Digital Commons Network^™

Investigation Of Dynamic Adsorption And Desorption Of Polymer Nanogel In Porous Media Through Microfluidics, Junchen Liu, Fuqiao Bai, Abdulaziz A. Almakimi, Mingzhen Wei, Xiaoming He, Ibnelwaleed A. Hussein, Baojun Bai

Mathematics and Statistics Faculty Research & Creative Works

Understanding the transport and retention of elastic nanogel and microgel particles in porous media has been a significant research subject for decades, essential to the application of enhanced oil recovery (EOR). However, a lack of dynamic adsorption and desorption studies, in which the kinetics in porous media are seldom investigated, hinders the design and application of polymer nanogel in underground porous media. In this work, we visualized and quantified the transport and dynamic adsorption of polymer nanogel in 3D glass micromodels that were manufactured by packing glass beads in capillaries. Calibrating the linearity of fluorescence intensity to concentration, we calculated …

Introducing Triangular Groups And Further Results On Magic Groups, Nicholas Charles Fleece

Doctoral Dissertations

In this research, we discuss two new topics in group theory. First, we define an n-magic square in a group to be a nxn array of group elements whose rows, columns, and diagonals have the same product. This definition is akin to the idea of magic squares in the integers. Groups that have an n-magic square are said to be n-magic. We begin with some preliminary results and focus much of our attention on 3-magic groups, though we also give some results for higher n. Through a series of propositions, we ultimately prove a characterization theorem for 3-magic finitely generated …

The Taylor Resolution Over A Skew Polynomial Ring, Luigi Ferraro, Desiree Martin, W. Frank Moore

School of Mathematical & Statistical Sciences Faculty Publications

Let k be a field and let I be a monomial ideal in the polynomial ring Q = k[x1, . . . , xn]. In her thesis, Taylor introduced a complex which provides a finite free resolution for Q/I as a Q-module. Later, Gemeda constructed a differential graded structure on the Taylor resolution. More recently, Avramov showed that this differential graded algebra admits divided powers. We generalize each of these results to monomial ideals in a skew polynomial ring R. Under the hypothesis that the skew commuting parameters defining R are roots of unity, we prove as an application that …

Golden Spirals Everywhere? Solutions For Fermi Questions, January 2025, John Adam

Mathematics & Statistics Faculty Publications

The article discusses different types of spirals, including Archimedean, hyperbolic, and logarithmic spirals, with a focus on the golden ratio and golden spirals. It addresses the misconception that golden rectangles and spirals can be found in various natural and man-made structures, emphasizing the importance of understanding the properties of logarithmic spirals. The article provides mathematical explanations and solutions for questions related to pitch angles and self-similarity in logarithmic spirals, using examples like the nautilus shell and an ammonite-like stone. It concludes by referencing additional sources for further exploration of the golden ratio and golden spiral myths.

Multipliers Between ℓᴾ Spaces, Raymond Cheng

Mathematics & Statistics Faculty Publications

For 0 < p ⩽ ∞ and 0 < r ⩽ ∞, the space 𝔐_p,r of (coefficient) multipliers from ℓ^p and ℓ^r is completely characterized. This is elementary in most instances. The interesting case 0 < r < p < ∞ requires more effort, and it is shown that a sequence of complex numbers belongs to 𝔐_p,r if and only if the sequence of their absolute values has a non increasing rearrangement (h₀,h₁,h₂,...) satisfying

(∞

Σ (k +1)^(p-r)/p (h^r_k - h^r_k+1)^1/r) < ∞

k = 0

In that case, the expression on the left is the norm of the multiplier, and it is a compact operator. Further upper and lower bounds are given for the multiplier norm.

A Bridge Too Low, John Adam

Mathematics & Statistics Faculty Publications

The article "A bridge too low" in the Physics Teacher journal discusses a low bridge near the River Greta in Keswick, England, with an arch shaped like a semiellipse. It presents questions about the maximum height a person of a certain height can walk under the bridge without hitting their head, the cross-sectional area of the arch, its eccentricity, and perimeter. The article also mentions the approximation by Indian mathematician Srinivasa Ramanujan for the perimeter of an ellipse and invites readers to find the answers online.

