Mathematics Commons^™

Ultra-Low Voltage Digital Circuits And Extreme Temperature Electronics Design, Aaron J. Arthurs

Graduate Theses and Dissertations

Certain applications require digital electronics to operate under extreme conditions e.g., large swings in ambient temperature, very low supply voltage, high radiation. Such applications include sensor networks, wearable electronics, unmanned aerial vehicles, spacecraft, and energyharvesting systems. This dissertation splits into two projects that study digital electronics supplied by ultra-low voltages and build an electronic system for extreme temperatures. The first project introduces techniques that improve circuit reliability at deep subthreshold voltages as well as determine the minimum required supply voltage. These techniques address digital electronic design at several levels: the physical process, gate design, and system architecture. This dissertation analyzes …

Sigtree: An Automated Meta-Analytic Approach To Find Significant Branches In A Phylogenetic Tree, Todd R. Jones

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

An experiment was performed on two groups of mice, the first group receiving a refined wheat diet, and the second group receiving a whole wheat diet. The levels of abundance of hundreds of bacteria in the guts of the mice were measured. Of interest was whether the levels of these bacteria were different depending on type of diet. In addition, it was desired to examine differences by diet in all of the families of bacteria. These family relationships are represented in a tree, and it was determined helpful to color the branches of this tree based on the differences of …

On The Occasion Of Your Graduation, Robert Dawson

Journal of Humanistic Mathematics

A letter from an absent supervisor to a doctoral student about to graduate reveals a terrible secret.

Math Moment, Paige S. Orland

Journal of Humanistic Mathematics

A short poem comparing Exponential and Logistic functions.

Confidence Interval, Ursula Whitcher

Journal of Humanistic Mathematics

A poem about estimating probabilities.

Joanne Growney's Poetry-With-Mathematics Blog -- An Appreciation, Gregory E. Coxson

Journal of Humanistic Mathematics

Now is a good time to work on the boundaries of practice and theory, of art and science. We are seeing a rising tide of interest in these boundaries. Witness the growing Bridges movement, which has been exploring the connections between mathematics and the arts. Similarly, JoAnne Growney's blog, Intersections -- Poetry with Mathematics, explores the connections between mathematics and poetry. Through this review, I aim to give readers a taste of what can be found in Intersections as a way of encouraging others, be they mathematicians, poets, or neither, to visit the blog.

Mathematics And The Hunger Games, Michael A. Lewis

Journal of Humanistic Mathematics

The Hunger Games plot features a dystopian future in which twelve outer districts are oppressed by a centralized capital. The story focuses on the heroism of a sixteen-year-old girl named Katniss and how she tries to rise above the oppression that she experiences. It also features a special lottery and other twists that are sources of mathematical interest. This essay focuses on some of the mathematical issues raised by The Hunger Games in an effort to show that this story can be used to teach students (as well as other interested parties) some important concepts from mathematics.

A Definition Of Mathematical Beauty And Its History, Viktor Blåsjö

Journal of Humanistic Mathematics

I define mathematical beauty as cognisability and trace the import of this notion through several episodes from the history of mathematics.

Report Supplement: Poetry Folder -- Selections From The Poetry Reading At Joint Mathematics Meetings 2012

Journal of Humanistic Mathematics

No abstract provided.

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.

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.

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 …

Assessing Readability Of College-Level Statistics Textbooks: A Quantitative Lexical And Grammatical Analysis, Ariel I. Gonzalez, Amy E. Wagler, Lawrence M. Lesser

COURI Symposium Abstracts, Summer 2012

This research was conceived because of the need to create and identify college level statistics textbooks (or other instructional materials)) that are written in a manner that is less intimidating and easier to read and understand for students, including English language learners. We selected a representative set of current editions of 15-20 well-known statistics textbooks (that varied in their incorporation of reform or literacy approaches) to assess and compare aspects and levels of readability. We then chose two topics for a manageable focus: measures of center and line of fit. The parts of the textbooks corresponding to these topics were …

Generating Minimal T-Wise Test Suites, Luis C. Gutierrez, Carlos Nieto, Francisco Zapata, Martine Ceberio

COURI Symposium Abstracts, Summer 2012

As the use of computing devices increases every day, users rely on the adequate functioning of software. When software is not tested properly, it can yield erroneous information or a complete failure of the system. The NIST estimates that defective software cost the United States economy close to $60 billion a year. Therefore, there is a need to develop software testing techniques that are time and cost effective. Fully testing software under all possible combinations of parameters values cannot be reduced. However, testing can focus on covering all combinations of subsets of parameters and empirical data shows that doing so …

An Intelligent System To Manage Soft Constraints, Gabriel Higareda, Eduardo Breijo, Martine Ceberio

COURI Symposium Abstracts, Summer 2012

Most problems can be expressed in terms of requirements that must be met by their expected solutions. Constraints are requirements and constraint programming is a declarative programming paradigm that simply consists in modeling problems as lists of their requirements. Many constraint solvers exist that provide solutions to such list of requirements.

However, constraint solvers are stiff: if a problem was ill modeled, no solution will be returned and the original problem called over-constrained. Nevertheless there is hope even in these cases: such overconstrained problems can be handled as soft constraints, meaning that their processing will not be stiff anymore and …

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 …

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.

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 …

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.

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 …

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

School of Mathematical & Statistical Sciences Faculty Publications

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 …

Unknotting Tunnels Of Hyperbolic Tunnel Number N Manifolds, Stephan Daniel Burton

Theses and Dissertations

Adams conjectured that unknotting tunnels of tunnel number 1 manifolds are always isotopic to a geodesic. We generalize this question to tunnel number n manifolds. We find that there exist complete hyperbolic structures and a choice of spine of a compression body with genus 1 negative boundary and genus n ≥ 3 outer boundary for which (n−2) edges of the spine self-intersect. We use this to show that there exist finite volume one-cusped hyperbolic manifolds with a system of n tunnels for which (n−1) of the tunnels are homotopic to geodesics arbitrarily close to self-intersecting. This gives evidence that the …

K-S-Rings, Emma Louise Turner

Theses and Dissertations

For a finite group G we study certain rings called k-S-rings, one for each non-negative integer k, where the 1-S-ring is the centralizer ring of G. These rings have the property that the (k+1)-S-ring determines the k-S-ring. We show that the 4-S-ring determines G when G is any group with finite classes. We show that the 3-S-ring determines G for any finite group G, thus giving an answer to a question of Brauer. We show the 2-characters defined by Frobenius and the extended 2-characters of Ken Johnson are characters of representations of the 2-S-ring of G. We find the character …

Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach, Rafik Aliev, Oleg H. Huseynov, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is either completely unable to select one of these alternatives, or selects one of the alternatives only "to some extent". How can we extend the traditional decision theory to such realistic interval and fuzzy cases? In their previous papers, the first two authors proposed a natural generalization of the usual decision theory axioms to interval and fuzzy cases, and described decision coming from this generalization. …