Gray Codes In Music Theory, 2020 University of Maine

#### Gray Codes In Music Theory, Isaac L. Vaccaro

*Electronic Theses and Dissertations*

In the branch of Western music theory called serialism, it is desirable to construct chord progressions that use each chord in a chosen set exactly once. We view this problem through the scope of the mathematical theory of Gray codes, the notion of ordering a finite set X so that adjacent elements are related by an element of some specified set R of involutions in the permutation group of X. Using some basic results from the theory of permutation groups we translate the problem of finding Gray codes into the problem of finding Hamiltonian paths and cycles in a Schreier ...

The Marshmallow Lab: A Project-Based Approach To Understanding Functional Responses, 2020 Utah State University

#### The Marshmallow Lab: A Project-Based Approach To Understanding Functional Responses, Melissa Pulley

*All Graduate Theses and Dissertations*

This paper presents a three-part lesson plan to improve student’s understanding of Holling’s type II functional response model. This model describes the interaction between a predator and how much it is able to consume given a constant number of prey. According to the model, while increased availability of prey allows predators to consume portionately more prey for low values, after some number of prey, predators will only be able to capture a limited number of prey even as the prey continues to increase. This phenomenon is known as saturation. Holling first develop this important ecological theory through his ...

Trees With Unique Italian Dominating Functions Of Minimum Weight, 2020 East Tennessee State University

#### Trees With Unique Italian Dominating Functions Of Minimum Weight, Alyssa England

*Electronic Theses and Dissertations*

An Italian dominating function, abbreviated IDF, of $G$ is a function $f \colon V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that for every vertex $v \in V(G)$ with $f(v)=0$, we have $\sum_{u \in N(v)} f(u) \ge 2$. That is, either $v$ is adjacent to at least one vertex $u$ with $f(u) = 2$, or to at least two vertices $x$ and $y$ with $f(x) = f(y) = 1$. The Italian domination number, denoted $\gamma_I$(G), is the minimum weight of an IDF in $G$. In this thesis, we use operations that join ...

An Analysis Of The First Passage To The Origin (Fpo) Distribution, 2020 East Tennessee State University

#### An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni

*Electronic Theses and Dissertations*

What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this ﬁrst passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a ﬁxed n and also the posterior distribution of m when ...

An Exploration In Ramsey Theory, 2020 University of Northern Iowa

#### An Exploration In Ramsey Theory, Jake Weber

*Dissertations and Theses @ UNI*

We present several introductory results in the realm of Ramsey Theory, a subfield of Combinatorics and Graph Theory. The proofs in this thesis revolve around identifying substructure amidst chaos. After showing the existence of Ramsey numbers of two types, we exhibit how these two numbers are related. Shifting our focus to one of the Ramsey number types, we provide an argument that establishes the exact Ramsey number for* h*(*k*, 3) for *k* ≥ 3; this result is the highlight of this thesis. We conclude with facts that begin to establish lower bounds on these types of Ramsey numbers for graphs ...

The Game Of Life On The Hyperbolic Plane, 2020 Rose-Hulman Institute of Technology

#### The Game Of Life On The Hyperbolic Plane, Yuncong Gu

*Mathematical Sciences Technical Reports (MSTR)*

In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3.

A Note On The Fine Structure Constant, 2020 University of Nebraska-Lincoln

#### A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan

*CSE Technical reports*

We derive the numerical value of the fine structure constant in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.

A Note On The Fine Structure Constant, 2020 University of Nebraska-Lincoln

#### A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan

*Sociology Department, Faculty Publications*

We derive the numerical value of the fine structure constant $\alpha$ in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.

A Note On The Fine Structure Constant, 2020 University of Nebraska-Lincoln

#### A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan

*Sociology Department, Faculty Publications*

We derive the numerical value of the fine structure constant in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.

Mathematic Modeling Of Covid-19 In The United States, 2020 Applied NanoFemto Technologies, LLC

#### Mathematic Modeling Of Covid-19 In The United States, Yuanji Tang, Shixia Wang

*Coronavirus COVID-19 Publications by UMMS Authors*

Since the early reports of COVID-19 cases in China in late January 2020 (1-2), the worst pandemic in 100 years has spread to the entire globe with approximately 2.4 million diagnosed cases and over 165,000 deaths up to April 20, 2020.

While scientists from various public and private groups use math and computer to simulate the course of this pandemic to try to predict how this outbreak might evolve (3), most of such analyses are either quite complicated or not publicly available.

Here a simple mathematic modeling approach is taken to track the outbreaks of COVID-19 in the ...

Infinite Sets Of Solutions And Almost Solutions Of The Equation N⋅M=Reversal(N⋅M) Ii, 2020 West Chester University of Pennsylvania

#### 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.

Computational Comparison Of Exact Solution Methods For 0-1 Quadratic Programs: Recommendations For Practitioners, 2020 Dickinson College

#### Computational Comparison Of Exact Solution Methods For 0-1 Quadratic Programs: Recommendations For Practitioners, Richard J. Forrester, Noah Hunt-Isaak

*Faculty and Staff Publications By Year*

This paper is concerned with binary quadratic programs (BQPs), which are among the most well-studied classes of nonlinear integer optimization problems because of their wide variety of applications. While a number of different solution approaches have been proposed for tackling BQPs, practitioners need techniques that are both efficient and easy to implement. We revisit two of the most widely used linearization strategies for BQPs and examine the effectiveness of enhancements to these formulations that have been suggested in the literature. We perform a detailed large-scale computational study over five different classes of BQPs to compare these two linearizations with a ...

Estimating Population Immunity Without Serological Testing, 2020 CUNY Bernard M Baruch College

#### 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, 2020 Clayton State University

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

*Theory and 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, 2020 Longwood University

#### 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 ...*

Universal Vector Neural Machine Translation With Effective Attention, 2020 SMU

#### 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 ...

Inductive Constructions In Logic And Graph Theory, 2020 Belmont University

#### Inductive Constructions In Logic And Graph Theory, Davis Deaton

*Honors Theses*

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 ...

An Investigation Of The Relationship Between Math Curricula And Students' College Readiness, 2020 Olivet Nazarene University

#### An Investigation Of The Relationship Between Math Curricula And Students' College Readiness, Nancy A. Deluca

*Scholar Week 2016 - present*

State learning standards with increased rigor have required higher levels of achievement from students on standardized tests, high-school grades, and national percentile ranks which are used for collegiate acceptance and course placement. As a result, preparation of students for standardized tests such as the ACT and SAT have become increasingly more challenging. The current quantitative, quasi-experimental study examined the relationship between the tangible math curricula used for instruction and students’ readiness for collegiate coursework. From sample sizes of 128 and 169 high-school students in two consecutive school years, there were several statistically significant relationship differences. Analysis of test results indicated ...

On A Vizing-Type Integer Domination Conjecture, 2020 Clayton State University

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

*Theory and 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 the vertices. The *{k}-domination ...*

Identifying Cloud Forest Landslides In Satellite Imagery: A Machine Learning Approach, 2020 Hope College

#### 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 ...