Homotopy invariance of coherent Witt groups

 We prove the following general homotopy invariance theorem for coherent Witt groups: Let be a flat morphism of separated Gorenstein schemes of finite Krull dimension with affine fibers,i.e. π⁻¹(y) is an affine space over the residue field k(y) for all yY, then the induced homomorphism of coherent Witt groups is an isomorphism. As an application we calculate the (classical) Witt group of the affine hyperbolic sphere over a regular local ring. Received: 22 August 2001; in final form: 22 June 2002 / Published online: 1 April 2003     

Non quasi-free classes of product states of the C.C.R.-algebra

Two exemples of pure states of Van Hove's Universal Receptacle in the boson case are presented with are not unitarily equivalent to any quasi-free state. In particular, it is shown that a discrete state is unitarily equivalent to some quasi-free state if and only if it is equivalent to the Fock state related to the chosen decomposition of the test function space.Attaché de Recherches — C.N.R.S. — Marseille.     

Chord length distributions and small-angle scattering

Chord length distributions describe size, shape and spatial arrangement of geometrical objects (particles). The chord length distribution is in principle proportional to the second derivative of the correlation function of small-angle scattering. It is calculable from a relative measurement of the scattering intensity I(h). In structure research, the characterization of numerous particle systems can be achieved by comparing experimental chord distributions with theoretical ones, provided the latter are available with sufficiently high precision for a lot of fundamental, universal shapes. Both sides of this concept are exemplified: – the step from a relative measurement of the scattering intensity of an isotropic two-phase sample to the chord length distribution (errors in and in , limited h-interval, corresponding to the region (1-2) nm < r in real space, must be observed); as well as the geometric matter of calculation of chord distributions as fingerprints for basic geometric figures, including the non-convex case. Received 15 March 1999 and Received in final form 26 April 2000     

Spécialisation de la -équivalence pour les groupes réductifs

Soit un groupe réductif défini sur un corps de caractéristique distincte de . On montre que le groupes des classes de -équivalence de ne change pas lorsque l'on passe de au corps des séries de Laurent , c'est-à-dire que l'on a un isomorphisme naturel .

ABSTRACT. Let be a reductive group defined over a field of characteristic . We show that the group of -equivalence for is invariant by the change of fields given by the Laurent series. In other words, there is a natural isomorphism .

     

Cohomologie galoisienne des groupes quasi-déployés sur des corps de dimension cohomologique ≤2; Galois cohomology of quasi-split groups over fields of cohomological dimension ≤ 2

Let k be a perfect field with cohomological dimension 2. Serre's conjecture II claims that the Galois cohomology set H ¹(k,G) is trivial for any simply connected semi-simple algebraic G/k and this conjecture is known for groups of type ¹ A _n after Merkurjev–Suslin and for classical groups and groups of type F ₄ and G ₂ after Bayer–Parimala. For any maximal torus T of G/k, we study the map H ¹(k, T) H ¹(k, G) using an induction process on the type of the groups, and it yields conjecture II for all quasi-split simply connected absolutely almost k-simple groups with type distinct from E ₈. We also have partial results for E ₈ and for some twisted forms of simply connected quasi-split groups. In particular, this method gives a new proof of Hasse principle for quasi-split groups over number fields including the E ₈-case, which is based on the Galois cohomology of maximal tori of such groups.     

Synthesis of alpha-trifluoromethylated nitrogen heterocycles

The syntheses of various alpha-trifluoromethylated nitrogen heterocycles have been achieved from readily available alpha-(trifluoromethyl)homoallylamine through a ring-closing metathesis.     

Comparison of gas chromatographic-mass spectrometric methods for screening of chlorotriazine pesticides in soil.

The performance of a coupled technique resulting from the combination of gas chromatography with a selective mass spectrometric technique (tandem mass spectrometry) (GC-MS-MS) with collisionally activated dissociation (CAD) and multi-reaction monitoring (MRM) was compared with that of GC-low resolution MS (GC-LRMS) at a resolving power of 1000 and GC-high-resolution MS (GC-HRMS) at resolving powers of 5000 and 10,000 for the determination of atrazine, simazine, cyanazine, deethylatrazine and deisopropylatrazine in polluted soil samples. GC-MS-MS daughter ion spectra for the parent ions [M]+. and [M - CH3]+ were generated using collisionally activated dissociation and studied. Also, by optimizing the collision energy for maximum sensitivity a method for screening chlorotriazines by MRM was developed. Analyses of soil sample extracts showed that GC-MS-MS overcomes interferences from other chlorotriazines and interfering compounds that could not be removed by GC-HRMS or GC-LRMS at resolving powers of 10,000 and 1000, respectively. The limits of detection for GC-MS-MS and GC-HRMS at a signal-to-noise ratio of 10 ranged between 1 and 24 pg, with a mean relative standard deviation of 25-30%. Soil samples known to contain chlorotriazines and their degradation products were analysed by GC-MS-MS and the results obtained were compared with those given by GC-HRMS at resolving powers of 5000 and 10,000, with quantification differences of 25-30%.     

A practical, solvent free, one-pot synthesis of C2-symmetrical secondary amines

A novel one-pot reductive amination of ketones using the combination Ti(OⁱPr)₄/H₂/Pd-C is reported. This practical procedure does not require any solvent, and affords C₂-symmetrical secondary amines in high yields and excellent diastereoselectivities.