Mathematics Commons^™

Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney

Euleriana

We give a brief history of the Euler Archive, an online database of the published works of Leonhard Euler (1707-1783). Furthermore, we describe the Archive's recent move to an academic repository, and the added functionality such a move allows.

A New Look At Euler And His Contemporaries, Christopher Goff, Erik Tou

Euleriana

Introducing Euleriana: Volume 1, Issue 1.

Traveling Wave Phenomena In A Nonlocal Dispersal Predator-Prey System With The Beddington-Deangelis Functional Response And Harvesting, Zhihong Zhao, Yan Li, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder's fixed point theorem, we show that there exists a positive constant c∗ such that the system possesses a traveling wave solution for any given c>c∗. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for c=c∗ is established by means of Corduneanu's theorem. The nonexistence of traveling wave …

Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, Nikos Mylonas, Basil K. Papadopoulos

Journal of Stochastic Analysis

No abstract provided.

Why Romans Sometimes Wrote 8 As Viii, And Sometimes As Iix: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most of us are familiar with Roman numerals and with the standard way of describing numbers in the form of these numerals. What many people do not realize is that the actual ancient Romans often deviated from these rules. For example, instead of always writing the number 8 as VIII, i.e., 5 + 3, they sometimes wrote it as IIX, i.e., as 10 − 2. Some of such differences can be explained: e.g., the unusual way of writing 98 as IIC, i.e., as 100 − 2, can be explained by the fact that the Latin word for 98 literally means …

Calculating The Virtual Cohomological Dimension Of The Automorphism Group Of A Raag, Matthew B. Day, Andrew W. Sale, Richard D. Wade

Mathematical Sciences Faculty Publications and Presentations

We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right-angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis-conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe–Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups.

What Is The Logic Behind Cistercian Numbers?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the 13-15 centuries, many European monasteries used an unusual number system developed originally by the Cistercian monks; later on, this system was used by winemakers. In this paper, we provide a possible explanation of why these particular symbols were used.

Graph Theoretic Aspects Of Minimum Distance And Equivalence Of Binary Linear Codes, Sudipta Mallik, Bahattin Yildiz

Mathematics Faculty Research

A binary linear [2n, n]-code with generator matrix [I_n|A] can be associated with a digraph on n vertices with adjacency matrix A and vice versa. We use this connection to present a graph theoretic formula for the minimum distance of codes with information rate 1/2. We also formulate the equivalence of such codes via new transformations on corresponding digraphs.

On The Burr Xii-Moment Exponential Distribution, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Menhui Sheng, Azeem Ali

Mathematical and Statistical Science Faculty Research and Publications

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue …

Predicting Circadian Misalignment With Wearable Technology: Validation Of Wrist-Worn Actigraphy And Photometry In Night Shift Workers, Philip Cheng, Olivia Walch, Yitong Huang, Caleb Mayer, Chaewon Sagong, Andrea Cuamatzi Castelan, Helen J. Burgess, Thomas Roth, Daniel B. Forger, Christopher L. Drake

Mathematics Sciences: Faculty Publications

Study Objectives: A critical barrier to successful treatment of circadian misalignment in shift workers is determining circadian phase in a clinical or field setting. Light and movement data collected passively from wrist actigraphy can generate predictions of circadian phase via mathematical models; however, these models have largely been tested in non-shift working adults. This study tested the feasibility and accuracy of actigraphy in predicting dim light melatonin onset (DLMO) in fixed night shift workers. Methods: A sample of 45 night shift workers wore wrist actigraphs before completing DLMO in the laboratory (17.0 days ± 10.3 SD). DLMO was assessed via …

Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes, Miquel Cueca, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan formula for the de Rham differential. This perspective allows us to develop the theory of Courant algebroid connections in a way that mirrors the classical theory of connections. Using a special class of connections, we construct secondary characteristic classes associated to any Courant algebroid.

Conformal Equivalence Of Visual Metrics In Pseudoconvex Domains, Luca Capogna, Enrico Le Donne

Mathematics Sciences: Faculty Publications

We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains in Cn are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between bounded smooth pseudoconvex domains. The proofs are inspired by Mostow’s proof of his rigidity theorem and are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the Bonk-Schramm hyperbolic fillings.

