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Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody 2021 William & Mary

Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody

Undergraduate Honors Theses

A graph has quantum symmetry if the algebra associated with its quantum automorphism group is non-commutative. We study what quantum symmetry means and outline one specific method for determining whether a graph has quantum symmetry, a method that involves studying planar algebras and manipulating planar tangles. Modifying a previously used method, we prove that the 5-cycle has no quantum symmetry by showing it has the generating property.


How Risk-Related Statistics, As Reported In News And Social Media, Are Linked To The Use Of The Public Transit System, Prashiddhi Pokhrel 2021 University of Southern Maine

How Risk-Related Statistics, As Reported In News And Social Media, Are Linked To The Use Of The Public Transit System, Prashiddhi Pokhrel

Thinking Matters Symposium

Due to the pandemic, people have started relying more on televisions, news, social media, and other news outlets for guidance. Moreover, with the increasing amount of news, data, and information there is also an increase in the amount of misleading statistics. People’s opinions and decisions significantly depend on the data, statistics, and information that they are exposed to, as well as their sources. For this project, we want to look at how information and its sources are affecting the decision made by the general public for the usage of the Portland Transit System. It is very important to know ...


Solving Parabolic Interface Problems With A Finite Element Method, Henry Brown 2021 West Chester University of Pennsylvania

Solving Parabolic Interface Problems With A Finite Element Method, Henry Brown

Mathematics Student Work

Partial differential equations (PDEs) dominate mathematical models given their effectiveness and accuracy at modeling the physical realities which govern the world. Though we have these powerful tools, analytic solutions can only be found in the simplest of cases due to the complexity of PDE models. Thus, efficient and accurate computational methods are needed to approximate solutions to PDE models. One class of these methods are finite element methods which can be used domain to provide close approximations to the PDE model in a finite domain. In this presentation, we discuss the use of a Discontinuous Galerkin (DG) Finite Element Methods ...


Modeling The Problem Of Integral Geometry On A Family Of Hyperbolic And Spherical Curves, Azamat Pirimbetov, N. Uteuliev, G. Djaykov 2021 Karakalpak State University

Modeling The Problem Of Integral Geometry On A Family Of Hyperbolic And Spherical Curves, Azamat Pirimbetov, N. Uteuliev, G. Djaykov

Karakalpak Scientific Journal

The problems of integral geometry in a strip on a family of curves of hyperbolic and spherical type are considered which have numerous applications in problems of geophysics, thermoacoustic and photoacoustic tomography. Explicit formulas are obtained for the Fourier image of the solution of integral geometry problems in the class of smooth compactly supported functions. Further, the obtained formulas are investigated for stability using numerical methods. To solve the problems, algorithms are constructed. Numerical and graphical results of applying these algorithms to solving the problems are presented.


Markov Chains And Their Applications, Fariha Mahfuz 2021 University of Texas at Tyler

Markov Chains And Their Applications, Fariha Mahfuz

Math Theses

Markov chain is a stochastic model that is used to predict future events. Markov chain is relatively simple since it only requires the information of the present state to predict the future states. In this paper we will go over the basic concepts of Markov Chain and several of its applications including Google PageRank algorithm, weather prediction and gamblers ruin.

We examine on how the Google PageRank algorithm works efficiently to provide PageRank for a Google search result. We also show how can we use Markov chain to predict weather by creating a model from real life data.


Classification Of Cayley Rose Window Graphs, Angsuman Das, Arnab Mandal 2021 Presidency University, Kolkata

Classification Of Cayley Rose Window Graphs, Angsuman Das, Arnab Mandal

Theory and Applications of Graphs

Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edge-transitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs.


Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid-19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos 2021 The University of Texas Rio Grande Valley

Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid-19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos

Mathematical and Statistical Sciences Faculty Publications and Presentations

At the beginning of August 2020, the Rio Grande Valley (RGV) of Texas experienced a rapid increase of coronavirus disease 2019 (abbreviated as COVID-19) cases and deaths. This study aims to determine the optimal levels of effective social distancing and testing to slow the virus spread at the outset of the pandemic. We use an age-stratified eight compartment epidemiological model to depict COVID-19 transmission in the community and within households. With a simulated 120-day outbreak period data we obtain a post 180-days period optimal control strategy solution. Our results show that easing social distancing between adults by the end of ...


Normality Properties Of Composition Operators, Grace Weeks, Hallie Kaiser, Katy O'Malley 2021 Taylor University

Normality Properties Of Composition Operators, Grace Weeks, Hallie Kaiser, Katy O'Malley

Celebration of Scholarship 2021

We explore two main concepts in relation to truncated composition matrices: the conditions required for the binormal and commutative properties. Both of these topics are important in linear algebra due to their connection with diagonalization.

We begin with the normal solution before moving onto the more complex binormal solutions. Then we cover conditions for the composition matrix to commute with the general matrix. Finally, we end with ongoing questions for future work.


Developing Better Instruction, Better Instructors, And New Investigators, Clay Vander Kolk, Abigail Pyle 2021 Taylor University

Developing Better Instruction, Better Instructors, And New Investigators, Clay Vander Kolk, Abigail Pyle

Celebration of Scholarship 2021

This research discusses how HAMTE and future educators collaborated to use the Principles to Action Professional Learning Toolkit in their classes and the tools they used to measure and gather conclusions about the development in the future teachers.