A Question Of Transparency, John Adam

Mathematics & Statistics Faculty Publications

Question 1: Why is it easier to see through rain than fog?

Start thinking about this by imagining a fixed volume (V) of water being dispersed into, say, N identical droplets of diameter d. Surface area and volume considerations should lead to the answer in terms of V and d.

Question 2: (a) How "long" (in meters) might such a rain shower or fog bank be?

Hint: Suppose you are looking along a linear stack of S cubes with 1-m sides (through the rain or fog). Each cube contains N drops. If p is the visibility (i.e., the fraction of …

A Question Of Transparency: Solutions For Fermi Questions, March 2025, John Adam

Mathematics & Statistics Faculty Publications

Question 1: Why is it easier to see through rain than fog?

Start thinking about this by imagining a fixed volume (V) of water being dispersed into, say, N identical droplets of diameter d. Surface area and volume considerations should lead to the answer in terms of V and d.

Solution to Question 1: N = VI(πd³/6) = 6V/πd³ ≈ 2V/d³.

The cross-sectional area A of each drop is πd²/4 ≈ 3d²/4, so the total area blocked off (assuming no overlapping drops—so this is an upper bound) is NA ≈ 1.5V/d, so the area blocked off is inversely proportional to …

A Bibliographic And Topic Modeling Analysis Of The P-Adic Theory Literature Using Latent Dirichlet Allocation, Humberto Llinás, Ismael Gutiérrez, Anselmo Torresblanca, Javier De La Hoz, Brian Llinás

Computer Science Faculty Publications

P-adic analysis, introduced by Kurt Hensel in the early 20th century, has developed into a fundamental area of mathematical research with broad applications in number theory, algebraic geometry, and mathematical physics. This study aims to examine the thematic evolution and scholarly impact of p-adic research through a comprehensive topic modeling and bibliometric analysis. Using classical bibliometric techniques (e.g., performance analysis, co-authorship, and co-citation networks) combined with Latent Dirichlet Allocation (LDA), we analyzed 7388 peer-reviewed documents published between 1965 and 2024. The computational workflow was conducted using R (version 4.4.1) and VOSviewer (version 1.6.20), which enabled the identification of 20 distinct …

Generalizations Of Some Q-Product Identities Of Ramanujan And Others, Timothy J. Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

By considering certain limiting cases of a WP-Bailey chain discovered by Andrews, and also limiting cases of certain classical summation formulae for basic hypergeometric series, we derive new expressions for certain Lambert series in terms of basic hypergeometric series. In some cases, the resulting series involve an arbitrary Bailey pair. This allows for the derivation of new basic hypergeometric expansions for some q-products and series that Ramanujan expressed in terms of Lambert series. Some of Ramanujan’s identities are extended to more general relations containing one or more free parameters.

Theoretical Foundations And Applied Performance Of Periodicity-Aware Imputation: Variable Bandpass Block Bootstrap Methods For Incomplete Time Series, Asmaa Ahmad

Electronic Theses & Dissertations (2024 - present)

Time series data are prevalent across a wide range of disciplines, including health surveillance, public policy, and environmental monitoring. In the presence of underlying cyclical patterns, the integrity of time series analysis depends critically on the ability to detect, model, and impute structured missing data without compromising the temporal structure. This dissertation introduces and validates a novel imputation framework that integrates the Variable Bandpass Periodic Block Bootstrap (VBPBB) into multiple imputation procedures, improving the accuracy, robustness, and interpretability of time series models under high rates of missingness and noise. The overarching goal of this dissertation was to develop and evaluate …

Hyper B-Ary Representations Of A Number, Mingway Wang

Masters Theses

In this work, we summarize combinatorial, analytical, and computational properties of Stern's diatomic sequence, and do the same for a generalization of a combinatorial property of this sequence to higher bases. We then construct special ``bit conversion'' functions $g_{b}$ that allows us to find a semi-explicit formula for the generalized sequences. Lastly, we analyze some of the properties of these $g_{b}$ functions.

