Physical Sciences and Mathematics Commons^™

Melting And Solidification Study Of As-Deposited And Recrystallized Bi Thin Films, M. K. Zayed, H. E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

Melting and solidification of as-deposited and recrystallized Bi crystallites, deposited on highly oriented 002-graphite at 423 K, were studied using reflection high-energy electron diffraction (RHEED). Films with mean thickness between 1.5 and 33 ML (monolayers) were studied. Ex situ atomic force microscopy was used to study the morphology and the size distribution of the formed nanocrystals. The as-deposited films grew in the form of three-dimensional crystallites with different shapes and sizes, while those recrystallized from the melt were formed in nearly similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting …

Strategies In Maximizing The Use Of Existing Technology In Philippine Schools, Debbie Marie Y. Bautista, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

One of the challenges that continue to confront teachers in Philippine schools is the accessibility of technology for the study and learning of mathematics. In this paper, we will look at several situations and actual experiences happening in Philippine schools. Strategies on how existing technological tools are to be maximized will be discussed, including the creation of lesson plans and classroom activities. The use of technology-based manipulatives in mathematics learning as alternatives to unavailable technology will also be looked at.

An Euler-Type Formula For Ζ(2k +1), Tian-Xiao He, Michael Dancs

Scholarship

In this short paper, we give several new formulas for ζ(n) when n is an odd positive integer. The method is based on a recent proof, due to H. Tsumura, of Euler’s classical result for even n. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult.

Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael Dancs

Scholarship

In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

On The Convergence Of The Summation Formulas Constructed By Using A Symbolic Operator Approach, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

This paper deals with the convergence of the summation of power series of the form Σa ≤ k ≤ bf(k)xk, where 0 ≤ a ≤ b < ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.

On The Generalized Möbius Inversion Formulas, Tian-Xiao He, Peter Shiue3, Leetsch Hsu

Scholarship

We provide a wide class of M¨obius inversion formulas in terms of the generalized M¨obius functions and its application to the setting of the Selberg multiplicative functions.

Shuffle Up And Deal: Should We Have Jokers Wild?, Kristen Lampe

Undergraduate Mathematics Day: Past Content

In the neighborhood poker games, one often hears of adding the Jokers as wild cards, or declaring deuces wild. In this talk, we’ll explore what happens mathematically when two Jokers are added to the deck. The probabilities for different hands change, in ways that might surprise you. Further, we will explore the mathematical consequences of playing poker with more or fewer than five cards. Finally, we will look at the historical beginnings of poker, and a mathematical anomaly that occurred along the way.

Bisections And Reflections: A Geometric Investigation, Carrie Carden, Jessie Penley

Undergraduate Mathematics Day: Past Content

This problem was first introduced as a challenge problem to high school geometry students. After receiving no responses from students, it was then taken to the collegial level. We were given this problem to investigate with the intent of generalizing the results to a broader question. This question being, what happens when we have a polygon with n sides? Before introducing the problem itself, we will recall some basic geometry definitions which will be used throughout this paper.

Methods Of Solution Of Second Order Linear Equations On Time Scales, Ashley Askew

Undergraduate Mathematics Day: Past Content

A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods is that we can obtain solutions on a system comprising of continuous and/or discrete elements. After restricting the time scale to be R, these solutions are equivalent to those obtained using differential equations methods.

A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods …

2006 Vol. 2 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

Mathematical And Numerical Modeling Of Inflammation, Joshua Sullivan, Ivan Yotov

Undergraduate Mathematics Day: Past Content

When the body is attacked by a bacterial infection, it initiates a series of events designed to eradicate the infection while causing minimal damage to the body. Our goal is to investigate the defenses of the organ walls to the spread of infection. To do this we have chosen to model a volume of the body that includes the organ wall, the lumen outside of it and the blood and tissue within it. We have also taken into account the varied responses of the body, and our model includes many interacting agents that are part of the infection and defense …

Adventures With Rubik's Ufo, Bill Higgins

Undergraduate Mathematics Day: Past Content

Enro Rubik invented the puzzle which is now known as Rubik’s Cube in the 1970’s. More than 100 million cubes have been sold worldwide. The mathematics behind solutions to the cube have been extensively studied by mathematicians and puzzle enthusiasts alike. In this article the mathematics behind a solution of the related puzzle known as Rubik’s UFO is analyzed.

An Investigation Of Continued Fractions, Kristi Patton, Sandra Schroeder, Richard Daquila

Undergraduate Mathematics Day: Past Content

The study of continued fractions has produced many interesting and exciting results in number theory and other related fields of mathematics. Continued fractions have been studied for centuries by many famous mathematicians such as Wallis, Euler, Gauss, Lagrange, Ramanujan, Cauchy, and Khinchin. A connection between continued fractions and the Fibonacci sequence can be revealed by examining functional parameters of various rational functions. This work makes use of existing results concerning continued fractions and Mathematica to explore the relationship between continued fractions and rational functions.

