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.     

Phenomena Affecting the Equilibrium of Al(III) and Zn(II) Extraction with Winsor II Microemulsions

The extraction of Al(III) and Zn(II) from an aqueous solution with two water-in-oil microemulsions, one containing di(2-ethylhexyl)phosphoric acid (DEHPA), was investigated to aid the understanding of the role of the extractant and the metal specific characteristics in the mechanism of microemulsion extraction. The extraction of Al with the DEHPA microemulsion increased by a factor of about 10 with respect to that in the conventional DEHPA system, whereas the extraction of Zn was lower than that in the single DEHPA system. Extraction with the DEHPA-free microemulsion was very low, showing that metal ion solubilization was not important in the mechanism of microemulsion extraction. It is proposed that the effect of the mixed microemulsion on the metal distribution coefficient is the result of the balance between a decrease in the complexation reaction yield due to the interaction between butanol and DEHPA, and the adsorption of the metal complex at the macro- and microinterfaces. The former leads to a decrease in Zn(II) extraction and the latter to Al(III) extraction synergism. Copyright 2000 Academic Press.     

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.     

Elektrolyse, Polarographie

Ohne Zusammenfassung     

Limit theorems for multipower variation in the presence of jumps

In this paper we provide a systematic study of how the probability limit and central limit theorem for realised multipower variation changes when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale.     

Carbonic acid: from polyamorphism to polymorphism

Layers of glassy methanolic (aqueous) solutions of KHCO3 and HCl were deposited sequentially at 78 K on a CsI window, and their reaction on heating in vacuo in steps from 78 to 230 K was followed by Fourier transform infrared (FTIR) spectroscopy. After removal of solvent and excess HCl, IR spectra revealed formation of two distinct states of amorphous carbonic acid (H2CO3), depending on whether KHCO3 and HCl had been dissolved in methanol or in water, and of their phase transition to either crystalline alpha- or beta-H2CO3. The main spectral features in the IR spectra of alpha- and beta-H2CO3 are observable already in those of the two amorphous H2CO3 forms. This indicates that H-bond connectivity or conformational state in the two crystalline phases is on the whole already developed in the two amorphous forms. The amorphous nature of the precursors to the two crystalline polymorphs is confirmed using powder X-ray diffraction. These diffractograms also show that alpha- and beta-amorphous H2CO3 are two distinct structural states. The variety of structural motifs found within a few kJ/mol in a computational search for possible crystal structures provides a plausible rationalization for (a) the observation of more than one amorphous form and (b) the retention of the motif observed in the amorphous form in the corresponding crystalline form. The polyamorphism inferred for carbonic acid from our FTIR spectroscopic and powder X-ray diffraction studies is special since two different crystalline states are linked to two distinct amorphous states. We surmise that the two amorphous states of H2CO3 are connected by a first-order-like phase transition.