Research: Art, Information, And Academic Inquiry, 2024 University of Maine

#### Research: Art, Information, And Academic Inquiry, Luke D. Mckinney

*Electronic Theses and Dissertations*

In light of the rapidly changing landscape of knowledge production and dissemination, this paper proposes a reformation of academic research that integrates artistic methodologies, emphasizes interdisciplinary collaboration, and prioritizes clear communication to both specialized and general audiences. By reconceptualizing research as a multidimensional, embodied practice that encompasses both rational and irrational elements, we can create a more inclusive, adaptable, and effective approach to scholarship that bridges the rational divide between artistic and scientific inquiry that allows for the engagement of Artistic Research from within the institution, ultimately leading to more innovative and impactful contributions to human knowledge.

An Introduction To Category Theory, 2024 University of Dayton

#### An Introduction To Category Theory, Joseph Kopp

*Electronic Proceedings of Undergraduate Mathematics Day*

Category theory is a relatively new field of mathematics that has grown much in popularity in recent years. It is a general theory of mathematical structure that lends itself to making overarching, yet deep, connections between many branches of mathematics. This power to make such wide-reaching statements is what has drawn many to study it. However, category theory has also been criticized for being "abstract nonsense," in that some believe the theory to be too abstract to carry meaning, much less be applied to the real world. The goal of this paper is to introduce the main ideas of category …

Derivation Of The Sliding Catenary Curve Via Calculus Of Variations, 2024 University of Dayton

#### Derivation Of The Sliding Catenary Curve Via Calculus Of Variations, Ethan Shade

*Electronic Proceedings of Undergraduate Mathematics Day*

Using the calculus of variations this paper derives the general equation for the "sliding catenary curve" — a hanging chain with terminal links free to slide along two poles, one tilted and one vertical. By applying physical assumptions along with the Euler-Lagrange equation, the Beltrami identity, the Legendre-Clebsch condition, the transversality condition, Lagrange multipliers, and the isoperimetric constraint, we derive the general equation for the sliding catenary curve through a functional that measures the potential energy of the hanging chain. This general equation is then compared to a real-life construction of a sliding catenary curve. Additionally the paper explores a …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, 2024 University of Arizona

#### Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

*CODEE Journal*

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

The Fundamental Groupoid In Discrete Homotopy Theory, 2024 Western University

#### The Fundamental Groupoid In Discrete Homotopy Theory, Udit Ajit Mavinkurve

*Electronic Thesis and Dissertation Repository*

Discrete homotopy theory is a homotopy theory designed for studying graphs and for detecting combinatorial, rather than topological, “holes”. Central to this theory are the discrete homotopy groups, defined using maps out of grids of suitable dimensions. Of these, the discrete fundamental group in particular has found applications in various areas of mathematics, including matroid theory, subspace arrangements, and topological data analysis.

In this thesis, we introduce the discrete fundamental groupoid, a multi-object generalization of the discrete fundamental group, and use it as a starting point to develop some robust computational techniques. A new notion of covering graphs allows us …

Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, 2024 University of Teacher Education Fukuoka

#### Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, Toshio Nakata, Hosam Mahmoud

*Journal of Stochastic Analysis*

No abstract provided.

#### Examining The Lived Experiences Of Educators Using Different Levels Of Support For Teaching Math To Students With Learning Disabilities In Math Computation And Problem-Solving For Teachers At Public Cyber Charter High Schools In The Northeastern United States: A Transcendental Phenomenological Study, Leeann E. Mccullough

*Doctoral Dissertations and Projects*

The purpose of this transcendental phenomenological study was to describe the lived experiences of educators using different levels of support for teaching math to students with learning disabilities in math computation and problem-solving for teachers at public cyber charter high schools in the Northeastern United States. The theory guiding this study was Sweller’s cognitive load theory, as it explained the learning process of students with learning disabilities and how educators developed instructional methods that complement the learner’s needs. The central research question was, “What is the lived experience of 9-12th-grade mathematics teachers in supporting students with differing learning abilities in …

On The Colorability Of The Sphere Complex, 2024 San Jose State University

#### On The Colorability Of The Sphere Complex, Bennett Haffner

*Master's Theses*

One of the most prominently studied groups in geometric group theory is the outer automorphism group of the free group Out(F). The sphere complex provides a topological model for Out(F). We demonstrate the chromatic number of the sphere complex is finite.

