Applied Mathematics Commons^™

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Libraries' Newsletters

No abstract provided.

Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

The Kabod

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.

Solitary Wave Solution Of Flat Surface Internal Geophysical Waves With Vorticity, Alan Compelli

Conference papers

A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is con-sidered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then considered and extended to produce a KdV approximation. Finally, a solitary wave solution is obtained.

Introduction To Random Processes Mth 453, Joanna Burkhardt

Library Impact Statements

No abstract provided.

Applied Calculus Mth 103, Joanna Burkhardt

Library Impact Statements

No abstract provided.

The Subject Librarian Newsletter, Mathematics, Fall 2016, Patti Mccall

Libraries' Newsletters

No abstract provided.

Creating Art Patterns With Math And Code, Boyan Kostadinov

Publications and Research

The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.

The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for …

The Evaluation Of Rhode Island Public High School Teachers: The Impact On Students, Stephen Lamontagne

Honors Projects in Mathematics

In 2012, the state of Rhode Island began the full implementation of a high-stakes teacher evaluation system. Its purpose is to increase teacher accountability and to improve student performance. However, a significant amount of literature casts doubt about the effectiveness and validity of teacher evaluation. This paper utilizes statistical methods including regression and decision trees in order to determine whether or not there is a relationship between teacher evaluation in Rhode Island and student performance, using RI Department of Education Data for each school from 2008-2015. Furthermore, this presentation investigates other factors that affect schools, to see if changes in …

What Is The True Cost To Stay In The Hospital?, Samantha Alicandro

Honors Projects in Mathematics

Currently, the unfortunate reality that receiving diverse health procedures can be extremely expensive is widely acknowledged and woefully accepted. However, have you inquired or been curious about the specific factors that influence the cost per day expensed by a hospital? Through examination, investigation, and evaluation operating SAS Enterprise Guide, SAS Enterprise Miner and Tableau I have attempted to arrive at a conclusion for this very question. Utilizing a 1.5 million row data set provided by Rhode Island, for the years 2003-2013, I analyzed the assorted elements conceivably bearing impact on the cost per day at a hospital. Regressions, decision trees, …

Catching Card Counters, Sarah French

Honors Projects in Mathematics

The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. …

A Weak Galerkin Method For Parabolic Equations, Yajie Yu

Theses and Dissertations

Parabolic equations have very broad applications in physics and engineering, such as heat diffusion and ocean acoustic propagation. Here we consider the 2D case with time dependent equations. Many numerical methods have been proposed to solve them, such as discontinuous Galerkin method, hybridized Galerkin method and so on. A weak Galerkin method is introduced by Dr. Wang and Dr. Ye by employing totally discontinuous functions in approximation space and an innovatively defined weak gradient operator which provide desirable flexibilities.In this thesis, we apply this method to solve parabolic equations. This method also has the energy conserva- tion property. Both continuous …

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.

3: Drugs And De's, Ruth Dover

Differential Equations

Making a connection between discrete recursion and differential equations.

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.

Optimal Placement Of Family Planning Centers, Kiera Dobbs

Senior Independent Study Theses

This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …

Strong Neutrosophic Graphs And Subgraph Topological Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilantheral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. Using these new structures special subgraph topological spaces are defined. Further special lattice graph of subgraphs of these graphs are defined and described. Several interesting properties using subgraphs of a strong neutrosophic graph are obtained. Several open conjectures are proposed. These new class of strong neutrosophic graphs will certainly find applications in NCMs, NRMs and NREs with appropriate modifications.

New Trends In Neutrosophic Theory And Applications - Vol. 1, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, …

Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu

Branch Mathematics and Statistics Faculty and Staff Publications

The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda

Williams Honors College, Honors Research Projects

Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z₉≀(Z₃ × Z₃) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.

Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher

LSU Doctoral Dissertations

Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work …

Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova

Physics Faculty Publications

This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

The Implications Of Self-Driving Cars On Insurance, Amanda Lobello

Honors Projects in Mathematics

Self-driving cars, also known as autonomous vehicles, are being researched and tested by automakers, technology industry leaders, and other institutions. Lawmakers and politicians are discussing the legislation that will affect the fate of such technology. Primary benefits include safety, mobility, free time, less traffic, and green effects. However, there are also obstacles to the implementation of self-driving vehicles including consumer acceptance, legal liability, and cost. With the potential shift in responsibility from driver to automaker, rating factors for insurance may change, weighing more heavily on the model of the car as a factor. The fate of auto insurance is in …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …

Standardized Testing: What Is It Good For? A Case Study In Connecticut, Megan Mapp

Honors Projects in Mathematics

The case study was developed in an attempt to shed more light on the debate of standardized testing. The goal of the study was to find evidence to support whether or not standardized testing is worth doing in public secondary schools. To investigate this question, the state standardized math test scores of three Connecticut public high schools were analyzed. The average math scores over thirteen years were observed and statistical analysis was performed to see if any significant differences existed between the three schools. Tests were performed before and after the change in standardized test. The graduation rates of the …

An Individual-Based Model Of Chaparral Vegetation Response To Frequent Wildfire, Timothy Lucas, Dayna Mann, Reanna Dona

Seaver College Research And Scholarly Achievement Symposium

In recent years, the Santa Monica Mountains (SMM) have been plagued by frequent wildfires which threaten the native chaparral species. Nonsprouting chaparral species are completely killed by a fire, but their seeds germinate in response to fire cues. Facultative sprouters both resprout after a wildfire and release seeds that germinate post-fire. This project is based on data collected since 1986 at a biological preserve adjacent to the Malibu campus of Pepperdine University with an average fire return interval of 7.5 years. We present a spatial model that simulates the growth, seed dispersal and resprouting behavior of individual shrubs that compete …