Digital Commons Network^™

On Weyl Representations Of Gl(N), Amairani Hernandez Garcia

Mathematics Dissertations - Archive

This thesis studies generalized Laurent polynomial representations of the general linear Lie algebra. These representations arise naturally as representations over the Weyl algebra consisting of differential operators on $\mathbb{C}^n$. Our main result is an explicit description of the socle filtration of $P_{\mu} = \Span \{x^{\bf m} \: | \: {\bf m} \in \mathbb Z^{n}, \: | \bf{m} | \: = \mu \}$ for $\mu \in \mathbb{Z}$.

A Study On The Correlation Between A Star's Rayleigh-Taylor Characteristic Timescale And Stellar Wind Activity, Fiona Klett

Undergraduate Journal of Mathematical Modeling: One + Two

In this paper, we investigate the correlations between a star's internal dynamics due to the Rayleigh-Taylor instability and episodes of stellar wind activity, using both a theoretical model and observational data from the NOAA.% \cite{NOAA}. Besides its relevance as an astrophysics problem, this study is also informative for models of climate change which include secular perturbations in the Sun's internal dynamics, as a potential source of solar activity variability.

Manifold Learning In Robotics: A Tutorial And Survey, Marcus Hawkins

Computer Science and Engineering Theses - Archive

In this article, we hope to represent the current state of the art of manifold learning in an understandable and approachable way. The authors will present a general overview core algorithms associated with linear and nonlinear dimensionality reduction techniques, give rudimentary definitions from differential geometry, and tenets of robotic perception, manipulation and path planning. Some of the historical applications of these algorithms will be presented, as well as conjectures about future uses, through examples from peer-reviewed journals.

Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, Te'a Riley

Mathematics Dissertations - Archive

This phenomenological study examines the role of undergraduate and graduate Real Analysis courses in shaping the mathematical trajectories of seven women Ph.D. mathematicians from groups historically disenfranchised in mathematics.Qualitative analysis of interviews explores various aspects of their development as mathematicians with a focus on their experiences in Real Analysis. This study applies Ryan & Deci’s (1985) Self-Determination Theory's Basic Psychological Need Theory and Critical Race Theory to analyze the trajectories of the participants. The research explores how the fulfillment of basic psychological needs in their Real Analysis courses may have influenced their academic and professional journeys. The basic psychological need …

Calculus Students’ Problem-Solving Strategies On Related Rates Of Change Problems Appearing In Online Versus Paper-And-Pencil Format, Tyson Bailey

Mathematics Dissertations - Archive

This study explores first-semester calculus students’ use of mathematical problem-solving strategies while working related rates of change problems in both an online homework format and a traditional pencil-paper format. We address two research questions: (1) How do students’ mathematical problem-solving strategies when working online homework on related rates of change problems compare with their problem-solving strategies when working paper-and-pencil homework related rates of change problems? (2) What influence does the ‘view an example’ feature in online homework have on a student’s problem-solving strategies when working an online RRC homework problem? Using scores on free-response midterm exam problems on related rates …

Quantifying Non-Primary Dna Formations Through Mechanical And Geometric Models, Sonia E. Teodorescu

Undergraduate Journal of Mathematical Modeling: One + Two

In this article, mechanical and geometric models for DNA strains (regarded as a helical structure in 3 dimensions, embedded into surfaces of various shapes (straight or curved cylinders, spheres, or projected into planes), are analyzed in order to obtain parameter estimates for DNA characteristics which can be used to detect the formation of secondary and tertiary formations in the presence of disorder. The models allow for the explicit representation of the DNA shape on constrained geometries and can therefore be implemented directly into {\it{ab initio}} or synthetic simulation studies.

