58 research outputs found
Kiri L Euler`ile, Taurini
http://tartu.ester.ee/record=b1867130~S1*es
On the alleged simplicity of impure proof
Roughly, a proof of a theorem, is âpureâ if it draws only on what is âcloseâ or âintrinsicâ to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is âextrinsic,â âextraneous,â âdistant,â âremote,â âalien,â or âforeignâ to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim
COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study
Background:
The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms.
Methods:
International, prospective observational study of 60â109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms.
Results:
âTypicalâ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (â€â18 years: 69, 48, 23; 85%), older adults (â„â70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each Pâ<â0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country.
Interpretation:
This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men
Mme. Ve. Courcier, imprimeur-libraire pour les mathématiques,
Las publicaciones de actualidad fueron una constante en la Academia de San Carlos. Esta obra, de reciente publicaciĂłn, es ejemplo de ello. Sin embargo, de mayor mĂ©rito para el acervo de la Academia es el tema que el autor aborda. La MĂ©canique analytique es un trabajo en el que el empeño del autor se dirige a reunir la teorĂa con el arte de resolver problemas, ofreciendo fĂłrmulas generales, de las que su simple desarrollo otorgue a todas las ecuaciones la soluciĂłn de cada problema. Una temĂĄtica como tal otorga el bagaje cultural y tĂ©cnico necesario a los estudiantes de la Academia de San Carlos.
IC
Vorlesungen ĂŒber die Functionen-Rechnung : mit Anmerkungen, ErlĂ€uterungen und ZusĂ€tzen
von J. L. Lagrange ; Deutsch herausgegeben von A. L. Crell
Analytische Mechanik
von ... Lagrange ; aus dem Französischen mit einigen Anmerkungen und erlÀuternden ZusÀtzen von Friedrich Wilhelm August Murhar
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