Mathematics Commons^™

Approximation Degree Of Durrmeyer-Bézier Type Operators, Purshottam N. Agrawal, Serkan Araci, Martin Bohner, Kumari Lipi

Mathematics and Statistics Faculty Research & Creative Works

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means of the unified Ditzian-Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed.

Italian Folk Multiplication Algorithm Is Indeed Better: It Is More Parallelizable, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, many ethnic groups had their own versions of arithmetic algorithms. Nowadays, most of these algorithms are studied mostly as pedagogical curiosities, as an interesting way to make arithmetic more exciting to the kids: by applying to their patriotic feelings -- if they are studying the algorithms traditionally used by their ethic group -- or simply to their sense of curiosity. Somewhat surprisingly, we show that one of these algorithms -- a traditional Italian multiplication algorithm -- is actually in some reasonable sense better than the algorithm that we all normally use -- namely, it is easier to parallelize.

Gradient Estimation For Attractor Networks, Thomas Flynn

Dissertations, Theses, and Capstone Projects

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the …

A Mean-Risk Mixed Integer Nonlinear Program For Transportation Network Protection, Jie Lu, Akshay Gupte, Yongxi Huang

Publications

This paper focuses on transportation network protection to hedge against extreme events such as earthquakes. Traditional two-stage stochastic programming has been widely adopted to obtain solutions under a risk-neutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a mean-risk two-stage stochastic programming model that allows for greater flexibility in handling risk preferences when allocating limited resources. In particular, the first stage minimizes the retrofitting cost by making strategic retrofit decisions whereas the second stage minimizes the travel cost. The conditional value-at-risk (CVaR) is included as the risk measure …

On The Removal Of Motivation And Structural Barriers In The Classroom And Across The Mathematics Curriculum, Benjamin Wiles, Chantal Levesque-Bristol

IMPACT Presentations

Presentation at the research roundtable discussion at the 2018 Critical Issues in Math Education Workshop, Mathematical Sciences Research Institute, in Berkeley, CA.

Presents data on the ability of active learning methods to impact motivation and promote learning outcomes in mathematics courses.

Infinitely Many Solutions To Asymmetric, Polyharmonic Dirichlet Problems, Edger Sterjo

Dissertations, Theses, and Capstone Projects

In this dissertation we prove new results on the existence of infinitely many solutions to nonlinear partial differential equations that are perturbed from symmetry. Our main theorems focus on polyharmonic Dirichlet problems with exponential nonlinearities, and are now published in Topol. Methods Nonlinear Anal. Vol. 50, No.1, (2017), 27-63. In chapter 1 we give an introduction to the problem, its history, and the perturbation argument itself. In chapter 2 we prove the variational principle of Bolle on the behavior of critical values under perturbation, and the variational principle of Tanaka on the existence of critical points of large augmented Morse …

Statistical Analysis Of Network Change, Teresa D. Schmidt, Martin Zwick

Complex Systems Faculty Publications and Presentations

Networks are rarely subjected to hypothesis tests for difference, but when they are inferred from datasets of independent observations statistical testing is feasible. To demonstrate, a healthcare provider network is tested for significant change after an intervention using Medicaid claims data. First, the network is inferred for each time period with (1) partial least squares (PLS) regression and (2) reconstructability analysis (RA). Second, network distance (i.e., change between time periods) is measured as the mean absolute difference in (1) coefficient matrices for PLS and (2) calculated probability distributions for RA. Third, the network distance is compared against a reference distribution …

Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier

Electronic Theses and Dissertations

Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …

Phytoforensics: Trees As Bioindicators Of Potential Indoor Exposure Via Vapor Intrusion, Jordan L. Wilson, V. A. Samaranayake, Matt A. Limmer, Joel Gerard Burken

Mathematics and Statistics Faculty Research & Creative Works

Human exposure to volatile organic compounds (VOCs) via vapor intrusion (VI) is an emerging public health concern with notable detrimental impacts on public health. Phytoforensics, plant sampling to semi-quantitatively delineate subsurface contamination, provides a potential non-invasive screening approach to detect VI potential, and plant sampling is effective and also time- and cost-efficient. Existing VI assessment methods are time- and resource-intensive, invasive, and require access into residential and commercial buildings to drill holes through basement slabs to install sampling ports or require substantial equipment to install groundwater or soil vapor sampling outside the home. Tree-core samples collected in 2 days at …

