Digital Commons Network^™

Machine Learning For Modeling In An Elementary Differential Equations Class, Nathan Albin, Andrew G. Bennett, Abhinav Chand

CODEE Journal

Mixing machine learning with modeling is an area of increasing importance. This paper presents a lesson where students model a spring-mass system both using traditional analysis with linear damping and using machine learning to learn the damping from real data. The machine learning is implemented in a Jupyter notebook hosted on Google Colab, allowing students to train the neural network without requiring the students to carry out coding. Students get experience with how machine learning can fail, how it can work, and the time and data requirements for machine learning to succeed, and are asked to apply this knowledge to …

Improving Explainability And Interpretability Of Neural Networks Via Hyperparameter-Extended Influence Functions, William Breslin

Dissertations and Theses

Understanding how model predictions and training outcomes vary with changes in data, features, and modeling choices is central to explainable artificial intelligence. This dissertation introduces a unified framework for explainability by generalizing classical influence functions to encompass user-defined hyperparameters embedded in the training loss, model architecture, or data representation. By extending influence functions in this way, the framework broadens their applicability and integrates multiple explainability techniques into a single, coherent approach. It provides a common mathematical foundation linking data impact, feature importance, and model design analysis, and supports a broad class of additional explainability analyses beyond these settings. The demonstrated …

Design And Implementation Of Error Estimators For Finite Element Eigenvalue Problems, Gabriel Esteban Pinochet Soto

Dissertations and Theses

We present three publications, all encompassed under the umbrella of a posteriori error estimation theory for eigenvalue problems for finite element discretizations. The central objective of the research is the development of a general framework for the study of reliable estimation of eigenvalues and eigenspaces. We introduce applications to problems of theoretical interest as well as problems arising in real-life scenarios, such as optical fibers. The first paper focuses on the implementation of a dual-weighted residual error estimator for a nonselfadjoint eigenvalue problems arising from the study of leaky modes in optical fibers---Maxwell's equations, Perfectly Matched Layers, and a conforming …

Bayesian Designs For Two-Arm Clinical Trials With Time-To-Event Endpoints: Incorporating Historical Data Through Power Priors, Sara Hajraf H. Almutiri

Mathematics & Statistics ETDs

Bayesian methods provide a flexible framework for time-to-event analysis by incorporating prior information. The power prior offers a systematic way to borrow information from historical data. This approach is especially valuable in clinical research, where historical data can enhance inference in early-phase trials with limited sample sizes. This dissertation develops Bayesian approaches for two-arm survival studies using both closed-form and simulation-based methods. The closed-form inference is derived under exponential and Weibull survival models. Under the proportional hazards framework, the posterior is derived through a normal approximation to the log hazard ratio, allowing inference on the treatment effect when the variance …

Degrees Of Access: The Role Of Family Education In Applying To Graduate School, Emma Tweed

Math and Computer Science Honors Theses

Access to graduate education in the United States remains heavily stratified by structural, financial, and informational barriers. While undergraduate first-generation student outcomes are widely studied, fewer structural analyses examine how graduate-level “educational inheritance” shapes prospective applicants' navigational capital, particularly within competitive STEM fields like mathematics. Drawing upon theories of social capital and the “hidden curriculum,” this study investigates the relationship between an individual's knowledge of the graduate school application process and the highest level of education attained by an immediate family member.

Using the Knowledge-GAP survey instrument funded by the National Science Foundation, data were collected from a diverse sample …

Exact Solution Of Steady Seepage In An Asymmetrical Domain Underneath A Cofferdam, Tan Nguyen

UNLV Theses, Dissertations, Professional Papers, and Capstones

For decades, the evaluation of steady state seepage beneath asymmetrical cofferdams has relied on numerical methods, such as Finite Element Methods (FEM), Finite Difference Method (FDM), Finite Volume Method (FVM), Mesh Reduction Method (MRM), Meshless Method (MM), Boundary Element Method (BEM), or geometric idealizations, most notably Griffiths' vertical Method of Fragments assumption. While exact closed form solutions via Schwarz-Christoffel (SC) conformal mapping have been well established for symmetrical geometries (Banerjee and Muleshkov), the generalized asymmetrical case has historically remained an intractable mathematical frontier. The primary barrier to an exact analytical solution has been the "crowding problem," a numerical phenomenon where …

Phase Field Modeling And A Fully Discrete Numerical Scheme For Two-Phase Incompressible Mhd Flows With Different Densities, Electric Conductivities And Viscosities, Xiaoyong Chen, Rui Li, Jian Li, Xiaoming He, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

