Géométrie diophantienne et variétés toriques

We present some results on projective toric varieties which are relevant in diophantine geometry. We interpret and study several invariants attached to these varieties by geometrical and combinatorial terms. We also give a Bézout theorem for Chow weights of projective varieties and an application to the theorem of successive algebraic minima. These results are extracted from the two texts of Philippon and Sombra mentioned in the references at the end of this Note (both downloadable from http://fr.arxiv.org). To cite this article: P. Philippon, M. Sombra, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Ensembles invariants non enlacés des difféomorphismes du tore et de l’anneau

We introduce the notion of unlinked invariant set for a diffeomorphism of the 2-torus or the closed annulus and we look at the properties of these sets which generalize the Aubry-Mather sets. We prove that for any irrational number in the rotation set of an area-preserving diffeomorphism of the annulus, there exists an unliked invariant set whose rotation set is reduced to . In the same way we prove that any minimal diffeomorphism of the 2-torus homotopic to the identity may be approximated in the C⁰-topology by a periodic diffeomorphism.

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Mathematics Subject Classification (2000) 37E30, 37E45, 37J10     

Practical guide for improving performance

Research has established that health care is not error free. The question facing perioperative units, as well as all health care services, is how to minimize the human factors that impact quality and safety. This two-part series on performance improvement in perioperative services was intended to help answer this question. Achieving performance excellence starts with a supportive work culture. The human issues of teamwork, communication, and leadership are crucial to achieving performance excellence. Next, perioperative caregivers must accept that all people make mistakes so systems and processes can be designed to be more "forgiving" of errors. Last, a planned and systematic approach must be used to measure, analyze, and improve performance. Successful implementation of performance improvement calls for strong partnerships between physicians, managers, and staff members. Performance excellence requires that everyone work together to ensure that perioperative care is safe, effective, appropriate, customer focused, and efficient.     

Mode dependent vibrational autoionization of Rydberg states of NO2. II. Comparing the symmetric stretching and bending vibrations

Triple-resonance excitation and high-resolution photoelectron spectroscopy are combined to characterize the mode selectivity of vibrational autoionization of the high Rydberg states of NO2. Photoelectron spectra and vibrational branching fractions are reported for autoionizing Rydberg states converging to the NO2+ X 1Sigmag +(110) state, that is, with one quantum in the symmetric stretch, nu1, and one quantum in the bending vibration, nu2. These results indicate that autoionization proceeds most efficiently through the loss of one quantum from the symmetric stretch rather than from the bending vibration. The implications of this result are discussed in terms of the autoionization mechanism.     

Theoretical and experimental study of differential group delay and polarization dependent loss of Bragg gratings written in birefringent fiber

In this paper, we completely study the wavelength dependency of differential group delay (DGD) and polarization dependent loss (PDL) for Bragg gratings written in birefringent fibers. Based on the coupled mode theory, we present analytical expressions for the evolution with wavelength of the transmission coefficient, the DGD and the PDL. The wavelength dependencies of these evolutions on the birefringence are then discussed. Experimental results are finally presented for an apodized FBG written in a bow-tie fiber. A very good agreement between theory and experience is reported, confirming the validity of the theoretical analysis.     

Design of the spatial filter window for digital holographic convolution reconstruction of object beam field

In the convolution reconstruction process of digital holographic object beam field, the object beam fields with different magnifications can be obtained when the reconstructing beams are spherical waves with different wave curvature radii. This paper presents a theoretical and experimental discussion on the useful spatial frequency spectrum of the hologram numerically illuminated by the spherical wave. The result shows that there would be an image in the spatial frequency spectrum of digital hologram, which is completely the same as the object, if the wave surface radius of the spherical wave is equal to the distance from the object to the CCD sensor. Taking this image as a reference and designing a filter, the position of the reconstructed images with different magnifications can be predicted correctly in the reconstructed plane. Additionally, since the spectrum distribution of zero-order diffraction can be forecasted accurately in theory, its contribution can be effectively eliminated through changing the spatial filter shape; then a reconstructed object field containing more high-frequency information can be obtained.     

Influence of the Metal Ion on the Two‐Photon Absorption Properties of Lanthanide Complexes Including Near‐IR Emitters

The synthesis of tris(2‐thenoyltrifluoroacetonate)lanthanide(III) complexes featuring a diethylaminostyryl‐2,2′‐bipyridine coligand was achieved for lanthanum; the near‐infrared (NIR) emitters neodymium, erbium, and ytterbium; and the transition‐metal yttrium. The photophysical properties were thoroughly studied, and it was demonstrated that the conjugated bipyridine ligand acts as a good antenna for the sensitization of the NIR emitters. The two‐photon absorption (TPA) properties of all five complexes were investigated by using both two‐photon excited fluorescence and the Z‐scan method. We demonstrate that the nature of the rare earth ion has almost no influence on the TPA properties centered on the conjugated bipyridyl ligand. Finally, we show that Yb^III is sensitized by a two‐photon antenna effect, and that Nd^III is mostly sensitized by a one‐photon process involving direct excitation of forbidden f–f transitions.     

Effect of alkyl chain length and hydroxyl group functionalization on the surface properties of imidazolium ionic liquids

Properties of the surface of ionic liquids, such as surface tension, ordering, and charge and density profiles, were studied using molecular simulation. Two types of modification in the molecular structure of imidazolium cations were studied: the length of the alkyl side chain and the presence of a polar hydroxyl group at the end of the side chain. Four ionic liquids were considered: 1-ethyl-3-methylimidazolium tetrafluoroborate, [C(2)C(1)im][BF(4)]; 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate, [C(2)OHC(1)im][BF(4)]; 1-octyl-3-methylimidazolium tetrafluoroborate, [C(8)C(1)im][BF(4)] and 1-(8-hydroxyoctyl)-3-methylimidazolium tetrafluoroborate, [C(8)OHC(1)im][BF(4)]. The surface tension was calculated using both mechanical and thermodynamic definitions, with consistent treatment of the long-range corrections. The simulations reproduce the available experimental values of surface tension with a maximum deviation of ±10%. This energetic characterization of the interface is completed by microscopic structural analysis of orientational ordering at the interface and density profiles along the direction normal to the interface. The presence of the hydroxyl group modifies the local structure at the interface, leading to a less organized liquid phase. The results allow us to relate the surface tension to the structural ordering at the liquid-vacuum interface.