Physical Sciences and Mathematics Commons^™

Essays On Economics Of Gender And Labour Market., Kanika Mahajan Dr.

Doctoral Theses

The differences in labor market outcomes between males and females have been of interest to the economists for at least past half a century. Gender inequality in the labor market manifests itself in the form of wage and employment gaps between males and females. However, little is understood about why these inequalities emerge. There are taste based theories of discrimination, occupational exclusion and theories of statistical discrimination. In this thesis, we study gender disparities in the labor market of rural India. The main objective of this thesis is to further our understanding about the existing wage and employment disparities in …

Mechanistic Plug-And-Play Models For Understanding The Impact Of Control And Climate On Seasonal Dengue Dynamics In Iquitos, Peru, Nathan Levick

Mathematics & Statistics ETDs

Dengue virus is a mosquito-borne multi-serotype disease whose dynamics are not precisely understood despite half of the world’s human population being at risk of infection. A recent dataset of dengue case reports from an isolated Amazonian city— Iquitos, Peru—provides a unique opportunity to assess dengue dynamics in a simpli- fied setting. Ten years of clinical surveillance data reveal a specific pattern: two novel serotypes, in turn, invaded and exclusively dominated incidence over several seasonal cycles, despite limited intra-annual variation in climate conditions. Together with mechanistic mathematical models, these data can provide an improved understand- ing of the nonlinear interactions between …

Sperner's Lemma, The Brouwer Fixed Point Theorem, The Kakutani Fixed Point Theorem, And Their Applications In Social Sciences, Ayesha Maliwal

Electronic Theses and Dissertations

Can a cake be divided amongst people in such a manner that each individual is content with their share? In a game, is there a combination of strategies where no player is motivated to change their approach? Is there a price where the demand for goods is entirely met by the supply in the economy and there is no tendency for anything to change? In this paper, we will prove the existence of envy-free cake divisions, equilibrium game strategies and equilibrium prices in the economy, as well as discuss what brings them together under one heading.

This paper examines three …

The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

Honors Theses

The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.

Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook

Electronic Theses and Dissertations

This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared …

Embedding Of Hypercube Graphs On Orientable Surfaces, Prateek Kunwar

Electronic Theses and Dissertations

The purpose of this thesis is to study hypercube graphs and their embeddings on orientable surfaces. We use rotation systems to represent these embeddings. We prove some results about the effect of adjacent switches in rotation system and create a rotation system called the ABC rotation system and prove general results about it. Using this rotation system, we give a general theorem about the minimal embedding of $Q_{n}$. We also look at some interesting types of maximal embedding of $Q_{n}$, such as the Eulerian walk embedding and the "big-face embedding". We prove a theorem that gives a recursively constructive way …

An Adapative Treecode-Accelerated Boundary Integral Solver For Computing The Electrostatics Of A Biomolecule, Andrew Joseph Szatkowski

Theses and Dissertations

The Poisson-Boltzmann equation (PBE) is a widely-used model in the calculation of electrostatic potential for solvated biomolecules. PBE is an interface problem defined in the whole space with the interface being a molecular surface of a biomolecule, and has been solved numerically by finite difference, finite element, and boundary integral methods. Unlike the finite difference and finite element methods, the boundary integral method works directly over the whole space without approximating the whole space problem into an artificial boundary value problem. Hence, it is expected to solve PBE in higher accuracy. However, so far, it was only applied to a …

Investigation Of Sparsifying Transforms In Compressed Sensing For Magnetic Resonance Imaging With Fasttestcs, Christopher Adams Baker

Theses and Dissertations

The goal of this contribution is to achieve higher reduction factors for faster Magnetic Resonance Imaging (MRI) scans with better Image Quality (IQ) by using Compressed Sensing (CS). This can be accomplished by adopting and understanding better sparsifying transforms for CS in MRI. There is a tremendous number of transforms and optional settings potentially available. Additionally, the amount of research in CS is growing, with possible duplication and difficult practical evaluation and comparison. However, no in-depth analysis of the effectiveness of different redundant sparsifying transforms on MRI images with CS has been undertaken until this work. New theoretical sparsity bounds …

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun

Theses and Dissertations

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas …

Pedagogical Moves As Characteristics Of One Instructor’S Instrumental Orchestrations With Tinkerplots And The Ti-73 Explorer: A Case Study, James L. Kratky

Dissertations

Those supporting contemporary reform efforts for mathematics education in the United States have called for increased use of technologies to support student-centered learning of mathematical concepts and skills. There is a need for more research and professional development to support teachers in transitioning their instruction to better meet the goals of such reform efforts.

