Mathematics Commons^™

Rapid Generation Of Jacobi Matrices For Measures Modified By Rational Factors, Amber Sumner

Dissertations

Orthogonal polynomials are important throughout the fields of numerical analysis and numerical linear algebra. The Jacobi matrix J for a family of n orthogonal polynomials is an n x n tridiagonal symmetric matrix constructed from the recursion coefficients for the three-term recurrence satisfied by the family. Every family of polynomials orthogonal with respect to a measure on a real interval [a,b] satisfies such a recurrence. Given a measure that is modified by multiplying by a rational weight function r(t), an important problem is to compute the modified Jacobi matrix Jmod corresponding to the new measure from knowledge of J. There …

The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

Honors Projects

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …

On Rugina’S System Of Thought, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article investigates Rugina's orientation table and gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's orientation table in systems which are s percent stable and 100 ÿ s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina's integrated logic, and then generalized in neutrosophic logic.

Non-Commutative Zero-Knowledge Protocols, Bailey Stewart

Departmental Honors & Graduate Capstone Projects

We examine zero-knowledge protocols working in non-commutative structures. Specifically, we will discuss the advantages and disadvantages of using invertible elements and elements that have a square root. An adaptation of the zero-knowledge protocol will be presented for working in symmetric groups and monoids of endomorphisms and matrices. Additionally, the security behind these zero-knowledge protocols will be discussed as well as showing different scenarios where invertible elements and elements with squares are vulnerable to attacks.

An Analysis Of Efficiency Measures Of The S/V Zodiac, Henry Darron

Departmental Honors & Graduate Capstone Projects

This paper concerns forecasting the performance of the S/V Zodiac, a two-masted schooner operating as a public and private charter vessel out of Bellingham, Washington. Two aspects of performance are discussed, namely the business cycle of the Zodiac and the operating efficiency of the Zodiac. For the business cycle, it is found that the best model for the business cycle is the one-year-ahead plan developed for the vessel in or around November each year. As for the operating efficiency, an original model is developed from techniques used for forecasting power outputs of wind farms and individual wind turbines. …

Jacobian Elliptic Kummer Surfaces And Special Function Identities, Elise Griffin, Andreas Malmendier

Mathematics and Statistics Faculty Publications

We derive formulas for the construction of all inequivalent Jacobian elliptic fibrations on the Kummer surface of two non-isogeneous elliptic curves from extremal rational elliptic surfaces by rational base transformations and quadratic twists. We then show that each such decomposition yields a description of the Picard-Fuchs system satisfied by the periods of the holomorphic two-form as either a tensor product of two Gauss' hypergeometric differential equations, an Appell hypergeometric system, or a GKZ differential system. As the answer must be independent of the fibration used, identities relating differential systems are obtained. They include a new identity relating Appell's hypergeometric system …

An Optimized Route For Q100'S Bert And Kristin To Visit All Jersey Mike's Subs In Atlanta For Charity

Symposium of Student Scholars

The Bert Show is a popular morning show on Atlanta’s Q100 radio station. They host a non-profit organization that provides a “magical, all-expenses-paid, five-day journey to Walt Disney World for children with chronic and terminal illnesses and their families” called “Bert’s Big Adventure.” On March 28^th, 2018, thirty-seven locations of Jersey Mike’s are participating in the their Jersey Mike’s Day of Giving to support Bert’s Big Adventure. The goal is to have two popular radio show hosts visit each of these locations for some photos and presence to draw in more customers! But how do we get two …

Non-Commutative Massey-Omura Encryption With Symmetric Groups, Shannon Haley

Departmental Honors & Graduate Capstone Projects

We introduce two non-commutative variations on the original Massey-Omura encryption system using conjugations in the symmetric group S_n. Patented in 1986, the original system was based on the cyclic group F^* of units in a finite field F. In place of the abelian group F^*, we will work in the non-abelian group S_nusing disjoint permutations as well as maximal abelian subgroups in order to potentially create a more secure system. Introducing the non-abelian group S_n presents the need to create a keyspace of commuting permutations and abelian subgroups of sufficient size. …

Abstraction And Infinity (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Abstraction and Infinity by Paolo Mancosu, Oxford University Press, 2017. 222 pp. ISBN: 9780198746829.