Meromorphic Continuations Of Euler Products With Polynomial Growth Coefficients, Kledis Ahmetaj

Senior Honors Theses and Projects

In this paper, we investigate the meromorphic continuation of Euler products, with a particular focus on those with polynomial growth coefficients. Building upon the classical example of the Riemann zeta function, we derive conditions under which Euler products can be extended beyond their regions of convergence to broader domains of the complex plane, revealing singularities and deepening our understanding of their analytic properties. We begin by establishing a framework for meromorphic continuation and then introduce a general theorem that applies to Euler products of the form

where the coefficients and exponents satisfy specific constraints. We prove that such Euler products …

Topological And Dynamic Properties Of The Sublinearly Morse Boundary And The Quasi-Redirecting Boundary., Jacob D. Garcia, Yulan Qing, Elliott Vest

Mathematics Sciences: Faculty Publications

Sublinearly Morse boundaries of proper geodesic spaces are introduced by Qing, Rafi and Tiozzo. Expanding on this work, Qing and Rafi recently developed the quasi-redirecting boundary, denoted ∂G, to include all directions of metric spaces at infinity. Both boundaries are topological spaces that consist of equivalence classes of quasi-geodesic rays and are quasi-isometrically invariant. In this paper, we study these boundaries when the space is equipped with a geometric group action. In particular, we show that G acts minimally on ∂κG and that contracting elements of G induces a weak north-south dynamic on ∂κG. We also prove, when ∂G exists …

Computational Methods For Oi-Modules, Michael Morrow

Theses and Dissertations--Mathematics

Computational commutative algebra has become an increasingly popular area of research. Central to the theory is the notion of a Gröbner basis, which may be thought of as a nonlinear generalization of Gaussian elimination. In 2019, Nagel and Römer introduced FI- and OI-modules over FI- and OI-algebras, which provide a framework for studying sequences of related modules defined over sequences of related polynomial rings. In particular, they laid the foundations of a theory of Gröbner bases for certain classes of OI-modules. In this dissertation we develop an OI-analog of Buchberger's algorithm in order to compute such Gröbner bases, as well …

First-Order Geometric Integer-Valued Autoregressive Model With Covariates, Adisak Seedamad

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we propose two integer-valued time series consisting of (1) the single parameter first-order geometric integer-valued autoregressive (SGINAR(1)) model with covariates and (2) the first-order geometric integer-valued autoregressive GINAR(1) model with covariates. In our study, we obtain the innovation distribution using stationary properties and obtain moment properties of two models. In addition, we obtain parameter estimation by using the conditional least squares (CLS) method and the penalized conditional least squares (PCLS) method. Finally, we conduct simulation studies and apply to real data.

Developing Machine Learning And Time-Series Analysis Methods With Applications In Diverse Fields, Muhammed Aljifri

Theses and Dissertations

This dissertation introduces methodologies that combine machine learning models with time-series analysis to tackle data analysis challenges in varied fields. The first study enhances the traditional cumulative sum control charts with machine learning models to leverage their predictive power for better detection of process shifts, applying this advanced control chart to monitor hospital readmission rates. The second project develops multi-layer models for predicting chemical concentrations from ultraviolet-visible spectroscopy data, specifically addressing the challenge of analyzing chemicals with a wide range of concentrations. The third study presents a new method for detecting multiple changepoints in autocorrelated ordinal time series, using the …

Integrating Contradictory Perspectives In Latin American Philosophy: A Multialism Approach, Maikel Yelandi Leyva Vázquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study explores the integration of indigenous philosophies and postcolonial modernist theories within the framework of MultiAlism, highlighting the potential for dialogue and synthesis between these diverse philosophical traditions in Latin America. MultiAlism, a concept developed by Florentin Smarandache, is utilized to bridge the gaps and contradictions between these systems by focusing on areas of neutrality such as cultural diversity and power structure critiques. The research emphasizes the importance of incorporating both ancestral wisdom and modern critiques to foster a deeper understanding and appreciation of Latin America’s rich philosophical heritage. This integrative approach offers practical insights for developing inclusive policies …

Fundamental Computational Problems And Algorithms For Superhypergraphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Hypergraphs extend traditional graphs by allowing edges (known as hyperedges) to connect more than two vertices, rather than just pairs. This paper explores fundamental problems and algorithms in the context of SuperHypergraphs, an advanced extension of hypergraphs enabling modeling of hierarchical and complex relationships. Topics covered include constructing SuperHyperGraphs, recognizing SuperHyperTrees, and computing SuperHyperTree-width. We address a range of optimization problems, such as the SuperHy-pergraph Partition Problem, Reachability, Minimum Spanning SuperHypertree, and Single-Source Shortest Path. Furthermore, adaptations of classical problems like the Traveling Salesman Problem, Chinese Postman Problem, and Longest Simple Path Problem are presented in the SuperHypergraph framework.