An Agent-Based Model To Evaluate The Effect Of Socioeconomic Status And Demographic Factors On Covid-19 Prevalence And Mortality, Jonathan Huang, Berke Nouri 2021 University of Richmond

An Agent-Based Model To Evaluate The Effect Of Socioeconomic Status And Demographic Factors On Covid-19 Prevalence And Mortality, Jonathan Huang, Berke Nouri

Arts & Sciences Student Symposium

The purpose of the project is to discover how the prevalence and mortality of a pandemic change depending on a population’s demographic factors as well as various intervention policies through a NetLogo agent-based model. This model will simulate how demographic factors affect the course of COVID-19 (infection rate, recovery rate, and death rate). Demographic factors of interest will include population density, income distribution, age distribution, and number of hospital beds per capita. Intervention policies include vaccination, social distancing, mask wearing, mass testing, and quarantining. Conclusions about the effect of demographic factors on the infection, recovery, and death rate will ...


Factoring: Difference Of Squares, Thomas Lauria 2021 CUNY College of Staten Island

Factoring: Difference Of Squares, Thomas Lauria

Open Educational Resources

This lesson plan will explain how to factor basic difference of squares problems


Preliminary Results On The Use Of Machine Learning For Advance Controls Of A Dielectric Elastomer Actuator, Nathanael Gentry, Carson Farmer, Hector Medina 2021 Liberty University

Preliminary Results On The Use Of Machine Learning For Advance Controls Of A Dielectric Elastomer Actuator, Nathanael Gentry, Carson Farmer, Hector Medina

Liberty University Research Week

Undergraduate

Applied


Potential Connections Between Graph Theory And Materials Modeling, Rachel Drake, Hector Medina 2021 Liberty University

Potential Connections Between Graph Theory And Materials Modeling, Rachel Drake, Hector Medina

Liberty University Research Week

Undergraduate

Applied


Translation Of: Isoparametrische Hyperflächen In Sphären Ii. Über Die Zerlegung Der Sphäre In Ballbündel, Math. Ann. 256, 215–232 (1981) By Hans Friedrich Münzner., Thomas E. Cecil 2021 College of the Holy Cross

Translation Of: Isoparametrische Hyperflächen In Sphären Ii. Über Die Zerlegung Der Sphäre In Ballbündel, Math. Ann. 256, 215–232 (1981) By Hans Friedrich Münzner., Thomas E. Cecil

Mathematics Department Faculty Scholarship

This is an English translation of the article "Isoparametrische Hyperflächen in Sphären II. Über die Zerlegung der Sphäre in Ballbündel" by Hans Friedrich Münzner, which was originally published in Math. Ann. 256, 215–232 (1981).

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in German. All references should be made to the original paper. I want to thank Cristina Ballantine for her help with the translation.


Translation Of: Isoparametrische Hyperflächen In Sphären, Math. Ann. 251, 57–71 (1980) By Hans Friedrich Münzner., Thomas E. Cecil 2021 College of the Holy Cross

Translation Of: Isoparametrische Hyperflächen In Sphären, Math. Ann. 251, 57–71 (1980) By Hans Friedrich Münzner., Thomas E. Cecil

Mathematics Department Faculty Scholarship

This is an English translation of the article "Isoparametrische Hyperflächen in Sphären" by Hans Friedrich Münzner, which was originally published in Math. Ann. 251, 57–71 (1980).

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in German. All references should be made to the original paper. I want to thank Cristina Ballantine for her help with the translation.


Reviving The Media Station: A Study In Reverse Engineering, Nathanael Gentry, Melesa Poole 2021 Liberty University

Reviving The Media Station: A Study In Reverse Engineering, Nathanael Gentry, Melesa Poole

Liberty University Research Week

Undergraduate

Applied


Emerald Ash Borer And The Application Of Biological Control In Virginia, Shuheng Chen, Yihui Wu, Shengjie Liu 2021 University of Richmond

Emerald Ash Borer And The Application Of Biological Control In Virginia, Shuheng Chen, Yihui Wu, Shengjie Liu

Arts & Sciences Student Symposium

The emerald ash borer (Agrilus planipennis; EAB) is an invasive wood-boring beetle whose larvae feed on ash phloem. After only 1-5 years of infestation, the larvae create extensive tunnels under the bark that disrupt the tree’s ability to transport water and nutrients, which eventually girdles and kills the tree. Since 2008, EAB has spread to all but the eastern-most counties in Virginia. Bological control is one strategy to limit EAB populations. In this project we study control by native agents (woodpeckers) and imported agents (parasitoid wasps).

Mathematical models of host-parasitoid interactions and simulations based on both models and field ...


Reducing The Maximum Degree Of A Graph: Comparisons Of Bounds, Peter Borg 2021 Department of Mathematics, Faculty of Science, University of Malta, Malta

Reducing The Maximum Degree Of A Graph: Comparisons Of Bounds, Peter Borg

Theory and Applications of Graphs

Let $\lambda(G)$ be the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. Let $\lambda_{\rm e}(G)$ be the smallest number of edges that can be removed from $G$ for the same purpose. Let $k$ be the maximum degree of $G$, let $t$ be the number of vertices of degree $k$, let $M(G)$ be the set of vertices of degree $k$, let $n$ be the number of vertices in the closed neighbourhood of $M(G)$, and let $m$ be the number of edges ...


Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson 2021 University of Richmond

Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson

Arts & Sciences Student Symposium

The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.


The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill 2021 University of Richmond

The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill

Arts & Sciences Student Symposium

This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of ...


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