Brownian Motion And Its Applications In The Stock Market, Angeliki Ermogenous

Undergraduate Mathematics Day: Past Content

Wilfrid Kendall notes on the complexity of the paths of Brownian motion: If you run Brownian motion in two dimensions for a positive amount of time, it will write your name. The oddness and complexity of Brownian motion reveal a really deep subject in the field of mathematics that cannot be fully understood and explained even until now. The purpose of this paper is to introduce the Brownian motion with its properties and to explain how it is applied in an everyday but totally unpredictable environment like the stock market.

Classifying E-Algebras Over Dedekind Domains, Brendan Goldsmith, R. Gobel

Articles

An R-algebra A is said to be a generalized E-algebra if A is isomorphic to the algebra EndR(A). Generalized E-algebras have been extensively investigated. In this work they are classified ‘modulo cotorsion-free modules’ when the underlying ring R is a Dedekind domain.

Discourse On The Interface Of Matheatics And Physics: A Panel Discussion Sponsored By Dit And The Ria., Brendan Goldsmith

Articles

No abstract available

Complex Symmetric Operators And Applications, Stephan Ramon Garcia, Mihai Putinar

Pomona Faculty Publications and Research

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

On Reduced And Semicommutative Modules, Muhi̇tti̇n Başer, Nazim Agayev

Turkish Journal of Mathematics

In this paper, various results of reduced and semicommutative rings are extended to reduced and semicommutative modules. In particular, we show: (1) For a principally quasi-Baer module, M_R is semicommutative if and only if M_R is reduced. (2) If M_R is a p.p.-module then M_R is nonsingular.

Review: Stability Of Bases And Frames Of Reproducing Kernels In Model Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06

Pomona Faculty Publications and Research

With advances in technology, biologists have been saddled with high dimensional data that need modern statistical methodology for analysis. DNA microarrays are able to simultaneously measure thousands of genes (and the activity of those genes) in a single sample. Biologists use microarrays to trace connections between pathways or to identify all genes that respond to a signal. The statistical tools we usually teach our undergraduates are inadequate for analyzing thousands of measurements on tens of samples. The project materials include readings on microarrays as well as computer lab activities. The topics covered include image analysis, filtering and normalization techniques, and …

Conjugation And Clark Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Yeast Through The Ages: A Statistical Analysis Of Genetic Changes In Aging Yeast, Alison Wise '05, Johanna S. Hardin, Laura Hoopes

Pomona Faculty Publications and Research

Microarray technology allows for the expression levels of thousands of genes in a cell to be measured simultaneously. The technology provides great potential in the fields of biology and medicine, as the analysis of data obtained from microarray experiments gives insight into the roles of specific genes and the associated changes across experimental conditions (e.g., aging, mutation, radiation therapy, drug dosage). The application of statistical tools to microarray data can help make sense of the experiment and thereby advance genetic, biological, and medical research. Likewise, microarrays provide an exciting means through which to explore statistical techniques.

Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor

Pomona Faculty Publications and Research

We prove that a graph is intrinsically linked in an arbitrary 3–manifold M if and only if it is intrinsically linked in S³. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S³.

Super Solutions Of The Dynamical Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r−matrices. A super dynamical r−matrix r satisfies the zero weight condition if

[h ⊗ 1 + 1 ⊗ h, r(λ)] = 0 for all h ∈ ɧ, λ ∈ ɧ ∗ .

In this paper we classify super dynamical r−matrices with zero weight.

What I Learned At The Maa Digital Library Workshop, Gizem Karaali

Pomona Faculty Publications and Research

Toward the end of July 2006, an item appeared briefly on the MAA website. This was the call for participants for the MAA Digital Library Workshop. Curious surfers like me clicked on it to find the description of this workshop, which was to be held over the course of a weekend in October 2006 in Washington, DC. The announcement included a cryptic sentence of the form “The primary aims of the workshop are to provide an overview of the two MAA digital libraries and of the National Science Digital Library, and to prepare participants to offer a short workshop on …

Pullbacks Of Crossed Modules And Cat^1- Commutative Algebras, Murat Alp

Turkish Journal of Mathematics

In this paper we first review the definitions of crossed module [10], pullback crossed module and cat^1-object in the category of commutative algebras. We then describe a certain pullback of cat^1- commutative algebras.

Chord Diagrams And Gauss Codes For Graphs, Thomas Fleming, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study of spatial graphs. We will define chord diagrams for planar embeddings of planar graphs and their intersection graphs, and prove some basic results. Then, as an application, we will introduce Gauss codes for immersions of graphs in the plane and give algorithms to determine whether a particular crossing sequence is …

Intersection Graphs For String Links, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show that these weight systems are related to the weight systems induced by the Conway and Homfly polynomials.

Tree Diagrams For String Links, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

In previous work, the author defined the intersection graph of a chord diagram associated with string links (as in the theory of finite type invariants). In this paper, we classify the trees which can be obtained as intersection graphs of string link diagrams.

Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S³. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S³.