One-Pot Synthesis of Analogues of Precocenes and Isoprenyl-Chromenes

A convenient one-pot synthesis of chromenes is described. It results from simultaneous addition and cyclization of differently parasubstituted monophenols and aldehydes of isoprenic type (5 or 10 carbons), heated for several hours in refluxing pyridine (or 4-methylpyridine).     

Application of NMR Spectroscopy and Mass Spectrometry to the Structural Elucidation of Modified Flavan‐3‐ols and Their Coupling Reaction Products*

NMR and MS techniques were used for the unambiguous structural elucidation of synthesized modified monomeric and dimeric flavan‐3‐ols presenting different substituents on the A‐ring C8 position. The full characterization of the synthesized compounds was achieved by concerted use of NMR and ESI‐MS techniques. Assignments of proton and carbon atoms was achieved through analysis of the 1D ¹H and ¹³C NMR spectra combined with homo‐ and heteronuclear 2D NMR experiments. In each case, HMBC correlation between proton H2 and carbon C8a was observed allowing assignment of this carbon, which represents the key for attribution of the A‐ring carbon atoms. The synthesis and structural characterization of activated monomeric and dimeric flavanols were also achieved and used as precursors for preparation of natural and modified dimeric procyanidin derivatives. The preparation of various dimeric species involving modified flavanols was explored through different coupling reactions. The structures of the compounds formed were characterized on the basis of their MS and NMR spectral analysis. Dimeric species were characterized through proton–proton and proton–carbon correlations, which distinguished between the different flavanol moieties and established their sequences.     

Towards a General Theory of Quantized Fields on the Anti-de Sitter Space-Time

 We propose a general framework for studying quantum field theory on the anti-de-Sitter space-time, based on the assumption of positivity of the spectrum of the possible energy operators. In this framework we show that the n-point functions are analytic in suitable domains of the complex AdS manifold, that it is possible to Wick rotate to the Euclidean manifold and come back, and that it is meaningful to restrict AdS quantum fields to Poincaré branes. We give also a complete characterization of two-point functions which are the simplest example of our theory. Finally we prove the existence of the AdS-Unruh effect for uniformly accelerated observers on trajectories crossing the boundary of AdS at infinity, while that effect does not exist for all the other uniformly accelerated trajectories. Received: 3 December 2001 / Accepted: 26 July 2002 Published online: 21 October 2002     

A nilregular element property

An element a of a commutative ring R is nilregular if and only if x is nilpotent whenever ax is nilpotent. More generally, an ideal I of R is nilregular if and only if x is nilpotent whenever ax is nilpotent for all a ∈ I . We give a direct proof that if R is Noetherian, then every nilregular ideal contains a nilregular element. In constructive mathematics, this proof can then be seen as an algorithm to produce nilregular elements of nilregular ideals whenever R is coherent, Noetherian, and discrete. As an application, we give a constructive proof of the Eisenbud-Evans-Storch theorem that every algebraic set in n-dimensional affine space is the intersection of n hypersurfaces.Received: 6 September 2004     

Response of plane viscous jet to entrance flow rate perturbation

A two‐dimensional numerical simulation solving unsteady incompressible Navier–Stokes equations is used to study the natural varicose instability of a plane jet in the Reynolds number range of 100–900. A transient train of vortices is observed at the beginning of the computation. It disappears yielding a steady flow. This flow is then used at the basis for forced excitation in order to study the space time development of instability. A Reynolds number dependant behaviour is observed which implies that viscosity directly affects the vortex dynamics. Copyright © 2001 John Wiley & Sons, Ltd.