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Register a new userEuler Analysis of a Machine for Raising Waters Proposed by Mr. de Mour
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Sylvio R. Bistafa
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We revisited an analysis made by Euler in a memoir of 1753 Sur une nouvelle maniere delever de leau propose par M. de Mour (On a new method to raise water proposed by Mr. de Mour), addressing a type of water sprinkler, consisting of an inclined tube with its lower end immersed into water, and discharging water at its top by turning a vertical axis to which the inclined tube is attached.
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This is an English translation of E579 in which the introductory remarks are in French, while Eulers original text is in Latin. By considering the balance of forces acting on a raising balloon on an isothermal atmosphere, namely the weight of the balloon, the buoyant force, and the aerodynamic drag force, Euler provides closed formulas for the calculation of the maximum altitude reached by the balloon, the altitude for which the velocity is maximum, the maximum velocity attained by the balloon, and the total ascending time.
Blue Waters is a Petascale-level supercomputer whose mission is to enable the national scientific and research community to solve grand challenge problems that are orders of magnitude more complex than can be carried out on other high performance computing systems. Given the important and unique role that Blue Waters plays in the U.S. research portfolio, it is important to have a detailed understanding of its workload in order to guide performance optimization both at the software and system configuration level as well as inform architectural balance tradeoffs. Furthermore, understanding the computing requirements of the Blue Waters workload (memory access, IO, communication, etc.), which is comprised of some of the most computationally demanding scientific problems, will help drive changes in future computing architectures, especially at the leading edge. With this objective in mind, the project team carried out a detailed workload analysis of Blue Waters.
A modification to the gnomonic factor using the concept of triangle of Plato is presented. With the aid of the platonic gnomonic factor (fgp) as we called it, we find that the oracles mentioned by Herodotus in his History, Dodona in Greece and Ammon in Oasis Siwa, Libya, were placed there because the noon shadow of Sun of a gnomon formed, back in 2500BC, the triangle of Plato the former, and the Egyptian sacred triangle the latter. This means that both concepts were known by Egyptians form Thebes long before they were formalized by the Greeks. The right angled triangle concept is an idealization, as said by D. Magdolen, of an astronomical observation; i. e. it is the shadow cast by a gnomon. ----- Se presenta una modificacion al factor gnomonico usando el concepto de triangulo de Platon. Con la ayuda de lo que llamamos factor gnomonico platonico (fgp) nosotros encontramos que los oraculos mencionados por Herodoto en su Historia, Dodona en Grecia, y Ammon en el Oasis Siwa, Libia, fueron ubicados ahi porque, hacia el anio 2500AC, la sombra proyectada por un gnomon vertical formo el triangulo de Platon en el primero y el triangulo sagrado Egipcio el ultimo. Esto significa que ambos conceptos eran conocidos por los Egipcios de Tebas, a decir de Herodoto, bastante antes de estos fueran formalizados por los griegos. El concepto de triangulo rectangulo seria la idealizacion, como dice D. Magdolen, de una observacion astronomica; esto es, la proyeccion de la sombra por un gnomon.
In 1998 a long-lost proposal for an election law by Gottlob Frege (1848--1925) was rediscovered in the Thuringer Universitats- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run. We find that through a slight modification of Freges original method even stronger proportionality guarantees can be achieved. This modified version of Freges method also provides a novel solution to the apportionment problem, which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties.
Background: The COVID-19 pandemic has uncovered the potential of digital misinformation in shaping the health of nations. The deluge of unverified information that spreads faster than the epidemic itself is an unprecedented phenomenon that has put millions of lives in danger. Mitigating this Infodemic requires strong health messaging systems that are engaging, vernacular, scalable, effective and continuously learn the new patterns of misinformation. Objective: We created WashKaro, a multi-pronged intervention for mitigating misinformation through conversational AI, machine translation and natural language processing. WashKaro provides the right information matched against WHO guidelines through AI, and delivers it in the right format in local languages. Methods: We theorize (i) an NLP based AI engine that could continuously incorporate user feedback to improve relevance of information, (ii) bite sized audio in the local language to improve penetrance in a country with skewed gender literacy ratios, and (iii) conversational but interactive AI engagement with users towards an increased health awareness in the community. Results: A total of 5026 people who downloaded the app during the study window, among those 1545 were active users. Our study shows that 3.4 times more females engaged with the App in Hindi as compared to males, the relevance of AI-filtered news content doubled within 45 days of continuous machine learning, and the prudence of integrated AI chatbot Satya increased thus proving the usefulness of an mHealth platform to mitigate health misinformation. Conclusion: We conclude that a multi-pronged machine learning application delivering vernacular bite-sized audios and conversational AI is an effective approach to mitigate health misinformation.
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