Encircling Chains Around 4- And 6-Clusters In Fullerenes,
2025
Syracuse University
Encircling Chains Around 4- And 6-Clusters In Fullerenes, Hannah Melissa Kimbrell
Dissertations - ALL
Fullerenes are purely carbon molecules which can be represented by a 3-regular planar graph consisting of only hexagonal and (exactly 12) pentagonal faces. Since carbon atoms have valence 4 but our graphs are trivalent we need to double the edges in a perfect matching to bring the valence up to 4. The edges in a perfect matching form a Kekulé structure and the hexagonal faces bound by three Kekulé edges are called benzene rings. A maximal independent set of benzene rings for a given Kekulé structure is called a Clar set, and the maximum possible size of a Clar set …
On The Embeddability Of Small Cubic Graphs Into The Torus,
2025
Syracuse University
On The Embeddability Of Small Cubic Graphs Into The Torus, Marie Kramer
Dissertations - ALL
The embeddability of graphs into different surfaces has been studied for nearly a century. In 1930, Kuratowski famously proved that a graph is planar if and only if it does not contain the complete graph K5 or the complete bipartite graph K3,3 as a topological minor. In particular, K3,3 is the only cubic obstructions for the plane. This sparked interest in two different directions: What are analogous results for other surfaces, and what can be said about embeddings of K5 and K3,3 into other surfaces? Regarding the first question, it was shown in the 1970s and 80s by Glover, Huneke, …
Pluricomplex Green Functions And Transform Methods For The Laplacian,
2025
Syracuse University
Pluricomplex Green Functions And Transform Methods For The Laplacian, Jesse Joel Hulse
Dissertations - ALL
There are two research themes within complex analysis presented. The first is developing generalizations of the Unified Transform Method as a novel way to compute fluid flows and numerically solve boundary value problems for holomorphic functions and solutions to the Laplacian and complex Helmholtz equation. The second is finding a formula for the pluricomplex Green function with two poles of equal weights for the bidisk. The Unified Transform Method (also sometimes known as the Fokas Method) is a technique for numerically solving boundary value problems for linear and integrable nonlinear PDEs. Crowdy reformulated the Unified Transform Method in the complex …
Exploration Into Homotopy Equivalence And Vietoris-Rips Complexes,
2025
University of Mississippi
Exploration Into Homotopy Equivalence And Vietoris-Rips Complexes, Alexander J. Mobley
Honors Theses
An important question in discrete topology and geometry is how to recover the structure and characteristics of a manifold when only given a finite set of points sampled from that manifold. Thus, if mathematicians have a point cloud of data which induces a discrete metric space, they look for some structure to these points. Understanding the structure of these points often gives needed insight to solve this problem. One such way to determine structure to these points is to use these points to construct a Vietoris-Rips complex. In abstract, Latschev shows that this allows us to recover the homotopy type …
Crystallization Of The Quantized Function Algebras Of Suq(N + 1),
2025
Indian Statistical Institute
Crystallization Of The Quantized Function Algebras Of Suq(N + 1), Manabendra Giri
Doctoral Theses
The $q$-deformation of a connected, simply connected Lie group $G$ is typically studied through two Hopf algebras associated with it: the quantized universal enveloping algebra $\mathcal{U}_q(\mathfrak{g})$ and the quantized function algebra $\mathcal{O}(G_q)$. If $G$ has a compact real form $K$, one can use the Cartan involution to give a $*$-structure on $\mathcal{O}(G_q)$. The QFA $\mathcal{O}(G_q)$ with this $*$ structure is denoted by $\mathcal{O}(K_q)$ and its $C^*$-completion by $C(K_q)$. Here we study the crystal limits of $\mathcal{O}(SU_q(n+1))$ and $C(SU_q(n+1))$ and classify all irreducible representations of the crystallized algebras. We also prove that the crystallized algebra carries a natural bialgebra structure.