Thinking Out Loud On Primeval Atom, Big Bang & Biblical Account Of Creation, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

In recent years, the Big Bang as described by the Lambda CDM-Standard Model Cosmology has become widely accepted by majority of physics and cosmology communities. Some people even have concluded that it has no serious alternative in horizon. Is that true? First, as we argued elsewhere, Big Bang relies on singularity, so, when we are able to describe the observed data without invoking singularity, then Big Bang model is no longer required. In this paper, we explore a few alternatives other than Big Bang which most cosmologists believe is the closest to biblical account of creation. We argue that re-reading …

Summary Of The Special Issue “Neutrosophic Information Theory And Applications” At “Information” Journal, Florentin Smarandache, Jun Ye

Branch Mathematics and Statistics Faculty and Staff Publications

Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to “Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489), located in Basel, Switzerland, was a success. The Guest Editors, Prof. Dr. Florentin Smarandache from the University of New Mexico (USA) and Prof. Dr. Jun Ye from the Shaoxing University (China), were happy to select—helped by a team of neutrosophic reviewers from around the world, and by the “Information” journal editors themselves—and publish twelve important neutrosophic papers, authored by 27 authors and coauthors. There were a variety of neutrosophic topics studied and used by the …

Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In …

Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

Branch Mathematics and Statistics Faculty and Staff Publications

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is …

Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

Branch Mathematics and Statistics Faculty and Staff Publications

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and …

Improved Kansa Rbf Method For The Solution Of Nonlinear Boundary Value Problems, Malgorzata A. Jankowska, Andreas Karageorghis, Ching-Shyang Chen

Faculty Publications

We apply the Kansa–radial basis function (RBF) collocation method to two-dimensional nonlinear boundary value problems. In it, the solution is approximated by a linear combination of RBFs and the governing equation and boundary conditions are satisfied in a collocation sense at interior and boundary points, respectively. The nonlinear system of equations resulting from the Kansa–RBF discretization for the unknown coefficients in the RBF approximation is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation may be included in the unknowns to be determined. The …

Cmsc 2018: 4th Creative Mathematical Sciences Communication Conference, Frances Rosamond

Journal of Humanistic Mathematics

Join scientists, researchers, teachers, and artists in developing new ways of communicating mathematical and computational thinking. Welcome are contributions in art forms such as dance, graphic art, theatre, and the myriad of ways to communicate science to the public. The conference will feature keynote talks by leading researchers and communicators in the mathematical sciences, sharing their experience, new initiatives, and ideas. The conference will be held in Wellington, New Zealand, at The Learning Connexion (TLC) on 21--23 July 2018. The conference website is http://www.cmsc.nz.

Mosaic: An Interdisciplinary Critical Journal Special Issue Call For Papers: Numbers, Shep Steiner

Journal of Humanistic Mathematics

Mosaic, an interdisciplinary critical journal, is pleased to announce a call for papers for a special issue on Numbers. Please submit your essay to the Editor using Mosaic’s online submission portal (http://umanitoba.ca/mosaic/submit) by March 9, 2018. The issue is currently scheduled to appear in September 2019.

Jesus And The Walnuts, Hugh C. Culik

Journal of Humanistic Mathematics

In “Jesus & the Walnuts,” a hapless English professor invokes fragments of mathematical thought to integrate his hunger for a knowable world with his affection for the logician with whom he shares an office. While “not even wrong” and horribly clumsy, his aspirations are iterations of the drive for order and meaning that are shared across disciplinary knowledge . . . and the hungers of the heart.

Paperback Vs. Cryptanalysis, Terry Trowbridge

Journal of Humanistic Mathematics

This poem is a defiant challenge against online and app based surveillance of readers. It also questions the guesses that are used to make claims about readers using text analyses.

Gradual Homicide, Jack Ritter

Journal of Humanistic Mathematics

A mathematical poem about asymptotic treachery.

Theremin, David Pritchard

Journal of Humanistic Mathematics

No abstract provided.

