Radiation conditions and uniqueness for stationary oscillations in elastic plates

Sommerfeld-type radiation conditions are indicated for the solutions of the system governing the small stationary oscillations in plates with transverse shear deformation, and a uniqueness theorem is proved in the case of the corresponding exterior Dirichlet and Neumann problems.

     

Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.     

Synthetic applications of 2-chlorooxiranes: preparation of thiazoles,dihydrothiazoles and selenazoles

The reaction of 2-chlorooxiranes 1 with thioamides and thioureas provides access to thiazoles, 4-hydroxy-4,5-dihydrothiazoles and 2-imino-2,3-dihydrothiazoles under mild conditions and with excellent yields. With 1 and selenourea, near quantitative yields of selenazoles are obtained.     

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.