A Review At Two Nuclear Reactor Problems In Asia, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The development of nuclear power plants (NPP) is often a heated debate, especially in developing countries [1]. In relation to this, it is worth the public's attention that lately, it seems that there have been increasingly frequent press releases from various parties representing the government regarding plans to build the first nuclear fission reactor in Indonesia in the not too distant future. Reportedly there will be a large amount of additional energy supply planned (around 100 GW to be built in Indonesia within the coming decade). For this reason, the authors would like to invite readers to take a moment …

Rado Numbers For Two Systems Of Linear Equations, Anthony Glackin

Electronic Theses and Dissertations

For any positive integer n and any equation E of either the form x1+x2+· · ·+xn = x0 or x1 + x2 + n = x0, the two-color Rado number R2(E) is the least integer such that any 2-coloring of the natural numbers 1 through R2(E) will contain a monochromatic solution to E. Let Ek be a system of k equations of the aforementioned form, where Ei represents the ith equation in Ek and the set I = {1, 2, . . . , k} is the set of indices of these equations. This thesis shows that the two-color Rado …

Principal Component Analysis With Application To Credit Card Data, Elenor Cain

Schultz-Werth Award Papers

Principal Component Analysis (PCA) is a type of dimension reduction technique used in data analysis to process the data before making a model. In general, dimension reduction allows analysts to make conclusions about large data sets by reducing the number of variables while retaining as much information as possible. Using the numerical variables from a data set, PCA aims to compute a smaller set of uncorrelated variables, called principal components, that account for a majority of the variability from the data. The purpose of this paper is to understand PCA and determine which principal components should be kept from a …

College Algebra, Leslie Bain

ATU Faculty OER Book Reviews

Review of OER College Algebra textbook by Carl Stitz, available at https://open.umn.edu/opentextbooks/textbooks/college-algebra

Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As many readers may know, graph theory is a fundamental branch of mathematics that explores networks made up of nodes and edges, focusing on their paths, structures, and properties [196]. A planar graph is one that can be drawn on a plane without any edges intersecting, ensuring planarity. Outerplanar graphs, a subset of planar graphs, have all their vertices located on the boundary of the outer face in their planar embedding. In recent years, outerplanar graphs have been formally defined within the context of fuzzy graphs. To capture uncertain parameters and concepts, various graphs such as fuzzy, neutrosophic, Turiyam, and …

The Independence Polynomial Of A Graph At −1, Phoebe Rose Zielonka

Theses, Dissertations and Culminating Projects

No abstract provided.

Implementation Of 1/2-Approximation Path Cover Algorithm And Its Empirical Analysis, Junyuan Lin, Guangpen Ren

Mathematics, Statistics and Data Science Faculty Works

In this paper, we demonstrate a deterministic algorithm that approximates the optimal path cover on various graphs and networks derived from a wide range of real world problems. Based on the 1-Approximation Path Cover Algorithm by Moran et al., we first organize the original algorithm into two versions - one with redundant edge removal and one without. To compare the two versions of algorithms, we prove the number of redundant edges for any general graphs to analyze the effects of edge removal. We also analyze theoretical guarantees of the two algorithms. To test the time complexity and performance, we conduct …

Experiencing Tensions Of Nepantla With Inner-Departmental Change Groups, Rachel Tremaine, Jess Ellis Hagman, Matthew Voigt, Amy Been Bennett, Fanatasi Nicole, Margaret Ann Bolick, Leilani Pai, Nancy Kress, Kelsey Quaisley, Rachel Funk, Patricia Wonch Hill, Wendy M. Smith

