Wavelets techniques for pointwise anti-Holderian irregularity

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one

Discrimination of five Tunisian cultivars by Mid Infra Red spectroscopy combined with chemometric analyses of olive Olea europaea leaves

The high biodiversity of olive tree and the economic needs require tools for the correct classification and identification of the different cultivars. Simple and rapid methods are in increasing demand. In the present work, FT-MIR spectroscopy associated to chemometric treatment is proposed as a direct and rapid tool to discriminate cultivars according to their olive leaves, a persistent tissue the whole year. A set of 75 samples of olive leaves representative of five Tunisian cultivars (Chemlali, Sayali, Meski, Zarrazi and Chetoui) cultivated in the same geographical area was analysed. Discrimination between the five Tunisian cultivars was performed by the chemometric approach, principal component analysis (PCA), based on the FT-MIR spectral data provided by olive leaves. Furthermore, a correct classification (100%) of the five Tunisian cultivars was obtained by the Partial Least Square Discriminate Analysis (PLS-DA) method