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.     

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.     

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.     

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 of a novel amphiphilic GdPCTA-[12] derivative as a potential micellar MRI contrast agent

A novel amphiphilic contrast agent, a GdPCTA-[12] derivative containing a dodecyl chain as lipophilic moiety, has been prepared. A convergent synthetic route from commercially available diethylene triamine and 3-hydroxypyridine is described. The target amphiphilic gadolinium complex was obtained in nine steps in 22% overall yield. Physicochemical properties and relaxivity measurements of this new contrast agent are described.     

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.     

Von den vielen Verfahren zum Nachweis von kleinsten Mengen Formaldehyd

Ohne Zusammenfassung     

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.     

Studies on the formation of porphyrinogens from monopyrroles in presence of the enzymes PBG deaminase and/or Uro’gen III synthase

The substrate-specificities of two enzymes in the biosynthetic pathway to vitamin B₁₂, PBG deaminase and Uro’gen III synthase, which are involved in the formation of Uro’gen III from the pyrrole PBG, are investigated for the preparation of Uroporphyrin analogs. Both enzymes display strong substrate-specificity. However, tetramerization of pyrroles with carboxylate β-substituents in mildly basic buffer represents the best and most rapid route to a family of Uro I analogs for enzymatic activity studies.