Action This Day: The Mathematics And Machinations That Bested The German Enigma, Jonah Weinbaum

Dartmouth College Master’s Theses

This thesis presents a comprehensive and chronological overview of cryptographic techniques designed to break Enigma, beginning in 1932 and culminating in the creation of the Turing-Welchman Bombe. We discuss the mathematical theory and electromechanical implements used to decode one of history's greatest ciphers.

Reexamining the Bombe through the lens of modern group theory, we critique Alan Turing's estimation of the number of "stops" that the Bombe produces for various plaintext-ciphertext pairing structures. To address its limitations, we introduce a new framework for estimating the number of stops by extending John Dixon's theorem concerning the probability that uniformly distributed elements of …

Strong Neighborhood-Prime Labelings Under Ordinary & Gaussian Integers, Micheal Arnal-Brown

Murray State Theses and Dissertations

This thesis introduces and studies the notion of a strong neighborhood-prime labeling, a strengthening of the neighborhood-prime labeling where the label 1 can be assigned to any vertex in a graph. We prove that several graph families—including paths, cycles (excluding those congruent to 2 modulo 4), caterpillars, helm graphs, closed helm graphs, gear graphs, and graphs with universal vertices—admit such labelings, and also provide results to more general classes of graphs. We extend this new labeling concept to the Gaussian integers using a spiral order- ing on Z[i] and define a Gaussian analogue of strongly neighborhood-primeness. To support this extension, …

A Computational Approach To The Game Of Cycles, Jocelyn Garcia, Mike Janssen, Eliza Kautz

Faculty Work Comprehensive List

In Mathematics for Human Flourishing, Francis E. Su introduced The Game of Cycles, a game played on a finite simple planar graph. In game play, opponents alternate adding direction to the edges of the graph with the goal of creating a cycle or making the last legal move. Recent work has sought to determine winning strategies on certain classes of graphs. We introduce a tabular representation of a game state and provide a computer program that determines which player has a winning strategy on any legal game board. The program builds a directed graph of all possible game states, utilizing …

On Higher Level Zhu Algebras Of N-Graded Vertex Algebras Associated With Simple Leibniz Algebras That Contain Sl2, Christian Soltermann

Theses and Dissertations

In this thesis, we study how the higher-level Zhu algebras of a vertex algebra reflect the structure of associated simple Leibniz algebras. In particular, we construct a vertex algebra from a vertex algebroid containing the simple Lie algebra sl₂ and analyze its higher level Zhu algebras. The irreducible modules of this vertex algebra were completely classified in [JY20b], but the structure of its indecomposable modules remains an open problem. Since modules for higher level Zhu algebras correspond to modules of vertex algebras, studying these algebras provides a method for understanding their broader representation theory.

The Impact Of Loss Function Topology On Gradient Descent, Robert B. Skudnig Jr.

Theses and Dissertations

Gradient descent is a popular optimization method that utilizes a model’s prediction error to iteratively improve its parameters for a given task. The functions that measure this error can be defined to align with the user’s goals and sometimes satisfy metric or norm properties. It is common for these functions to measure over Rn, but any differentiable space allows for gradient descent to occur. There has been some research investigating the influence of topological spaces on optimization methods, but it is a limited field of study. This thesis further explores this phenomenon by applying a transformation prediction model to multiple …

A New G Family: Properties, Characterizations, Different Estimation Methods And Port-Var Analysis For U.K. Insurance Claims And U.S. House Prices Data Sets, Ahmad M. Aboalkhair, Gholamhossein Hamedani, Nazar Ali Ahmed, Mohamed Ibrahim, Mohammad A. Zayed, Haitham M. Yousof

