Mathematics Commons^™

For The Love Of Poetry And Mathematics: January 6, 2012, Charlotte Henderson

Journal of Humanistic Mathematics

Together we combine to become twice what 60 could ever be.
The same ghost looked into my eyes.
Also, the center of the circle is inside the circle.
There is no way to draw a line, other than a border line,
A language as precise as poetry to delineate universe and being,
Deceptive as one over n as n goes to infinity, summed.
The world is a complex system
not defined by any voice factored out of my voicelessness,
the hypotenuse of course is the man who came between us
doubting every figured guess,
so, inductively, all of God’s natural …

Raphael's School Of Athens: A Theorem In A Painting?, Robert Haas

Journal of Humanistic Mathematics

Raphael's famous painting The School of Athens includes a geometer, presumably Euclid himself, demonstrating a construction to his fascinated students. But what theorem are they all studying? This article first introduces the painting, and describes Raphael's lifelong friendship with the eminent mathematician Paulus of Middelburg. It then presents several conjectured explanations, notably a theorem about a hexagram (Fichtner), or alternatively that the construction may be architecturally symbolic (Valtieri). The author finally offers his own "null hypothesis": that the scene does not show any actual mathematics, but simply the fascination, excitement, and joy of mathematicians at their work.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Essays On Group Deviation., Conan Mukherjee Dr.

Doctoral Theses

No abstract provided.

Multilevel And Multidimensional Hadamard Matrices, Sarah Adams, Matthew Crawford, Caitlin Greeley, Bryce Lee, Mathav Murugan

Sarah Spence Adams

Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code division multiple access systems. We answer the open question concerning the maximum number of distinct elements permissible in an order n MHM by proving the existence of an order n MHM with n elements of distinct absolute value for all n. We also define multidimensional MHMs and prove an analogous existence result.

On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland

Sarah Spence Adams

An L(2,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G so that adjacent vertices get labels at least distance two apart and vertices at distance two get distinct labels. A hole is an unused integer within the range of integers used by the labeling. The lambda number of a graphG, denoted λ(G), is the minimum span taken over all L(2,1)-labelings of G. The hole index of a graph G, denoted ρ(G), is the minimum number of holes taken over all L(2,1)-labelings with span exactly λ(G). Georges and Mauro [On the structure of graphs …

Convergence Analysis Of A Fully Discrete Family Of Iterated Deconvolution Methods For Turbulence Modeling With Time Relaxation, Iuliana Stanculescu, R. Ingram, N Mays, C. C. Manica

Mathematics Faculty Articles

We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the (modified) Tikhonov-Lavrentiev and (modified) Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An existence theory is derived for the family of models and a rigorous convergence theory is derived for the resulting algorithms. Our theoretical results are supported by numerical testing with the Taylor-Green vortex problem, presented for the special operator cases mentioned above.

A Homogeneous Solution Of The Einstein-Maxwell Equations, Charles G. Torre

Research Vignettes

We exhibit and analyze a homogeneous spacetime whose source is a pure radiation electromagnetic field [1]. It was previously believed that this spacetime is the sole example of a homogeneous pure radiation solution of the Einstein equations which admits no electromagnetic field (see [2] and references therein). Here we correct this error in the literature by explicitly displaying the electromagnetic source. This result implies that all homogeneous pure radiation spacetimes satisfy the Einstein-Maxwell equations.

PDF and Maple worksheets can be downloaded from the links below.

Communicating Quantitative Literacy: An Examination Of Open-Ended Assessment Items In Timss, Nals, Ials, And Pisa, Karl Kosko, Jesse Wilkins

Karl W Kosko

Quantitative Literacy (QL) has been described as the skill set an individual uses when interacting with the world in a quantitative manner. A necessary component of this interaction is communication. To this end, assessments of QL have included open-ended items as a means of including communicative aspects of QL. The present study sought to examine whether such open-ended items typically measured aspects of quantitative communication, as compared to mathematical communication, or mathematical skills. We focused on public-released items and rubrics from four of the most widely referenced assessments: the Third International Mathematics and Science Study (TIMSS-95): the National Adult Literacy …

Nitrated Fibrinogen Is A Biomarker Of Oxidative Stress In Venous Thromboembolism, Marissa Martinez, Adam Cuker, Angela Mills, Richard Lightfoot, Yiying Fan, W.H. Wilson Tang, Stanley L. Hazen, Harry Ischiropoulos

Mathematics and Statistics Faculty Publications

The pathogenesis of venous thromboembolism (VTE) is linked to inflammation and oxidant production, although specific markers for these pathways with pathological relevance to VTE have not been explored. The coagulant protein fibrinogen is posttranslationally modified by nitric oxide-derived oxidants to nitrated fibrinogen in both acute and chronic inflammatory states. Therefore, nitrated fibrinogen may serve as a marker of inflammation and oxidative stress in VTE. To test this hypothesis we enrolled subjects (n=251) presenting with suspected VTE at the University of Pennsylvania Hospital emergency department, 50 (19.9%) of whom were positive by imaging or 90-day follow-up. Mean nitrated fibrinogen was elevated …

Dark Solitons And Vortices In Pt-Symmetric Nonlinear Media: From Spontaneous Symmetry Breaking To Nonlinear Pt Phase Transitions, V. Achilleos, Panos Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´Alez

