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2017

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Articles 721 - 750 of 1334

Full-Text Articles in Mathematics

A Minus Sign That Used To Annoy Me But Now I Know Why It Is There (Two Constructions Of The Jones Polynomial), Peter Tingley Feb 2017

A Minus Sign That Used To Annoy Me But Now I Know Why It Is There (Two Constructions Of The Jones Polynomial), Peter Tingley

Mathematics and Statistics: Faculty Publications and Other Works

We consider two well known constructions of link invariants. One uses skein theory: you resolve each crossing of the link as a linear combination of things that don’t cross, until you eventually get a linear combination of links with no crossings, which you turn into a polynomial. The other uses quantum groups: you construct a functor from a topological category to some category of representations in such a way that (directed framed) links get sent to endomorphisms of the trivial representation, which are just rational functions. Certain instances of these two constructions give rise to essentially the same invariants, but …

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Q-Stirling Identities Revisited, Yue Cai, Richard Ehrenborg, Margaret Readdy Feb 2017

Q-Stirling Identities Revisited, Yue Cai, Richard Ehrenborg, Margaret Readdy

Mathematics Faculty Publications

We give combinatorial proofs of q-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the q-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel q-Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.

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A Variant Of Clark's Theorem And Its Applications For Nonsmooth Functionals Without The Palais-Smale Condition, Shaowei Chen, Zhaoli Liu, Zhi-Qiang Wang Feb 2017

A Variant Of Clark's Theorem And Its Applications For Nonsmooth Functionals Without The Palais-Smale Condition, Shaowei Chen, Zhaoli Liu, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

By introducing a new notion of the genus with respect to the weak topology in Banach spaces, we prove a variant of Clark's theorem for nonsmooth functionals without the Palais-Smale condition. In this new theorem, the Palais-Smale condition is replaced by a weaker assumption, and a sequence of critical points converging weakly to zero with nonpositive energy is obtained. As applications, we obtain infinitely many solutions for a quasi-linear elliptic equation which is very degenerate and lacks strict convexity, and we also prove the existence of infinitely many homoclinic orbits for a second-order Hamiltonian system for which the functional is …

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Stable Computations With Flat Radial Basis Functions Using Vector-Valued Rational Approximations, Grady B. Wright, Bengt Fornberg Feb 2017

Stable Computations With Flat Radial Basis Functions Using Vector-Valued Rational Approximations, Grady B. Wright, Bengt Fornberg

Mathematics Faculty Publications and Presentations

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast …

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The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila Feb 2017

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Libraries' Newsletters

No abstract provided.

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Controlling Viral Outbreaks: Quantitative Strategies, Anna Mummert, Howard Weiss Feb 2017

Controlling Viral Outbreaks: Quantitative Strategies, Anna Mummert, Howard Weiss

Mathematics Faculty Research

Preparing for and responding to outbreaks of serious livestock infectious diseases are critical measures to safeguard animal health, public health, and food supply. Almost all of the current control strategies are empirical, and mass culling or “stamping out” is frequently the principal strategy for controlling epidemics. However, there are ethical, ecological, and economic reasons to consider less drastic control strategies. Here we use modeling to quantitatively study the efficacy of different control measures for viral outbreaks, where the infectiousness, transmissibility and death rate of animals commonly depends on their viral load. We develop a broad theoretical framework for exploring and …

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Anonpri: A Secure Anonymous Private Authentication Protocol For Rfid Systems, Farzana Rahman, Md. Endadul Hoque, Sheikh Iqbal Ahamed Feb 2017

Anonpri: A Secure Anonymous Private Authentication Protocol For Rfid Systems, Farzana Rahman, Md. Endadul Hoque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Privacy preservation in RFID systems is a very important issue in modern day world. Privacy activists have been worried about the invasion of user privacy while using various RFID systems and services. Hence, significant efforts have been made to design RFID systems that preserve users' privacy. Majority of the privacy preserving protocols for RFID systems require the reader to search all tags in the system in order to identify a single RFID tag which not efficient for large scale systems. In order to achieve high-speed authentication in large-scale RFID systems, researchers propose tree-based approaches, in which any pair of tags …

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On Benacerraf’S Dilemma, Again, Marco Panza Feb 2017

On Benacerraf’S Dilemma, Again, Marco Panza

MPP Published Research

In spite of its enormous influence, Benacerraf’s dilemma admits no standard unanimously accepted formulation. This mainly depends on Benacerraf’s having originally presented it in a quite colloquial way, by avoiding any compact, somehow codified, but purportedly comprehensive formulation (Benacerraf 1973 cf. p. 29).

