La surjectivité de l'application moyenne pour les espaces préhomogènes

Let ? be an homogeneous polynomial on $\text{R}$ⁿ. First an analog of the Borel theorem is proved for the distributions which appear at the poles of the distribution |?|^s (s ∈ $\text{C}$). If ? is the relative invariant of an irreducible regular prehomogeneous vector space, the preceding result is used to characterize the functions which are obtained by integration on the fibers of ?.     

Electrochemical Study of Phase-Transfer Catalysis Reactions: The Williamson ether synthesis

The transfer properties of the ionic species involved in the Williamson ether synthesis by phase-transfer catalysis were investigated using electrochemical techniques developed for the study of polarised liquid/liquid interfaces. This approach allows the measurement of the apparent partition coefficients of the transferring species. From these data, it is proposed that the role of the phase-transfer catalyst salt in the reaction mechanism is to establish a Galvani distribution potential difference between the two phases which in turn acts as the driving force for transferring the reactive aqueous ions to the organic phase.     

The Catline for Deep Regression

Motivated by the notion of regression depth (Rousseeuw and Hubert, 1996) we introduce thecatline, a new method for simple linear regression. At any bivariate data setZ_n={(x_i, y_i);i=1, …, n} its regression depth is at leastn/3. This lower bound is attained for data lying on a convex or concave curve, whereas for perfectly linear data the catline attains a depth ofn. We construct anO(n log n) algorithm for the catline, so it can be computed fast in practice. The catline is Fisher-consistent at any linear modely=βx+α+ein which the error distribution satisfies med(e | x)=0, which encompasses skewed and/or heteroscedastic errors. The breakdown value of the catline is 1/3, and its influence function is bounded. At the bivariate gaussian distribution its asymptotic relative efficiency compared to theL¹line is 79.3% for the slope, and 88.9% for the intercept. The finite-sample relative efficiencies are in close agreement with these values. This combination of properties makes the catline an attractive fitting method.     

Nonprobabilistic entropies and indetermination measures in the setting of fuzzy sets theory

Our purpose in this paper is first of all to build an axiomatic generalization for the nonprobabilistic entropy of De Luca and Termini in the setting of fuzzy sets theory.We then build from this entropy an indetermination measure which can be used like discriminant function in Pattern Recognition when patterns are described by means of fuzzy sets.