On a problem of Nirenberg concerning expanding maps

Let X be a Banach space and T:X → X a continuous map, which is expanding (i.e., ∥Tu ? Tv∥ ? ∥u ? v∥ for all u, v?X) and such that T(X) has a nonempty interior. Does this guarantee that T is onto? We give a counterexample in the case of X=L¹(N).     

Adjustment of piezoelectric transducer parameters for bandwidth enhancement

The enhancement of the efficiency bandwidth for ultrasonic transducers used in echographic applications is investigated. Analytical and experimental results are given which show the availability of simple conditions on the mechanical impedance ratio and the radiation resistance for the design of broadband transducers.     

Harmonic maps with defects

Two problems concerning maps with point singularities from a domain C ³ toS ² are solved. The first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed. In the second problem is the unit ball and =g is given on ; we show that the only cases in whichg(x/|x|) minimizes the energy isg=const org(x)=±Rx withR a rotation. Extensions of these problems are also solved, e.g. points are replaced by holes, ³,S ² is replaced by ^N ,S ^N–1 or by ^N , P ^N–1, the latter being appropriate for the theory of liquid crystals.Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A02     

Reaction Dynamics of Electronically Excited Alkali Atoms with Simple Molecules

The reactions of electronically excited sodium atoms with simple molecules have been studied in crossed molecular beams experiments. Electronically excited Na(3²P_3/2,4²D_5/2, and 5²S_1/2) were produced by optical pumping using single frequency dye lasers. The effects of the symmetry, and the orientation and alignment of the excited orbital on the chemical reactivity, and detailed information on the reaction dynamics were derived from measurements of the product angular and velocity distributions.     

Successive removal of chloride ions from organic polychloride pollutants. Mechanisms of reductive electrochemical elimination in aliphatic gem-polychlorides,alpha,beta-polychloroalkenes,and alpha,beta-polychloroalkanes in mildly protic medium

The factors that control the successive reductive expulsion of chloride ions from aliphatic gem-polychlorides are investigated, taking as examples the electrochemical reduction of polychloromethanes and polychloroacetonitriles in N,N-dimethylformamide. At each elimination stage, the reaction involves, as a rate-determining step, the transfer of one electron concerted with the cleavage of the carbon-chloride bond. The second step is an immediate electron transfer to the ensuing radical, taking place at a potential more positive than the potential at which the first electron transfer occurs. The carbanion thus formed is sufficiently basic to be protonated by any trace weak acid present in the reaction medium. The three successive elimination steps require increasingly negative potentials. Application of the "sticky" dissociative electron transfer model allows one to quantitatively unravel the factors that control the energetics of the successive reductive expulsion of chloride ions. The large potential gaps between each stage stem primarily from large differences in the dissociative standard potentials. They are also strongly affected by two cumulative intrinsic activation barrier factors, namely, the bond dissociation energy of the substrate that decreases with the number of chlorine atoms and the interaction between chloride ion and the radical that increases in the same direction. In the case of alpha,beta-polychloroethanes (Cl(3)C-CCl(3), Cl(2)HC-CCl(3), Cl(2)HC-CHCl(2), ClH(2)C-CHCl(2)) too, the first step is a dissociative electron transfer with sizable ion-radical interactions in the product cluster. Likewise, a second electron transfer immediately leads to the carbanion, which however prefers to expel a second chloride ion, leading to the corresponding olefin, than to be protonated to the hydrogenolysis product. The ion-radical interaction in the product cluster plays a major role in the control of the reduction potential. The reduction of the alpha,beta-polychloroethenes (Cl(2)C=CCl(2), ClHC=CCl(2), ClHC=CHCl) follows a similar 2e(-)-2Cl(-) reaction sequence, leading then to the corresponding alkynes. However, unlike the polychloroethane case, the expulsion of the first chloride ion follows a stepwise electron transfer/bond cleavage mechanism. The reduction potential is thus essentially governed by the thermodynamics of the anion radical formation.     

Sur quelques nouveaux oxyfluorures de structure rutile

Transition metal oxyfluorides with rutile structure have been obtained by various synthesis methods: NiM′³⁺TiO₃F₃, CoM′³⁺TiO₃F₃ (M′³⁺ = V³⁺, Fe³⁺); NiVTiO₄F₂, CoVTiO₄F₂ and NiCoTiO₂F₄. Electric and magnetic measurements indicate a semiconducting and antiferromagnetic behavior.     