Forcing Number, Maximum Nullity, And Minimum Rank Theorems Concerning The Generalized Petersen Graph And Related Observations, Hobert J. Holbrook, R. Duane Skaggs

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Mathematical Surfaces And 3d Printing, Haily A. Slone, R. Duane Skaggs

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashuwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

In this paper, we explore the notion of simplicity. We use definitions of simplicity proposed by philosophers, scientists, and economists. In an age when the rapidly growing human population faces an equally rapidly declining energy/material resources, there is an urgent need to consider various notions of simplicity, collective and individual, which we believe to be a sensible path to restore our planet to a reasonable state of health. Following the logic of mathematicians and physicists, we suggest that simplicity can be related to sustainability. Our efforts must therefore not be spent so much in pursuit of growth but in achieving …

Measuring A Rifle’S Recoil Using Wireless Dynamics Sensor System, Seth Baker, Ignacio Birriel

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Efficient Reduced Bias Genetic Algorithm For Generic Community Detection Objectives, Aditya Karnam Gururaj Rao

Theses

The problem of community structure identification has been an extensively investigated area for biology, physics, social sciences, and computer science in recent years for studying the properties of networks representing complex relationships. Most traditional methods, such as K-means and hierarchical clustering, are based on the assumption that communities have spherical configurations. Lately, Genetic Algorithms (GA) are being utilized for efficient community detection without imposing sphericity. GAs are machine learning methods which mimic natural selection and scale with the complexity of the network. However, traditional GA approaches employ a representation method that dramatically increases the solution space to be searched by …

Effect Of A Pre-Dinner Walnut Snack On Nutrient Intake Among University Students, Michelle E. Lacasse, Mackenzie J. Weis, Lauren S. Devaan, Gabrielle L. Schnellman, Elizabeth M. Gile, Molly D. Ahmann, Ted Wilson, Tisha L. Hooks

Undergraduate Research Celebration 2018

No abstract provided.

Optimization Of Biogas Production Process In Solid State Digesters In Semiarid Areas Of Northern Tanzania, Debora J Mahushiab, Alfred Nn Muzukaa, Revocatus L Machunda

Tanzania Journal of Science

Solid state digestion process has received much attention due to its low water requirements, making it preferred in semi-arid areas as well. In this study, the performance of the household solid state digesters was evaluated through monitoring of the feedstock mixing ratios and using the digester gas pressure as a measure of performance. Additionally, a batch study to verify the appropriate and optimal mixing ratio of feedstocks was also done. The mixing ratios of cow dung to water were 2:1, 3:1 and 4:1. Total solids determined were 120, 150 and 170 mg/g for the ratios 2:1, 3:1 and 4:1, respectively. …

Mathematics Of The Significant Tornado Parameter, Aaron Baker

Undergraduate Research Conference

The idea of this project came from my curiosity of weather and especially how severe storms are predicted. There are many parameters used to predict severe weather that use mathematical formulas. After sorting through the parameters, the STP was the one selected due to its use of other parameters for prediction of tornadoes, as well as concepts used in Single and Multi-Variable Calculus, such as areas between curves and vector magnitude and direction, and learning how to use new graphs than what is normally used.

Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation, Gizem Yuce

Theses and Dissertations

There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and …

On A Generalization Of The Hanoi Towers Group, Rachel Skipper

Graduate Dissertations and Theses

In 2012, Bartholdi, Siegenthaler, and Zalesskii computed the rigid kernel for the only known group for which it is non-trivial, theHanoi towers group. There they determined the kernel was the Klein 4 group. We present a simpler proof of this theorem. In thecourse of the proof, we also compute the rigid stabilizers and present proofs that this group is a self-similar, self-replicating, regular branch group.

We then construct a family of groups which generalize the Hanoi towers group and study the congruence subgroup problem for the groups in this family. We show that unlike the Hanoi towers group, the groups …

Using Random Forests To Describe Equity In Higher Education: A Critical Quantitative Analysis Of Utah’S Postsecondary Pipelines, Tyler Mcdaniel

Butler Journal of Undergraduate Research

The following work examines the Random Forest (RF) algorithm as a tool for predicting student outcomes and interrogating the equity of postsecondary education pipelines. The RF model, created using longitudinal data of 41,303 students from Utah's 2008 high school graduation cohort, is compared to logistic and linear models, which are commonly used to predict college access and success. Substantially, this work finds High School GPA to be the best predictor of postsecondary GPA, whereas commonly used ACT and AP test scores are not nearly as important. Each model identified several demographic disparities in higher education access, most significantly the effects …