Mathematics Commons^™

Fundamental Results On S-Closures, William D. Taylor

Mathematical Sciences Faculty Research

This paper establishes the fundamental properties of the s-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the s-closure of homogeneous ideals in graded rings is studied, and criteria are given for when the s-closure of an ideal can be described exactly in terms of its tight closure and rational powers. Sufficient conditions are established for the weak s-closure to equal to the s-closure. A generalization of the Briancon-Skoda theorem is given which compares any two different s-closures applied to powers of the same ideal.

Infinite Sets Of Solutions And Almost Solutions Of The Equation N⋅M=Reversal(N⋅M) Ii, Cem Ekinci

Mathematics Student Work

Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover a method for producing infinite sets of solutions and almost solutions of the equation N⋅M=reversal(N⋅M), our results are valid in a general numeration base b>2.

"Birds And Polynomial Functions”, Kelly W. Remijan

Teacher Resources

No abstract provided.

"Bouncing Balls And Linear Functions”, Kelly W. Remijan

Teacher Resources

No abstract provided.

Deterministic And Stochastic Models For Hiv-1 Dynamics, Amy Creel

Research and Creativity Symposium

In this research project, I investigated deterministic and stochastic versions of a model for Human Immunodeficiency Virus Type 1 (HIV-1) dynamics. First, the deterministic model is introduced, and numerical techniques are used to obtain an approximate solution to the system. Then, a stochastic model is developed from the deterministic system. Patient data is introduced, and the Monte Carlo Method is used to find an approximate solution to the stochastic system. The results of this project demonstrate the behavior of HIV-1 in an infected patient under the effects of reverse transcriptase and protease inhibitors, and the introduction of randomness to the …

Estimating Population Immunity Without Serological Testing, Andrew Lesniewski

Publications and Research

We propose an approximate methodology for estimating the overall level of immunity against COVID-19 in a population that has been affected by the recent epidemic. The methodology relies on the currently available mortality data and utilizes the properties of the SIR model. We illustrate the application of the method by estimating the recent levels of immunity in 10 US states with highest case numbers of COVID-19.

An Improvement In The Two-Packing Bound Related To Vizing's Conjecture, Kimber Wolff

Theory & Applications of Graphs

Vizing's conjecture states that the domination number of the Cartesian product of graphs is at least the product of the domination numbers of the two factor graphs. In this note we improve the recent bound of Breŝar by applying a technique of Zerbib to show that for any graphs G and H, γ(G x H)≥ γ (G) 2/3(γ(H)-ρ(H)+1), where γ is the domination number, ρ is the 2-packing number, and x is the Cartesian product.

Volume 12, Haleigh James, Hannah Meyls, Hope Irvin, Megan E. Hlavaty, Samara L. Gall, Austin J. Funk, Karyn Keane, Sarah Ghali, Antonio Harvey, Andrew Jones, Rachel Hazelwood, Madison Schmitz, Marija Venta, Haley Tebo, Jeremiah Gilmer, Bridget Dunn, Benjamin Sullivan, Mckenzie Johnson

Incite: The Journal of Undergraduate Scholarship

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Immortality in the Mortal World: Otherworldly Intervention in "Lanval" and "The Wife of Bath's Tale" by Haleigh James

Analysis of Phenolic Compounds in Moroccan Olive Oils by HPLC by Hannah Meyls

Art by Hope Irvin

The Effects of Cell Phone Use on Gameplay Enjoyment and Frustration by Megan E. Hlavaty, Samara L. Gall, and Austin J. Funk

Care, No Matter What: Planned Parenthood's Use of Organizational Rhetoric to Expand its Reputation by Karyn Keane

Analysis of Petroleum Products for …

Simplexity Of The N-Cube, Peter Graziano

Mathematics & Computer Science Student Scholarship

Major: Mathematics and Classics

Faculty Mentor: Dr. Su-Jeong Kang, Mathematics

The process of dividing shapes into triangles is called triangulation, and it is possible to abstract the idea of a triangle to higher dimensions, where it will be called a simplex in n-dimensions, or an n-simplex. I studied this process of generalized triangulation, or decomposition, in order to find an optimal decomposition of a 5-cube to help improve the bounds on the general case of an n-cube.

Self-Supervised Learning For Single-Molecule Localization Microscopy, Clare Minnerath

Mathematics & Computer Science Student Scholarship

Major: Mathematics and Computer Science

Faculty Mentor: Dr. Lynette Boos, Mathematics

We evaluate the ability of self-supervised deep learning for Poisson denoising of Single-Molecule Localization Microscopy (SMLM) in addition to the impact denoising can have on the ability to locate molecules within the Single-Molecule Localization Microscopy images. SMLM images are predominantly corrupted with Poisson noise. There is a need for a superior technique to provide accurate SMLM images in order for scientists to gain a better understanding of the functions of live cells at the nanoscale. By denoising SMLM images prior to the images undergoing the current state- of-the-art super-resolution …

Application Of Black-Scholes-Merton Model In Option Pricing And Intangibles Assets, Giang Nguyen-Hoang

