Mathematics Commons^™

Eleventh Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Every Time I Turn Around There's Dr. Schraut Or You Can't Take Mathematics Out Of A U. D. Mathematics Major (Abstract), Eugene Steuerie

Kenneth C. Schraut Memorial Lectures

In this lecture, Gene Steurele, a math major from the 1968 graduating class, will discuss the many ways that mathematics & statistics crop up in almost every major public policy debate in which he has participated.

Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger

CMC Senior Theses

Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.

Uniqueness Of Derivatives Of Meromorphic Functions Sharing Two Or Three Sets, Abhijit Banerjee, Pranab Bhattacharjee

Turkish Journal of Mathematics

In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained five results which will improve all the existing results.

Climbing Eements In Finite Coxeter Groups, Colum Watt, Thomas Brady, Aisling Kenny

Articles

We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.

Schrödinger Operators With Δ'Interactions And The Krein–Stieltjes String, Aleksey Kostenko, M. M. Malamud

Articles

We investigate one dimensional symmetric Schrödinger operator HX, β with δ' interactions of strength β = ⊂ on a discrete set X = ⊂ [0, b), b ≤ +∞ (xn ↑ b). We consider HX, β as an extension of the minimal operator Hmin := –d2/dx2 (\X) and study its spectral properties in the frame work of the extension theory by using the technique of boundary triplets and the corresponding Weyl functions. The construction of a boundary triplet for is given in the case d∗ := infn ∈ |xn – xn – 1| = 0. We show that spectral properties …

Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza

MPP Published Research

"Both historians and philosophers of mathematics frequently speak of mathematical objects. Are they speaking of the same or of similar things? Better: are they appealing to the same notion or to similar notions?"

Packing Rates Of Measures And A Conjecture For The Packing Density Of 2413, C. B. Presutti, Walter Stromquist

Mathematics & Statistics Faculty Works

We give a new lower bound of 0.10472422757673209041 for the packing density of 2413, justify it by a construction, and conjecture that this value is actually equal to the packing density. Along the way we define the packing rate of a permutation with respect to a measure, and show that maximizing the packing rate of a pattern over all measures gives the packing density of the pattern.

Whitehead Products In Function Spaces: Quillen Model Formulae, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We study Whitehead products in the rational homotopy groups of a general component of a function space. For the component of any based map f : X→Y, in either the based or free function space, our main results express the Whitehead product directly in terms of the Quillen minimal model of f. These results follow from a purely algebraic development in the setting of chain complexes of derivations of differential graded Lie algebras, which is of interest in its own right. We apply the results to study the Whitehead length of function space components.

Heat Transfer Through The Boundary Layer On A Moving Cylindrical Fibre, Brendan Redmond, David Mcdonnell

Articles

This paper applies boundary layer theory to the process of manufacturing polymer fibres known as the melt spinning process. The rate of heat loss of the fibre during this process, characterised by the local Nusselt number, is evaluated by means of a Pohlhausen integral method.

The Wright Message, 2010, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2010 - 2011 Tenure-Stream Faculty
-- Spotlight on Undergraduates
-- Projects and Grants
-- Secondary Mathematics Education Programs
-- UNI I-Teach
-- Crane Scholarship
-- Actuarial Science and the Actuarial Science Fund
-- Alliance Project
-- Mathematics Contribution Form
-- Additional Mathematics Funds
-- Around Wright Hall
-- In Memoriam
-- Dr. Ridenhour Retires

Gender And Mathematics Education In Pakistan: A Situation Analysis, Anjum Halai

The Mathematics Enthusiast

This paper reports from a situation analysis of gender issues in mathematics education in Pakistan. It was undertaken at the initiation of a large scale project which aimed to understand how curriculum change in mathematics and science education may be implemented in ways that contribute to poverty alleviation and promote gender equity in disadvantaged rural settings. The paper posits that issues of access, achievement and quality of mathematics education are integrally linked with questions of equity, in this case gender equity. It identifies several questions and arenas for further research and makes recommendations for policy and practice in mathematics education.

