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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...

Wavelet analysis of the multivariate fractional brownian motion

Jean-François Coeurjolly, Pierre-Olivier Amblard, Sophie Achard (2013)

ESAIM: Probability and Statistics

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behaviour of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral...

Weak difference property of functions with the Baire property

Tamás Mátrai (2003)

Fundamenta Mathematicae

We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h) - f(x) has the Baire property for every h ∈ ℝ can be written in the form f = g + H + ϕ where g has the Baire property, H is additive, and for every h ∈ ℝ we have ϕ(x+h) - ϕ (x) ≠ 0 only on a meager set. We also discuss the weak difference property of some subclasses of the class of functions with the Baire property, and the consistency of the difference...

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.

Weakly Increasing Zero-Diminishing Sequences

Bakan, Andrew, Craven, Thomas, Csordas, George, Golub, Anatoly (1996)

Serdica Mathematical Journal

The following problem, suggested by Laguerre’s Theorem (1884), remains open: Characterize all real sequences {μk} k=0...∞ which have the zero-diminishing property; that is, if k=0...n, p(x) = ∑(ak x^k) is any P real polynomial, then k=0...n, p(x) = ∑(μk ak x^k) has no more real zeros than p(x). In this paper this problem is solved under the additional assumption of a weak growth condition on the sequence {μk} k=0...∞, namely lim n→∞ | μn |^(1/n) < ∞. More precisely, it is established that...

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.

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