Mathematics Commons^™

Empirical Bayes Estimators And Borel-Tanner Distribution, Celestina Ruby Soltero

Theses and Dissertations

The motivation for this paper stems from the role Borel-Tanner (BT) distribution has as the distribution of the total outbreak number in epidemics modeled by branching processes. We briefly review Borel-Tanner distribution and its applications. In Chapter II we outline the Bayes decision problem, a construction for an Empirical Bayes (EB) estimator proposed by Liang [9] and discuss risk analysis. In Chapter III, the importance of randomization addressed and a classical construction of a monotonized EB estimator proposed by Houwalingen [14] is outlined. Lastly in Chapter IV we use R software to perform a Monte Carlo simulation and conduct a …

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 …

Optimal Inequalities For Submanifolds Of An Indefinite Space Form, Rıfat Güneş, Mehmet Gülbahar, Sadık Keleş, Erol Kılıç

Applications and Applied Mathematics: An International Journal (AAM)

Optimal inequalities involving the scalar curvature, the mean curvature vector and the second fundamental form for pseudo Riemannian submanifolds are proved and the equality cases of these inequalities are discussed. These results are studied for submanifolds of various indefinite contact space forms.

On General Matrix Application Of Quasi Power Increasing Sequences, Hikmet S. Özarslan, Ahmet Karakaş

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we give a general theorem dealing with absolute matrix summability by using quasi-power increasing sequences. This theorem includes some results concerning absolute summability methods.

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 Frenet Frame And Space Curves, Catherine Elaina Eudora Ross

Graduate Theses/Dissertations

Essential to the study of space curves in Differential Geometry is the Frenet frame. In this thesis we generate the Frenet equations for the second, third, and fourth dimensions using the Gram-Schmidt process, which allows us to present the form of the Frenet equations for n-dimensions. We highlight several key properties that arise from the Frenet equations, expound on the class of curves with constant curvature ratios, as well as characterize spherical curves up to the fourth dimension. Methods for generalizing properties and characteristics of curves in varying dimensions should be handled with care, since the structure of curves often …

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

AOER Course Materials

No abstract provided.

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 …

On Fractional Realizations Of Tournament Score Sequences, Kaitlin S. Murphy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Contrary to popular belief, we can’t all be winners.

Suppose 6 people compete in a chess tournament in which all pairs of players compete directly and no ties are allowed; i.e., 6 people compete in a ‘round robin tournament’. Each player is assigned a ‘score’, namely the number of games they won, and the ‘score sequence’ of the tournament is a list of the players’ scores. Determining whether a given potential score sequence actually is a score sequence proves to be difficult. For instance, (0, 0, 3, 3, 3, 6) is not feasible because two players cannot both have …

Chapter 1: Finite Elements For 1d Second Order Elliptic Equation, Xiaoming He

AOER Course Materials

No abstract provided.

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 …

An Application Of Conformal Mapping To The Boundary Element Method For Unconfined Steady Seepage With A Phreatic Surface, Jorge Eduardo Reyes

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, numerical results using the Boundary Element Method (BEM) for groundwater flow in a domain with a boundary that contains numerous singularities with a phreatic surface are developed. The flow in the domain is modeled using Darcy’s law for a homogeneous isotropic porous medium. The boundary conditions are a combination of Dirichlet and Neumann with the phreatic surface having both boundary conditions. Exact solutions by Conformal Mapping for simplified domains with the same singularity as the original domain allow for modifications to the BEM resulting in an improvement to the numerical solution.

An iterative process is used to …

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 …

A Study Of Big Field Multivariate Cryptography., Ryann Cartor

Electronic Theses and Dissertations

As the world grapples with the possibility of widespread quantum computing, the cryptosystems of the day need to be up to date. Multivariate Public Key Cryptography is a leading option for security in a post quantum society. One goal of this work is to classify the security of multivariate schemes, especially C*variants. We begin by introducing Multivariate Public Key Cryptography and will then discuss different multivariate schemes and the main types of attacks that have been proven effective against multivariate schemes. Once we have developed an appropriate background, we analyze security of different schemes against particular attacks. Specifically, we …

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 …

One-Note-Samba Approach To Cosmology, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

Inspired by One Note Samba, a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology. Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also briefly discuss possible link with our previous paper which describes Newtonian Universe with Vortex in terms of Ermakov equation.

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.

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.

Tartaglia Re-Imagined, Aja Juola

Journal of Humanistic Mathematics

Niccolo Fontana wrote that he wore a beard because he feared his appearance was monstrous. No one should ever feel such shame about their physical appearance so I figured after all these years I would tell him to bare his scars proudly as a reminder of what he had endured and the life he led.

Applied Scientific Demiurgy I – Entrance Examination Information Sheet, Mario Daniel Martín

Journal of Humanistic Mathematics

This document provides all the required information needed by aspiring demiurges to sit the entrance examination for the foundation course Applied Scientific Demiurgy I in the scientific stream of the Bachelor of Applied Demiurgy at the Topological Hyper-university of Technological Cosmology.