Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.

Découvrez-en plus sur les applications Graph.

Graph
Search

fr|en

Se Connecter

Concept

Rapport (mathématiques)

Résumé

En sciences, un rapport est le quotient de deux valeurs qui se rapportent à des grandeurs de la même espèce. Quand le quotient se rapporte à des grandeurs d'espèces différentes, on parle de taux. Un rapport est une grandeur sans dimension : il ne conserve aucune trace des grandeurs qu'il compare. Usage Un rapport s'exprime souvent en pourcentage. Dans les spécialités les plus en relation avec l'aire anglophone, on emploie souvent le mot d'origine latine , dont la définition est identique. Dans des textes anciens, et dans certains cas particuliers, le rapport (mathématique) s'appelle raison. On parle ainsi de la raison d'une suite définie par récurrence. En physique et en technologie, un , comme l'indice de réfraction est un rapport. En statistique et en économie, un indice est le rapport, généralement multiplié par cent, entre une grandeur et une de ses valeurs prise comme référence. Usage approximatif Il faut constater que la définition rigoureuse n'i

Source officielle

https://fr.wikipedia.org/wiki/Rapport_(math%C3%A9matiques)

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (71)

Chargement

Afficher plus

Publications associées

Chargement

Personnes associées (110)

Personnes associées

Chargement

Unités associées (50)

Unités associées

Chargement

Concepts associés (37)

Concepts associés

Chargement

Cours associés (37)

In systems biology, proteomics represents an essential pillar. The understanding of protein function and regulation provides key information to decipher the complexity of living systems. Proteomic technology now enables deep quantitative proteome mapping via mass spectrometry.

Ce cours traite des 3 sujets suivants : la perspective, la géométrie descriptive, et une initiation à la géométrie projective.

The student will acquire the basis for the analysis of static structures and deformation of simple structural elements. The focus is given to problem-solving skills in the context of engineering design.

Afficher plus

Cours associés

Chargement

Séances de cours associées (73)

Séances de cours associées

Chargement

Publications associées (71)

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

Lars Rohwedder

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. The input consists of a set of jobs, characterized by their processing times, release times, and weights and we want to compute a (possibly preemptive) schedule for them. The objective is to minimize the sum of the weighted flow times of the jobs, where the flow time of a job is the time between its release date and its completion time. It had been a long-standing open problem to find a polynomial time O(1)-approximation algorithm for this setting. In a recent break-through result, Batra, Garg, and Kumar (FOCS 2018) found such an algorithm if the input data are polynomially bounded integers, and Feige, Kulkarni, and Li (SODA 2019) presented a black-box reduction to this setting. The resulting approximation ratio is a (not explicitly stated) constant which is at least 10000. In this paper we improve this ratio to 2 + epsilon. The algorithm by Batra, Garg, and Kumar (FOCS 2018) reduces the problem to DEMAND MULTICUT ON TREES and solves the resulting instances via LP-rounding and a dynamic program. Instead, we first reduce the problem to a (different) geometric problem while losing only a factor 1 + epsilon, and then solve its resulting instances up to a factor of 2 + epsilon by a dynamic program. In particular, our reduction ensures certain structural properties, thanks to which we do not need LP-rounding methods. We believe that our result makes substantial progress towards finding a PTAS for weighted flow time on a single machine.

ASSOC COMPUTING MACHINERY2021

Chargement

Influence of silica fume on the microstructure of cement pastes: New insights from H-1 NMR relaxometry

Arnaud Charles Albert Muller, Karen Scrivener

H-1 NMR has been used to characterise white Portland cement paste incorporating 10 wt.% of silica fume. Samples were measured sealed throughout the hydration without sample drying. Paste compositions and C-S-H characteristics are calculated based on H-1 NMR signal intensities and relaxation analysis. The results are compared with a similar study of plain white cement paste. While the presence of silica fume has little influence on C-S-H densities, the chemical composition is impacted. After 28 days of sealed hydration, the Ca/(Si + Al) ratio of the C-S-H is 1.33 and the H2O/(Si + Al) ratio is 1.10 when 10% of silica fume is added to the white cement. A densification of the C-S-H with time is observed. There are no major changes in capillary, C-S-H gel and interlayer pore sizes for the paste containing silica fume compared to the plain white cement paste. However, the gel/interlayer water ratio increases in the silica fume blend. (C) 2015 Elsevier Ltd. All rights reserved.

Pergamon-Elsevier Science Ltd2015

Chargement

Tight Approximation Algorithms for Scheduling with Fixed Jobs and Nonavailability

Klaus Jansen, Ola Nils Anders Svensson

We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.

Assoc Computing Machinery2012

Chargement

Afficher plus