Mathematics Commons^™

Covers For Leo Moser's Worm Problem, Thitipong Kanchai

Chulalongkorn University Theses and Dissertations (Chula ETD)

Leo Moser’s worm problem was posted in 1966 stating that “What is the region of the smallest area that can cover every unit are?”. In 2018, N. Ploymaklam and W. Wichiramala illustrated a new cover, which is currently smallest. Their cover was adapted from the cover of R. Norwood and G. Poole. In this work, we modify the region from the work of R. Norwood and G. Poole and the work of N. Ploymaklam and W. Wichiramala. Our regions are modified by changing their upper boundary. However, the regions remain satisfying properties in the work of R. Norwood and G. …

Some Intuition Behind Large Cardinal Axioms, Their Characterization, And Related Results, Philip A. White

Theses and Dissertations

We aim to explain the intuition behind several large cardinal axioms, give characterization theorems for these axioms, and then discuss a few of their properties. As a capstone, we hope to introduce a new large cardinal notion and give a similar characterization theorem of this new notion. Our new notion of near strong compactness was inspired by the similar notion of near supercompactness, due to Jason Schanker.

Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.

Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty

Graduate Theses, Dissertations, and Problem Reports (ETD)

The differential is a symbol that is common in first- and second-year calculus. It is perhaps expected that a common mathematical symbol would be interpreted universally. However, recent literature that addresses student interpretations of differentials, usually in the context of definite integration, suggests that this is not the case, and that many interpretations are possible. Reviews of textbooks showed that there was not a lot of discussion about differentials, and what interpretations there were depended upon the context in which the differentials were presented. This dissertation explores some of these issues. Since students may not have the experience necessary to …

Infinite Matroids And Transfinite Sequences, Martin Andrew Storm

Graduate Theses, Dissertations, and Problem Reports (ETD)

A matroid is a pair M = (E,I) where E is a set and I is a set of subsets of E that are called independent, echoing the notion of linear independence. One of the leading open problems in infinite matroid theory is the Matroid Intersection Conjecture by Nash-Williams which is a generalization of Hall’s Theorem. In [31] Jerzy Wojciechowski introduced µ- admissibility for pairs of matroids on the same ground set and showed that it is a necessary condition for the existence of a matching. A pair of matroids (M,W) with common ground set E is µ-admissible if a …

The Impact Of College Athletic Success On Donations And Applicant Quality, Benjamin Baumer, Andrew Zimbalist

Mathematics Sciences: Faculty Publications

For the 65 colleges and universities that participate in the Power Five athletic conferences (Pac 12, Big 10, SEC, ACC, and Big 12), the football and men’s basketball teams are highly visible. While these programs generate tens of millions of dollars in revenue annually, very few of them turn an operating “profit.” Their existence is thus justified by the claim that athletic success leads to ancillary benefits for the academic institution, in terms of both quantity (e.g., more applications, donations, and state funding) and quality (e.g., stronger applicants, lower acceptance rates, higher yields). Previous studies provide only weak support for …

Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

Michigan Tech Publications, Part 1

Certain excess versions of the Minkowski and Hölder inequalities are given.

The Relationship Between Housing Affordability And Demographic Factors: Case Study For The Atlanta Beltline, Chapman T. Lindstrom

College of Graduate Studies: Theses & Dissertations

Housing affordability has been a widely examined subject for populations residing in major metropolitan regions around the world. The relationship between housing affordability and the city’s demographics and its volume of urban development are important to take into consideration. In the past two decades there has been an increasing volume of literature detailing Atlanta Georgia’s large-scale redevelopment project, the Atlanta BeltLine (ABL), and its relationship with Atlanta’s Metropolitan population and housing affordability. The first objective of this paper is to study the relationship between housing affordability at two scales within the Atlanta Metropolitan Area (AMA) for both renters and homeowners. …

The Predictive Performance Of Objective Measures Of Physical Activity Derived From Accelerometry Data For 5-Year All-Cause Mortality In Older Adults: National Health And Nutritional Examination Survey 2003-2006, Ekaterina Smirnova, Andrew Leroux, Quy Cao, Lucia Tabacu, Vadim Zipunnikov, Ciprian Crainiceanu, Jacek Urbanek

Mathematics & Statistics Faculty Publications

Background: Declining physical activity (PA) is a hallmark of aging. Wearable technology provides reliable measures of the frequency, duration, intensity, and timing of PA. Accelerometry-derived measures of PA are compared to established predictors of 5-year all-cause mortality in older adults in terms of individual, relative, and combined predictive performance.

Methods: Participants between 50 and 85 years old from the 2003-2006 National Health and Nutritional Examination Survey (NHANES, n = 2978) wore a hip-worn accelerometer in the free-living environment for up to 7 days. A total of 33 predictors of 5-year all-cause mortality (number of events = 297), including 20 measures …

On Hybrid Temporal Basis Functions For Stable Numerical Solution Of Time Domain Boundary Integral Equations, Fang Q. Hu

Mathematics & Statistics Faculty Publications

Problems in unsteady aerodynamics and aeroacoustics can sometimes be formulated as integral equations, such as the boundary integral equations. Numerical discretization of integral equations in the time domain often leads to so-called March-On-in-Time (MOT) schemes. In the literature, the temporal basis functions used in MOT schemes have been largely limited to low-order shifted Lagrange basis functions. In order to evaluate the accuracy and effectiveness of the temporal basis functions, a Fourier analysis of the temporal interpolation schemes is carried out. Based on the Fourier analysis, the spectral resolutions of various temporal basis functions are quantified. It is argued that hybrid …

