Bi-fonctions moment.

An Alternating Moment Condition for Bi-freeness

In this note we demonstrate an equivalent condition for bi-freeness, inspired by the well-known “vanishing of alternating centred moments” condition from free probability. We show that all products satisfying a centred condition on maximal monochromatic χ-intervals have vanishing moments if and only if the family of pairs of faces they come from is bi-free. In addition, we construct a bi-free u...

Fonctions Thêta

Bi-substitution-induced magnetic moment distribution in spinel Bi(x)Co(2-x)MnO(4) multiferroic.

We report the near-edge x-ray absorption spectroscopy (NEXAFS) at the Co/Mn L(3,2) edge and oxygen K edge of the well-characterized Bi-substituted Co(2)MnO(4) multiferroic samples. The evolution of peak features in NEXAFS spectra of the Co/Mn L(3,2) edge and O K edge show the Bi-induced redistribution of magnetic cations (Co/Mn). The variation in valence states of Co and Mn in all the substitut...

Fonctions génératrices et applications

On utilisera principalement cette fonction génératrice comme une fonction définie sur [0, 1]. gX est C∞ sur ]− 1, 1[ on a gX(0) = P(X = 0), gX(1) = 1,P(X = n) = g X (0)/n!. Proposition 1. Soient X et Y de variables aléatoires indépendantes, de fonctions génératrices respectives gX et gY . Alors la fonction génératrice de X + Y est gX+Y = gXgY . Démonstration. Pour tout s, gX+Y (s) = E[sX+Y ] = ...

Fonctions zêta des hauteurs

The paper surveys recent progress towards the Height zeta functions related to the Manin’s conjecture. In particular, it details some cases where one can prove meromorphic continuation of these functions.