Understanding Student And Teacher Perceptions Of A Checking For Accuracy Method In Algebra Class,
2025
Abilene Christian University
Understanding Student And Teacher Perceptions Of A Checking For Accuracy Method In Algebra Class, Abigail A. Jameson
Masters of Education in Teaching and Learning
Mathematics encompasses learning from one’s mistakes and developing accuracy with problem-solving. This action research study analyzed the classroom teacher’s and students' perceptions of a checking for accuracy math method that was implemented in an eighth-grade algebra classroom. Additionally, the researcher wanted to understand how the participants felt about the accuracy method and its influence on students’ attitudes toward math and mastery of math concepts. Student surveys, individual teacher (with student artifacts) and student interviews and focus groups (with individual artifacts) were the qualitative data collected using the constant comparative method. Descriptive statistics was used to collect quantitative data with calculated …
Derived $P$-Adic Heights And The Leading Coefficient Of The Bertolini–Darmon–Prasanna $P$-Adic $L$-Function,
2025
The University of Texas Rio Grande Valley
Derived $P$-Adic Heights And The Leading Coefficient Of The Bertolini–Darmon–Prasanna $P$-Adic $L$-Function, Francesc Castella, Chi-Yun Hsu, Debanjana Kundu, Yu-Sheng Lee, Zheng Liu
School of Mathematical & Statistical Sciences Faculty Publications
Let E/Q be an elliptic curve and let p be an odd prime of good reduction for E. Let K be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which p splits. The goal of this paper is two-fold: (1) we formulate a p-adic BSD conjecture for the p-adic L-function LBDP p introduced by Bertolini–Darmon–Prasanna [Duke Math. J. 162 (2013), pp. 1033–1148]; and (2) for an algebraic analogue F BDP p of LBDP p , we show that the “leading coefficient” part of our conjecture holds, and that the “order of vanishing” part follows from the expected …
Statistics - What Does My Data Say About Me?,
2025
Chapman University
Statistics - What Does My Data Say About Me?, Taylor Gadsden-Deterville
Student Scholar Symposium Abstracts and Posters
For my Introduction to Statistics Class, I have been tasked with collecting unique, personal data to give insight into my daily routine. I decided to record nine different outcomes (two qualitative and seven quantitative). On February 6, 2025, I began with a blank Excel sheet, and so far, I have 57 full days of data collected. I will continue monitoring my findings for the remainder of the Spring 2025 Semester. Per my project instructions, I must include tables and graphs for my qualitative and quantitative outcomes. So far, I have collected daily quantitative data on my screen time (Instagram and …
A Preliminary Study Of Hilbert–Kunz Functions: Coefficient Behavior In A Normal Affine Semigroup Ring,
2025
Texas A&M International University
A Preliminary Study Of Hilbert–Kunz Functions: Coefficient Behavior In A Normal Affine Semigroup Ring, Jesus A. Mendiola Herrera
Theses and Dissertations
In 1890, David Hilbert published a set of notes on what now constitutes one of the bases of Commutative Algebra; his work would eventually influence the efforts of mathematicians like Ernst Kunz. In 1969, Ernst Kunz introduced a particular mapping regarding modules of regular local rings. His goal was to characterize Noetherian local rings of prime characteristic by computing the length of the composition series under Frobenius power transformations. In this thesis, the focus will be on stating the initial steps on finding the coefficients of the Hilbert-Kunz function of the normal affine semigroup ring of the form R = …
Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians,
2025
Butler University
Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians, Jennifer L.C. Burke, Elizabeth C. Novosel, Daniel G. Kipnis, Rasitha R. Jayesekere
Libraries Scholarship