This article establishes a phase field model for governing the two-phase incompressible MHD flows with different densities, electric conductivities, and viscosities. In addition to the coupling between the Cahn–Hilliard phase field equations and the single-phase MHD equations together with the varying parameters, it is physically faithful and mathematically rigorous for the modeling to incorporate a relative flux term, which is related to the diffusion of the components, into the coupled system, inspired by Abels et al. and Shen and Yang. We present a linear fully discrete numerical scheme for this complex multi-physics system, which leverages the artificial compressibility method, an …

Unbounded Derivations On Algebras Associated With Monothetic Groups: An Expository Thesis, Britton Phillips

Theses and Dissertations

This thesis is an expository exploration of the paper Unbounded Derivations in Algebras Associated with Monothetic Groups. Monothetic groups will be utilized to create a minimal system that gives rise to two C*-algebras, and once we have these algebras, unbounded derivations will be able to be defined on them. These derivations are able to be classified and decomposed into ”special” derivations, and these decompositions help simplify the comparisons between derivations on different algebras. In particular, we emphasize the classification, covariance properties, innerness and approximate innerness, and the lifting behavior of these derivations.

Dynamic Homeostasis In Relaxation And Bursting Oscillations, Christopher J. Ryzowicz

Biology and Medicine Through Mathematics Conference

No abstract provided.

College Algebra With Review, Lanee Young Ph.D., Jayme Goetz

All Open Educational Resources

This text is disseminated via the Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org) and like the thousands of other texts available within this powerful platform, it is freely available for reading, printing, and "consuming." The LibreTexts mission is to bring together students, faculty, and scholars in a collaborative effort to provide an accessible, and comprehensive platform that empowers our community to develop, curate, adapt, and adopt openly licensed resources and technologies; through these efforts we can reduce the financial burden born from traditional educational resource costs, ensuring education is more accessible for students and communities worldwide. Most, but …

Effectiveness Of The Guided Discovery Method In Teaching The Surface Area Of A Cylinder, Paul Ahortu

2026 Symposium

This study investigates the impact of the guided discovery instructional method on students’ understanding of the surface area of a cylinder. A quasi-experimental pre-test–post-test design was conducted with 100 senior high school students in Cape Coast, Ghana, divided into experimental and comparison groups..

Results showed a substantial improvement in performance for students exposed to guided discovery, with mean scores increasing from 1.25 (pre-test) to 9.43 (post-test) and a large effect size (Cohen’s d = 2.70). Statistical analysis also revealed significant gender differences in achievement.

These findings indicate strong improvement following the guided discovery intervention and suggest its potential to enhance …

Dynamical Systems Modeling To Determine The Role Of Crosstalk In Shaping Stat Signaling Profiles, Laura F. Strube, Anamarie Martinez, Neha Cheemalavagu, Karsen Shoger, James Faeder, Rachel Gottschalk

Biology and Medicine Through Mathematics Conference

No abstract provided.

Adaptive Two-Derivative Runge–Kutta–Nyström Method With Trigonometric Fitting Approach, Nur Nabila Huda, Khai Chien Lee, Nurul Huda Abdul Aziz

Turkish Journal of Mathematics

A fifth-order trigonometrically-fitted explicit two-derivative Runge–Kutta–Nyström method with an adaptive step size strategy, denoted as ATFRKN5, is proposed for efficiently solving second-order ordinary differential equations of the form u^″(x) = f(x, u(x)) that exhibit oscillatory behavior. The order conditions of the method are derived using Taylor series expansion, enabling the construction of two-derivative Runge–Kutta–Nyström schemes up to orders four and five. Trigonometric fitting is applied by incorporating the basis functions e^iλx and e^−iλx, λ ∈ ℝ, allowing the method to adapt naturally to problems with dominant frequencies. …

On Sequences Arising From The Action Of Modular Group, Tuncay Köroğlu, Bahadir Özgür Güler

Turkish Journal of Mathematics

This paper examines the sequences produced by the natural action of specific elements of the modular group on extended rational numbers. The polynomial sequences Pr(c) and Qr(c) are derived from the orbit of the point at infinity under a specific modular transformation. These sequences satisfy linear recurrence relations, which are analyzed using generating functions. The polynomials encode k-Fibonacci numbers, and studying their behavior modulo a fixed integer m reveals notable arithmetic and combinatorial properties. We also explore the connection between these modular actions and Farey graphs, illustrating the hyperbolic transformations as nested geodesic paths in the upper half-plane.

A Module Theoretic Approach To (B,C)-Invertibility, Tuğba Pakel, Burcu Üngör, Handan Köse, Sai̇t Halicioğlu, Abdullah Harmanci

Turkish Journal of Mathematics

In this paper, we introduce and investigate the concept of an (r, f)-inverse in the context of modules, drawing inspiration from the (b, c)-inverse, which is the analogous notion in ring theory. We demonstrate the uniqueness of (r, f)-inverses in modules whenever they exist. We provide some necessary and sufficient conditions for the existence of (r, f)-inverses in modules.