High School Teachers Use Of Dynamic Software To Generate Serendipitous Mathematical Relations, Manuel Santos-Trigo, Hugo Espinosa-Pérez

The Mathematics Enthusiast

In this study, we document and analyse problem-solving approaches that high school teachers exhibited as a result of using dynamic software (Cabri-Geometry) to construct and examine geometric configurations. What type of questions do teachers pose and pursue while representing and exploring mathematical tasks or objects dynamically? To what extent their initial problem solving strategies are enhanced with the use of the tools? Results indicate that the use of the tool offered the participants the opportunity of constructing geometric configuration (formed by simple mathematical objects) that led them to identify and explore key mathematical relations.

“What Was Really Accomplished Today?” Mathematics Content Specialists Observe A Class For Prospective K–8 Teachers, Andrew M. Tyminksi, Sarah Ledford, Dennis Hembree

The Mathematics Enthusiast

One of the important activities mathematics teacher educators engage in is the development of teachers at both the in-service and pre-service levels. Also of importance is the professional development of these professional developers. In the summer of 2004, a summer institute was held that allowed mathematics teacher educators watch the teaching of a mathematics content course for prospective K–8 teachers. This paper examines the manner in which a specific group of mathematics content specialists experienced this professional development.

Randomness: Developing An Understanding Of Mathematical Order, Steve Humble

The Mathematics Enthusiast

Is randomness merely the human inability to recognise a pattern that may in fact exist?

The three activities described show how order can be found in seemly random activities. The author has found that by using these activities on randomness, his students have developed a greater understanding of mathematical pattern and sequence. The teaching mathematical concepts in this way, engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can sometimes occur in the classroom. By taking the maths beyond the classroom, …

The Constructs Of Phd Students About Infinity: An Application Of Repertory Grids, Serdar Aztekin, Ahmet Arikan, Bharath Sriraman

The Mathematics Enthusiast

Infinity has been one of the more difficult concepts for humanity to grasp. A major component of the research on mathematics education related to infinity has been the study of student’s conceptions and reasoning about calculus subjects, particularly limits and series. Some related studies are about Cantor’s ordinal and cardinal infinity. However since most students at the high school and college level are unfamiliar with symbolic representations and terminology, such as a set theoretic approach, a context (generally geometric) is used for investigating notions of infinity indirectly. In this paper we report on a study on the constructs of PhD …

When Is .999... Less Than 1?, Karin Usadi Katz, Mikhail G. Katz

The Mathematics Enthusiast

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999... be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.

Bringing Toric Codes To The Next Dimension, Ivan Soprunov, Jenya Soprunova

Mathematics and Statistics Faculty Publications

This paper is concerned with the minimum distance computation for higher dimensional toric codes defined by lattice polytopes in $\mathbb{R}^n$. We show that the minimum distance is multiplicative with respect to taking the product of polytopes, and behaves in a simple way when one builds a k-dilate of a pyramid over a polytope. This allows us to construct a large class of examples of higher dimensional toric codes where we can compute the minimum distance explicitly.

Alternative Technical Efficiency Measures: Skew, Bias, And Scale, William Clinton Horrace, Qu Feng

Center for Policy Research

In the fixed-effects stochastic frontier model an efficiency measure relative to the best firm in the sample is universally employed. This paper considers a new measure relative to the worst firm in the sample. We find that estimates of this measure have smaller bias than those of the traditional measure when the sample consists of many firms near the efficient frontier. Moreover, a two-sided measure relative to both the best and the worst firms is proposed. Simulations suggest that the new measures may be preferred depending on the skewness of the inefficiency distribution and the scale of efficiency differences.

Regular Functions On The Space Of Cayley Numbers, Graziano Gentili, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions.

Hybridization And Postprocessing Techniques For Mixed Eigenfunctions, Bernardo Cockburn, Jay Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, Jaume Peraire

Mathematics and Statistics Faculty Publications and Presentations

We introduce hybridization and postprocessing techniques for the Raviart–Thomas approximation of second-order elliptic eigenvalue problems. Hybridization reduces the Raviart–Thomas approximation to a condensed eigenproblem. The condensed eigenproblem is nonlinear, but smaller than the original mixed approximation. We derive multiple iterative algorithms for solving the condensed eigenproblem and examine their interrelationships and convergence rates. An element-by-element postprocessing technique to improve accuracy of computed eigenfunctions is also presented. We prove that a projection of the error in the eigenspace approximation by the mixed method (of any order) superconverges and that the postprocessed eigenfunction approximations converge faster for smooth eigenfunctions. Numerical experiments using …

