We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, th...

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a strong law for L2-mixingales that seems to have gone unnoticed in the econometrics literature, and also a new strong law for Lp-mixingales. These results greatly relax the dependence and heterogeneity conditions relative to the results that are cur...

This paper concerns the third-orderm-point boundary-value problem u′′′(t) + f(t, u(t), u′(t), u′′(t)) = 0, a.e. t ∈ (0, 1), u(0) = u′(0) = 0, u′′(1) = m−2 X i=1 kiu (ξi), where f : [0, 1] × R3 → R is Lp-Carathéodory, 1 ≤ p < +∞, 0 = ξ0 < ξ1 < · · · < ξm−2 < ξm−1 = 1, ki ∈ R (i = 1, 2, . . . ,m− 2) and Pm−2 i=1 ki 6= 1. Some criteria for the existence of at least one solution are established by ...

Here we report the synthesis, pharmacological and pharmacokinetic evaluation of a pilot set of compounds structurally related to the potent and selective 5-HT7 ligand LP-211. Among the studied compounds, N-pyridin-3-ylmethyl-3-[4-[2-(4-methoxyphenyl)phenyl]piperazin-1-yl]ethoxy]propanamide (4b) showed high affinity for 5-HT7 receptors (K(i)=23.8 nM), selectivity over 5-HT1A receptors (>50-fold)...

We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. ...

We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. ...