Mathematical and Statistical Science Faculty Research and Publications

This paper introduces a new class of probability distributions, termed the generated log exponentiated polynomial (GLEP) family, designed to enhance flexibility in modeling complex real financial data. The proposed family is constructed through a novel cumulative distribution function that combines logarithmic and exponentiated polynomial structures, allowing for rich distributional shapes and tail behaviors. We present comprehensive mathematical properties, including useful series expansions for the density, cumulative, and quantile functions, which facilitate the derivation of moments, generating functions, and order statistics. Characterization results based on the reverse hazard function and conditional expectations are established. The model parameters are estimated using various …

A Bayesian Complex-Valued Latent Variable Model Applied To Functional Magnetic Resonance Imaging, Chase J. Sakitis, D. Andrew Brown, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic …

Bayesian Merged Utilization Of Grappa And Sense (Bmugs) For In-Plane Accelerated Reconstruction Increases Fmri Detection Power, Chase J. Sakitis, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In fMRI, capturing brain activity during a task is dependent on how quickly the k-space arrays for each volume image are obtained. Acquiring the full k-space arrays can take a considerable amount of time. Under-sampling k-space reduces the acquisition time, but results in aliased, or “folded,” images after applying the inverse Fourier transform (IFT). GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) and SENSitivity Encoding (SENSE) are parallel imaging techniques that yield reconstructed images from subsampled arrays of k-space. With GRAPPA operating in the spatial frequency domain and SENSE in image space, these techniques have been separate but can …

Lipschitz Conditions On Operators And Matrices, Ryan Farrell

UNF Graduate Theses and Dissertations

Lipschitz functions on the real line find various applications across mathematics, including in differential equations, optimization, and machine learning. The goal of this thesis is to investigate functions which satisfy certain Lipschitz conditions when ap- plied to operators and matrices. Our study will review two classes of such functions, the class of Operator Lipschitz functions with respect to a given matrix norm, and the class consisting of functions which do not meet Lipschitz conditions in the traditional sense but satisfy inequalities which are Lipschitz in nature – we call such conditions ”Lipschitz-like”. The thesis concludes with a survey of these …

Fourier Transformation Of Non-Periodic Functions And Its Application In Computed Tomography, Sabrina Hossain

UNF Graduate Theses and Dissertations

Fourier analysis plays an important role in signal processing and imaging applications,

with computed tomography (CT) being a prominent example. CT imaging relies on recon-

structing cross-sectional images of objects from multiple projections, a process deeply rooted

in the mathematical framework of the Fourier series and its extensions. This thesis explores

the mathematical principle behind CT, demonstrating how periodic and non-periodic func-

tions can be decomposed into sinusoidal components to facilitate image reconstruction. We

begin by reviewing the Fourier series and its ability to represent periodic signals, and then

extend this concept to non-periodic functions through Fourier transforms. The connection …

Geometric Properties Of Positive Definite Matrices: Means, Order, And Metrics, Blaine Dubois

UNF Graduate Theses and Dissertations

In this thesis, we study matrix means from a geometric point of view. In particular, we consider divergences of the form Tr[A + B − 2G(A, B)] for certain Geometric-Type matrix means G(A, B). We derive alternative formulations of this distance function through the application of one-sided inverses of G(A, B). When G(A, B) = A#B, we give a curve parametrization of the straight-line path between two points with respect to this semi-metric and present conditions under which this holds for other Geometric-Type means. For read- ability and self-containment, we introduce most of the preliminary concepts to build up to …

Polar Decompositions And Spectral Properties Of Linear Operator Pencils, Slaviša Djordjević, Jaewoong Kim, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair T=(T1,T2) . Using this decomposition, we define the generalized spherical Aluthge transforms for the linear pencil of an ordered pair T=(T1,T2) and give spectral properties between the linear pencil and the generalized spherical Aluthge transform of it. In detail, we study whether the spectral properties of the linear pencil of an ordered pair T=(T1,T2) are invariant under the generalized spherical Aluthge transform.

