Synthesis of tetrahydrothiopyrano[3,2-c]pyrazole derivatives from 3-thianones

The synthesis of bicyclic pyrazoles and pyrazolones in which the fused ring contains a sulfur atom in different oxidation states is reported.     

La classification des immersions combinatories

Sans résumé Ce travail a été subventionné par le Fonds national de la Recherche scientifique suisse.     

High precision spectrum of N2O at 4.5 μm and determination of molecular constants for the ν3 and the (ν2 + ν3 − ν2) bands

A high precision wavenumber calibration has been achieved for the spectrum of N₂O at 4.5 μm. The values of the wavenumbers are reported for the (00°1-00°0) and for the (01¹1-01¹0) transitions. A new set of molecular constants is given for the upper and lower levels of these two transitions. In particular, the value of the H constant for the ground state (?2.02 ± 0.4) × 10^?13 cm^?1 determined in this work is significantly different from previous results.     

A Three Squares Theorem with almost Primes

As an application of the vector sieve and uniform estimateson the Fourier coefficients of cusp forms of half-integral weight,it is shown that any sufficiently large number n 3 (mod 24)with 5 n is expressible as a sum of three squares of integershaving at most 521 prime factors. 2000 Mathematics Subject Classification11P05, 11N36, 11N75, 11E25.     

Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous ${\mathbb{P}}_1/{\mathbb{P}}_1$ finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method. To cite this article: G.R. Barrenechea, F. Valentin, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Sur la stabilité du fibré de PicardOn the stability of the Picard bundle

We study the stability of the Picard bundle on the moduli space of stable vector bundles of fixed rank and determinant, over an irreducible, smooth, algebraic curve of genus g?2. To cite this article: V. Savin, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 885–888.     

Strong paracompactness and multi-selections

We characterize strong paracompactness in terms of usco multi-selections for closed-valued lower semi-continuous mappings into completely metrizable spaces, thus generalizing recent results obtained by Choban, Mihaylova and Nedev [M. Choban, E. Mihaylova, S. Nedev, On selections and classes of spaces, Topology Appl. 155 (2008) 797-804]. Related results and applications are achieved as well.