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Fractional Bernstein Polynomial Approximations For Nonlinear Timefractional Partial Differential Equations, Reem Abdul Quzli

Theses

This thesis studies the numerical approximation of nonlinear time-fractional partial differential equations using fractional Bernstein polynomials. The main model considered is the nonlinear time-fractional foam drainage equation, in which the classical time derivative is replaced by the Caputo fractional derivative. This formulation introduces memory effects into the model and allows the present drainage behavior to depend on the previous evolution of the liquid fraction.

The proposed method approximates the solution by a finite expansion of fractional Bernstein basis functions. After substituting this approximation into the governing equation, the residual is expanded in powers of t^�� . The unknown coefficient …

C*-Extreme Quantum Instruments; Completion And Disintegration Of Completely Positive Maps, Arghya Chongdar

Doctoral Theses

This thesis develops a comprehensive operator-algebraic framework for the study of completely positive (CP) instruments, with contributions spanning convexity theory, integration theory, completion problems, and disintegration theory. We begin by laying the foundational groundwork in the theory of C*-algebras and von Neumann algebras, introducing key structures such as CP maps, positive operator-valued measures (POVMs), and CP instruments, along with their dilation-theoretic properties. Pure and decomposable instruments are characterized via minimal bi-dilations, and CP instruments are realized as bivariate maps, providing a rigorous quantum analogue of classical joint measures. The thesis then investigates convexity-theoretic aspects of instruments. A structural characterization of …

Fostering Innovation At The Intersection Of Maker Education And Extended Reality (Xr), Jewoong Moon, Yong Ju Jung, Soo Hyeon Kim, Younggon Bae, Bertrand Schneider

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

Hyper-Bishops, Hyper-Rooks, And Hyper-Queens: Percentage Of Safe Squares On Higher Dimensional Chess Boards, Caroline Cashman, Joseph Cooper, Raul Marquez, Steven J. Miller, Jenna Shuffelton

School of Mathematical & Statistical Sciences Faculty Publications

Chess has inspired an abundance of mathematical problems, especially in combinatorics and probability. One such problem, initially studied by Miller, Sheng, and Turek, considers the proportion of safe spaces when randomly placing n rooks on an 𝑛×𝑛 chess board. They show that as n approaches infinity, the proportion of safe spaces converges to 1/𝑒2. We first generalize their results to bishops and queens. This problem is significantly more interesting and difficult; while a rook attacks the same number of spaces regardless of its position, this is not so for bishops and queens. We prove that the proportion of safe spaces …

Analytical And Numerical Methods For Solving Fractional Integro-Differential Equations Using The Modified Operational Matrix Method, Nour Alzoubi

Theses

Fractional calculus has attracted considerable attention in recent years because of its wide applicability to model a variety of linear and nonlinear physical phenomena across different scientific disciplines. In particular, fractional diferential equation systems have proven to be effective in describing processes with memory and hereditary properties. However, the solvability and analysis of such systems strongly depend on the type of fractional operator employed, especially in the presence of nonlocal fractional derivatives with singular kernels, which remain an open and challenging area of research.

The main objective of this thesis is to develop efficient analytical and numerical techniques for solving …

Advanced Mathematical Modeling And Data-Driven Techniques For The Diagnosis Of Diabetes Using Continuous Glucose Monitoring (Cgm) Data, Farah Morsi

Theses

Diabetes mellitus is a major and growing health challenge, particularly in the Middle East and North Africa (MENA) region. Continuous Glucose Monitoring (CGM) provides high-resolution time-series data that capture detailed glucose fluctuations over time. However, conventional CGM summary measures, such as mean glucose, standard deviation, and time-in-range, may not fully describe the nonlinear temporal structure of glucose dynamics.

