Une Conjecture de Lebesgue

Let A > 0 be an integer. The equation x⁵–y⁵ = Az⁵ wasfirst studied by Dirichlet and Lebesgue. Lebesgue conjecturedin 1843 that if A has no prime divisors of the form 10k+1, theequation has no solutions except the visible ones. Partial resultswere obtained by Lebesgue and by Terjanian in 1987. The purposeof the paper is to prove Lebesgue's conjecture. The main toolused is the method known as the elliptic Chabauty method.     

Numerical predictions and experiments on the free-plate edge mode

In this paper, te edge mode variation is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S(0). Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied.     

On the characterization of disordered and heterogeneous carbonaceous materials by Raman spectroscopy

The applicability of Raman spectroscopy to characterize disordered and heterogeneous carbonaceous materials (CM) is discussed, by considering both natural and synthetic CM. First, different analytical mismatches during the measurement are discussed and technical indications are provided in order to eliminate them. Second, the accuracy and relevance of the different parameters obtained by the decomposition of spectra by conventional fitting procedure, is reviewed. Lastly, a new Raman technique (Raman area mode microspectroscopy) giving an homogeneous repartition of power within a large laser beam is presented, this technique being powerful to study strongly heterogeneous CM and/or photosensitive samples.     

A new paclitaxel prodrug for use in ADEPT strategy

A new paclitaxel prodrug intended for use in Antibody-Directed Prodrug Therapy (ADEPT) or Prodrug Monotherapy (PMT) has been prepared. This prodrug was originally designed to be activated into the drug by human beta-glucuronidase. In order to enhance the liberation rate of paclitaxel, an elongated spacer system including a nitro-aromatic derivative and a N,N'-methylethylenediamine was incorporated between the sugar moiety and the drug. Indeed, this new prodrug proved to be activated significantly faster than a former paclitaxel prodrug containing a conventional spacer.     

On the capacity of sets of divergence associated with the spherical partial integral operator

In this article, we study the pointwise convergence of the spherical partial integral operator when it is applied to functions with a certain amount of smoothness. In particular, for , , , we prove that -quasieverywhere on , where is such that almost everywhere. A weaker version of this result in the range as well as some related localisation principles are also obtained. For and , we construct a function such that diverges everywhere.