Oscillation In Mathematical Epidemiology, 2019 Bates College

#### Oscillation In Mathematical Epidemiology, Meredith Greer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

2019 Petersheim Academic Exposition Schedule Of Events, 2019 Seton Hall University

#### 2019 Petersheim Academic Exposition Schedule Of Events, Seton Hall University

*Petersheim Academic Exposition*

2019 Petersheim Academic Exposition

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), 2019 Central Washington University

#### How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

*Pre-calculus and Trigonometry*

No abstract provided.

Greatest Common Divisor: Algorithm And Proof, 2019 University of St. Thomas - Houston

#### Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

*Number Theory*

No abstract provided.

Connectedness- Its Evolution And Applications, 2019 Ursinus College

#### Connectedness- Its Evolution And Applications, Nicholas A. Scoville

*Topology*

No abstract provided.

The Knill Graph Dimension From Clique Cover, 2019 Pepperdine

#### The Knill Graph Dimension From Clique Cover, Evatt Salinger, Dr. Kassahun Betre

*Seaver College Research And Scholarly Achievement Symposium*

In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim (G1 + G2) = 1 + dim G1 + dim G2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order KN will have dimension N − 1.

Critical Mathematical Inquiry, 2019 Bank Street College of Education

#### Critical Mathematical Inquiry

*Occasional Paper Series*

Welcome to Issue 41 of Bank Street’s *Occasional Paper Series*. The issue features a collection of papers by authors with a shared affinity for the work of critical mathematical inquiry (CMI). In what follows, we present our framing of mathematics education as a participatory venue for CMI and situate it in the context of another, perhaps more familiar approach to teaching mathematics for social justice (TMfSJ).

Student-Faculty Connection And Stem Identity In The Flipped Classroom, 2019 University of Southern Indiana

#### Student-Faculty Connection And Stem Identity In The Flipped Classroom, Adrian P. Gentle, William Wilding

*ASEE IL-IN Section Conference*

Students who arrive at college intending to major in a STEM discipline are often required to complete a college-level precalculus course, despite evidence that these courses are not always successful in preparing students for calculus. The implementation of evidence-based teaching strategies, such as the flipped classroom, provides an avenue for improving the effectiveness of precalculus. This quasi-experimental study explores the effect of a flipped precalculus classroom on students' degree of connection with their instructor and other students, together with their sense of motivation and enjoyment of mathematics, which we treat as an indicator of a developing STEM identity. Validated survey ...

Secure Passwords Using Combinatorial Group Theory, 2019 Fairfield University

#### Secure Passwords Using Combinatorial Group Theory, Gilbert Baumslag, Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger

*Benjamin Fine*

Password security is a crucial component of modern internet security. In this paper, we present a provably secure method for password verification using combinatorial group theory. This method relies on the group randomizer system, a subset of the MAGNUS computer algebra system and corrects most of the present problems with challenge response systems, the most common types of password verification. Theoretical security of the considered method depends on several results in asymptotic group theory. We mention further that this method has applications for many other password situations including container security.

Monoidal Supercategories And Superadjunction, 2019 University of Ottawa

#### Monoidal Supercategories And Superadjunction, Dene Lepine

*Rose-Hulman Undergraduate Mathematics Journal*

We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.

Strengthening Relationships Between Neural Ideals And Receptive Fields, 2019 Texas A&M University

#### Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant

*Rose-Hulman Undergraduate Mathematics Journal*

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code *C *can be represented by its neural ideal *J*_{C}. In turn, the polynomials in *J*_{C }can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were related ...

Triangle Packing On Tripartite Graphs Is Hard, 2019 University of Kansas

#### Triangle Packing On Tripartite Graphs Is Hard, Peter A. Bradshaw

*Rose-Hulman Undergraduate Mathematics Journal*

The problem of finding a maximum matching on a bipartite graph is well-understood and can be solved using the augmenting path algorithm. However, the similar problem of finding a large set of vertex-disjoint triangles on tripartite graphs has not received much attention. In this paper, we define a set of vertex-disjoint triangles as a “tratching.” The problem of finding a tratching that covers all vertices of a tripartite graph can be shown to be NP-complete using a reduction from the three-dimensional matching problem. In this paper, however, we introduce a new construction that allows us to emulate Boolean circuits using ...

