Mathematics Commons^™

Permutohedra, Configuration Spaces And Spineless Cacti, Yongheng Zhang

Open Access Dissertations

It has been known that the configuration space F(R², n) of n distinct ordered points in R² deformation retracts to a regular CW complex with n!permutohedra P_n as the top dimensional cells. In this paper, we show that there exists a similar but different permutohedral structure of the spaceCact(n) of spineless cacti with n lobes. Based on these structures, direct homotopy equivalences between F (R², n) and Cact(n) are then given. It is well known that the little 2-discs space D₂(n) is homotopy equivalent toF(R², n). …

Investigating Synergy: Mathematical Models For The Coupled Dynamics Of Hiv And Hsv-2 And Other Endemic Diseases, Christina M Alvey

Open Access Dissertations

This dissertation presents epidemiological models that investigate synergy: synergy between HIV and HSV-2 or between humans and mosquitoes in a malaria study. Each of the three coupled disease models addresses different epidemiological questions with regard to gender or disease structure in the context of sexually-transmitted diseases (STDs), while the malaria model focuses on age-structure of the human population. ^ Mounting evidence indicates that HSV-2 infection may increase susceptibility to HIV infection and that co-infection may increase infectiousness. Accordingly, antiviral treatment of people with HSV-2 may mitigate the incidence of HIV in populations where both pathogens occur. To better understand the …

Two Rosa-Type Labelings Of Uniform K-Distant Trees And A New Class Of Trees, Kimberly Wenger Diller

Honors Projects

A k-distant tree consists of a main path, called the spine, such that each vertex on the spine is joined by an edge to an end-vertex of at most one path on at most k vertices. Those paths, along with the edge joining them to the spine, are called tails. When every vertex on the spine has exactly one incident tail of length k we call the tree a uniform k-distant tree. We show that every uniform k-distant tree admits both a graceful- and an α-labeling.

For a graph G and a positive integer …

The Atiyah Class Of A Dg-Vector Bundle, Rajan Amit Mehta, Mathieu Stiénon, Ping Xu

Mathematics Sciences: Faculty Publications

We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields X(M) on a dg-manifold M with homological vector field Q admits a structure of L_∞[1]-algebra with the Lie derivative L_Q as unary bracket λ₁, and the Atiyah cocycle At_M corresponding to a torsion-free affine connection as binary bracket λ₂.

Estimating The Extreme Low-Temperature Event Using Nonparametric Methods, Anisha D'Silva

Master's Theses (2009 -)

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. …

2015 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2015 Spring Colloquium.

On Products Of Generalized Geometries, Ralph R. Gomez, Janet Talvacchia

Mathematics & Statistics Faculty Works

In this paper we address what generalized geometric structures are possible on products of spaces that each admit generalized geometries. In particular we consider, first, the product of two odd dimensional spaces that each admit a generalized almost contact structure, and then subsequently, the product of an odd dimensional space that admits a generalized almost contact structure and an even dimensional space that admits a generalized almost complex structure. We also draw attention to the relationship of the Courant bracket to the classical notion of normality for almost contact structures.

Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. Mccarthy

Mathematics Faculty Research

We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.

My Math Gps: Elementary Algebra Guided Problem Solving, Jonathan Cornick, G Michael Guy, Karan Puri

Open Educational Resources

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors. In a paper to appear in PRIMUS, this textbook and accompanying pedagogy showed significant increases in learning outcomes.

Betti Sequences Over Local Rings And Connected Sums Of Gorenstein Rings, Zheng Yang

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis consists of two parts:

1) Polynomial growth of Betti sequences over local rings (Chapter 2),

2) Connected sums of Gorenstein rings (Chapter 3).

Chapter 1 gives an introduction for the two topics discussed in this thesis.

The first part of the thesis deals with modules over complete intersections using free resolutions. The asymptotic patterns of the Betti sequences of the finitely generated modules over a local ring R reflect and affect the singularity of R. Given a commutative noetherian local ring and an integer c, sufficient conditions and necessary conditions are obtained for all Betti sequences …

A P-Adic Spectral Triple, Sumedha Hemamalee Rathnayake

Open Access Dissertations

We construct a spectral triple for the C*-algebra of continuous functions on the space of p-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative D on the tree. Our spectral triple satisfies the properties of a compact spectral metric space and the metric on the space of p-adic integers induced by the spectral triple is equivalent to the usual p-adic metric. Furthermore, we show that the spectrum of the operator D*D is closely related to the roots of a certain …

Hurwitz's Theorem, Marianna Malek

Masters Essays

No abstract provided.

