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Euler In Wartime: Publishing In The Seven Years' War, Erik R. Tou 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, Cynthia J. Huffman Ph.D. 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, Larry G. Blaine, Susan Ferré 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, Sylvio R. Bistafa 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, Sylvio R. Bistafa 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'', Christopher Goff, Michael Saclolo 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, Daniel J. Curtin 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, Daniel J. Curtin 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, Erik R. Tou, Christopher Goff, Michele Gibney 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, Christopher Goff, Erik Tou 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, Zhihong Zhao, Yan Li, Zhaosheng Feng 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, Nikos Mylonas, Basil K. Papadopoulos 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, Brennan Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Adil Al-Rubaye, Jesse Wheeler, Scout Jarman, Miranda Rogers 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 ...


Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes, Miquel Cueca, Rajan Amit Mehta 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, Christopher James Natoli 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 ...


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 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 ...


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


Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey 2021 Fitchburg State University

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 2021 Ariana Investment Management

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 2021 St. John Fisher College

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 influenced ...


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