Existence Results And Uniqueness For Some Caputo-Hadamard Fractional Differential Equations Via The Measures Of Noncompactness, Manochehr Kazemi, Mohammad Esmael Samei, Hamid Reza Sahebi, Osman Tunç

Turkish Journal of Mathematics

In this paper, the existence of solutions to Caputo–Hadamard fractional differential equations is investigated using measures of noncompactness and the Petryshyn fixed point theorem. Several new results are established, recovering certain earlier results under weaker conditions. Finally, two illustrative examples are presented.

Proportion Of Nilpotent Subgroups In Finite Groups And Their Properties, João Victor Monteiros De Andrade, Leonardo Santos Da Cruz

Turkish Journal of Mathematics

​This work introduces and investigates the function J(G) = Nil(G) / L(G) , where Nil(G) denotes the number of nilpotent subgroups and L(G) the total number of subgroups of a finite group G. The function J(G), defined on the interval (0,1], represents the proportion of nilpotent subgroups relative to the total number of subgroups, including trivial ones. It serves as a tool for analyzing structural patterns in finite groups, particularly in nonnilpotent families such as supersolvable and dihedral groups. Analytical results reveal the distribution of J(G) values across products of dihedral groups, emphasizing its density over (0,1]. Additionally, a probabilistic …

Optimal Control Of An Inverse Two-Point Boundary Value Problem For A Pseudoparabolic Equation With Samarskii–Ionkin-Type Boundary Conditions, Khanlar R. Mamedov, Tursun K. Yuldashev, Zholdoshbek Zh. Shermamatov

Turkish Journal of Mathematics

This paper investigates an inverse optimal control problem for a pseudoparabolic equation governed by nonlinear control function in a two-point boundary condition. The differential equation is considered under Samarskii Ionkin-type boundary value conditions with respect to the spatial variable x. Necessary optimality conditions are derived, and the associated nonlinear functional equations are analyzed. Using the contraction mapping principle, the existence and uniqueness of the control function are established. Subsequently, the redefinition function and the state function are determined. The convergence of their respective Fourier series representations is rigorously proven.

Close-To-Convexity Properties Of Inverse Hypergeometric Functions, Ijlal Hussain, Wasim Ul Haq, Janusz Sokol

Turkish Journal of Mathematics

The normalized inverse hypergeometric function zF_ν⁻¹(d, e, f; z) = ∑_s=0^∞ A_sz^s+1 is considered, where A_s = (f)_s(ν + 1)_s / (d)_s(e)_s. We aim to provide constraints on d, e, f, and ν under which zF_ν⁻¹(d, e, f; z) belongs to various subclasses of the class of close-to-convex functions. Coefficient characterizations of these families are derived under additional conditions. Some associated operators …

Ricci Solitons On Manifolds With Norden Golden Structure, Bang-Yen Chen, Foued Aloui, Mohammed Nisar, Majid Ali Choudhary

Turkish Journal of Mathematics

​The concept of golden structure is a compelling area with wide-ranging applications. In this paper, we introduce and investigate the notion of Norden golden Ricci solitons. In particular, we investigate Ricci solitons on a Norden golden Riemannian manifold of constant sectional curvature. Furthermore, we explore Ricci solitons and Norden golden Ricci solitons on Norden golden Riemannian manifolds whose potential vector fields are killing, conformal killing, concurrent, or homothetic.

Comparisons Of Some Weighted Mixed Biased Estimators For The Linear Regression Model, Dünya Karapinar, Murat Polat, Ni̇met Özbay, Selahatti̇n Kaçiranlar

Turkish Journal of Mathematics

This paper presents comparative results on the two-parameter weighted mixed estimator, which is a distinct class of estimator defined to address the problem of multicollinearity. The two-parameter weighted mixed estimator is a general estimator that includes the weighted mixed estimator, the weighted mixed Liu estimator, and the weighted mixed ridge estimator. Detailed comparisons among the mentioned estimators are carried out based on the matrix mean square error. Theoretical findings are supported by two numerical examples in addition to a Monte Carlo simulation study.

Improved Oscillation Criteria For A Class Of Neutral Differential Equations In The Canonical Case, Abdulaziz Khalid Alsharidi, Ali Muhib

Turkish Journal of Mathematics

This paper develops an analytical framework based on comparison with first-order equations to derive new oscillation criteria for all solutions of a class of second-order differential equations with multiple delays. These criteria extend and improve upon previously published results. Illustrative examples are provided to validate the theoretical findings and to demonstrate the significance and applicability of the proposed criteria.

