v-Triazolines. Part XIX. Thiocino[4,5-d]-1,2,3-triazole and thiocino[4,5-d]isoxazole derivatives

5-Amino-2,3,6,7-tetrahydrothiocines were reacted with arylazides yielding 1-aryl-9a-amino-1,3a,4,5,7,8,9,9a-octahydrothiocino[4,5-d]-1,2,3-triazoles which could be deaminated to 1-aryl-1,4,5,7,8,9-hexahydrothiocino-[4,5-d]-1,2,3-triazoles. Similarly, the above enamines yielded, with nitrile oxides, 3-aryl-9a-amino-3a,4,5,8,9,9a-hexahydrothiocino[4,5-d]isoxazoles which were transformed with acids into 3-aril-4,5,8,9-tetrahydrothiocino-[4,5-d]isoxazoles.     

Surface‐enhanced Raman spectroscopy for trace‐level detection of explosives

The detection of explosives and their associated compounds for security screening is an active area of research and a wide variety of detection methods are involved in this very challenging area. Surface‐enhanced Raman scattering (SERS) spectroscopy is one of the most sensitive tools for the detection of molecules adsorbed on nano‐scale roughened metal surface. Moreover, SERS combines high sensitivity with the observation of vibrational spectra of species, giving complete information on the molecular structure of material under study. In this paper, SERS was applied to the detection of very small quantities of explosives adsorbed on industrially made substrates. The spectra were acquired with a compact Raman spectrometer. Usually, a high signal‐to‐noise (S/N) spectrum, suitable for identification of explosive molecules down to few hundreds of picograms, was achieved within 30 s. Our measurements suggest that it is possible to exploit SERS using a practical detection instrument for routine analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Spherical orbits and quantized enveloping algebras

Let lbe an odd integerl>1 and let ? be a primitive l^th -root of unity. In this paper we prove that every U_?(sl(n))-irreducible module parametrized by a spherical, unipotent conjugacy class О of SL(n) has dimension divisible by l ^½dimОresuit was conjectured by De Concini, Kac and Procesi in [DC-K-P 1].     

A finite difference scheme on a non commutative group

Summary. We propose and analyze a finite difference scheme for the Kohn Laplacian operator associated with the Heisenberg group, which is a degenerate elliptic operator of H?rmander type. We give a complete analysis for a periodic problem in a cube. In particular, we prove a discrete Poincaré-Wiertinger inequality which yields the stability. Numerical tests are presented. Received June 1, 1999 / Revised version received June 7, 2000 / Published online March 20, 2001     

The stochastic heat equation: Feynman-Kac formula and intermittence

We study, in one space dimension, the heat equation with a random potential that is a white noise in space and time. This equation is a linearized model for the evolution of a scalar field in a space-time-dependent random medium. It has also been related to the distribution of two-dimensional directed polymers in a random environment, to the KPZ model of growing interfaces, and to the Burgers equation with conservative noise. We show how the solution can be expressed via a generalized Feynman-Kac formula. We then investigate the statistical properties: the two-point correlation function is explicitly computed and the intermittence of the solution is proven. This analysis is carried out showing how the statistical moments can be expressed through local times of independent Brownian motions.     

Rearrangement of 2-aminofuro[3,2-b]pyridine-3-carboxylic esters

Ethyl 2-aminofuro[3,2-b]pyridine-3-carboxylate rearranges with sodium ethoxide in ethanol to 2-oxo-3-cyano-2,3-dihydro[3,2-b]furopyridine; the corresponding p-nitrophenyl ester undergoes the same rearrangement by dilute aqueous sodium hydroxide. In the first case it was possible to isolate the labile intermediate, which was shown to be the hemiacetal of the above mentioned cyanolactone.     

The Dissociation Constants of 1,1′-Bis (pyridinium-4-aldoxime)trimethylene dibromide

Summary. The dissociation constants of the two oxime groups of 1,1-bis(pyridinium-4-aldoxime)trimethylene dibromide (TMB-4) were determined using spectrophotometric data. Two numerical methods were applied to treat the overlapping equilibria. The results obtained by both agreed with each other and their mean values at 25°C corrected for the ionic strength of 0.05moldm^–3 are pK_a1=7.49±0.11 and pK_a2=8.96±0.09. These values were discussed in terms of the pK_as of 1,1-bis(pyridinium-4-aldoxime)oxydimethylene dichloride (Toxogonin), a similar dioxime, which were derived by extrapolation of literature data.