A Measure Of Interactive Complexity In Network Models, 2024 Binghamton University

#### A Measure Of Interactive Complexity In Network Models, Will Deter

*Northeast Journal of Complex Systems (NEJCS)*

This work presents an innovative approach to understanding and measuring complexity in network models. We revisit several classic characterizations of complexity and propose a novel measure that represents complexity as an interactive process. This measure incorporates transfer entropy and Jensen-Shannon divergence to quantify both the information transfer within a system and the dynamism of its constituents’ state changes. To validate our measure, we apply it to several well-known simulation models implemented in Python, including: two models of residential segregation, Conway’s Game of Life, and the Susceptible-Infected-Susceptible (SIS) model. Our results reveal varied trajectories of complexity, demonstrating the efficacy and sensitivity …

A Measurement Of The Differential Drell-Yan Cross Section As A Function Of Invariant Mass In Proton–Proton Collisions At √ S = 13 Tev, 2024 University of Nebraska-Lincoln

#### A Measurement Of The Differential Drell-Yan Cross Section As A Function Of Invariant Mass In Proton–Proton Collisions At √ S = 13 Tev, William Robert Tabb

*Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–*

The Drell-Yan process, a crucial mechanism for producing lepton pairs in highenergy hadron collisions, serves as an essential probe for testing the Standard Model of particle physics. This dissertation presents a comprehensive measurement of the differential cross section with respect to the invariant mass of the lepton pairs, utilizing data collected by the CMS experiment at CERN from 2016 to 2018. Cross sections are essential for refining our understanding of parton distribution functions and the underlying quantum chromodynamics processes, thereby providing constraints on theoretical predictions. In this analysis, the cross sections are compared to theoretical models and simulations, offering new …

Relating Elasticity And Other Multiplicative Properties Among Orders In Number Fields And Related Rings, 2024 Clemson University

#### Relating Elasticity And Other Multiplicative Properties Among Orders In Number Fields And Related Rings, Grant Moles

*All Dissertations*

This dissertation will explore factorization within orders in a number ring. By far the most well-understood of these orders are rings of algebraic integers. We will begin by examining how certain types of subrings may relate to the larger rings in which they are contained. We will then apply this knowledge, along with additional techniques, to determine how the elasticity in an order relates to the elasticity of the full ring of algebraic integers. Using many of the same strategies, we will develop a corresponding result in the rings of formal power series. Finally, we will explore a number of …

Probabilistic Frames And Concepts From Optimal Transport, 2024 Clemson University

#### Probabilistic Frames And Concepts From Optimal Transport, Dongwei Chen

*All Dissertations*

As the generalization of frames in the Euclidean space $\mathbb{R}^n$, a probabilistic frame is a probability measure on $\mathbb{R}^n$ that has a finite second moment and whose support spans $\mathbb{R}^n$. The p-Wasserstein distance with $p \geq 1$ from optimal transport is often used to compare probabilistic frames. It is particularly useful to compare frames of various cardinalities in the context of probabilistic frames. We show that the 2-Wasserstein distance appears naturally in the fundamental objects of frame theory and draws consequences leading to a geometric viewpoint of probabilistic frames.

We convert the classic lower bound estimates of 2-Wasserstein distance \cite{Gelbrich90, …

Exploring Intraplate Seismicity In The Midwest, 2024 University of Nebraska-Lincoln

#### Exploring Intraplate Seismicity In The Midwest, Alexa Fernández

*Department of Earth and Atmospheric Sciences: Dissertations, Theses, and Student Research*

Intraplate seismicity represents a notable occurrence within the stable North American Craton. This research explores the potential sources of stresses that could reactivate older faults and influence seismic activity within this region. Among these sources, the enduring impact of the last glacial period is considered, which includes continued glacial isostatic adjustments (GIA). During GIA the lithosphere rebounds due to the retreating ice, and the forebulge caused by far-field flexure in response to the glacial load, collapses. This results in significant faulting, fracturing, and seismic activity associated with the deglaciation phase. The adjustment of the lithosphere manifests as both near surface …

Convex Ancient Solutions To Anisotropic Curve Shortening Flow, 2024 University of Tennessee, Knoxville

#### Convex Ancient Solutions To Anisotropic Curve Shortening Flow, Benjamin Richards

*Doctoral Dissertations*

We construct ancient solutions to Anisotropic Curve Shortening Flow, including a

noncompact translator and compact solution that lives in a slab. We then show that

these are the unique ancient solutions that exist in a slab of a given width.