Mathematics & Computer Science Student Scholarship

Major: Finance and Mathematics

Faculty Mentor: Dr. Joseph Shomberg, Mathematics

The Black-Scholes model was developed by Fisher Black and Myron Scholes in the 1970s to price stock options. Since then the model has been suited to price so-called intangible assets such as trademarks and patents. In this paper, we investigate the related Black-Scholes-Merton model and the relevant characteristics of patents in order to associate patents as real options. After describing patents as options, we apply the Black-Scholes-Merton model to the valuation of the intangible assets. Special attention is given to modeling volatility and the cost of delay in order to …

Research In Sabermetrics: The Cape Cod Baseball League, Thomas Zinzarella

Mathematics & Computer Science Student Scholarship

Major: Sports Media

Faculty Mentor: Fr. Humbert Kilanowski O.P, Mathematics and Computer Science

We analyzed data from the Cape Cod Baseball League, a prestigious summer baseball league, where we looked at sabermetric statistics such as WAR (Wins above replacement). Stats like these can help evaluate a player and project whether they are a future MLB player or not. Especially on the Cape, where 1 in 7 current Major League Baseball players have played in the league.

Universal Vector Neural Machine Translation With Effective Attention, Joshua Yi, Satish Mylapore, Ryan Paul, Robert Slater

SMU Data Science Review

Neural Machine Translation (NMT) leverages one or more trained neural networks for the translation of phrases. Sutskever intro- duced a sequence to sequence based encoder decoder model which be- came the standard for NMT based systems. Attention mechanisms were later introduced to address the issues with the translation of long sen- tences and improving overall accuracy. In this paper, we propose two improvements to the encoder decoder based NMT approach. Most trans- lation models are trained as one model for one translation. We introduce a neutral/universal model representation that can be used to predict more than one language depending on …

Inductive Constructions In Logic And Graph Theory, Davis Deaton

Honors Scholars Collaborative Projects

Just as much as mathematics is about results, mathematics is about methods. This thesis focuses on one method: induction. Induction, in short, allows building complex mathemati- cal objects from simple ones. These mathematical objects include the foundational, like logical statements, and the abstract, like cell complexes. Non-mathematicians struggle to find a common thread throughout all of mathematics, but I present induction as such a common thread here. In particular, this thesis discusses everything from the very foundations of mathematics all the way to combina- torial manifolds. I intend to be casual and opinionated while still providing all necessary formal rigor. …

On A Vizing-Type Integer Domination Conjecture, Elliot Krop, Randy R. Davila

Theory & Applications of Graphs

Given a simple graph G, a dominating set in G is a set of vertices S such that every vertex not in S has a neighbor in S. Denote the domination number, which is the size of any minimum dominating set of G, by γ(G). For any integer k ≥ 1, a function f : V (G) → {0, 1, . . ., k} is called a {k}-dominating function if the sum of its function values over any closed neighborhood is at least k. The weight of a {k}-dominating function is the sum of its values over all …

Identifying Cloud Forest Landslides In Satellite Imagery: A Machine Learning Approach, Eric Leu

19th Annual Celebration of Undergraduate Research and Creative Activity (2020)

Landslide formation is a significant contributor to montane rainforest biodiversity, opening gaps in the tree canopy and leading to the germination of pioneer plants. In order to study the spatio-temporal patterns of landslide formation, we developed a technique using a machine learning algorithm (random forest) to automatically identify landslides in high resolution satellite imagery. Using 4-band Planetscope and 5-band RapidEye satellite imagery, we identified landslides associated with major rain events over the Monteverde Cloud Forest Reserve in Costa Rica. The classifier uses reflectance values along with texture measures and topographic slope to sort pixels into different landscape classes. Slope was …

Entropy In Quantum Mechanics And Applications To Nonequilibrium Thermodynamics, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Classical formulations of the entropy concept and its interpretation are introduced. This is to motivate the definition of the quantum von Neumann entropy. Some general properties of quantum entropy are developed, such as the quantum entropy which always increases. The current state of the area that includes thermodynamics and quantum mechanics is reviewed. This interaction shall be critical for the development of nonequilibrium thermodynamics. The Jarzynski inequality is developed in two separate but related ways. The nature of irreversibility and its role in physics are considered as well. Finally, a specific quantum spin model is defined and is studied in …

"Using A Multimeter And Graphing: Voltage And Math”, Kelly W. Remijan

Teacher Resources

No abstract provided.

Response To Pitkanen’S Solar System Model: Towards Gross-Pitaevskiian Description Of Solar System And Galaxies And More Evidence Of Chiral Superfluid Vortices, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

In a new paper in recent issue of this journal (PSTJ), Prof. M. Pitkanen describes a solar system model inspired by spiral galaxies. While we appreciate his new approach, we find it lacks substantial discussion on the nature of vortices and chirality in galaxy. Therefore we submit a viewpoint that Gross-Pitaevskii model can be a more complete description of both solar system and also spiral galaxies, especially taking into account the nature of chirality and vortices in galaxies. In this article, we also hope to bring out some correspondence among existing models, so we discuss shortly: the topological vortice approach, …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …