Mathematics Commons^™

K -Isocoronal Tilings, Eduard C. Taganap, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s k. A tiling T is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of T is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k- transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then …

Positive Subreducts In Finitely Generated Varieties Of Mv-Algebras, Leonardo M. Cabrer, Peter Jipsen, Tomáš Kroupa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Positive MV-algebras are negation-free and implication-free subreducts of MV-algebras. In this contribution we show that a finite axiomatic basis exists for the quasivariety of positive MV-algebras coming from any finitely generated variety of MV-algebras.

Remarks On Suzuki's Epimorphism Number, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

A partial order on prime knots can be defined by declaring ��≥��, if there exists an epimorphism from the knot group of �� onto the knot group of ��. Suppose that �� is a 2-bridge knot that is strictly greater than �� distinct, nontrivial knots. In this paper, we determine a lower bound on the crossing number of �� in terms of ��. Using this bound, we answer a question of Suzuki regarding the 2-bridge epimorphism number EK(��) which is the maximum number of nontrivial knots which are strictly smaller than some 2-bridge knot with crossing number ��. We establish …

Finite N-Quandles Of Torus And Two-Bridge Links, Alissa Crans, Blake Mellor, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

We compute Cayley graphs and automorphism groups for all finite n-quandles of two-bridge and torus knots and links, as well as torus links with an axis.

On The Structure Of Hom Quandles, Alissa Crans

Mathematics, Statistics and Data Science Faculty Works

We continue the study of the quandle of homomorphisms into a medial quandle begun in [2]. We show that it suffices to consider only medial source quandles, and therefore the structure theorem of [11] provides a characterization of the Hom quandle. In the particular case when the target is 2-reductive this characterization takes on a simple form that makes it easy to count and determine the structure of the Hom quandle

Improved Prediction Of Periodicity Using Quartet Approximation In A Lattice Model Of Intracellular Calcium Release, Robert J. Rovetti

Mathematics, Statistics and Data Science Faculty Works

This study uses a probabilistic cellular automata (PCA) to model the spatial and temporal dynamics of calcium release units (CRUs) within cardiac myocytes. The CRUs are subject to random activation, nearest-neighbor recruitment, and temporal refractoriness, and their interactions produce a physiologically-important condition called calcium alternans, a beat-to-beat oscillation in the amount of calcium released. In the PCA this manifests as a transition to period-2 behavior in the fraction of activated lattice sites. We investigate this phenomenon using PCA simulations and moment-closure approximation methods of zero order (mean-field), first order (pair), and second order (quartet). We show that only the quartet …

Associated Primes And Syzygies Of Linked Modules, Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahaski

Department of Mathematics: Faculty Publications

Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring R, if a Cohen-Macaulay R-module M of grade g is linked to an R-module N by a Gorenstein ideal c, such that AssR(M)\AssR(N) = ;, then M R N is isomorphic to direct sum of copies of R=a, where a is a Gorenstein ideal of R of grade g + 1. We give a criterion for the depth of a local ring (R;m; k) in terms of the homological dimensions of the modules linked to the syzygies of the residue eld k. As a …

Persistence Metrics For A River Population In A Two-Dimensional Benthic-Drift Model, Yu Jin, Qihua Huang, Julia Blackburn, Mark A. Lewis

Department of Mathematics: Faculty Publications

The study of population persistence in river ecosystems is key for understanding population dynamics, invasions, and instream flow needs. In this paper, we extend theories of persistence measures for population models in one-dimensional rivers to a benthic-drift model in two-dimensional depth- averaged rivers. We define the fundamental niche and the source and sink metric, and establish the net reproductive rate R₀ to determine global persistence of a population in a spatially heterogeneous two-dimensional river. We then couple the benthic-drift model into the two-dimensional computational river model, River2D, to study the growth and persistence of a population and its source …

A Self-Contained Course In The Mathematical Theory Of Statistics For Scientists & Engineers With An Emphasis On Predictive Regression Modeling & Financial Applications., Tim Smith

Open Access Textbooks

Preface & Acknowledgments

This textbook is designed for a higher level undergraduate, perhaps even first year graduate, course for engineering or science students who are interested to gain knowledge of using data analysis to make predictive models. While there is no statistical perquisite knowledge required to read this book, due to the fact that the study is designed for the reader to truly understand the underlying theory rather than just learn how to read computer output, it would be best read with some familiarity of elementary statistics. The book is self-contained and the only true perquisite knowledge is a solid …

Rationality In Bargaining By Finite Automata, Jim Bell

Theses and Dissertations (Comprehensive)

Aspects of behavioral decision-making can be integrated into game-theoretic models of two-player bargaining using finite automata which can represent bargaining strategies in combination with various behavioral traits. The automata are used as bargaining agents who must jointly agree upon a fixed allocation of transferable utility in an infinite-horizon Rubinstein bargaining game. At each turn, the automata are given the opportunity to accept a proposed portion of the transferable utility, or to reject the proposal and make a counter-offer of their own. A round-robin tournament and ecological simulations were run to explore strategic dominance under different conditions. Principles of bargaining strategy …

What Is The Shape Of A Traditional Rapanui House On Easter Island? A Multicultural Mathematical Activity Involving Ellipses, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

The Rapanui people of the island Rapa Nui, also known as Easter Island, at one time had a system of “writing” called Rongorongo. Unfortunately, the ability to read Rongorongo has since been lost. So currently archaeology and oral tradition are the only available sources for information about the early people of the island. Oral tradition states that the houses originally had upside down canoes for their roofs, and thus they are called hare paenga, or in English, boat-houses. In the literature, these boat-houses are said to be elliptical in shape. In this activity, we will investigate the shape of archaeological …

The Game Of Ur: An Exercise In Strategic Thinking And Problem Solving And A Fun Math Club Activity, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

In this Open Educational Resource activity, students learn a little about the history of the Royal Game of Ur, the first board game, and get to practice critical thinking and problem solving by playing the game. Instructions are given along with a template for the game and game pieces and tetrahedral die.

Cgi (Computer Generated Imagery) Matrix Multiplication Activity, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

Many students are motivated by real world applications of mathematics, and most students are familiar with the term CGI from watching movies and playing video games. This particular activity ties matrix multiplication to CGI (Computer Generated Imagery). It has been used successfully with high school students in an Algebra II course who had just learned how to do matrix multiplication, middle school and high school students (some of whom were seeing matrix multiplication for the first time) attending a special Math Day on a university campus, and with College Algebra students (during a unit about matrices).

Block-Avoiding Sequencings Of Points In Steiner Triple Systems, Donald L. Kreher, Douglas R. Stinson

Michigan Tech Publications, Part 1

Given an STS(v), we ask if there is a permutation of the points of the design such that no l consecutive points in this permutation contain a block of the design. Such a permutation is called an l-good sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v>3 and 4-good sequencings exist for any STS(v) with v>71. Similar re-sults also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v =7, 9, 13 and 15.

Three Formative Questions In The Quantitative Literacy Movement, Dorothy Wallace

Numeracy

In this essay we remember early discussions attempting to answer three questions that played a formative role in our understanding of and approach to numeracy, quantitative literacy, and quantitative reasoning: (1) What is numeracy? (2) Should the QL movement promote any specific kind of pedagogy? (3) What organizational structure will best support QL?

As the QL movement has progressed, these three questions continue to be difficult to answer. As a result, they have been useful formative guides for institutions and organizations seeking to improve the quantitative reasoning of students. Now that the quantitative literacy movement has a firmer standing in …

Cardinal Characteristics Associated With Families Of Functions And Permutations, Nattapon Sonpanow

Chulalongkorn University Theses and Dissertations (Chula ETD)

The Continuum Hypothesis (CH) states that the size of the set of real numbers c is the least uncountable cardinal, i.e. c = N₁. In the absence of CH, it is possible that there are cardinals that lie between N₁ and c. Many of them are cardinals of infinite families related to some concepts in infinite combinatorics, called cardinal characteristics. Most of these cardinals are defined on families of infinite sets of natural numbers. We study families of functions and permutations on the set of natural numbers with some combinatorial properties and associated cardinal characteristics. We give relations among these …

A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

This project aims to identify a possible statistical relationship between the stock market and incidences of financial crime in Illinois, Texas, and Utah through big data analysis techniques using data from the FBI’s Federal Bureau of Investigation’s National Incident-Based Reporting System (NIBRS) database. By analyzing the occurrences of financial crime by location, year, and type in relation to the S&P 500’s percent change in close price on the first day of the calendar year, it will be possible to determine if a statistical relationship exists between the two. In addition, regression analysis was performed in order to predict financial crime …

Aligning Best Practices In Student Success And Career Preparedness: An Exploratory Study To Establish Pathways To Stem Careers For Undergraduate Minority Students, Kimberly D. Kendricks, Anthony A. Arment, K. V. Nedunuri, Cadance A. Lowell

Journal of Research in Technical Careers

Undergraduate minority retention and graduation rates in STEM disciplines is a nationally recognized challenge for workforce growth and diversification. The Benjamin Banneker Scholars Program (BBSP) was a five-year undergraduate study developed to increase minority student retention and graduation rates at an HBCU. The program structure utilized a family model as a vehicle to orient students to the demands of college. Program activities integrated best K-12 practices and workforce skillsets to increase academic preparedness and career readiness. Findings revealed that a familial atmosphere improved academic performance, increased undergraduate research, and generated positive perceptions of faculty mentoring. Retention rates among BBSP participants …

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method For A Transient Stokes Interface Problem With Jump Coefficients, Andrew Lundberg, Pengtao Sun, Cheng Wang, Chen-Song Zhang

Mathematical Sciences Faculty Research

The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated.

Volume 11, Jacob Carney, Ryan White, Joseph Hyman, Jenny Raven, Megan Garrett, Ibrahim Kante, Summer Meinhard, Lauren Johnson, William "Editha" Dean Howells, Laura Gottschalk, Christopher Siefke, Pink Powell, Natasha Woodmancy, Katharine Colley, Abbey Mays, Charlotte Potts

Incite: The Journal of Undergraduate Scholarship

Table of Contents:

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Synthesis of 3,5-substituted Parabens and their Antimicrobial Properties, Jacob Coarney, Ryan White

Chernobyl: Putting "Perestroika" and "Glasnot" to the Test, Joseph Hyman

Art by Jenny Raven

Watering Down Accessibility: The Issue with Public Access to Alaska's Federal Waterways, Meagan Garrett

Why Has the Democratic Republic of the Congo outsourced its Responsibility to Educate its Citizens? Ibrahim Kante

Art by Summer Meinhard

A Computational Study of Single Molecule Diodes, Lauren Johnson

Satire of …