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Wallis entre Hobbes et Newton. La question de l’angle de contact chez les anglais

François Loget (2002)

Revue d'histoire des mathématiques

Cet article traite d’un aspect de la controverse qui a opposé Hobbes et Wallis dans la deuxième moitié du xviie siècle, celui portant sur l’angle de contact. Wallis a publié deux traités sur l’angle de contact, l’un en 1656, l’autre en 1685. Entre ces deux dates sa position sur la question de l’angle de contact a sensiblement évolué. Durant la même période, il s’est opposé à Hobbes sur divers sujets de mathématiques, dont l’angle de contact. J’étudie les positions des deux protagonistes à travers...

Weaker forms of continuity and vector-valued Riemann integration

M. A. Sofi (2012)

Colloquium Mathematicae

It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.

Weierstrass division theorem in quasianalytic local rings

Abdelhafed Elkhadiri, Hassan Sfouli (2008)

Studia Mathematica

The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy-Carleman classes.

Weighted extended mean values

Alfred Witkowski (2004)

Colloquium Mathematicae

The author generalizes Stolarsky's Extended Mean Values to a four-parameter family of means F(r,s;a,b;x,y) = E(r,s;ax,by)/E(r,s;a,b) and investigates their monotonicity properties.

Weighted means and weighting functions

Radko Mesiar, Jana Špirková (2006)

Kybernetika

We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non- decreasing operators, in general.

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