Sur les translations biunivoques

Mémoire Sur Les Probabilités∗

I intend to treat in this Memoir two important points in the analysis of chances which do not seem yet to have been sufficiently deeply studied: the first has for object the manner of calculating the probability of events composed of simple events of which one does not know the respective probabilities; the object of the second is the influence of past events on the probability of future events...

Mémoire Sur Les Suites

The theory of series is one of the most important objects of Analysis: all problems which reduce to some approximations, and consequently nearly all the applications of Mathematics to Nature, depend on this theory; thus we see that it has principally fixed the attention of the geometers; they have found a great number of beautiful theorems and ingenious methods, either in order to expand functi...

Résonance paramagnétique sur les phosphores

Marches Aléatoires sur les Groupes

Dans cet article, on va étudier les marches aléatoires sur les graphes et sur les groupes. Enfin, on trouvera une condition nécessaire et suffisante pour la récurrence des marches aléatoires sur les groupes. La condition est très similaire à celle des marches aléatoires sur Zd. La démonstration qu’on donnera est la plus courte. Cependant, on admet le théorème 4.15 de Gromov sur la relation entr...

Oscillations localisées sur les diviseurs

Let f be a real arithmetic function and ∆(n, f) := sup u2R, 06v61 ���� X d|n eu<d6eu+v f(d) ���� denote the corresponding generalization of Hooley’s Delta-function. We investigate weighted moments of ∆(n; f) for oscillating functions f , typical cases being those of a non principal Dirichlet character or of the Möbius function. We obtain, in particular, sharp bounds up to factors (log x)o(1) fo...