This thesis investigates nonlinear dynamical approaches for analyzing CGM time series, with a focus on recurrence-based analysis and ordinal-network analysis. Recurrence-based methods, including recurrence quantification analysis (RQA), are used to characterize geometric and temporal patterns in reconstructed phase space, while ordinal networks …

Heat Transfer And Micropolar Characteristic Analysis For Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder: A Fractional Derivative Study, Khalid Al Homran

Theses

This study presents a comprehensive analysis of heat transfer and micropolar fluid characteristics for flow over a contracting permeable infinite-length cylinder using fractional derivative modeling. The micropolar fluid model accounts for microstructure effects that are prevalent in many practical applications, such as polymeric fluids, colloidal suspensions, and biological fluids. The inclusion of fractional derivatives allows the analysis to incorporate memory effects, which provide a more accurate depiction of the physical phenomena compared to classical integer-order models. The governing partial differential equations, representing the momentum, micropolar momentum and energy transport processes, are transformed into a set of nonlinear ordinary differential equations …

On The Fractional Laplacian Type Operator, Maysam Abdulnaser Zain

Theses

In this thesis, we study analytical structures arising from Dunkl theory and their

applications to harmonic analysis and fractional Laplacian operators. Dunkl operators are differential–difference operators associated with finite reflection groups, providing a natural generalization of the classical Fourier analysis through the introduction of root systems and multiplicity functions. Within this framework, several classical transforms appear as special cases of the (k,a)-generalized Fourier transform. We study the generalized Fourier transform ��ₖ,ₐ, its kernel B_k,a (x,y), and the associated translation operator and convolution structures. Using these tools, we construct the corresponding heat …

Assessing The Effectiveness Of Tilt-Informed Assessments In Calculus I, Samuel Horelick

Inquiry: The Journal of the Virginia Community Colleges

Transparent Design in Learning and Teaching (TILT) is widely promoted as an evidence-based framework intended to clarify expectations, promote equity, and improve student learning. While prior research reports positive outcomes across many disciplines, less is known about how transparency functions in quantitative, problem-solving courses such as calculus, where students often value efficiency and autonomy. This study examines the effects of a TILT-informed assignment redesign in two sections of Calculus I at a Virginia Community College System institution. One section completed a traditional assignment, while the other completed an equivalent task redesigned to make the purpose, task, and evaluation criteria explicit. …

Differential-Geometric Methods For Neural Signed Distance Fields: Parameterized Surface Extraction And Curvature Regularization For Cad Models, Haotian Yin

Dissertations

Neural signed distance fields have emerged as a powerful framework for representing three-dimensional geometry through continuous and differentiable neural functions. Their flexibility, resolution independence, and compatibility with gradient-based optimization make them especially attractive for surface reconstruction and geometric learning. However, despite these advantages, two fundamental challenges remain for engineering-grade applications. First, higher-order geometric properties such as curvature are difficult to model reliably during training and often require computationally expensive second-order differentiation. Second, while neural signed distance fields provide implicit surface representations, they do not directly yield a globally consistent forward map or parameterization for downstream geometric processing.

This dissertation addresses …

A Symbolic Model Of Proof Acquisition In Act-R, Beckett Morris, Kerstin Haring

DU Undergraduate Research Journal Archive

Learning to construct mathematical proofs—formal arguments demonstrating the truth of a mathematical statement using logical deductions and previously established facts—is one of the most challenging skills in STEM education. This research aims to build the foundations for a symbolic cognitive model, using the ACT-R cognitive architecture and implementing in Python with the pyactr package, to explore how different proof strategies can be thought through with only symbols and rules. The model observes simple proofs, and its abilities are assessed based on its generalization capabilities, efficiency, and error patterns. By developing and analyzing such a model, this research provides new insights …

Measuring Stock Market Inefficiency Using A Multilayer Composite Efficiency Index: A Case Of The Egyptian Exchange, Patrick K. Owido, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

Financial markets play a critical role in resource allocation. Their performance depends on the decisions of millions of independent investors constantly reacting to one another. Their informational efficiency remains a subject of debate across economic systems. When informational efficiency is present at the weak form, historical price information should not consistently predict future returns. Several empirical tests of this hypothesis often focus on the behavior of aggregate market indices, and use individual efficiency proxies such as autocorrelation, GARCH-type volatility, or entropy-based measures to measure efficiency. This has often yielded mixed results, particularly in emerging markets. Here we show that testing …

