Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

Application of B–E time-of-flight mass spectrometry to the detection of high-energy neutral atoms following the photoexcitation of Ar

A novel instrument which combines high-resolution double-focusing mass spectrometry with time-of-flight detection was applied to the study of cluster ion photofragmentation. Using this apparatus, kinetic energy measurements were made on neutral photofragments following the excitation of Ar at 532 nm. The results show that one and possibly two argon atoms with high centre of mass kinetic energies emerge from the cluster within a few picoseconds of the photon being absorbed.     

Investigations of a highly crowded phosphino-substituted biphenyl: A precursor for a λ3, λ5-diphosphaphenanthrene

The synthesis of 2,2′-bis(bis(dimethylamino)-phosphino)-3,3′5,5′-tetra-tert-butylbiphennyl ( 5 ) is described. It was extensively studied by ¹H, ¹³C, and ³¹P NMR spectroscopy. Furthermore, the X-ray analysis of 5 is reported. Crystals of 5 are tetragonal, space group P¯42₁c, a = b = 24.770 (3) Å, c = 12.658 (4) Å, Z = 8. The surprising reaction of 5 with proton acids leading to the formation of various phosphorus containing five- and six-membered ring compounds is discussed. On reaction of one of the six-membered ring compounds ( 9 ) with magnesium in THF, a λ³, λ⁵-diphosphaphenanthrene ( 19 ) was obtained.     

New chiral ionic liquids based on imidazolinium salts

The preparation and application of a new series of chiral ionic liquids are described. The salts are based on imidazolinium cations. Some of the cations also incorporated an axial chirality at the C(2) position next to the central chirality. These cations display a very high rotational barrier along the arene–imidazolinium axis. Furthermore, an analogue with a chiral anion was prepared. The salts have low melting points. Their potential as solvents and as chiral shift reagents was explored, resulting for the first time in an example of a chiral ionic liquid as a shift reagent for a neutral compound.