Instrumental approaches to conceptualizing technology use in mathematics education, arising out of the theoretical and empirical work in France and other European nations, show promise for use to frame studies on school mathematics in the United States. Instrumental genesis is used to describe the bidirectional and …

Estimating The Selection Gradient Of A Function-Valued Trait, Tyler John Baur

Theses and Dissertations

Kirkpatrick and Heckman initiated the study of function-valued traits in 1989. How to estimate the selection gradient of a function-valued trait is a major question asked by evolutionary biologists. In this dissertation, we give an explicit expansion of the selection gradient and construct estimators based on two different samples: one consisting of independent organisms (the independent case), and the other consisting of independent families of equally related organisms (the dependent case).

In the independent case we first construct and prove the joint consistency of sieve estimators of the mean and covariance functions of a Gaussian process, based on previous developments …

Density Estimation For Lifetime Distributions Under Semi-Parametric Random Censorship Models, Carsten Harlass

Theses and Dissertations

We derive product limit estimators of survival times and failure rates for randomly right censored data as the numerical solution of identifying Volterra integral equations by employing explicit and implicit Euler schemes. While the first approach results in some known estimators, the latter leads to a new general type of product limit estimator. Plugging in established methods to approximate the conditional probability of the censoring indicator given the observation, we introduce new semi-parametric and presmoothed Kaplan-Meier type estimators. In the case of the semi-parametric random censorship model, i.e. the latter probability belonging to some parametric family, we study the strong …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

Laboratory Experiences In Mathematical Biology For Post-Secondary Mathematics Students, Matthew Lewis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In addition to the memorization, algorithmic skills and vocabulary which is the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher level skills through Laboratory Experiences in Mathematical Biology (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical …

Latin Squares And Their Applications To Cryptography, Nathan O. Schmidt

Boise State University Theses and Dissertations

A latin square of order-n is an n x n array over a set of n symbols such that every symbol appears exactly once in each row and exactly once in each column. Latin squares encode features of algebraic structures. When an algebraic structure passes certain "latin square tests", it is a candidate for use in the construction of cryptographic systems. A transversal of a latin square is a list of n distinct symbols, one from each row and each column. The question regarding the existence of transversals in latin squares that encode the Cayley tables of finite groups …

Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson

Masters Theses

This study has been written to illustrate the development from early mathematical learning (grades 3-8) to secondary education regarding the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. It investigates the progression of the mathematics presented to the students by the current curriculum adopted by the Rhea County School System and the mathematics academic standards set forth by the State of Tennessee.

Solving Boundary Value Problems On Various Domains, Ibraheem Otuf

MSU Graduate Theses

Domain-sensitivity is a hallmark in the realm of solving boundary value problems in partial differential equations. For example, the method used in solving a boundary value problem on an finite cylindrical domain is very different from one that arises from a rectangular domain. The difference is also reflected in the types of functions employed in the processes of solving these boundary value problems, as are the mathematical tools utilized in deriving an analytic solution. In this thesis, we solve an important class of partial differential equations with boundary conditions coming from various domains, such as the n dimensional cube, circles, …

Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little

Honors Theses

Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes …

Some Spectral Properties Of A Quantum Field Theoretic Hamiltonian, Devin Burnell Mcghie

Theses and Dissertations

We derive the ground-state eigenvalues and eigenvectors for a simplified version of the 1-D QED single electron-photon model that Glasgow et al recently developed [2]. This model still allows for meaningful interaction between electrons and photons while keeping only the minimum needed to do so. We investigate the interesting spectral properties of this model. We determine that the eigenvectors are orthogonal as one would expect and normalize them.