An Analysis Of Lake Erie’S Near Shore Habitats With The Benthic Diatom Metric, Kenjon Yeong

Masters Essays

No abstract provided.

Existence And Uniqueness Of Solutions For A Class Of Non-Linear Boundary Value Problems Of Fractional Order, Arwa Abdulla Omar Salem Ba Abdulla

Theses

In this thesis, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1

Local Well-Posedness Of Periodic Fifth Order Kdv-Type Equations, Yi Hu, Xiaochun Li

Mathematical Sciences: Faculty Publications

In this paper, the local well-posedness of periodic fifth order dispersive equation with nonlinear term P1(u)∂xu + P2(u)∂xu∂xu. Here P1(u) and P2(u) are polynomials of u. We also get some new Strichartz estimates.

Restricted Sum Formula Of Alternating Euler Sums, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

In this paper, we study restricted sum formulas involving alternating Euler sums which are defined by ζ(s1,…,sd;ε1,…,εd)=∑n1>⋯>nd≥1εn11⋯εnddns11⋯nsdd,

for all positive integers s 1,…,s d and ε 1=±1,…,ε d =±1 with (s 1,ε 1)≠(1,1). We call w=s 1+⋯+s d the weight and d the depth. When ε j =−1 we say the jth component is alternating. We first consider Euler sums of the following special type: ξ(2s1,…,2sd)=ζ(2s1,…,2sd;(−1)s1,…,(−1)sd).

For d≤n, let Ξ(2n,d) be the sum of all ξ(2s 1,…,2s d ) …

Armstrong Calculus, Michael Tiemeyer, Jared Schlieper

Mathematics Open Textbooks

Authors' Description:

An open-source textbook for calculus.

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.

The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text …

Volume 07, Rachel C. Lombardi, Ben Osterhout, Lindsay Graybill, Rebecca E. Dey, Skyler T. Carpenter, Emma Beckett, Jason Ware, Mollie Andrews, James Bates, Landon Cooper, Tiffani Jeffries, Maria Wheaton, Dallas Price, Laura Kahler, Sarah Charlton, Anna Bultrowicz, Emily Spittle, Erin Godwin, Eamon Brokenbrough

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Spatial Analysis of Potential Risk Factors Associated with Addition of Atlantic Coast Pipeline Through Virginia by Rachel C. Lombardi

"Delicate Matters with No Speaking," "Hope and Nothing," "Mono Duality" by Ben Osterhout

"Connect" Graphic Design Senior Project by Lindsay Graybill

Phenolic Acids in Brassicaceae Plants: Ovipositional Stimulants or Deterrents for Cabbage White Butterfly, Pieris Rapae? by Rebecca E. Dey And Skyler T. Carpenter

"Abecedarian Cards" by Emma Beckett, Jason Ware, And Mollie Andrews

Helvetica: A Type Specimen Book by James Bates, Landon Cooper, Tiffani Jeffries, And Maria Wheaton

“Things Left Behind” by Dallas …

On The Fattening Of Lines In P3, Mike Janssen

Faculty Work Comprehensive List

We follow the lead of Bocci and Chiantini and show how differences in the invariant alpha can be used to classify certain classes of subschemes of P^3. Specifically, we will seek to classify arithmetically Cohen-Macaulay codimension 2 subschemes of P^3 in the manner Bocci and Chiantini classified points in P^2. The first section will seek to motivate our consideration of the invariant alpha by relating it to the Hilbert function and gamma, following the work of Bocci and Chiantini, and Dumnicki, et. al. The second section will contain our results classifying arithmetically Cohen-Macaulay codimension 2 subschemes of P^3. This work …

An Efficient Method For Solving A Discrete Orthogonal Approximation To Fractional Boundary Value Problems, Mwaffag Husein Nahar Sharadga

Theses

In this thesis we developed a numerical method for solving a class of nonlinear fractional boundary value problems using the fractional order Legendre Tau-path following method. Theoretical and numerical analyses are presented. The numerical results showed that this method works properly and efficiently.