Oscillation Properties Of First-Order Difference Equations With Nonmonotone Delays: New Insights And Criteria, Emad Attia, George Chatzarakis

Turkish Journal of Mathematics

In this paper, we examine the oscillatory behavior of the first-order linear delay difference equation Δy(n) + p(n) y(τ(n)) = 0, n ∈ ℕ₀. It is known in the literature that, for any C > 0, the condition lim sup_n→∞ ∑_i=τ(n)ⁿ p(i) > C, with τ(n) nonmonotone, is not, in general, sufficient to establish the oscillation of the difference equation. We prove that, for certain classes of difference equations, the aforementioned condition is sufficient to ensure the …

On The Number Of Exact Factorization Of Finite Groups, Jesus Alonso Ochoa Arango, Maria Angelica Umbarila Martin

Turkish Journal of Mathematics

In this work, the function f2(G), which counts the number of exact factorizations of a finite group G, is studied. The value of  f2(G) is computed for several well-known families of finite groups, and an asymptotic expression is derived for the number of exact factorizations of the alternating group A2n .

Λ-Fold Near-Factorizations Of Groups, Donald L. Kreher, Shuxing Li, Douglas R. Stinson

Michigan Tech Publications

We initiate the study of λ-fold near-factorizations of groups with λ>1. While λ-fold near-factorizations of groups with λ=1 have been studied in numerous papers, this is the first detailed treatment for λ>1. We establish fundamental properties of λ-fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of λ-fold near-factorizations, including upper bounds on λ. We present three constructions of infinite families of λ-fold near-factorizations, highlighting the characterization of two subfamilies of λ-fold near-factorizations. We discuss a computational approach to λ-fold near-factorizations and tabulate computational results for abelian groups of small order.

Relation Subspaces In Vertex Operator Algebras: Residue Generators For O_N^\Circ(V) And Intersections With (L(−1) +L(0))V, Junghyun Kim

Undergraduate Research Journal

We study the relation subspace 𝑂◦𝑛 (𝑉) that appears in the definition o f the level-𝑛 Zhu algebra 𝐴𝑛 (𝑉) = 𝑉/𝑂𝑛 (𝑉), where 𝑂𝑛 (𝑉) = 𝑂𝐿 (𝑉) + 𝑂◦𝑛 (𝑉) and 𝑂𝐿 (𝑉) =(𝐿(−1) + 𝐿(0))𝑉. Using residue calculus, we introduce operators 𝑅𝑛,𝑘 that encode the circle products 𝑢◦𝑛 𝑣 and prove explicit change-of-generators formulas between the standard generators (𝑢−𝑚1)◦𝑛 𝑣 and the residue generators 𝑢 𝑅𝑛,0𝑣, together with a binomial inversion. These identities provide a practical framework for computing 𝑂◦𝑛 (𝑉), especially in strongly generated VOAs. As progress toward understanding the overlap 𝑂◦𝑛 (𝑉) ∩ 𝑂𝐿 (𝑉), …

Identifiability, Sequentiality And Infinity, Jose L. Menaldi

Mathematics Faculty Research Publications

Abstract: A definition of identifiable-sets is used with sequential analysis to establish a realm of mathematics. Within this imaginary world, a specific consonant between infinite sets and sequentiality is reached.  This consonant allows some mathematical constructions to model pieces of the reality, based on dual philosophy and physics itself.  There is an effort made to render this understandable for the scientific community.

Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard

LSU Doctoral Dissertations

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …

Global Invertibility Of Sobolev Mappings And Energy Minimizers With Prescribed Jacobian, Sabrina Traver

Dissertations - ALL

We prove two main results at the intersection of Geometric Function Theory and Nonlinear Elasticity. The first is a Sobolev variant of the Inverse Function Theorem, which generalizes a famous result of John Ball. It uses Classical Sobolev Theory as well as the Degree Function, which was initially a topological tool. The second result is the existence and uniqueness (up to rotation) of a radially-symmetric minimizer for Sobolev mappings with prescribed Jacobian. This result generalizes recent work of André Guerra, Lukas Koch, and Sauli Lindberg.

Dg Algebra Techniques For Tor Algebras And Edge Ideals, Desiree Martin

Dissertations - ALL

This thesis is comprised of two projects. The first is individual work where I use semifree Gamma-extensions to show, for an ideal I with infinite projective dimension over a Noetherian local ring R, there exists a splitting morphism from a Tor algebra Tor(R/I,R/I) to the exterior algebra of the R/I-free summands of the conormal module. In particular, when the conormal module is free over R/I, we see that the exterior algebra of the conormal module splits completely from Tor(R/I,R/I) as algebras. For the second project my collaborators, Hugh Geller and Henry Potts-Rubin, and I completely classify all trees and cycle …