Making Sandwiches: A Novel Invariant In D-Module Theory, 2024 University of Nebraska-Lincoln

#### Making Sandwiches: A Novel Invariant In D-Module Theory, David Lieberman

*Department of Mathematics: Dissertations, Theses, and Student Research*

Say I hand you a shape, any shape. It could be a line, it could be a crinkled sheet, it could even be a the intersection of a cone with a 6-dimensional hypersurface embedded in a 7-dimensional space. Your job is to tell me about the pointy bits. This task is easier when you can draw the shape; you can you just point at them. When things get more complicated, we need a bigger hammer.

In a sense, that “bigger hammer” is what the ring of differential operators is to an algebraist. Then we will say some things and stuff …

A Study On The Vanishing Of Ext, 2024 University of Nebraska-Lincoln

#### A Study On The Vanishing Of Ext, Andrew J. Soto Levins

*Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–*

This thesis has two goals. The first is to study an Ext analog of the rigidity of Tor, and the second is to study Auslander bounds.

In Chapter 2 we show that if *R* is an unramified hypersurface, if *M* and *N* are finitely generated *R*-modules, and if the nth Ext modules of *M* against *N* is zero for some *n* less than or equal to the grade of *M*, then the ith Ext module of *M* against *N* is zero for all *i* less than or equal to *n*. A corollary of this says that if …

Spreads And Transversals And Their Connection To Geproci Sets, 2024 University of Nebraska-Lincoln

#### Spreads And Transversals And Their Connection To Geproci Sets, Allison Joan Ganger

*Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–*

Spreads of [set of prime numbers]^{3} over finite fields can yield geproci sets. We study the existence of transversals to such spreads, proving that spreads with two transversals exist for all finite fields, before further considering the groupoids coming from spreads when transversals do or do not exist. This is further considered for spreads of higher dimensional projective spaces. We also consider how certain spreads might generalize to characteristic zero and the connection to the previously known geproci sets coming from the root systems *D*_{4} and *F*_{4}.

Advisor: Brian Harbourne

On Regularity Of Graph C*-Algebras, 2024 University of Nebraska-Lincoln

#### On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot

*Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–*

We prove that for any countable directed graph *E* with Condition (K), the corresponding graph *C**-algebra *C**(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for *O*_{∞} -stability of graph algebras, and prove some partial results for *Z*-stability.

Advisor: Christopher Schafhauser

Gevrey Class Estimates Towards Null Controllability Of A Fluid Structure Interaction System, 2024 University of Nebraska-Lincoln

#### Gevrey Class Estimates Towards Null Controllability Of A Fluid Structure Interaction System, Dylan Mcknight

*Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–*

Fluid-Structure Interaction concerns the interaction of parabolic fluids and hyperbolic elastic structures via numerous mechanisms such as boundary coupling and pressure. These models find application in blood flow, fluid flow in the eye, and air flow over plane wings. Parabolic equations are well known for “infinite speed of propagation,” which manifests itself via a uniform bound on the resolvent of the infinitesimal generator of the associated strongly continuous semigroup. Qualitatively, a solution of a parabolic pde with rough initial data is immediately smooth for any positive time. A priori, it is not clear whether a fluid structure interaction inherits any …

On Neumann Boundary Conditions For Nonlocal Models With Finite Horizon, 2024 University of Nebraska-Lincoln

#### On Neumann Boundary Conditions For Nonlocal Models With Finite Horizon, Scott Alex Hootman-Ng

*Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–*

Nonlocal models are have recently seen an explosive interest and development in the context of fracture mechanics, diffusion, image processing, population dynamics due to their ability to approximate differential-like operators with integral operators for inherently discontinuous solutions. Much of the work in the field focuses on how concepts from partial differential equations (PDEs) can be extended to the nonlocal domain. Boundary conditions for PDEs are crucial components for applications to physical problems, prescribing data on the domain boundary to capture the behavior of physical phenomena accurately with the underlying model. In this thesis we specifically examine a Neumann-type boundary condition …