Mathematics Commons^™

Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc

Faculty Publications

We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.

Volumetric Lattice Boltzmann Method For Wall Stresses Of Image-Based Pulsatile Flows, Xiaoyu Zhang, Joan Gomez-Paz, Xi Chen, James M. Mcdonough, Md Mahfuzul Islam, Yiannis Andreopoulos, Luoding Zhu, Huidan Yu

Mechanical Engineering Faculty Publications

Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route …

Subclasses Of Multivalent Meromorphic Functions With A Pole Of Order P At The Origin, Daniel Breaz, Kadhavoor R. Karthikeyan, Elangho Umadevi

All Works

In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. …

Lipschitz Regularity For The Parabolic P-Laplacian In The Heisenberg Group, Luca Capogna, Giovanna Citti, Xiao Zhong

Mathematics Sciences: Faculty Publications

In this paper we establish the local Lipschitz regularity of weak solutions of a certain class of quasilinear, degenerate parabolic equations in the Heisenberg group Hn , or more in general in contact subRiemannian manifolds. In particular we extend to the non-stationary setting.

Reproducing Kernel Method For Solving Fuzzy Initial Value Problems, Qamar Kamel Dallashi

Theses

In this thesis, numerical solution of the fuzzy initial value problem will be investigated based on the reproducing kernel method. Problems of this type are either difficult to solve or impossible, in some cases, since they will produce a complicated optimized problem. To overcome this challenge, reproducing kernel method will be modified to solve this type of problems. Theoretical and numerical results will be presented to show the efficiency of the proposed method.

A Phenomenological Study: The Lived Experience Of Self-Described Math-Anxious Students Attending College Online, Toni Nicole Sawhill

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study is to describe the lived experience of mathematics anxiety for self-described math-anxious students who completed an undergraduate mathematics course online at a university in the Pacific Northwest part of the United States. The theory guiding this study is community of inquiry (COI) introduced by early pragmatist philosophers C. S. Peirce and John Dewey and further developed by D. Randy Garrison, Terry Anderson, and Walter Archer as mathematics anxiety is a learned behavior based on students’ experiences. This research study answers the central research question: What are the lived experiences of mathematics anxiety for …

Inverse Scattering Transform For The Complex Coupled Short-Pulse Equation, Aikaterini Gkogkou, Bao-Feng Feng, A. David Trubatch

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we develop the Riemann–Hilbert approach to the inverse scattering transform (IST) for the complex coupled short-pulse equation on the line with zero boundary conditions at space infinity, which is a generalization of recent work on the scalar real short-pulse equation (SPE) and complex short-pulse equation (cSPE). As a byproduct of the IST, soliton solutions are also obtained. As is often the case, the zoology of soliton solutions for the coupled system is richer than in the scalar case, and it includes both fundamental solitons (the natural, vector generalization of the scalar case), and fundamental breathers (a superposition …

Starlike Functions Of Complex Order With Respect To Symmetric Points Defined Using Higher Order Derivatives, Kadhavoor R. Karthikeyan, Sakkarai Lakshmi, Seetharam Varadharajan, Dharmaraj Mohankumar, Elangho Umadevi

All Works

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.

Euclidean Quantum Field Formulation Of P-Adic Open String Amplitudes, A. R. Fuquen-Tibatá, H. García-Compeán, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's local zeta function. The lowest term in this series is a regularized version of the p-adic open Koba-Nielsen string amplitude.

Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity, Troy Smith

Dissertations, Theses, and Capstone Projects

For much of American history, literacy has been prioritized in K-12 education and society, at large, at the expense of numeracy. This lack of numerical emphasis has established innumeracy as an American cultural norm that has resulted in America not producing a sufficient number of numerate citizens, and ranking poorly on mathematical performance in international comparisons. This paper investigates the decisions and circumstances that led to this under prioritization, along with the public and cultural impact of said actions. Toward this end, literature regarding contemporary and historical influences on American mathematics education (e.g., civic, policy, and parental) was reviewed. The …

Special Issue Call For Papers: Mathematics And Society, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez, Tian An Wong

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics (http://scholarship.claremont.edu/jhm/) is pleased to announce a call for papers for a special issue on Mathematics and Society. Please send your initial proposal submissions via email to the guest editors by August 15, 2022. Initial submission of complete manuscripts is due December 15, 2022. The issue is currently scheduled to appear in July 2023.

Journal For Mathematics And The Arts Call For Papers: Special Issue On The Mathematics Of Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro

Journal of Humanistic Mathematics

The Journal for Mathematics and the Arts (https://www.tandfonline.com/journals/tmaa20) a peer-reviewed journal that focuses on connections between mathematics and the arts, is pleased to announce a call for papers for a special issue on Mathematics of Fiber Arts. Please send your queries via email to the guest editors. Initial submission of complete manuscripts is due August 1, 2022. The issue is currently scheduled to appear in Fall 2023.

A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto

Journal of Humanistic Mathematics

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.

As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …

So Long My Friend, Bryan Mcnair

Journal of Humanistic Mathematics

No abstract provided.

Heuristic Or Stochastic?, E Laura Golberg

Journal of Humanistic Mathematics

This is a poem about laying odds on the outcome of weddings.

The Solipsist’S First Paper, Sabrina Sixta

Journal of Humanistic Mathematics

The angst of a graduate student who has not yet written a paper, but really wants to.

Wrong Way, Joseph Chaney

Journal of Humanistic Mathematics

No abstract provided.

