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.     

Homogeneity and Canonical Connections of Isoparametric Manifolds

On every isoparametric submanifold M a connection with parallel second fundamental form is constructed geometrically such that M is an orbit of an s-representation if and only if the connection is a canonical one. If the rank of M is greater than one this connection is in case of homogeneity the canonical connection of the reductive decomposition given by the orbit of s-representation. This revised version was published online in June 2006 with corrections to the Cover Date.     

MgF(3)(-) as a transition state analog of phosphoryl transfer

The formation of complexes between small G proteins and certain of their effectors can be facilitated by aluminum fluorides. Solution studies suggest that magnesium may be able to replace aluminum in such complexes. We have determined the crystal structure of RhoA.GDP bound to RhoGAP in the presence of Mg(2+) and F(-) but without Al(3+). The metallofluoride adopts a trigonal planar arrangement instead of the square planar structure of AlF(4)(-). We have confirmed that these crystals contain magnesium and not aluminum by proton-induced X-ray emission spectroscopy. The structure adopted by GDP.MgF(-) possesses the stereochemistry and approximate charge expected for the transition state. We suggest that MgF3(-) may be the reagent of choice for studying phosphoryl transfer reactions.     

Laccase-catalyzed carbon-carbon bond formation: oxidative dimerization of salicylic esters by air in aqueous solution

The laccase catalyzed oxidative dimerization of salicylic esters, a rare example of a laccase-catalyzed carbon-carbon bond formation, was studied. This reaction allows the use of air as stoichiometric oxidant and proceeds in aqueous solution. The preparative scope and the mechanism of the method, which provides a new and convenient access to functionalized biaryls under mild conditions, were investigated.     

Definitive Proof for the Operation of Isotopically Sensitive Branching (‘Metabolic Switching’) in FeI-Mediated C?H Bond Activation in the Gas Phase Short Communication

Rigorous regio- and stereospecific labeling experiments are performed to demonstrate the operation of the previously suggested operation of ‘isotopically sensitive branching’ in Fe^I-mediated C? H bond activation. For the hexane-1,6-diol/Fe⁺-complex, it is shown that dehydrogenation involves specifically the central C(3)/C(4) position, and the study of the stereospecifically labeled D ,L - and meso-[3,4-D₂]-isotompomers 1e and 1f demonstrates that dehydrogenation proceedes via two competing pathways (i.e. ‘anti’- vs. ‘syn’-route). The contribution of these routes to the product formation is – due to a kinetic isotope effect – controlled by the relative configuration at the labeled positions C(3)/C(4). For the D ,L -form 1e , we estimate a ratio of 49:1 in favor of the ‘anti’-route; due to an isotope effect, this ratio drops to 4.3:1 for the meso-form 1f .     

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.     

Gas Phase Catalysis by Metal Nanoparticles in Nanoporous Alumina Membranes

Nanoporous alumina membranes, loaded with palladium and ruthenium nanoparticles of various size, were used for gas phase hydrogenation of 1, 3‐butadiene and for oxidation of carbon monoxide, respectively. Those membranes contain 10⁹ ‐ 10¹¹ pores per cm², all running perpendicular to the surface. Membrane discs of 20 mm in diameter and only 60 μm thick, incorporated in a reactor in which the reactants can be pumped in a closed circuit through the pores, turned out to very actively catalyze hydrogenation of butadiene (Pd) and oxidation of CO (Ru). The activity of the Pd catalysts depends characteristically on the particles size, the gas flow, and of the educts ratio. As could be expected, larger particles are less active than smaller ones, whereas increasing gas flows in case of hydrogenation accelerates the reactions. Excessive hydrogen reduces selectivity with respect to the various butenes, but favours formation of butane.     

Synthesis of Chiral Cyclohexenones from α-Campholenic,Fencholenic, and β-Campholenic Derivatives

Summary. Optically active dimethylcyclohexenones, potential building blocks for enantioselective syntheses of various naturally active substances, were prepared. These compounds were obtained by oxidation with KMnO₄/Pb(OAc)₄ or ozonolysis of the corresponding cyclopentenic precursors, followed by aldol condensation. During the course of the preparation intermediate diols and chiral polyfunctional carbonyl derivatives were separated and identified analytically.     

Dynamic alterations of fibronectin layers on copolymer substrates with graded physicochemical characteristics

Desorption and exchange of preadsorbed fibronectin layers in pure buffer solution and solutions of human serum albumin or fibronectin, respectively, were studied in dependence on the physicochemical characteristics of maleic acid copolymer films used as substrates. Although the preadsorbed amount of fibronectin differed only slightly, the protein was found to exhibit a significantly enhanced anchorage at the more hydrophobic polymer surface as compared to the more hydrophilic and more negatively charged polymer surface. The preadsorbed fibronectin layer was most efficiently exchanged by fibronectin (i.e., in the homodisplacement process) while pure buffer solution and human serum albumin solutions induced desorption or exchange of fibronectin to lower and similar degrees. An increase of the total adsorbed amount of protein due to additional adsorption of fibronectin or human serum albumin accompanied the partial exchange of the preadsorbed fibronectin in the displacement experiments. Evaluation of the kinetics of desorption and exchange of fibronectin at any of the substrates revealed two kinds of surface-attached protein populations--a fast desorbing species and a species with a slow desorption and exchange rate. By a multivariate regression analysis the surface characteristics of the polymer substrate were confirmed to determine the degree of protein desorption and exchange while the dynamics of the layer alteration was found to solely depend on the diffusion behavior of the proteins.     

Evaluation of molten inorganic salt hydrates as reaction medium for the derivatization of cellulose

Molten inorganic salt hydrates are highly efficient solvents forcellulose. The carboxymethylation of the polymer dissolved in this new group ofcellulose solvents was investigated. The homogeneous carboxymethylation ofcellulose in molten LiClO₄3H₂O using sodiummonochloroacetate in the presence of NaOH is possible. The formation of CMC wasconfirmed by FT- Raman spectroscopy. Structure analysis by means of HPLC afterchain degradation showed the formation of CMC with a DS of 2 after a shortreaction time of 4 h. The derivatives exhibit a statisticaldistribution of substituents along the polymer chain if prepared in moltenLiClO₄3H₂O as solvent. A substituent distributioninthe order C-6 > C-2 C-3 for anhydroglucose units (AGU) was concludedfrom ¹H-NMR measurements. The synthesis of CMC in the swellingmediumLiClxH₂O (2 x 5) yields polymers with astatistical distribution of functional groups along the chain. The watercontentof the salt melts has a dramatic influence on the DS_CMC.