The 2020 National Snow Load Study, Brennan L. Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Al-Rubaye, Jesse Wheeler, Scout Jarman, Miranda Rogers

Mathematics and Statistics Faculty Publications

The United States has a rich history of snow load studies at the state and national level. The current ASCE 7 snow loads are based on studies performed at the Cold Regions Research and Engineering Laboratory (CRREL) ca. 1980 and updated ca. 1993. The map includes large regions where a site-specific case study is required to establish the load. Many state reports attempt to address the "case-study regions" designated in the current ASCE 7 design snow load requirements. The independently developed state-specific requirements vary in approach, which can lead to discrepancies in requirements at state boundaries. In addition, there has …

Ovals And Niho Bent Functions In Small Dimensions, Rasha M. E. Issa Shat

Theses

In this thesis hyperovals and ovals are considered in the projective plane PG(2,q), q = 2^m even. Traditionally these objects are studied algebraically via o-polynomials. In our work, a different approach is used by means of g-functions. These functions also provide a natural description of Niho bent functions. Using g-functions, all ovals and Niho bent functions are listed up to equivalency for dimensions m ≤ 6.

Symbolic Rees Algebras, Eloísa Grifo, Alexandra Seceleanu

Department of Mathematics: Faculty Publications

We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.

Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …

Global-In-Time Solvability And Blow-Up For A Non-Isospectral Two-Component Cubic Camassa-Holm System In A Critical Besov Space, Lei Zhang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we prove the global Hadamard well-posedness of strong solutions to a non-isospectral two-component cubic Camassa-Holm system in the critical Besov space B2,11/2(T). Our results show that in comparison with the well-known work for classic Camassa-Holm-type equations, the existence of global solution only relies on the L1-integrability of the variable coefficients α(t) and γ(t), but nothing to do with the shape of the initial data. The key ingredient of the proof hinges on the careful analysis of the mutual effect among two component forms, the uniform bound of approximate solutions, and several crucial estimates of cubic nonlinearities in …

Some Model Theory Of Free Groups, Christopher James Natoli

Dissertations, Theses, and Capstone Projects

There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form A-Fraisse classes and that the class of non-abelian limit groups fails to form a strong A-Fraisse class.

The second main result is that if a countable group is elementarily …

Math In The Time Of Covid: An Open Call For Contributions, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics invites submissions of essays, reflections, poetry, and artwork for an upcoming thematic folder tentatively titled Math in the Time of COVID and scheduled to appear in July 2021. Please send your submissions via email to the editors by May 1, 2021. Publication decisions will be made by June 15, 2021.

Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Ethics in Mathematics. Please send your abstract submissions via email to the guest editors by September 1, 2021. Initial submission of complete manuscripts is due December 1, 2021. The issue is currently scheduled to appear in July 2022.

Once Upon A Party - An Anecdotal Investigation, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians and Physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imitates their craft, and we must simply observe the deep truths hiding in their party-going behavior...

Deterministic Republic, Kris H. Green

Journal of Humanistic Mathematics

This story is an extension of the paper "Mathematics and Voter Choice" published in this same issue of the Journal of Humanistic Mathematics. It explores what elections and politics might look like from the voter perspective if some of the ideas from the paper were implemented. The story is also an attempt to highlight how mathematics and data science are done, much the way a colleague of mine refers to shows like CSI as recruiting tools that use "dramatic pipetting" in the labs to show day-to-day science in action. The story is, as you will no doubt see, heavily …

Iterations Of Emptying, Marian Christie

Journal of Humanistic Mathematics

Successive iterations of the Sierpinski carpet fractal are used to explore how we---our history, experiences, thoughts and memories---occupy spaces that we once inhabited.

Turing's Machine, Mike Curtis

Journal of Humanistic Mathematics

The musings of a Turing Machine.

One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef

Journal of Humanistic Mathematics

No abstract provided.

Proof Theory, Stan Raatz

Journal of Humanistic Mathematics

No abstract provided.

Early Morning Mathematics Classes, Angelina Schenck

Journal of Humanistic Mathematics

No abstract provided.

Permission To Add: Math-Teaching Limericks, Marion D. Cohen

Journal of Humanistic Mathematics

Throughout my years and decades of being a teacher, I have written limericks about every course I’ve taught, and sometimes courses I haven’t taught but reviewed textbooks in. Here I share several of these limericks.

Peter Hilton En Passant, Richard Delaware

Journal of Humanistic Mathematics

This is a decades-long tale of my glancing friendship with distinguished mathematician and mathematics educator Peter Hilton and his constant collaborator Jean Pedersen. Peter’s wit, compassion, and support are in full display, though in truth I knew him only “in passing.”

The Number, Arati Nanda Pati

Journal of Humanistic Mathematics

This is a story from the heart on COVID-19, penned around April 4, 2020, in the early days of the pandemic.