Academic librarians do not engage with all disciplinary departments equally. Despite equal or even greater efforts, some departments are less responsive to librarian outreach. One such department is mathematics. To understand mathematics departments’ relationships with their academic librarians, three mathematics librarians created a 20-question survey that was disseminated to mathematics faculty, instructors, and instructional staff in the United States and Canada. Of the 188 survey participants, more than a third reported that they never engage with their librarians, approximately half only do so occasionally, and a mere eight percent of participants collaborated with librarians to provide information literacy instruction (IL) …
Oriented Matroid Circuit Polytopes,
2025
Washington University in St. Louis
Oriented Matroid Circuit Polytopes, Jodi Mcwhirter
Arts & Sciences Graduate Student Theses and Dissertations
Matroids give rise to several natural constructions of polytopes. Inspired by this, we examine polytopes that arise from the signed circuits of an oriented matroid. We give the dimensions of these polytopes arising from graphical oriented matroids and their duals. Moreover, we consider polytopes constructed from cocircuits of oriented matroids generated by the positive roots in any type A root system. We give an explicit description of their face structure and determine the Ehrhart series. We also study an action of the symmetric group on these polytopes, giving a full description the subpolytopes fixed by each permutation. These type A …
A Zariski-Nagata Theorem For Smooth Toric Surfaces,
2025
University of Nebraska-Lincoln
A Zariski-Nagata Theorem For Smooth Toric Surfaces, Jordan Vincent Barrett
Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–
The Affine Zariski-Nagata theorem is a classical result in commutative algebra that gives an expression for the nth symbolic power of a radical ideal I in a polynomial ring over a field in terms of the nth ordinary powers of the maximal ideals in [affine variety]max(I). In this thesis we discuss a well-known projective analog of Zariski-Nagata and provide the necessary background on toric varieties to present a generalization of this result to toric surfaces. We conclude with a brief discussion about work toward characterizing which abstract toric varieties have smooth point fibers with …
Transformations Of Bound Quivers,
2025
Macalester College
Transformations Of Bound Quivers, Ari Pincus-Kazmar
Mathematics, Statistics, and Computer Science Honors Projects
A quiver Q is a directed multigraph. Representations of Q are assignments of vector spaces and linear maps to the vertices and arrows of Q; these are categorically equivalent to the modules over the path algebra kQ. The indecomposable representations of a given quiver and the irreducible morphisms between them are summarized combinatorially in the Auslander-Reiten quiver which, in the case of algebras of finite representation type, gives almost complete information about the category of representations. We introduce an intuitive transformation from a family of bound quivers to a family of A-type quivers which preserves properties of the Auslander-Reiten quiver.
Modeling Literary Connections: Exploring Transregional Resistance In Dalit Poetry,
2025
Macalester College
Modeling Literary Connections: Exploring Transregional Resistance In Dalit Poetry, Antara Bhattacharyay
Mathematics, Statistics, and Computer Science Honors Projects
Structuring socio-political identities, the caste system (a graded form of hierarchy) remains entrenched in contemporary Indian society. Dalits, marginalized by the caste system, have expressed their resistance through literature, envisioning substantive equality and social change. In this thesis, I draw on digital humanities methods to examine regional variation in translated Dalit poetry from Bengali, Hindi/Urdu, Marathi, and Tamil languages. I utilize topic modeling—a machine learning algorithm that detects latent semantic structures in a text—as a point of departure for poetry analysis. I observe how topic modeling enables newer readings of the poems, revealing regionally resonant and broader Dalit themes.