Global Existence And Asymptotic Behaviors For Some Nonlinear Partial Differential Equations., Ismahan Dhaw Binshati

Graduate Theses, Dissertations, and Problem Reports (ETD)

We study global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler-Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical and we also add the friction between two fluids. In addition, we discuss the rates of decay of $L^{p}-L^{q}$ norms for a linear system. Moreover, we use the result for $L^{p}-L^{q}$ estimates to prove the decay rates for the nonlinear systems. In addition, we prove existence of heteroclinic orbits for the nonlinear Vlasov and the one-dimensional Vlasov-Poisson systems. In the nonlinear Vlasov case with …

Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn Stehr Maher, Ha Nguyen, Gregory Chamblee, Sharon Taylor

Mathematical Sciences: Faculty Publications

Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of …

Taking A Canon To The Adjunction Formula, Paul M. Harrelson

College of Graduate Studies: Theses & Dissertations

In this paper, we show how the canonical divisor of a graph is related to the canonical divisor of its subgraph. The use of chip firing and the adjunction formula for graphs ex- plains said relation and even completes it. We go on to show the difference between the formula for full subgraphs and that of non-full subgraphs. Examples are used to simplify these results and to see the adjunction formula in action. Finally, we show that though the adjunction formula seems simple at first glance, it is somewhat complex and rather useful.

Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson

College of Graduate Studies: Theses & Dissertations

We study various homological constructions over a ring $R$ of characteristic $2$. We construct chain complexes over a field $K$ of characteristic $2$ using polynomials rings and partial derivatives. We also provide a link from the homology of these chain complexes to the simplicial homology of simplicial complexes. We end by showing how to construct all finitely-generated commutative differential graded $R$-algebras using polynomial rings and partial derivatives.

Proceedings Of Thirteenth Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Front Matter

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Contents of 13th Annual GAMTE Proceedings Front Matter:

• Officers of GAMTE
• Reviewers
• Copyright & Licensing Terms
• Purposes and Goals of GAMTE
• Conference Schedule
• Dedication
• Table of Contents

Conceptualizing And Interpreting Mean And Median With Future Teachers, Eryn M. Stehr, Ha Nguyen, Gregory Chamblee, Sharon Taylor

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Mathematical Education of Teachers II (METII), echoed by the American Statistical Association publication, Statistical Education of Teachers, recommended teacher preparation programs support future teachers in developing deep understandings of mean and median, such that middle grades teachers may use them to “summarize, describe, and compare distributions” (Conference Board of Mathematical Sciences, 2012, p. 44; Franklin et al., 2015). Georgia Standards of Excellence require statistical reasoning from students beginning as early as 6-7 years old, including interpretation of measures of center and statistical reasoning about best measures of center (Georgia Department of Education, 2015). This level of understanding and interpretation of …

K-2 Mathematicians & Writers: Professional Learning Communities For Developing Conceptual Understanding, Doris Santarone, Angel R. Abney, Sandra M. Webb

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

National Council of Teachers of Mathematics (NCTM) has long supported the use of children’s literature, writing, and manipulatives to improve conceptual understanding of mathematics (2000). In a professional learning community for K-2 teachers, professional development was designed and implemented on ways to incorporate literacy and manipulatives into a mathematics lesson. The teachers were charged with collaboratively planning lessons that included multiple components: the standard(s), a mathematics activity, manipulatives, a writing task, and children’s literature. As the data were analyzed, it became apparent that while most of the lessons were well connected, this did not happen for all of the lessons. …

Econophysics And Fractional Calculus: Einstein's Evolution Equation, The Fractal Market Hypothesis, Trend Analysis And Future Price Prediction, Jonathan Blackledge, Derek Kearney, Marc Lamphiere, Raja Rani, Paddy Walsh

Articles

This paper examines a range of results that can be derived from Einstein’s evolution equation focusing on the effect of introducing a Lévy distribution into the evolution equation. In this context, we examine the derivation (derived exclusively from the evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov–Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent and volatility. In this way, we provide a collection of results (which includes the derivation of certain fractional partial …

Pressure Versus Impulse Graph For Blast-Induced Traumatic Brain Injury And Correlation To Observable Blast Injuries, Barbara Rutter

Doctoral Dissertations

"With the increased use of explosive devices in combat, blast induced traumatic brain injury (bTBI) has become one of the signature wounds in current conflicts. Animal studies have been conducted to understand the mechanisms in the brain and a pressure versus time graph has been produced. However, the role of impulse in bTBIs has not been thoroughly investigated for animals or human beings.

This research proposes a new method of presenting bTBI data by using a pressure versus impulse (P-I) graph. P-I graphs have been found useful in presenting lung lethality regions and building damage thresholds. To present the animal …

Dendrites Or Lambda-Dendroids As Generalized Inverse Limits, Faruq Abdullah Mena

Doctoral Dissertations

"This research centers on the study of generalized inverse limits. We show that all members of an infinite family of inverse limit spaces are homeomorphics to one particularly complicated inverse limit space known as "The Monster". Further, properties of factor spaces and graphs of bonding functions which are preserved in generalized inverse limit spaces with upper semi-continuous bonding functions with appropriate restrictions are investigated. Some of the properties are locally connectedness, hereditary decomposability, hereditary indecomposability, hereditary unicoherence, arc-likeness, and tree-likeness. The theorems are illustrated by several examples"--Abstract, page iv.