Classes Of Analytic Functions Defined By Salagean Derivative Operator Associated With Neutrosophic Generalized Poisson Distribution, Soliu O. Opeyemi Okunola, Olushola Adeyemo, Sayo A. Abidemi Gbangbala, Folorunso I. Isola Akinwale

Neutrosophic Systems with Applications

This study introduces and analyses new subclasses of analytic functions by applying the Salagean derivative operator to the Neutrosophic Generalized Poisson Distribution (NGPD) series. We develop a model where the mean parameter is treated as an interval or set to account for indeterminacy in complex systems. By employing Stirling numbers of the second kind and decreasing factorials, we derive necessary and sufficient coefficient inequalities and inclusion relations for these new subclasses. Numerical results and graphical illustrations demonstrate the sensitivity of these functions to orientation and the neutrosophic parameter, providing a framework for applications in fields like medical imaging and network …

1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, ..., Annemarie Torresen

Masters Theses

1

I invite you to see it and feel it and sit in it and breathe it in and

hold it in your lap. Art isn’t too scary, and neither is math.

2

bouncing between bounds of a binary

bippity boppity! let’s break brains and bread

balance or belly flop, what’s mine is yours:

bumptious and bumbling and barely able

i offer it broken and let you like it that way

Goodness-Of-Fit Test For The Kumaraswamy Distribution Via Energy Distance Approach With Applications To Real Data, Joseph Njuki, Thomas Gilbert

Mathematics and Statistics

In this article, we develop a goodness-of-fit test for the Kumaraswamy distribution based on energy statistics. Due to the availability of its quantile (inverse) function, the Kumaraswamy distribution has been shown to be the preferred alternative to the Beta distribution, since both have bounded support in the (0,1) interval. The proposed test procedure is simple and more powerful against general alternatives. Under different settings, simulations show that the proposed test is capable of being well controlled for any given significance (nominal) levels. In terms of power comparisons, the proposed test outperforms other existing methods in different settings. We then apply …

New Developments In Space-Filling Designs, Xiankui Yang

USF Tampa Graduate Theses and Dissertations

This dissertation presents three methodological advancements to improve the construction of space-filling designs for meeting different needs of computer experiments. Traditional space-filling designs focus on achieving uniform coverage in the input space, ensuring that design points are spread evenly throughout. However, in some scientific and engineering applications, varied density of design points may be desired for more efficient data collection when prior knowledge implies different emphases. In other cases, ensuring good coverage and/or spread of the response values allows better performance of fitted models in the next stage of applications. Many processes involve variation in response values. Therefore, incorporating variation …

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

Design Considerations For Hypertension Chronotherapy Trials: Insights From Experience And Modelling, Olivia Walch, Amy Rogers, Yitong P. Huang, Marc D. Ruben, Kenneth A. Dyar, Robert W. V. Flynn, Isla S. Mackenzie, Roberto Manfredini, Francesco P. Cappuccio, Filippo Pigazzani

Mathematics Sciences: Faculty Publications

Chronotherapy aims to maximise treatment efficacy while minimising side effects by scheduling treatment according to personal biological rhythms. In recent years, randomised clinical trials (RCTs) have been conducted to evaluate whether scheduled blood pressure interventions can improve patient outcomes. However, reports of time-of-day effects have attracted rebuttals and engendered methodological debate. A perfectly controlled chronotherapy trial (i.e., a trial that assesses the effect of assigning time of intervention) will never be feasible in the real world; yet some factors may be more critical to consider and control for than others. To advance the conversation about how best to evaluate the …

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 …

Parameter Estimation In Ode Models Using Least-Squares Regression, Ulrich A. Hoensch

CODEE Journal

We present a method of estimating model parameters for non-linear ODEs using least-squares regression. The coefficient of determination can be used as a measure of model fit. The method is demonstrated using US population data to fit a logistic growth model. Also, a competing species model is used to describe the interaction of two different species of yeast.

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 …