Regular Round Matroids, Svetlana Borissova

Electronic Theses, Projects, and Dissertations

A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we …

Bio-Mathematics: Introduction To The Mathematical Model Of The Hepatitis C Virus, Lucille J. Durfee

Electronic Theses, Projects, and Dissertations

In this thesis, we will study bio-mathematics. We will introduce differential equations, biological applications, and simulations with emphasis in molecular events. One of the first courses of action is to introduce and construct a mathematical model of our biological element. The biological element of study is the Hepatitis C virus. The idea in creating a mathematical model is to approach the biological element in small steps. We will first introduce a block (schematic) diagram of the element, create differential equations that define the diagram, convert the dimensional equations to non-dimensional equations, reduce the number of parameters, identify the important parameters, …

Discrete And Continuous Operational Calculus In Stochastic Games, Kenneth Ibe Iwezulu

Theses and Dissertations

First, we consider a class of antagonistic stochastic games between two players A and B. The game is specified in terms of two "hostile" stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. This game is observed upon random epochs of time and the outcome of the game is not known in real time. The game ends at the time when the underlying fixed threshold of either player is crossed (referred to as the first passage time). The first passage time is then shifted to an epoch, i.e. upon one of the observation instants of time. …

An Introduction To Boolean Algebras, Amy Schardijn

Electronic Theses, Projects, and Dissertations

This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and proved many properties involving Boolean algebras and related structures.

We …

Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon

Electronic Theses, Projects, and Dissertations

A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.

On Rational Subgroups Of Exceptional Groups., Neha Hooda Dr.

Doctoral Theses

The main theme of this thesis is the study of exceptional algebraic groups via their subgroups. This theme has been widely explored by various authors (Martin Leibeck, Gary Seitz, Adam Thomas, Donna Testerman to mention a few), mainly for split groups ([26], [27], [28], [60] ). When the field of definition k of the concerned algebraic groups is not algebraically closed, the classification of k-subgroups is largely an open problem. In the thesis, we mainly handle the cases of simple groups of type F4 and G2 defined over an arbitrary field. These may not be split over k. We first …

Essays On The Economics Of Education., Soham Sahoo Dr.

Doctoral Theses

This thesis consists of three empirical essays that investigate issues related to the economics of education. The main focus of this thesis is to study schooling outcomes of children in a developing country: India. The first chapter explores the effect of mothers’ labour force participation on children’s educational outcomes in the context of a large employment guarantee program in India. This study finds that workfare schemes enhancing women’s access to economic opportunities have implications for intra-household resource allocation which in turn lead to a positive effect on children’s education. The second essay investigates the effect of better access to secondary …

Efficacy Of Math Video Tutorials On Student Perception And Achievement, Carol R. Kahrmann

Doctor of Education in Teacher Leadership Dissertations

Abstract

The purpose of this mixed methods research study is to explore how teacher-made video tutorials in one middle school mathematics classroom are being used and what enables/impedes their effectiveness. A quantitative, quasi-experimental design investigates how video tutorial usage relates to students’ self-efficacy and achievement in mathematics. The sample consisted of 55 students in the experimental group and 65 students in the control group. Results found parents wanted the tutorials even if they did not view them. Students did actually use the video tutorials for remediation and learning. Videos longer than ten minutes impeded the effectiveness of the videos. The …

Spherical Tropicalization, Anastasios Vogiannou

Doctoral Dissertations

In this thesis, I extend tropicalization of subvarieties of algebraic tori over a trivially valued algebraically closed field to subvarieties of spherical homogeneous spaces. I show the existence of tropical compactifications in a general setting. Given a tropical compactification of a closed subvariety of a spherical homogeneous space, I show that the support of the colored fan of the ambient spherical variety agrees with the tropicalization of the closed subvariety. I provide examples of tropicalization of subvarieties of GL(n), SL(n), and PGL(n).

Skein Theory And Algebraic Geometry For The Two-Variable Kauffman Invariant Of Links, Thomas Shelly

Doctoral Dissertations

We conjecture a relationship between the Hilbert schemes of points on a singular plane curve and the Kauffman invariant of the link associated to the singularity. Specifcally, we conjecture that the generating function of certain weighted Euler characteristics of the Hilbert schemes is given by a normalized specialization of the difference between the Kauffman and HOMFLY polynomials of the link. We prove the conjecture for torus knots. We also develop some skein theory for computing the Kauffman polynomial of links associated to singular points on plane curves.

Series Solutions Of Multi-Layer Boundary Value Problems, Amr Saad Hassan Bolbol

Theses

It is well known that differential equations (DEs) play an important role in many sciences. They are mathematical representations of many physical systems. By studying such DEs, one gains many important insights about the physical system. Solutions of DEs provide information on the physical system behavior. As many physical systems are nonlinear in nature, this naturally gives rise to nonlinear differential equations (NLDEs). Such NLDEs are, in most cases, hard or sometimes impossible to solve analytically. In such situations, we resort to numerical techniques to approximate the solutions. The purpose of this thesis is to consider nonlinear multi-layer boundary value …