Mathematics, Statistics and Data Science Faculty Works

This study explores the experiences of three Networked Improvement Communities (NICs) within mathematics departments as they work to critically transform their introductory mathematics programs. Drawing on the framework of dominant and critical axes of equity, we identify three key tensions experienced by the NICs: identity neutrality versus identity centrality, power over versus power with, and students as novices versus students as experts. These tensions are framed as productive enactments of working to change systems from within, highlighting the challenges and opportunities inherent in navigating the liminal space of nepantla. We argue that engaging with these tensions is crucial for fostering …

Effect Of Fluid Elasticity On The Emergence Of Oscillations In An Active Elastic Filament, Kathryn G. Link, Robert D. Guy, Becca Thomases, Paulo E. Arratia

Mathematics Sciences: Faculty Publications

Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This …

A Note On Three-Fold Branched Covers Of S4, Ryan Blair, Patricia Cahn, Alexandra Kjuchukova, Jeffrey Meier

Mathematics Sciences: Faculty Publications

We show that any 4-manifold admitting a (g;k₁,k₂,0)-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in S⁴, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property.

Nonequational Stable Groups, Isabel Müller, Rizos Sklinos

Faculty Journal Articles

We introduce a combinatorial criterion for verifying whether a formula is not the conjunction of an equation and a co-equation. Using this, we give a proof for the nonequationality of the free group. Furthermore, we generalize the latter result to the first-order theory of any free product of groups of the form G * Fω.

Cryptographic Algorithms, Cryptocurrencies, And A Predictive Model Of Bitcoin Value By Pls Regression, Paul Kenneth O'Connor

Masters Theses

"With the invention of Bitcoin in 2009, as a seemingly timed response to the ongoing financial crisis, the popularity of the cryptocurrency has since continued to grow. Just this year, the Security Exchange Commission approved Bitcoin for exchange traded funds, allowing major investment firms to begin product trading. With this approval, and during this very moment of writing, Bitcoin has entered a bull market and reached a record value of over 72,000 USD. In addition, the Bitcoin halving event in April of 2024 is expected to increase demand even further. It has been anticipated that Bitcoin and other cryptocurrencies will …

The Exponential Function In Discrete Fractional Calculus Under The Delta Operator, Brayton James Link

Masters Theses

"Previously the exponential problem in discrete fractional calculus under the nabla operator was solved with the discrete Mittag--Leffler function. We now show the solution to the exponential problem in discrete fractional calculus under the delta operator, providing multiple derivations of the solution with recursion and Laplace transforms. We also share some computational and numerical results of experiments with different orders of difference to display the nature of the solution" -- Abstract, p. iii

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar

Honors College Theses

Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon …

Enumeration Of Increasing Trees, Garrett M. Southwood

Honors College Theses

We consider the generating function for increasingly labelled trees. By generalizing the proof through symbolic method, we are able to study various statistics regarding binary increasing trees with respect to height restrictions. We then apply our approach to special colorings of increasing trees in order to obtain their generating functions and, from there, derive the counting sequence for (ak+a)-colored recursive trees. We also present some interesting bijections between colored and non-colored increasing trees.

Accessing And Assessing Components Of Elementary And Middle School Students’ Mathematical Disposition Through Metaphors, Emily Deal, Edward Mooney, Amanda Cullen, Neet Priya Bajwa, Allison M. Kroesch, Julien Corven, Beth Macdonald

Faculty Publications – Mathematics

This study examined student-generated metaphors comparing food to math as a means of accessing and assessing components of prekindergarten through Grade 8 students’ (N = 306) mathematical disposition. Previous research provided insight into predominantly affective components of older students’ mathematical disposition (i.e. Grade 4 through college). However, we extend these findings to include nonaffective components and younger students. Our study highlights the value in conceptualizing mathematical disposition as the sum of three mental functions, namely cognitive (e.g., mental processes such as reasoning), affective (e.g., attitudes, feelings, beliefs about mathematics or oneself as a learner), and conative (e.g., effort, grit, …