Moyenne arithmétique

Résumé

En mathématiques, la moyenne arithmétique d'une liste de nombres réels est la somme des valeurs divisée par le nombre de valeurs. Il s’agit de la moyenne au sens usuel du terme, sans coefficients, l’adjectif « arithmétique » la distinguant d’autres moyennes mathématiques moins courantes. Expression La moyenne peut être notée à l’aide de son initiale m, M ou avec la lettre grecque correspondante μ. Lorsque la moyenne est calculée sur une liste notée (x, x, ... , x), on la note habituellement à l’aide du diacritique macron, caractère unicode u+0304. Son expression mathématique s’écrit : \overline{x}=\frac{x_1+x_2+\ldots+x_n}n=\frac1n\sum_{i=1}^n{x_i}. Par exemple, le nombre moyen de jours par mois dans une année non bissextile s’écrit 31+28+31+30+31+30+31+31+30+31+30+31/12 soit environ 30,4. La moyenne arithmétique de la liste (x, x, ... , x) peut être vue comme son isobarycentre. Le calcul de moyenne est implanté dans

Source officielle

https://fr.wikipedia.org/wiki/Moyenne_arithm%C3%A9tique

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Computing Cyclic Isogenies between Principally Polarized Abelian Varieties over Finite Fields

Marius Lorenz Vuille

Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While the interest in abelian varieties has long time been of purely theoretic nature, they saw their first real-world application in cryptography in the mid 1980's, and have ever since lead to broad research on the computational and the arithmetic side. The most instructive examples of abelian varieties are elliptic curves and Jacobian varieties of hyperelliptic curves, and they come naturally equipped with some additional structure, called a principal polarization. Morphisms between abelian varieties that respect both the geometric and the arithmetic structure are called isogenies. In this thesis we focus on the computation of isogenies with cyclic kernel between principally polarized abelian varieties over finite fields.

EPFL2020

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Universal Bounds And Semiclassical Estimates For Eigenvalues Of Abstract Schrodinger Operators

Joachim Stubbe

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operators of much more general form. In particular, we allow for the presence of continuous spectrum, which is a necessary underpinning for new proofs of Lieb-Thirring inequalities. We both sharpen and extend universal bounds on spectral gaps and moments of eigenvalues {lambda(k)} of familiar types, and in addition we produce novel kinds of inequalities that are new even in the model cases. These include a family of differential inequalities for generalized Riesz means and a theorem stating that arithmetic means of {lambda(p)(k)}(k=1)(n) with p 8.

2010

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A Continuation Multi Level Monte Carlo (C-MLMC) method for uncertainty quantification in compressible inviscid aerodynamics

Pénélope Leyland, Fabio Nobile, Michele Pisaroni

In this work we apply the Continuation Multi-Level Monte Carlo (C-MLMC) algorithm proposed in Collier et al. (2014) to efficiently propagate operating and geometric uncertainties in inviscid compressible aerodynamics numerical simulations. The key idea of MLMC is that one can draw MC samples simultaneously and independently on several approximations of the problem under investigations on a hierarchy of nested computational grids (levels). The expectation of an output quantity is computed as a sample average using the coarsest solutions and corrected by averages of the differences of the solutions of two consecutive grids in the hierarchy. By this way, most of the computational effort is transported from the finest level (as in a standard Monte Carlo approach) to the coarsest one. The continuation algorithm (C-MLMC) is a robust and self-tuning version that estimates on the fly the optimal number of level and realizations per level. In this work we describe in detail how C-MLMC can be adapted to perform uncertainty quantification analysis in compressible aerodynamics and we apply it to the relevant test cases of a quasi 1D convergent–divergent Laval nozzle and the 2D transonic RAE-2822 airfoil.

Elsevier2017

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