Mathematics Commons^™

Roman Domination Cover Rubbling, Nicholas Carney

Electronic Theses and Dissertations

In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the …

Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley

Master's Theses

For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent …

Machine Learning Techniques As Applied To Discrete And Combinatorial Structures, Samuel David Schwartz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Machine Learning Techniques have been used on a wide array of input types: images, sound waves, text, and so forth. In articulating these input types to the almighty machine, there have been all sorts of amazing problems that have been solved for many practical purposes.

Nevertheless, there are some input types which don’t lend themselves nicely to the standard set of machine learning tools we have. Moreover, there are some provably difficult problems which are abysmally hard to solve within a reasonable time frame.

This thesis addresses several of these difficult problems. It frames these problems such that we can …

Interval-Valued Kriging Models With Applications In Design Ground Snow Load Prediction, Brennan L. Bean

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One critical consideration in the design of buildings constructed in the western United States is the weight of settled snow on the roof of the structure. Engineers are tasked with selecting a design snow load that ensures that the building is safe and reliable, without making the construction overly expensive. Western states use historical snow records at weather stations scattered throughout the region to estimate appropriate design snow loads. Various mapping techniques are then used to predict design snow loads between the weather stations. Each state uses different mapping techniques to create their snow load requirements, yet these different techniques …

Chapter 2: 2d/3d Finite Element Spaces, Xiaoming He

AOER Course Materials

No abstract provided.

A Framework Of Integrating Manufacturing Plants In Smart Grid Operation: Manufacturing Flexible Load Identification, Md. Monirul Islam, Zeyi Sun, Wenqing Hu, Cihan H. Dagli

Engineering Management and Systems Engineering Faculty Research & Creative Works

In the deregulated electricity markets run by Independent System Operator (ISO), a two-settlement (day-ahead and real-time) process is typically used to determine the electricity price to the end-use customers at different buses. In the day-ahead settlement, the demand is predicted at each bus based on the previous consumption behavior of the consumers and thus, Locational Marginal Price (LMP) can be determined and shared to the consumers. A significant gap is usually observed between the planned and real-time demands due to the uncertainties of the weather (temperature, wind-speed etc.), the intensity of business, and everyday activities. Therefore, a large price variation …

Global Existence And Propagation Speed For A Generalized Camassa-Holm Model With Both Dissipation And Dispersion, Qiaoyi Hu, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study a generalized Camassa–Holm (gCH) model with both dissipation and dispersion, which has (N+1)-order nonlinearities and includes the following three integrable equations: the Camassa–Holm, the Degasperis–Procesi, and the Novikov equations, as its reductions. We first present the local well-posedness and a precise blow-up scenario of the Cauchy problem for the gCH equation. Then, we provide several sufficient conditions that guarantee the global existence of the strong solutions to the gCH equation. Finally, we investigate the propagation speed for the gCH equation when the initial data are compactly supported.

Joint Manufacturing And Onsite Microgrid System Control Using Markov Decision Process And Neural Network Integrated Reinforcement Learning, Wenqing Hu, Zeyi Sun, Y. Zhang, Y. Li

Mathematics and Statistics Faculty Research & Creative Works

Onsite microgrid generation systems with renewable sources are considered a promising complementary energy supply system for manufacturing plant, especially when outage occurs during which the energy supplied from the grid is not available. Compared to the widely recognized benefits in terms of the resilience improvement when it is used as a backup energy system, the operation along with the electricity grid to support the manufacturing operations in non-emergent mode has been less investigated. In this paper, we propose a joint dynamic decision-making model for the optimal control for both manufacturing system and onsite generation system. Markov Decision Process (MDP) is …

Family Math Night: Increasing Engagement In University Mathematics Courses For Prospective Teachers, Eva Thanheiser

Mathematics and Statistics Faculty Publications and Presentations

Prospective elementary school teachers (PSTs) often do not perceive mathematics activities as fun or engaging and perceive the mathematics tasks in their university content courses as inauthentic and irrelevant. Both these points were addressed by connecting the university classroom tasks to the K–5 environment via a Family Math Night (FMN). Survey results from 23 PSTs showed that PSTs were excited about the authenticity of the tasks, learned about children’s mathematical thinking, and reconceptualized mathematics learning as potentially enjoyable. In combination, these results may lead to PSTs’ increased engagement in the mathematics content course and, thus, result in their increased mathematics …

The Topp-Leone Generalized Odd Log-Logistic Family Of Distributions: Properties, Characterizations And Applications, Mustafa Ç. Korkmaz, Haitham M. Yousof, Morad Alizadeh, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

A new family of distributions called the Topp-Leone generalized odd log-logistic-G family is introduced and studied. We provide some mathematical properties of the new family including ordinary and incomplete moments, generating function and order statistics. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of two simulation studies. Finally, the usefulness of the family is il lustrated by means of two real data sets. The new model provides consistently better fits than other competitive models for these data sets.