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Partitioning Random Graphs Into Monochromatic Components, Deepak Bal, Louis Debiasio Feb 2017

Partitioning Random Graphs Into Monochromatic Components, Deepak Bal, Louis Debiasio

Department of Mathematics Faculty Scholarship and Creative Works

Erdős, Gyàrfàs, and Pyber (1991) conjectured that every r-colored complete graph can be partitioned into at most r – 1 monochromatic components; this is a strengthening of a conjecture of Lovàsz (1975) and Ryser (1970) in which the components are only required to form a cover. An important partial result of Haxell and Kohayakawa (1995) shows that a partition into r monochromatic components is possible for sufficiently large r-colored complete graphs. We start by extending Haxell and Kohayakawa’s result to graphs with large minimum degree, then we provide some partial analogs of their result for random graphs. In particular, we …

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Arithmetic: Math As 'Pure' And 'Applied', Sunil Chetty Feb 2017

Arithmetic: Math As 'Pure' And 'Applied', Sunil Chetty

Forum Lectures

One often hears mathematics classified into two categories: pure or applied, abstract or concrete, elementary or modern. We explore how arithmetic can dismantle such highly artificial distinctions. More specifically, we play with tiles and draw pictures to highlight how arithmetic can be both good mental exercise and a very useful tool for modern communication.

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From Acoustic Analog Of Space, Cancer Therapy, To Acoustic Sachs-Wolfe Theorem: A Model Of The Universe As A Guitar, Victor Christianto, Florentin Smarandache, Yunita Umniyati Feb 2017

From Acoustic Analog Of Space, Cancer Therapy, To Acoustic Sachs-Wolfe Theorem: A Model Of The Universe As A Guitar, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such an acoustic model of cosmology is rarely developed fully into a complete framework from the notion of space, cancer therapy up to the sky. This paper may be the first attempt towards such a complete description of the Universe based on classical wave equation of sound. It is argued that one can arrive at a consistent description of space, elementary particles, Sachs-Wolfe acoustic theorem, up to a novel approach for cancer …

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Ichme-5: Fifth International Conference On The History Of Mathematics Education, Jenneke Krüger Feb 2017

Ichme-5: Fifth International Conference On The History Of Mathematics Education, Jenneke Krüger

Journal of Humanistic Mathematics

No abstract provided.

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Ladies' Night, Robert Dawson Feb 2017

Ladies' Night, Robert Dawson

Journal of Humanistic Mathematics

"Lady" Jane is an expert at her racket. The Joint Statistical Meetings are in Vegas, and she reckons it's payday. But she's taking on the professionals.

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The University Of Montana Department Of Mathematics Post-Apocalyptic Working Seminar, Kenan A. Ince Feb 2017

The University Of Montana Department Of Mathematics Post-Apocalyptic Working Seminar, Kenan A. Ince

Journal of Humanistic Mathematics

No abstract provided.

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16, Dan Mcquillan Feb 2017

16, Dan Mcquillan

Journal of Humanistic Mathematics

This 15 word poem suggests that the reader count the words of the poem. Since every line has half as many words as the previous line, and since the poem urges the reader to keep counting forever, one imagines a total of 16 words.

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The Geometry Of Morning, Greg Huteson Feb 2017

The Geometry Of Morning, Greg Huteson

Journal of Humanistic Mathematics

No abstract provided.

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Book Review: Realizing Reason: A Narrative Of Truth And Knowing By Danielle Macbeth, Emily R. Grosholz Feb 2017

Book Review: Realizing Reason: A Narrative Of Truth And Knowing By Danielle Macbeth, Emily R. Grosholz

Journal of Humanistic Mathematics

This review examines Danielle Macbeth’s novel and compelling account of the formal languages of mathematics, from Euclid’s geometrical diagrams to the algebraic equations of Descartes and the differential equations of Newton and Leibniz, to the much more abstract language of Galois, Bolzano and Riemann. She argues that the practice of those 19th century mathematicians, reasoning deductively from abstract concepts like ‘group’ and ‘manifold’, inspired the philosophical logician Gottlob Frege, whose Begriffsschrift captures the procedures of those who reasoned in concepts. However, his way of formalizing mathematical reasoning was obscured by the success of Bertrand Russell and Alfred North Whitehead’s …

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Solving Equations: A Make-Work Project For Math Teachers And Students, Egan J. Chernoff Feb 2017

Solving Equations: A Make-Work Project For Math Teachers And Students, Egan J. Chernoff