Math In Seventeen Syllables: A Folder Of Mathematical Haiku

Journal of Humanistic Mathematics

In our July 2017 issue, we issued an open call for mathematical haiku, which we defined to be a three-line poem in the “5-7-5” syllabic form that expressed a mathematical idea or experience, and hopefully connected it to the human condition. In deference to traditional Japanese haiku, we encouraged poets to consider using allusions to nature or the seasons in their work, or what is known as a caesura or kire represented by punctuations, space, line-break, or other grammatical break that is intended to compare two images implicitly.

We received haiku on an amazing variety of themes and subjects, from …

Book Review: Algebra In Context: Introductory Algebra From Origins To Applications By Amy Shell-Gellasch And J. B. Thoo, Cindia D. Stewart

Journal of Humanistic Mathematics

This is a review of Algebra in Context: Introductory Algebra from Origins to Applications, a textbook authored by Amy Shell-Gellasch and J.B. Thoo. The text presents traditional mathematics through the lens of history, allowing students to gain a rich understanding of how mathematics works and where it comes from. In addition to providing the reader with a summary of the book contents, the reviewer suggests why and how the text may be incorporated into college-level mathematics courses.

Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö

Journal of Humanistic Mathematics

Recent attempts at defining mathematical beauty fall roughly into two schools of thought. One takes its starting point in the subjective experience of the mathematician and characterises mathematical beauty in cognitive terms. The other seeks to reduce beauty to objective notions such as truth, symmetry, or simplicity. This second approach is popular among analytic philosophers, who are committed to seeing mathematics and science as prototypically rational enterprises. I criticise this stance on the grounds that this commitment makes its supporters approach beauty in mathematics not with a genuine desire to sympathetically understand it, but with the preconceived goal of explaining …

The Origin Of The Group In Logic And The Methodology Of Science, Paolo Mancosu

Journal of Humanistic Mathematics

The Group in Logic and the Methodology of Science at UC Berkeley was founded in 1957. It has been a key institutional element in carrying out Tarski’s vision for making UC Berkeley one of the most important centers of logical research in the world. In this brief history, I look at the emergence of the Group in Logic with an eye towards understanding the circumstances that made it possible.

My Sets And Sexuality, Andres Sanchez

Journal of Humanistic Mathematics

It was only with the application of set theory to my own personal life that I discovered my true identity and sexuality. In this exploratory, personal essay, I detail my own discovery of my sexuality through mathematics and how this math has become a lens through which I view the world. And, with new knowledge of literary criticism in hand, I can now retroactively describe the thoughts I had in this discovery process.

Fun, Not Competition: The Story Of My Math Club, Johanna Hardin

Journal of Humanistic Mathematics

For almost three years, I have spent most of my Sunday afternoons doing math with my daughters and a group of their school friends. Below I detail why and how the math club is run. Unlike my day job, which is full of (statistical) learning objectives for my college students, my math club has only the objective that the kids I work with learn to associate mathematics with having fun. My math club has its challenges, but the motivation comes from love of mathematics, which makes it fun, and worth every minute.

In Memory Of Professor Andrei Nikolaievitch Tikhonov (1906-1993) On The 25th Anniversary Of His Death, Hayat Rezgui

Journal of Humanistic Mathematics

Thursday, November 8, 2018, is the twenty-fifth anniversary of the death of the celebrated Professor A. N. Tikhonov, one of my most favorite mathematicians. The idea of writing this paper to honor his life and scientific activities came to me as I was reading many of his works; I was impressed by his knowledge, amazing research, profound scholarship, perspicuity and eloquence of expression, painstaking accuracy, and big ideas. My aim is to be clear and evocative, for in this way I feel more in touch with my subject that is very interesting.

Cello Tangents Of Quartic Polynomials, Robert Haas Ph.D.

Journal of Humanistic Mathematics

This note uses easy calculus and linear algebra to analyze the situation of a line being tangent to two points of a fourth-degree polynomial curve.

Seen With Other Eyes: A Service Learning Project For High School Mathematicians Working With Visually Impaired Learners, Özgür Akas

Journal of Humanistic Mathematics

Seen With Other Eyes (SWOE) is a community involvement project that focuses on mathematics education for the visually impaired. In this essay I describe this project, which I developed together with my students at Robert College, a private high school in Turkey, and share some of our story. In the past few years, our work was welcomed by the global mathematics education community, as a testimony to the power of social media to connect like-minded educators with one another.