The Integer-Antimagic Spectra Of Graphs With A Chord, 2021 San Jose State University

#### The Integer-Antimagic Spectra Of Graphs With A Chord, Richard M. Low, Dan Roberts, Jinze Zheng

*Theory and Applications of Graphs*

Let $A$ be a nontrival abelian group. A connected simple graph $G = (V, E)$ is $A$-antimagic if there exists an edge labeling $f: E(G) \to A \setminus \{0\}$ such that the induced vertex labeling $f^+: V(G) \to A$, defined by $f^+(v) = \sum_{uv\in E(G)}f(uv)$, is injective. The integer-antimagic spectrum of a graph $G$ is the set IAM$(G) = \{k\;|\; G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic}$ $\textnormal{and } k \geq 2\}$. In this paper, we determine the integer-antimagic spectra for cycles with a chord, paths with a chord, and wheels with ...

Modeling The Effect Of Lockdown Timing As A Covid‑19 Control Measure In Countries With Differing Social Contacts, 2021 The University of Texas Rio Grande Valley

#### Modeling The Effect Of Lockdown Timing As A Covid‑19 Control Measure In Countries With Differing Social Contacts, Tamer Oraby, Michael G. Tyshenko, Jose Campo Maldonado, Kristina Vatcheva, Susie Elsaadany, Walid Q. Alali, Joseph C. Longenecker, Mustafa Al‑Zoughool

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

The application, timing, and duration of lockdown strategies during a pandemic remain poorly quantified with regards to expected public health outcomes. Previous projection models have reached conflicting conclusions about the effect of complete lockdowns on COVID-19 outcomes. We developed a stochastic continuous-time Markov chain (CTMC) model with eight states including the environment (SEAMHQRD-V), and derived a formula for the basic reproduction number, R0, for that model. Applying the R 0 formula as a function in previously-published social contact matrices from 152 countries, we produced the distribution and four categories of possible R 0 for the 152 countries and chose one ...

Noncentral Limit Theorem For Large Wishart Matrices With Hermite Entries, 2021 CNRS, Université de Lille, Laboratoire Paul Painlevé UMR 8524, F-59655 Villeneuve d’Ascq, France

#### Noncentral Limit Theorem For Large Wishart Matrices With Hermite Entries, Charles-Philippe Diez, Ciprian A. Tudor

*Journal of Stochastic Analysis*

No abstract provided.

Euler In Wartime: Publishing In The Seven Years' War, 2021 University of Washington, Tacoma

#### Euler In Wartime: Publishing In The Seven Years' War, Erik R. Tou

*Euleriana*

At the outbreak of the Seven Years' War in 1756, Leonhard Euler (1707-1783) was a successful and prolific scholar at the Berlin Academy of Sciences, well on his way to producing many significant contributions to 18th century science and mathematics. However, once the war began his opportunities were sharply curtailed. Most of the war did not go well for Prussia, and Euler's place in the midst of this conflict limited his ability to publish his work. With the Euler Archive available online, Gustaf Eneström's index may be analyzed more deeply to uncover the effects of the conflict on ...

Euler Archive Spotlight, 2021 Pittsburg State University

#### Euler Archive Spotlight, Cynthia J. Huffman Ph.D.

*Euleriana*

A spotlight on the Euler Archive, including recent translations.

Euler’S Theories Of Musical Tuning With An English Translation Of Du Véritable Caractère De La Musique Moderne, 2021 Plymouth State University

#### Euler’S Theories Of Musical Tuning With An English Translation Of Du Véritable Caractère De La Musique Moderne, Larry G. Blaine, Susan Ferré

*Euleriana*

*Du Véritable Caractère de la Musique Moderne *(E315), a work almost unknown to musical scholars, is an extremely interesting document in the history of *tuning systems*. A tuning system is simply an arrangement of sound frequencies for use in music. A *just tuning* is an arrangement in which the ratios of these frequencies are all ratios of whole numbers- preferably small ones. Classically, these ratios involve only factors of 2, 3, and 5. In particular, a very fundamental chord in music of many genres, the so-called *major triad*, Has frequency ratios 4:5:6. Euler proposes introducing the prime 7 ...

Principles For Determining The Motion Of Blood Through Arteries, 2021 University of Sao Paulo

#### Principles For Determining The Motion Of Blood Through Arteries, Sylvio R. Bistafa

*Euleriana*

Translation of* Principia pro motu sanguinis per arterias determinando *(E855). This work of 1775 by L. Euler is considered to be the first mathematical treatment of circulatory physiology and hemodynamics.

Euler, Father Of Haemodynamics, 2021 University of Sao Paulo

#### Euler, Father Of Haemodynamics, Sylvio R. Bistafa

*Euleriana*

This article is being published in conjunction with the translation and synopsis of E855. *Principia pro motu sanguinis per arterias determinando* of 1775 - view the translation and synopsis by clicking here.

A History And Translation Of Lagrange's "Sur Quelques Problèmes De L'Analyse De Diophante'', 2021 University of the Pacific

#### A History And Translation Of Lagrange's "Sur Quelques Problèmes De L'Analyse De Diophante'', Christopher Goff, Michael Saclolo

*Euleriana*

Among Lagrange's many achievements in number theory is a solution to the problem posed and solved by Fermat of finding a right triangle whose legs sum to a perfect square and whose hypotenuse is also a square. This article chronicles various appearances of the problem, including multiple solutions by Euler, all of which inadequately address completeness and minimality of solutions. Finally, we summarize and translate Lagrange's paper in which he solves the problem completely, thus successfully proving the minimality of Fermat's original solution.

On The Surface Area Of Scalene Cones And Other Conical Bodies, 2021 Northern Kentucky University

#### On The Surface Area Of Scalene Cones And Other Conical Bodies, Daniel J. Curtin

*Euleriana*

This paper first appeared in the *Novi Commentarii academiae scientiarum Petropolitanae* vol. 1, 1750, pp. 3-19 and is reprinted in the *Opera Omnia*: Series 1, Volume 27, pp. 181–199. Its Eneström number is E133. This translation and the Latin original are available from the Euler Archive.

The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, 2021 Northern Kentucky University

#### The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin

*Euleriana*

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon's in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz's solution, which he corrected, after extending Varignon's solution in the case of circular base. Euler then used Leibniz ...

Collecting Works: A History Of The Euler Archive, 2021 University of Washington – Tacoma

#### 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, 2021 University of the Pacific

#### 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, 2021 The University of Texas Rio Grande Valley

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

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

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 ...

Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, 2021 Democritus University of Thrace, Kimeria, Xanthi, 67100, Greece

#### 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.

The 2020 National Snow Load Study, 2021 Utah State University

#### The 2020 National Snow Load Study, Brennan Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Adil 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 ...

Global-In-Time Solvability And Blow-Up For A Non-Isospectral Two-Component Cubic Camassa-Holm System In A Critical Besov Space, 2021 The University of Texas Rio Grande Valley

#### 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

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

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 ...

Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes, 2021 Georg-August-Universität Göttingen

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

*Mathematics and Statistics: 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.

Some Model Theory Of Free Groups, 2021 The Graduate Center, City University of New York

#### 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, 2021 Claremont McKenna College

#### 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.