Large Cardinals, Oliver Pechenik

Honors Papers

Infinite sets are a fundamental object of modern mathematics. Surprisingly, the existence of infinite sets cannot be proven within mathematics. Their existence, or even the consistency of their possible existence, must be justified extra-mathematically or taken as an article of faith. We describe here several varieties of large infinite set that have a similar status in mathematics to that of infinite sets, i.e. their existence cannot be proven, but they seem both reasonable and useful. These large sets are known as large cardinals. We focus on two types of large cardinal: inaccessible cardinals and measurable cardinals. Assuming the existence of …

The Fundamental Gap For Hyperbolic Triangles, Dennis Stuart Fillebrown

Honors Theses

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Gliomapredict: A Clinically Useful Tool For Assigning Glioma Patients To Specific Molecular Subtypes, Aiguo Li, Serdar Bozdag, Yuri Kotliarov, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Advances in generating genome-wide gene expression data have accelerated the development of molecular-based tumor classification systems. Tools that allow the translation of such molecular classification schemas from research into clinical applications are still missing in the emerging era of personalized medicine.

Results: We developed GliomaPredict as a computational tool that allows the fast and reliable classification of glioma patients into one of six previously published stratified subtypes based on sets of extensively validated classifiers derived from hundreds of glioma transcriptomic profiles. Our tool utilizes a principle component analysis (PCA)-based approach to generate a visual representation of the analyses, quantifies …

Edge Coloring Bibds And Constructing Moelrs , John S. Asplund

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well.

In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic K_v into copies of K_k such that each copy of the K_k contains at most one edge from each K_v. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of …

On Osgood's Criterion For Classical Wave Equations And Nonlinear Shallow Water Wave Equations, Timothy Smith, Greg Spradlin

Publications

The problem on classical solutions for the wave equation and the BBM equation is considered. The equations are considered with a forcing term and sufficient conditions of solvability, existence and uniqueness are established.

Ethnomathematics For Capacity Building In Mathematics Education, Catherine P. Vistro-Yu

Mathematics Faculty Publications

The Mathematics Framework for Philippine Basic Education (MATHTED and SEI, in press), a document that aims to guide the development of curricular contents in mathematics, identifies cultural-rootedness as one of the cognitive values that mathematics education in the Philippines must inculcate. Cultural-rootedness is defined as ?appreciating the cultural value of mathematics and its origins in many cultures, its rich history and how it has grown and continues to evolve?. Ethnomathematics, described as the ?mathematics which is practiced among identifiable cultural groups, such as national tribal societies, labor groups, children of a certain age bracket, professional classes and so on? (D?Ambrosio, …

Situating Sotl Within The Disciplines: Mathematics In The United States As A Case Study, Jacqueline Dewar, Curtis Bennett

Mathematics, Statistics and Data Science Faculty Works

After two decades of work, many in the SoTL community are pondering the future of the SoTL movement. Will it sustain its influence? Will it continue to attract new participants? What role should the disciplines play? From the perspective of mathematics, this paper examines efforts by the Carnegie Academy and individuals within the mathematical community to build disciplinary support for the scholarship of teaching and learning. The authors, both mathematicians and Carnegie scholars, restrict their observations to the efforts undertaken in the United States during the last decade and examine the situation in mathematics in greater depth than has heretofore …

On The Construction Of Explicit Solutions To The Matrix Equation X2ax = Axa, Ed Mosteig, Aihua Li

Mathematics, Statistics and Data Science Faculty Works

In a previous article by Aihua Li and Duane Randall, the existence of solutions to certain matrix equations is demonstrated via nonconstructive methods. A recurring example appears in that work, namely the matrix equation AXA=X2AX, where A is a fixed, square matrix with real entries and X is an unknown square matrix. In this paper, the solution space is explicitly constructed for all 2×2 complex matrices using Gr ̈obner basis techniques. When A is a 2×2 matrix, the equation AXA=X2AXis equivalent to a system of four polynomial equations. The solution space then is the variety defined by the polynomials involved. …

Derived Categories And The Analytic Approach To General Reciprocity Laws. Part Iii, Michael Berg

Mathematics, Statistics and Data Science Faculty Works

Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structures situated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for proving n-Hilbert reciprocity by means of singularity analysis.