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     

L'acide hydroxylamine-O-sulfonique,réactif de choix pour la conversion d'aldéhydes en nitriles

Hydroxylamine-O-sulfonic acid: a convenient reagent for the conversion of aldehydes into nitriles . Hydroxylamine-O-sulfonic acid (HAS) proved to be an excellent reagent for the conversion of aliphatic, aromatic and heteroatomic aldehydes into nitriles. There, aldehydes in the form of suspension in HAS water solution, react rapidely to give the corresponding nitriles in high yield. Only with formylpyridines could the intermediate oxime-O-sulfonic acids be isolated.     

Dérivés propargyliques,XII et dérivés de la décahydroquinoléine,II Alkynyl-4, alkényl-4 et alkyl-4-décahydroquinolinols-4 N-substitués

The authors describe the synthesis of decahydro-4-quinolinones and N-substituted 4-alkynyl-, 4-allyl- and 4-alkyldecahydro-4-quinolinols and discuss the stereochemical problems of this compounds.     

Configurational bias Monte Carlo simulation of phase segregation in block copolymer networks

Cross-linked block copolymers are used as adhesives in fiber-reinforced composite material manufactures for automotive applications. Good adhesion between the polymer matrix and fibers in the interphase region is required for the structural integrity of these materials. Experimental evidence indicates that superior adhesion is obtained when phase segregation occurs between the two matrix phase block copolymers. It is therefore desirable to predict the conditions under which phase segregation is expected to occur. Configurational bias Monte Carlo simulations of two-component, trifunctional block copolymer networks were carried out to investigate phase segregation in these materials. The effects of four principal parameters on phase segregation were examined: the weight fractions of the two components, the cross-link length, the connectivity of the network, and the ratio of the square-well interactions. The molecular simulation results confirmed trends observed in laboratory measurements.     

Sequentially photocleavable protecting groups in solid-phase synthesis

[reaction: see text] A sequential solid-phase peptide synthesis was developed using both photolabile linker and protecting groups. The chromatic sequential lability between a tert-butyl ketone-derived linker (sensitive to irradiation at 305 nm) and a nitroveratryloxycarbonyl (NVOC) group (sensitive at 360 nm) was exploited to prepare Leu-Enkephalin in a 55% overall yield. This new strategy allows the preparation of peptides in essentially neutral medium, by avoiding the use of common deprotection reagents such as trifluoroacetic acid or piperidine.     

Review coupling of capillary electrochromatography to mass spectrometry

This review discusses the development of capillary electrochromatography (CEC) coupled to mass spectrometric (MS) detection over the last few years. Major topics addressed are instrumental setups employed and applications of this technology published in the recent literature. The instrumental section includes a discussion of the most commonly used interfaces for the hyphenation of CEC and MS as well as ionization techniques. Applications reviewed in this paper come from a variety of different fields such as the analysis of biomolecules like proteins, peptides, amino acids or carbohydrates, chiral separations or the analysis of pharmaceutical an their metabolites in a series of matrices.     

Vibrational and high pressure conformational studies of 1,1,2-trichloroethane

The infrared spectra of 1,1,2-trichloroethane were recorded from 4000 to 50 cm^?1 in the vapour and liquid states. Additional spectra above 200 cm^?1 of the low temperature crystal and of two crystalline solids, prepared by compressing the sample in a diamond anvil cell, were obtained. Also, infrared spectra of the liquid and of the compound dissolved in CS₂ were recorded at increased pressures. Raman spectral data of the liquid (including polarization measurements) and of the low temperature crystal were obtained.The fundamental frequencies for each of the two conformers, C₁ and C_s, were assigned and the results checked by normal coordinate analysis. The same diagonal and off-diagonal force constants were employed for the two conformers and the force fields were derived by means of a least squares refinement, including data for chloroethane, 1,1-dichloroethane and various deuterated species. A standard deviation of 3 % was obtained in the final fit.From the changes in relative intensities for infrared bands belonging to the C₁ and C_s conformers with increasing pressure, the volume differences (ΔV¯between the conformers were determined in CS₂ solution and in the pure liquid.     

Rare Events in Random Geometric Graphs

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating rare-event probabilities on this basis. We prove rigorously a reduction in variance when compared to the crude Monte Carlo estimators and illustrate the magnitude of the improvements in a simulation study. In higher dimensions, we use conditional Monte Carlo to remove the fluctuations in the estimator coming from the randomness in the Poisson number of nodes. Finally, building on conceptual insights from large-deviations theory, we illustrate that importance sampling using a Gibbsian point process can further substantially reduce the estimation variance.

     

Ergodicity of a Class of Cocycles Over Irrational Rotations

It is proved that if is irrational and L²(S¹) with o(l/n)then for each mZ\{0} the corresponding skew product is ergodic. The rigidity of specialflows over irrational rotations with roof functions whose Fouriercoefficients are in o(l/n) is also shown.