The Signaling Problem: Using Exploding Dots To Solve An Accessible Mystery In An Elementary-Aged Math Circle, Rodi Steinig

Journal of Math Circles

Many people want to facilitate Math Circles for younger students but don’t know how. This article provides a model for how to create an engaging Math Circle for students aged 8-10 to explore different number bases and gives a detailed narrative to guide prospective instructors through the class. The narrative follows a group of eight students spending six weeks joyfully discovering underlying mathematical structure without being told what to do.

Exploding Dots At The Msu-Billings Math Circle, Tien Chih

Journal of Math Circles

Global Math Week is an annual event started by Dr. James Tanton and the Global Math Project, connecting students around the world with the mathematics of Exploding Dots. Exploding Dots is a reconceptualization of the mechanics of arithmetic, which allows for a visually intuitive and accessible representation of a variety of mathematical topics ranging from different base representations to the arithmetic of polynomials and series. In this manuscript, we describe the first implementation of Exploding Dots at the MSU-Billings Math Circle. The actual itemized agenda of the session is described, followed by highlights of the session and observations by the …

Commentary From The Field: Elimu Haina Mwisho “Education Has No Limits”, Erick Mathew

Journal of Math Circles

Commentary From the Field: ELIMU HAINA MWISHO “Education has no Limits”

A Message From The Global Math Project Team, James Tanton

Journal of Math Circles

A Message From the Global Math Project Team

Editorial Introduction To The Journal Of Math Circles, Emilie Hancock, Brandy Wiegers

Journal of Math Circles

Editorial Introduction to the Journal of Math Circles.

Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds

Department of Math & Statistics Faculty Publications

In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …

Bulk Spectrum And K-Theory For Infinite-Area Topological Quasicrystals [Dataset], Terry A. Loring

Math and Statistics Datasets

Archived here are files, data and program files, that are supplementary the following article, expected to be published in 2019:

* Terry A. Loring. Bulk Spectrum and K-theory for Infinite-Area Topological Quascrystal. Journal of Mathematical Physics, (2019 est.).

The files, in Matlab format, allow the user to create approximate eigenvalues for a topological Hamilontian on a round patch of a quasicrystal. The data files describe pathes of the Ammann-Bennkeer tiling. One of the data files is really large. Read the file README.txt first (available via the main download button), so see if you can avoid downloading the largest file.

Recommended …

An Analysis Of The Effect Of Tooth Wear On Bovid Identification, Juliet K. Brophy, Gregory J. Matthews, George K. Thiruvathukal

Mathematics and Statistics: Faculty Publications and Other Works

Previous research provides a method for reducing the subjectivity in taxonomic identification of species in the family Bovidae by quantifying the occlusal surface of molar teeth using elliptical Fourier analysis. In this current study, we specifically test what effect medium to late tooth wear has on the identification of bovids when using the form (size and shape) of the occlusal surface to classify specimens. To achieve this, the classification results of teeth with ≥85% of their occlusal surface (training data set) were compared with the results of teeth with <85% of their occlusal surface (test data set) due to wear. In the training data set, all tribes classified correctly >87% of the time with both Alcelaphini and Reduncini classifying correctly …

Third Voices Conference On Teaching Stem With Music, September 22-23, 2019, Lawrence M. Lesser

Journal of Humanistic Mathematics

The third annual VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song; https://www.causeweb.org/voices/) conference will be held online September 22-23, 2019. Chaired by Tiffany Getty, this conference will explore the use of song to teach STEM (science, technology, engineering, and mathematics) at the postsecondary (or secondary) level.

How To Bake A Theorem, Cache Dexter

Journal of Humanistic Mathematics

We bake bread to satisfy our hunger, and we prove theorems to satisfy our hunger for knowledge and existence. Here I explore this analogy.