Editorial Insights: Reflections On The Volume And Charge To The Field, Heather Howell, Meghan Shaughnessy, Barbara Stengal, Carrie Wilkerson Lee, Liza Bondurant, Bima Sapkota, Gregory Benoit, Yvonne Lai

School of Mathematical & Statistical Sciences Faculty Publications

In this, the final chapter of Section 3, the authors document an interview that took place in June of 2024, as the editorial team wrapped up reviews of the chapters submitted to this volume. The interview was led by two of the advisory board members, Meghan Shaughnessy and Barbara Stengal, and included the editorial group, Heather Howell, Carrie Wilkerson Lee, Liza Bondurant, and Bima Sapkota, and other members of the advisory board, Greg Benoit and Yvonne Lai. The motivation to create this interview-based chapter was to capture some of the authors' own learning and reflection as they brought the volume …

Bifurcation And Index Theory With Applications To Nonlinear Differential Equations, Asrafi Yesmin

UNF Graduate Theses and Dissertations

This thesis presents a rigorous framework for the study of bifurcation phenomena in nonlinear differential equations. Semigroup theory and index theory are introduced to examine qualitative changes in the solution structures of the nonlinear dynamic system as the parameters vary. The theoretical framework is then applied to several nonlinear differential equations from biology and physics.

Generalizations Of Finiteness Conditions And Extension Monads In Algebras With Infinitely Many Or Infinitary Operations, Danielle Christienne Bowerman

Doctoral Dissertations

In this work, we extend the results of finiteness conditions and extension monads found in Insall from finitely many finitary operations to infinitely many finitary operations, as well as touching on infinitary operations. We also examine varieties of algebras, including the notion of strong varieties introduced in Insall, and common constructions of extension monads in varieties of algebras. We see that for finite collections of algebras of the same signature, the extension monad operation on a variety of algebras commutes with the direct product operation, and all retractions from an enlargement or extension monad are trivial. We also see that …

Development Of Conceptual Scaffolding-Assisted Formative Assessment For Enhancing Understanding Of Temperature And Heat, Ana Lailatul Fitriyah, Sentot Kusairi, Markus Diantoro

Jurnal Pendidikan Sains

This research aims to develop formative assessment media assisted by conceptual scaffolding to improve students’ understanding of temperature and heat, test its validity and practicality, and gauge student responses. Utilizing the ADDIE model, the research follows five stages: Analysis, Design, Development, Implementation, and Evaluation. In the Analysis stage, a literature review was conducted to identify critical components, including formative assessment, conceptual scaffolding, concept mastery, and previous research. The Design stage involved identifying users, defining competencies and indicators, creating a storyboard, integrating assessment components, and determining mastery levels. During the Development stage, the assessment media were developed into a functional product. …

Composite Volume Learning Media Based On Augmented Reality To Enhance Students’ Visual-Spatial Intelligence, Ria Kurniawati, Susiswo Susiswo, Syamsul Hadi

Jurnal Pendidikan Sains

Augmented Reality (AR) technology, a three-dimensional visual tool that integrates virtual objects or environments into real-world displays in real time (Azuma et al., 2001), is particularly useful for grasping complex concepts such as the composite volume of solids, which often confuses students when they need to decompose solids into their individual components. While previous research has predominantly focused on the introduction of solids, spatial nets, and the volume of singular shapes, this study aims to develop composite volume learning media based on AR to enhance students’ visual-spatial intelligence in a valid, practical, and effective manner, aligning with their concrete operational …

Students’ Concept Maps Profile On Environmental Pollution Material During The Covid-19 Pandemic, Sunarni Sunarni, Sri Widoretno, Puguh Karyanto, Bowo Sugiharto, Sri Dwiastuti, Chandra Adi Prabowo

Jurnal Pendidikan Sains

The study investigates the performance of students in constructing Concept Maps (CM) related to environmental pollution material during the COVID-19 pandemic. The data reveals that the overall achievement in CM construction was suboptimal, with no component reaching more than half of its maximum potential. The highest achievement was recorded in the valid relationship component, which attained 9.75% of its maximum possible score. This was followed by the hierarchy component, achieving 7.34%, and the branching component at 3.42%. The pattern component ranked fourth with 1.31%, closely followed by the example component at 1.30%. The lowest performance was observed in the crosslink …