigation focuses on the construction of a finite difference implementation of a Peaceman- Rachford and a Glowinski-Le Tallec splitting procedures for solving the …

New Fueter-Type Variables Associated To The Global Operator In The Quaternionic Case, Daniel Alpay, Kamal Diki, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

The purpose of this paper is to develop a new theory of three non-commuting quaternionic variables and its related Schur analysis theory for a modified version of the quaternionic global operator.

Using Academic Librarians And The Academic Library: Survey Results From Mathematics Faculty In United States And Canada, Elizabeth Novosel, Daniel G. Kipnis, Jenni Burke, Rasitha Jayesekera

Libraries Scholarship

Presented at STEM Librarian South Conference, November 6, 2024

Despite our diligent outreach and relationship-building efforts, certain groups of faculty within STEM disciplines remain hesitant to engage with academic librarians and utilize library resources. This challenge raises a critical question: How can librarians effectively support a department when faculty members are unresponsive?

Our research team, composed of three frustrated mathematics librarians and one mathematics faculty member, recognized the need for a fresh approach. Mathematics, a department known for its independence, has received limited attention in scholarly Library and Information Science (LIS) literature. To address this gap, we embarked on a …

On The Work Of Cartan And Münzner On Isoparametric Hypersurfaces, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface Mⁿ in a real space form Rⁿ⁺¹, Sⁿ⁺¹, or Hⁿ⁺¹ is isoparametric if it has constant principal curvatures. This paper is a survey of the fundamental work of Cartan and Münzner on the theory of isoparametric hypersurfaces in real space forms, in particular, spheres. This work is contained in four papers of Cartan [3]–[6] published during the period 1938–1940, and two papers of Münzner [47]–[48] that were published in preprint form in the early 1970’s, and as journal articles in 1980–1981. These papers of Cartan and Münzner have been the …

Purely Pseudo-Anosov Subgroups Of The Genus Two Handlebody Group, Marissa E. Chesser, Christiopher J. Leininger

Faculty Work Comprehensive List

We prove that finitely generated, purely pseudo-Anosov subgroups of the genus 2 handlebody group are convex cocompact.