How Much Should Consumers With Mild To Moderate Hearing Loss Spend On Hearing Devices?,
2025
The University of Texas Rio Grande Valley
How Much Should Consumers With Mild To Moderate Hearing Loss Spend On Hearing Devices?, Vinaya Manchaiah, Steve Taddei, Abram Bailey, De Wet Swanepoel, Hansapani Rodrigo, Andrew Sabin
School of Mathematical & Statistical Sciences Faculty Publications
Background: This study examined the relationship between hearing device price and sound quality. Method: A novel consumer-centric metric of sound quality (“SoundScore”) was used to assess hearing devices’ audio performance. Each hearing device is tested with two fittings. The “Initial Fit” is designed to approximate the most likely fitting for an individual with a mild-to-moderate sloping sensorineural hearing loss. The “Tuned Fit” includes adjusting parameters optimized to hit prescriptive fitting targets (NAL NL2) on an acoustic manikin. Each fitting is evaluated across five dimensions. Both fittings are combined using a weighted average to create a single number from 0 to …
Studies In Algebraic Cycles: Hodge Theory Of Degenerations, Regulators, And Cluster Varieties,
2025
Washington University in St. Louis
Studies In Algebraic Cycles: Hodge Theory Of Degenerations, Regulators, And Cluster Varieties, Ricardo Jaime Acuna
Arts & Sciences Graduate Student Theses and Dissertations
This dissertation brings together results in Hodge theory and the theory of cluster varieties. The second chapter, based on a paper written in collaboration with Devin Akman and Matt Kerr, uses admissible normal functions to establish the first finiteness result for zero-dimensional components of the Hodge locus. The third chapter, based on joint work with Matt Kerr, shows that weak polar- ized relations constrain possible adjacencies of mixed Hodge structures across boundary strata in geometric compactifications. The fourth chapter gives a geometric construction of a 6-dimensional cluster variety with a disconnected mutation graph, as discovered by Yan Zhou. These three …
Some Interpolation Problems In The Projective Plane,
2025
University of Arkansas, Fayetteville
Some Interpolation Problems In The Projective Plane, Lilah Estes
Mathematical Sciences Undergraduate Honors Theses
Given some set of r general points in the projective plane, we want to better understand: what is the smallest degree of any polynomial passing through the points m times? How many linearly independent equations of this degree pass through the points m times? The investigation of these questions, particularly for the case of m=3 and r< 16, motivates the development of several results. We translate Terracini's inductive argument, a tool for evaluating the expectedness of certain sets of double points, into a version which can be used for triple points, and prove that the argument holds. We compute the minimal graded free resolutions for the ideals corresponding to up to 15 points, for m up to 6, and we conjecture a connection between the expectedness of these ideals and what their resolutions look like. Further, we prove that this conjecture holds when m=1, and we either fully or partially prove that these ideals are …
On The Hexgame,
2025
Rose-Hulman Institute of Technology
On The Hexgame, Corwin Jones
Mathematical Sciences Technical Reports (MSTR)
The SOMA Cube has been studied by mathematicians for a number of decades, but so far methods for solving three-dimensional space-filling puzzles like the SOMA cube remain numerical; we do not have a means to predict the number of solutions to SOMA-like puzzles. We present a two-dimensional puzzle that shares certain features of the SOMA Cube, with the hope that it will be a more convenient object of study for future research into space-filling/space-covering puzzles.
Math Course Placement Models At Csbsju Using Data Analysis,
2025
College of Saint Benedict and Saint John's University
Math Course Placement Models At Csbsju Using Data Analysis, Josephine Jackson
Celebrating Scholarship and Creativity Day (2018-)
Many majors at the College of Saint Benedict and Saint John’s University (CSBSJU) require students to complete a course in calculus or statistics, however incoming students have various levels of preparation for these courses. This research investigates strategies for predicting student success in these courses and potential recommendations for remediation courses, e.g., pre-calculus or pre-statistics. The research uses data analysis to make this determination based on their previous math coursework and other data incoming students provide. Trends for success in math classes at CSBSJU have previously been based on outdated and inequitable methods. This project identifies correlations between prior coursework …
Logic's Modern British Up-Enders, Defenders, And Extenders: Whately's Revitalization Of Logic,
2025
Dordt University
Logic's Modern British Up-Enders, Defenders, And Extenders: Whately's Revitalization Of Logic, Calvin Jongsma
Faculty Work Comprehensive List
Logic developed dramatically during the last half of the nineteenth century. The baseline for these transformations in Great Britain was the revival of logic by Richard Whately around 1825. Whately successfully defended syllogistic logic as the science of valid reasoning against potent seventeenth and eighteenth-century detractors—Bacon, Locke, Reid, Campbell, Stewart, and others. In so doing, he made logic an intellectually respectable field of investigation for the next generation of logicians to explore and extend. This included John Stuart Mill (inductive logic), Augustus De Morgan (logic of relations), and George Boole (algebraic logic; propositional logic).