Journal of Humanistic Mathematics

The purpose of this article is to share a particular view that I have towards solving equations in the school mathematics classroom. Specifically, I contend that solving equations in the math classroom is a make-work project for math teachers and students. For example, math teachers take a predetermined value that makes a statement true, and then proceed to make it harder and harder and harder for their students to determine the value that makes the statement true. However, math teachers do so with the explicit purpose of teaching their students how to reveal the solution that they themselves have concealed. …

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Does Society Need Imo Medalists?, Man Keung Siu Feb 2017

Does Society Need Imo Medalists?, Man Keung Siu

Journal of Humanistic Mathematics

With a title that sounds provocative but with no intention to embarrass the organizers and participants of the event of IMO (International Mathematical Olympiad) this article should be seen as the sharing of some thoughts on this activity, or more generally on mathematical competitions, by a teacher of mathematics who had once helped in the coaching of the first Hong Kong Team to take part in the 29th IMO held in Canberra in 1988 and in the coordination work of the 35th IMO held in Hong Kong in 1994. The author tries to look at the issue in …

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Basketball, Algebra, And Probabilities, Gunhan Caglayan Feb 2017

Basketball, Algebra, And Probabilities, Gunhan Caglayan

Journal of Humanistic Mathematics

This article is an attempt to illustrate some humanistic aspects of mathematics in context, in particular, sports and scoring (basketball). The intriguing and dynamic illustrations demonstrate innovative and creative ways of integrating basketball snapshots into the pedagogy of a high school or college-level mathematics-in-context course. I have used this activity with several mathematics education students in a mathematics-in-context class as they worked in groups of five. I include here a presentation and a discussion of their explorations and analyses.

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The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz Feb 2017

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

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The Hidden Symmetries Of The Multiplication Table, Zoheir Barka Feb 2017

The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

Journal of Humanistic Mathematics

In this article we explore some of the symmetries that hide in the distribution of numbers in the multiplication table of positive integers when viewed through modulo k arithmetic as we vary k.

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Some Comments On Multiple Discovery In Mathematics, Robin W. Whitty Feb 2017

Some Comments On Multiple Discovery In Mathematics, Robin W. Whitty

Journal of Humanistic Mathematics

Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, categories, etc. With this in view we unearth many more examples, find some tenuous connections and draw some tentative conclusions.

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The Graduate Student Blues, Marion D. Cohen Feb 2017

The Graduate Student Blues, Marion D. Cohen

Journal of Humanistic Mathematics

This is a memoir about my rather unconventional path to a mathematics Ph.D. There were difficulties, due partly to university politics, partly to my youth and immaturity, and partly to the thesis material itself – it was, in the words of some of my fellow students, “not what’s being done now”. I had written the thesis entirely on my own, without help from my Master’s thesis advisor or any other professor at my school. This is not the usual procedure of course. Nobody in my department could understand the thesis or was willing to vouch for it. There followed three …

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Every Minute Of Your Life Has Been Interesting, Susan D'Agostino Feb 2017

Every Minute Of Your Life Has Been Interesting, Susan D'Agostino

Journal of Humanistic Mathematics

In this short paper, we prove that every minute of your life has been interesting. We also provide four exercises intended to solidify understanding of this result, including one exercise related to the torturously boring family road trip you took as a child.

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From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev Feb 2017

From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev

Journal of Humanistic Mathematics

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.

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Badiou’S Logics: Math, Metaphor, And (Almost) Everything, Vladimir Tasic Feb 2017

Badiou’S Logics: Math, Metaphor, And (Almost) Everything, Vladimir Tasic

Journal of Humanistic Mathematics

Mathematics plays a central role in the philosophical system of Alain Badiou. The aim of this essay is to situate this appeal to mathematics in the broader context of his work, including its literary and political elements.

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Mathematical Identities, Mark Huber, Gizem Karaali Feb 2017

Mathematical Identities, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Feb 2017

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Why Mixture Of Probability Distributions, Andrzej Pownuk, Vladik Kreinovich Feb 2017

Why Mixture Of Probability Distributions, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

If we have two random variables ξ1 and ξ1, then we can form their mixture if we take ξ1 with some probability w and ξ2 with the remaining probability 1 − w. The probability density function (pdf) ρ(x) of the mixture is a convex combination of the pdfs of the original variables: ρ(x) = w * ρ1(x) +( 1 − w) * ρ2(x). A natural question is: can we use other functions f(ρ1, ρ2) to combine the pdfs, i.e., to produce a new pdf ρ(x) =f(ρ1 …

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