Resolution of β-aminophosphines with chiral cyclopalladated complexes

Resolution of the racemic chiral β-aminophosphines Ph₂PCH₂CH(Ph)NH(Ar) (L¹ for Ar = C₆H₅ and L² for Ar = 2,6-C₆H₃ⁱPr₂) has been investigated by use of different cyclopalladated complexes as chiral agents. The resulting complexes afford diastereomeric adducts in a 1:1 ratio. After successive crystallizations from ethanol, a d.e. of 98% was achieved for one aminophosphine palladium complex, while no significant d.e. was obtained after crystallizations from chlorinated solvents. The X-ray structure analysis has pointed out intermolecular hydrogen interactions N-H?Cl between the P,N ligand and the chloride ion, which are responsible for the formation and stabilization of the diastereomeric adducts. Thus, the use of oxygenated solvents cancels such hydrogen interactions by their stronger donor character and makes the diastereomers separation possible, allowing to isolate the optically pure (R)-Ph₂PCH₂CH(Ph)NH(Ph) L¹ of which the absolute configuration has been determined from the X-ray structure analysis of the related palladium dichloride complex.     

Connecting terminal carboxylate groups in nine-coordinate lanthanide podates: consequences on the thermodynamic,structural, electronic,and photophysical properties

The hydrolysis of terminal (t)butyl-ester groups provides the novel nonadentate podand tris[2-[N-methylcarbamoyl-(6-carboxypyridine-2)-ethyl]amine] (L13) which exists as a mixture of slowly interconverting conformers in solution. At pH = 8.0 in water, its deprotonated form [L13 - 3H](3-) reacts with Ln(ClO(4))(3) to give the poorly soluble and stable podates [Ln(L13 - 3H)] (log(beta(110)) = 6.7-7.0, Ln = La-Lu). The isolated complexes [Ln(L13 - 3H)](H(2)O)(7) (Ln = Eu, 8; Tb, 9; Lu, 10) are isostructural, and their crystal structures show Ln(III) to be nine-coordinate in a pseudotricapped trigonal prismatic site defined by the donor atoms of the three helically wrapped tridentate binding units of L13. The Ln-O(carboxamide) bonds are only marginally longer than the Ln-O(carboxylate) bonds in [Ln(L13 - 3H)], thus producing a regular triple helix around Ln(III) which reverses its screw direction within the covalent Me-TREN tripod. High-resolution emission spectroscopy demonstrates that (i) the replacement of terminal carboxamides with carboxylates induces only minor electronic changes for the metallic site, (ii) the solid-state structure is maintained in water, and (iii) the metal in the podate is efficiently protected from interactions with solvent molecules. The absolute quantum yields obtained for [Eu(L13 - 3H)] (Phi(Eu)(tot)= 1.8 x 10(-3)) and [Tb(L13 - 3H)] (Phi(Eu)(tot)= 8.9 x 10(-3)) in water remain modest and strongly contrast with that obtained for the lanthanide luminescence step (Phi(Eu) = 0.28). Detailed photophysical studies assign this discrepancy to the small energy gap between the ligand-centered singlet ((1)pi pi*) and triplet ((3)pi pi*) states which limits the efficiency of the intersystem crossing process. Theoretical TDDFT calculations suggest that the connection of a carboxylate group to the central pyridine ring prevents the sizable stabilization of the triplet state required for an efficient sensitization process. The thermodynamic and electronic origins of the advantages (stability, lanthanide quantum yield) and drawbacks (solubility, sensitization) brought by the "carboxylate effect" in lanthanide complexes are evaluated for programming predetermined properties in functional devices.     

Hydrogen and proton exchange at carbon. Imbalanced transition state and mechanism crossover

A recent remarkable study of the C–H oxidation of substituted fluorenyl-benzoates together with the transfer of a proton to an internal receiving group by means of electron transfer outer-sphere oxidants, in the noteworthy absence of hydrogen-bonding interactions, is taken as an example to uncover the existence of a mechanism crossover, making the reaction pass from a CPET pathway to a PTET pathway as the driving force of the global reaction decreases. This was also the occasion to stress that considerations based on “imbalanced” or “asynchronous” transition states cannot replace activation/driving force models based on the quantum mechanical treatment of both electrons and transferring protons.

Using the remarkable study of C–H oxidation of substituted fluorenyl-benzoates as an example, we have shown that a mechanism crossover takes place upon decreasing the driving force, from a CPET pathway to a PTET pathway.