Panos Kevrekidis

We consider nonlinear analogs of parity-time- (PT-) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and odd excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter ɛ controlling the strength of the PT-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as ɛ is further increased, the ground state and first excited state, as well as branches of higher multisoliton (multivortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear PT phase transition—thus …

On Principal Minors Of Bezout Matrix, Ruben G. Hayrapetyan

Mathematics Publications

Let $x_1,...,x_{n}$ be real numbers, $P(x)=p_n(x-x_1)...(x-x_n)$, and $Q(x)$ be a polynomial of degree less than or equal to $n$. Denote by $\Delta(Q)$ the matrix of generalized divided differences of $Q(x)$ with nodes $x_1,...,x_n$ and by $B(P,Q)$ the Bezout matrix (Bezoutiant) of $P$ and $Q$. A relationship between the corresponding principal minors, counted from the right-hand lower corner, of the matrices $B(P,Q)$ and $\Delta(Q)$ is established. It implies that if the principal minors of the matrix of divided differences of a function $g(x)$ are positive or have alternating signs then the roots of the Newton's interpolation polynomial of $g$ are real …

Carrying Biomath Education In A Leaky Bucket, James A. Powell, Brynja R. Kohler, James W. Haefner, Janice Bodily

Mathematics and Statistics Faculty Publications

In this paper, we describe a project-based mathematical lab implemented in our Applied Mathematics in Biology course. The Leaky Bucket Lab allows students to parameterize and test Torricelli’s law and develop and compare their own alternative models to describe the dynamics of water draining from perforated containers. In the context of this lab students build facility in a variety of applied biomathematical tools and gain confidence in applying these tools in data-driven environments. We survey analytic approaches developed by students to illustrate the creativity this encourages as well as prepare other instructors to scaffold the student learning experience. Pedagogical results …

Methods Of Music Classification And Transcription, Jonathan Peter Baker

Theses and Dissertations

We begin with an overview of some signal processing terms and topics relevant to music analysis including facts about human sound perception. We then discuss common objectives of music analysis and existing methods for accomplishing them. We conclude with an introduction to a new method of automatically transcribing a piece of music from a digital audio signal.

Analytical Upstream Collocation Solution Of A Quadratically Forced Steady-State Convection-Diffusion Equation, Stephen Brill, Eric Smith

Stephen H. Brill

Purpose – The purpose of this paper is to present the analytical solution to the Hermite collocation discretization of a quadratically forced steady-state convection-diffusion equation in one spatial dimension with constant coefficients, defined on a uniform mesh, with Dirichlet boundary conditions. To improve the accuracy of the method “upstream weighting” of the convective term is used in an optimal way. The authors also provide a method to determine where the forcing function should be optimally sampled. Computational examples are given, which support and illustrate the theory of the optimal sampling of the convective and forcing term. Design/methodology/approach – The authors: …

A Maple Program For Computing Landau-Ginzburg A- And B-Models And An Exploration Of Mirror Symmetry, Evan D. Merrell

Theses and Dissertations

Mirror symmetry has been a significant area of research for geometry and physics for over two decades. Berglund and Hubsch proposed that for a certain family of singularities W, the so called "transposed" singularity WT should be the mirror partner of W. cite{BH} The techniques for constructing the orbifold LG models to test this conjecture were developed by FJR in cite{FJR} with a cohomological field theory generalized from the study of r-spin curves. The duality of LG A- and B-models became more elaborate when Krawitz cite{Krawitz} generalized the Intriligator-Vafa orbifold B-model to include contributions from more than one sector.This thesis …

How To Create A Lie Algebra, Ian M. Anderson

How to... in 10 minutes or less

We show how to create a Lie algebra in Maple using three of the most common approaches: matrices, vector fields and structure equations. PDF and Maple worksheets can be downloaded from the links below.

The 2-Component Dispersionless Burger's Equation Arising In The Modelling Of Bloodflow, Tony Lyons

Articles

This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood- ow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well as applications of the model to clinical conditions.

Negative-Order Korteweg–De Vries Equations, Zhijun Qiao, Engui Fan

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, based on the regular Korteweg–de Vries (KdV) system, we study negative-order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs, conservation laws, and explicit multisoliton and multikink wave solutions thorough bilinear B¨acklund transformations. The NKdV equations studied in our paper are differential and actually derived from the first member in the negative-order KdV hierarchy. The NKdV equations are not only gauge equivalent to the Camassa-Holm equation through reciprocal transformations but also closely related to the Ermakov-Pinney systems and the Kupershmidt deformation. The bi-Hamiltonian structures and a Darboux transformation of the NKdV equations are constructed with the aid …

Total Character Groups, Chelsea Lorraine Kennedy

Theses and Dissertations

The total character of a finite group G is the sum of the irreducible characters of G. When the total character of a finite group can be written as a monic polynomial with integer coefficients in an irreducible character of G, we say that G is a total character group. In this thesis we examine the total character of the dicyclic group of order 4n, the non-abelian groups of order p^3, and the symmetric group on n elements for all n ≥ 1. The dicyclic group of order 4n is a total character group precisely when n is congruent to …