Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.     

On a conjecture of R. E. Miles about the convex hull of random points

Denoty byp _d+i (B _d ,d+m) the probability that the convex hull ofd+m points chosen independently and uniformly from ad-dimensional ballB _d possessesd+i(i=1,...,m) vertices. We prove Mile's conjecture that, given any integerm, p _d+m (B _d ,d+m)»1 asd». This is obvious form=1 and was shown by Kingman form=2 and by Miles form=3. Further, a related result by Miles is generalized, and several consequences are deduced.Dedicated to Professor E. Halwaka on the occasion of his seventieth     

X-ray structure and variable temperature NMR spectra of [meso-triarylcorrolato]copper(III)

The diamagnetic square planar d(8) complexes [meso-arylcorrolato]copper(III) become paramagnetic upon warming, indicative of the equilibrium between the [corrolato]copper(III) and the [corrolato](+)* copper(II) forms of the complex. [meso-Triphenylcorrolato]copper(III) was structurally characterized and found to be saddled.     

Réductions chimique et électrochimique de 5H-benzopyranno[4,3-d]pyrimidines

The chemical reduction of 5H-[1]benzopyranno[4,3-d]pyrimidines with lithium aluminum hydrrde leads to 3,4-dihydro derivations. The electro-chemical reducation in acidic medium shows two monoelectronic cathodic waves. In netural or basic medium, substituted compounds in 2 position show a single bielectronic wave while two bielectronic waves are observed for unsubstituted compounds In all cases, preparative electrolysis lead to a hydrodimer in the 4,4′-positiom.     

Use of solid-phase microextraction-capillary-gas chromatography (SPME-CGC) for the varietal characterization of wines by means of chemometrical methods

The extraction of wine aroma compounds was studied by direct-SPME (DI/SPME), headspace-SPME (HS/SPME) and multiple-headspace-extraction-SPME (MHE/SPME). The aromagrams obtained by HS/SPME-CGC were evaluated with chemometrical methods for the varietal classification of wines. Received: 25 July 1997 / Revised: 24 September 1997 / Accepted: 7 October 1997     

Speciation and biosynthetic variation in four dictyoceratid sponges and their cyanobacterial symbiont, Oscillatoria spongeliae

Four species of marine sponges (Phylum Porifera, Order Dictyoceratida), which contain the filamentous cyanobacterial symbiont Oscillatoria spongeliae, were collected from four locations in Palau. The halogenated natural products associated with the symbiont were characterized from each sample, revealing that each species contained either chlorinated peptides, brominated diphenyl ethers, or no halogenated compounds. Analysis of the host sponges and the symbionts indicated that each species of sponge contained a distinct strain of morphologically similar cyanobacteria. Although cospeciation may be present in this group, we have identified that at least one host switching event has occurred in this symbiosis. Only the strain of O. spongeliae in the sponge containing the chlorinated compounds possessed genes involved in the biosynthesis of chlorinated leucine precursors, indicating that the chemical variation observed in these animals has a genetic foundation.     

Synthesis and molecular structure of methyl 4-O-methyl-alpha-D-glucopyranuronate

A method for the preparation of methyl 4-O-methyl-alpha-D-glucopyranuronate and its single crystal X-ray structure determination are reported. The molecule adopts an almost ideal (4)C1 ((degree)C3) conformation.