Graphs, Random Walks, And The Tower Of Hanoi, 2019 Baldwin Wallace University, Berea

#### Graphs, Random Walks, And The Tower Of Hanoi, Stephanie Egler

*Rose-Hulman Undergraduate Mathematics Journal*

The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”, that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself ...

Asymptotically Optimal Bounds For (T,2) Broadcast Domination On Finite Grids, 2019 Williams College

#### Asymptotically Optimal Bounds For (T,2) Broadcast Domination On Finite Grids, Timothy W. Randolph

*Rose-Hulman Undergraduate Mathematics Journal*

Let *G = (V,E)* be a graph and *t,r* be positive integers. The *signal* that a tower vertex *T* of signal strength *t* supplies to a vertex *v* is defined as *sig(T, v) = max(t − dist(T,v),0)*, where *dist(T,v)* denotes the distance between the vertices *v* and *T*. In 2015 Blessing, Insko, Johnson, and Mauretour defined a *(t, r) broadcast dominating set*, or simply a *(t, r) broadcast*, on *G* as a set *T ⊆ V* such that the sum of all signal received at each vertex *v ∈ V* from the set of towers *T ...*

New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, 2019 University of California, Davis

#### New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano

*Rose-Hulman Undergraduate Mathematics Journal*

The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences ...

A Generalized Newton-Girard Identity, 2019 University of Maryland, College Park

#### A Generalized Newton-Girard Identity, Tanay Wakhare

*Rose-Hulman Undergraduate Mathematics Journal*

We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.

Decomposing Graphs Into Edges And Triangles, 2019 University of Warwick

#### Decomposing Graphs Into Edges And Triangles, Daniel Kral, Bernard Lidicky, Taisa L. Martins, Yanitsa Pehova

*Mathematics Publications*

We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C1,. . .,Cℓ of orders two and three such that |C1|+···+|Cℓ| ≤ (1/2+o(1))n2. This result implies the asymptotic version of the old result of Erdős, Goodman and Pósa that asserts the existence of such a decomposition with ℓ ≤ n2/4.

Analytical Wave Solutions Of The Space Time Fractional Modified Regularized Long Wave Equation Involving The Conformable Fractional Derivative, 2019 Jessore University of Science and Technology

#### Analytical Wave Solutions Of The Space Time Fractional Modified Regularized Long Wave Equation Involving The Conformable Fractional Derivative, M. Hafiz Uddin, Md. Ashrafuzzaman Khan, M. Ali Akbar, Md. Abdul Haque

*Karbala International Journal of Modern Science*

The space time fractional modified regularized long wave equation is a model equation to the gravitational water waves in the long-wave occupancy, shallow waters waves in coastal seas, the hydro-magnetic waves in cold plasma, the phonetic waves in dissident quartz and phonetic gravitational waves in contractible liquids. In nonlinear science and engineering, the mentioned equation is applied to analyze the one way tract of long waves in seas and harbors. In this study, the closed form traveling wave solutions to the above equation are evaluated due to conformable fractional derivatives through double (G'⁄G,1⁄G)-expansion method and the ...

Dissertation_Davis.Pdf, 2019 University of Kentucky

#### Dissertation_Davis.Pdf, Brian Davis

*brian davis*

Positive Solutions Of Boundary Value Dynamic Equations, 2019 Marshall University

#### Positive Solutions Of Boundary Value Dynamic Equations, Olusegun Michael Otunuga, Basant Karna, Bonita Lawrence

*Basant Karna*

In this paper, we deal with the existence of a positive solution for 2^{nd} and 3^{rd} order boundary value problem by first defining their respective Green’s function. The Green’s function is used to derive the Green’s function for the 2nth and 3nth order boundary value problem, respectively, where *n* is a positive integer. The Green’s function is also used to derive conditions for positive solution of the 2*n*th and 3*n*th order eigen value differential equation, respectively.