Synthesis of cyclic mono- and bis-disulfides and their selective conversion to mono- and bis-thiosulfinates

Twelve-membered ring pseudopeptidic cyclic disulfides have been prepared by iodine oxidation of the parent dithiols. However, oxidation of N,N′-(1,2-phenylene)bis(2-mercapto-2-methylpropanamide) afforded a 25/75 mixture of cyclic mono- and bis-disulfides that were separated by selective precipitation in CHCl₃. The cyclic bis-disulfide was selectively prepared by iodine oxidation of the Ni complex of this dithiol and crystallized. Its crystal structure was solved by X-ray diffraction. All these cyclic mono- or bis-disulfides were selectively converted to cyclic mono- and bis-thiosulfinates upon stoichiometric oxidation with dimethyldioxirane at low temperature. ¹H NMR of the cyclic bis-thiosulfinate revealed the presence of four isomers, two couples of stereoisomers, as expected from the insertion of two oxygen atoms in this compound, one on each disulfide bond. The two couples of cis/trans isomers were separated by preparative TLC and identified after alkaline cleavage of the two S(O)-S bonds and metalation with Ni(II). As HO⁻ attack is selective for the sulfinyl sulfur, the nature of the Ni complexes obtained is a signature of each couple of stereoisomers.     

On energy densities reached in heavy-ion collisions at the CERN SPS

We present a few estimates of energy densities reached in heavy-ion collisions at the CERN SPS. The estimates are based on data and models of proton-nucleus and nucleus-nucleus interactions. In all of these estimates the maximum energy density in central Pb+Pb interactions is larger than the critical energy density GeV/fm³ following from lattice gauge theory computations. In estimates which we consider as realistic the maximum energy density is about . In this way our analysis gives some support to claims that deconfined matter has been produced at the CERN SPS. Any definite statement requires a deeper understanding of formation times of partons and hadrons in nuclear collisions. We also compare our results with implicit energy estimates contained in earlier models of anomalous suppression in nuclear collisions. Received: 3 February 2003 / Revised version: 5 March 2003 / Published online: 5 May 2003     

A Multidimensional Branch-and-Prune Method for Interval Global Optimization

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

On covering bridged plane triangulations with balls

We show that every plane graph of diameter 2r in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius r. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 65–80, 2003     

A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties

We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO₂/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO₂ is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sn, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices.     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.