What's So Great About Non-Orientable Manifolds?, Michael Mccormick

Journal of Humanistic Mathematics

No abstract provided.

Poetry In The Glade: Bridges 2021 Fib Collection

Journal of Humanistic Mathematics

A Fibonacci poem follows the Fibonacci sequence to any length in its count of syllables per line, or words per line, or lines per stanza, or any other countable thing connected with the poem. A Fib is a special case of Fibonacci poem, a poem of 6 lines whose syllable line count follows the first 6 numbers of the Fibonacci sequence: 1; 1; 2; 3; 5; 8. The present collection of Fibs arose out of the Bridges poetry community in response to the Bridges organization’s efforts to make the Bridges 2021 conference more interactive.

Mathematics For The Masses: Door-To-Door Missionaries Of Math And Twelve-Step Recovery Programs, Daniel S. Helman

Journal of Humanistic Mathematics

Conversion of strangers, or proselytizing, is a feature of a range of groups for religious, organizational and other aims. In twelve-step recovery programs, such as Alcoholics Anonymous, belief in a higher power is a requirement for working the steps to recovery. People are encouraged to find a higher power of their own understanding. This paper presents a model for using mathematics as a higher power, and shows how recovery works with mathematics in that role instead of a more traditional higher power such as God. A contemplative definition of math is given along with a description of a three-categoried epistemology: …

An Urgent Plea For More Graduate Programs In Statistics Education, David Eli Drew, Sam Behseta, Cherie L. Ichinose

Journal of Humanistic Mathematics

Lately, much has been written about the importance of amplifying statistics-related content in the K-12 curricula. This can be viewed in parallel or as an addendum to the existing mathematics curricula in the United States. Nevertheless, a key component of this debate is the lack of robust and cutting-edge academic programs in statistics education. In this piece, we emphasize the urgent need for investing in creating strong statistics education programs, which would significantly contribute to nurturing quantitative literacy as well as preparing a more informed citizenry in the 21^st century.

A Reflection On Growth Mindset And Meritocracy, Rachel L. Petrik, Julianne Vega, Andrés R. Vindas-Meléndez

Journal of Humanistic Mathematics

As mathematicians working in higher education we reflect on meritocracy and growth mindset with a focus on the relationship between the two. We also note the subtle differences between growth mindset and grit. Our reflection ends with suggestions for how to move forward in the math classroom and throughout the collegiate level.

Life Of A Working Ramsey Theorist: Conversation With Thomas C. Brown, Kyle Singh, Veselin Jungic, Jun Bo Mei

Journal of Humanistic Mathematics

This interview, conducted in November 2020, explores the fascinating life and work of Ramsey theorist Thomas Craig Brown. We hope, through our conversation with Dr. Brown, to show that mathematics is not a discipline that is only concerned with numbers, but that it is, in a fundamental way, also about people and connections.

Decisions, Decisions: How Should The Votes Be Counted?, Michael J. Caulfield

Journal of Humanistic Mathematics

It is a simple matter for the members of a group to decide among two options. When there are three or more options among which to choose, the situation is much more complicated. This is precisely what faces the electorate each time there are more than two candidates running for a single office. And while there is debate over which voting method should be used, there is wide agreement over the method that should not be used: plurality, the most common approach taken in the United States. This article presents a simple classroom activity which provides students the opportunity to …

A Cognitive View Of "Pandemic Meditation" (A Mathematical Visual Poem), Kazmier Maslanka

Journal of Humanistic Mathematics

Mathematical visual poetry is a poetic genre whereby metaphorical expressions are created using mathematical structures. Within the structure, the poetics are understood by the cross-mapping of numerous conceptual domains including visual, lexical, and mathematical. Here I focus on one particular mathematical visual poetic structure: what I call a Similar Triangles Poem or Proportional Poem. To illustrate the ideas discussed, I present "Pandemic Meditations," a mathematical visual poem; in particular I discuss how this mathematical poem uses the mechanisms of poetic metaphor in the context of the embodied mind. The intent of this paper is not to explain "Pandemic Meditation," …

Twisting The Cube: Art-Inspired Mathematical Explorations, Lingguo Bu

Journal of Humanistic Mathematics

A cube can be twisted in a playful manner for visual and algebraic insights. The twisting process and the resulting ruled surfaces can be demonstrated using 3D modeling tools (e.g., GeoGebra® and Autodesk Fusion 360®) or elastic cords on a 3D-printable scaffold. The twisted cube is aesthetically appealing, posing interesting questions that are worthwhile at multiple levels. Algebraically, the volume of the twisted cube is shown to be two-thirds of the reference cube. The twisted faces are parts of hyperbolic paraboloids, whose implicit and parametric equations can be established from diverse perspectives in support of further dynamic explorations and discussions …

Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala

Journal of Humanistic Mathematics

In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll's famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley's thesis and expound upon Carroll's artful use of symbolism to attack excessive use of symbolism in mathematics.

The Nature Of Numbers: Real Computing, Bradley J. Lucier

Journal of Humanistic Mathematics

While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both …

Accidental World Teacher, Richard Delaware

Journal of Humanistic Mathematics

When the College Algebra and Calculus I video courses I created were posted on my university’s YouTube channel in 2009, I suddenly began to receive dozens of heartfelt emails from students around the world thanking me. Here I tell the story of the creation of those videos and sample the effect they seem to have had over the last decade, as I accidentally became a teacher available to the entire planet.

The Problem Of Words: Learning To Teach Mathematics When Numbers And Languages Mix, Gladys Krause

Journal of Humanistic Mathematics

In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.