Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equation

We consider the propagation of wave packets for the nonlinear Schrödinger equation, in the semi-classical limit. We establish the existence of a critical size for the initial data, in terms of the Planck constant: if the initial data are too small, the nonlinearity is negligible up to the Ehrenfest time. If the initial data have the critical size, then at leading order the wave function propagates like a coherent state whose envelope is given by a nonlinear equation, up to a time of the same order as the Ehrenfest time. We also prove a nonlinear superposition principle for these nonlinear wave packets.     

A rhenium tris-carbonyl derivative as a single core multimodal probe for imaging (SCoMPI) combining infrared and luminescent properties

A rhenium tris-carbonyl derivative has been designed to couple infrared and luminescent detection in cells. Both spectroscopies are consistent with one another; they point out the reliability of the present SCoMPI (for Single Core Multimodal Probe for Imaging) for bimodal imaging and unambiguously indicate a localization at the Golgi apparatus in MDA-MB-231 breast cancer cells.     

Comparison of uranyl extraction mechanisms in an ionic liquid by use of malonamide or malonamide-functionalized ionic liquid

The extraction of uranyl from acidic (HNO(3)) aqueous solutions toward an ionic liquid phase, C(1)-C(4)-imTf(2)N (1-methyl,3-butylimidazolium Tf(2)N), has been investigated as a function of initial acid concentration and ligand concentration for two different extracting moieties: a classical malonamide, N,N'-dimethyl-N,N'-dibutylmalonamide (DMDBMA) and a functionalized IL composed of the Tf(2)N(-) anion and an imidazolium cation on which a malonamide pattern has been grafted (FIL-MA). The extraction mechanism, as demonstrated through the influence of added C(1)-C(4)-imCl or added LiTf(2)N in the aqueous phase, is slightly different between the DMDBMA and FIL-MA extracting agents. Modeling of the extraction data evidences a double extraction mechanism, with cation exchange of UO(2)(2+)versus 2 H(+) for DMDBMA or versus C(1)-C(4) -im(+) and H(+) for FIL-MA at low acidic values, and through anion exchange of [UO(2)(NO(3))(3)](-)versus Tf(2)N(-) for both ligands at high HNO(3) concentrations. The FIL-MA molecule is more efficient than its classical DMDBMA parent.     

Refined inequalities on graded Lie groups

We construct a Littlewood–Paley decomposition associated to a Rockland operator on graded Lie groups, which allows us to deduce refined Gagliardo–Nirenberg, Sobolev and Hardy inequalities.     

Structural and magnetic properties of carboxylato-bridged manganese(II) complexes involving tetradentate ligands: discrete complex and 1D polymers. Dependence of J on the nature of the carboxylato bridge

The crystal structure of an inorganic linear polymer consisting of Mn(II) and an N-centered tripodal ligand N,N-bis(2-(6-methyl)pyridylmethyl)glycinate is presented (1, C(16)H(20)N(3)O(3)F(6)P(1)Mn(1), a = 9.993(2) A, b = 13.285(3) A, c = 16.040(3) A, orthorhombic, Pnam, Z = 4). The polymeric structure is ensured by carboxylato ligands connecting two Mn(II) in a rather rare syn-anti geometry. The magnetic properties of this infinite chain have been investigated, together with the magnetic properties of a dimeric Mn(II) compound (3) from a closely related ligand [N,N-bis[(1-methylimidazol-2-yl)-methyl)glycinate] involving an unusual bis(monatomic-carboxylato) bridge. The inorganic polymer 1 shows a pseudo-2D magnetic structure, with a major interaction pathway along the chain (J/k = -0.172 +/- 0.005 K) and an interchain minor one (zJ'/k = -0.006 +/- 0.004 K). These properties are reminiscent of those from a closely related previously reported inorganic Mn(II) polymer (2 obtained from manganese(II) and N,N-(2-pyridylmethyl)((1-methylimidazol-2-yl)methyl)glycinate). The dimer 3 shows a small antiferromagnetic coupling of J/k = -0.693 +/- 0.016 K. To address the influence of the carboxylato bridging mode on the magnetic properties, these complexes are compared to a series of compounds involving carboxylato bridges of several geometries between Mn(II) ions. Carboxylato bridges induce usually antiferromagnetic coupling, with the magnitude of the interaction (/J/) increasing with the number of bridges. The J value is dependent on the bridging mode. The syn-syn bridge is an efficient pathway, even by comparison with the monatomic [(mu-eta(1)-carboxylato)] bridge.     

Synthesis, characterization and dioxygen reactivity of copper(I) complexes with glycoligands

A new family of copper(I) complexes with "glycoligands" containing a central saccharide scaffold, with 2-picolyl ether groups or 2-picolylamine or N-imidazolylamine groups, has been prepared and characterized. For this purpose, the following tetradentate ligands have been synthesized: methyl 2,3-di-O-(2-picolyl)-alpha-D-lyxofuranoside (L1), 1,5-anhydro-2-deoxy-3,4-di-O-(2-picolyl)-d-galactitol (L2), 5-(amino-N-(2-salicyl))-5-deoxy-1,2-O-isopropylidene-3-O-(2-picolyl)-alpha-D-xylofuranose (L3), and 5-(amino-N-(2-salicyl))-5-deoxy-1,2-O-isopropylidene-3-O-(methylimidazol-2-yl)-alpha-D-xylofuranose (L4). The ligands and the complexes were characterized by elemental analysis, IR, 1H and 13C NMR spectroscopies, ESI mass spectrometry, and cyclic voltammetry. Collaterally with the experimental work, HF-DFT(B3LYP/6-31G*) computations were performed to obtain additional structural information. The Cu(I) complexes are found to be pentacoordinated. The redox properties and the O2-reactivity of the Cu(I)Ln complexes have been studied. Reactions of Cu(I) complexes with dioxygen in ethanol yield stable Cu(II) complexes as confirmed by UV-visible spectrophotometry and EPR spectroscopy.     

Liquid–liquid extraction of actinides,lanthanides, and fission products by use of ionic liquids: from discovery to understanding

Liquid–liquid extraction of actinides and lanthanides by use of ionic liquids is reviewed, considering, first, phenomenological aspects, then looking more deeply at the various mechanisms. Future trends in this developing field are presented.     

Une formule de Landau–Zener pour un croisement non dégénéré et involutif de codimension 3Landau–Zener formula for non-degenerate involutive codimension 3 crossings

In this Note, we study a 2×2 system of evolution equations with some codimension 3 crossing. We derive two conditions of non-degeneracy. We focus on one of them and reduce our system to some Landau–Zener's type system. Using this reduction, we describe the energy transfer at the crossing by Landau–Zener formula for 2-scales semi-classical measures. To cite this article: C. Fermanian Kammerer, P. Gérard, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 915–920.     

Semi-Classical Analysis of a Dirac Equation Without Adiabatic Decoupling

We study adiabatic decoupling for Dirac equation with some scaling which yields that the mass appears with a coefficient where is the semi-classical parameter and > 0. Therefore, the system presents an avoided crossing. The scale = 1/2 is critical: adiabatic decoupling holds for (0,1/2) while for 1/2, there is energy transfer at leading order between the two modes. We describe this transfer in terms of two-scale Wigner measures by means of Landau-Zener formula which takes into account the change of polarization of the measures after the crossing.     

Von den vielen Verfahren zum Nachweis von kleinsten Mengen Formaldehyd

Ohne Zusammenfassung