Lipschitz equivalence of self-similar sets

In 1997 David and Semmes asked whether there exists a bilipschitz map between the two compact self-similar subset M and $M^{\prime }$ of the real line defined by the relations $M=(M/5)\cup (M/5+2/5)\cup (M/5+4/5)$ and $M^{\prime }=(M^{\prime }/5)\cup (M^{\prime }/5+3/5)\cup (M^{\prime }/5+4/5)$. We answer this question positively. To cite this article: H. Rao et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

A new guaiane diterpenoid from Euphorbia wallichii

A new guaiane-type diterpenoid, (1alpha,5beta,7alpha)-3,10(18),11-dictytriene-19-acid, was obtained from the roots of Euphorbia wallichii. This is the first isolation of guaiane diterpene from this genus of Euphorbia. The structure was elucidated by spectral methods. And the compound was tested for the cytotoxicities on the cancer cell line P-388 and A-549 in vitro.     

Edge plane sites on highly ordered pyrolytic graphite as templates for making palladium nanowires via electrochemical decoration

An approach for the fabrication of metal nanowires is presented. Palladium wires with diameters less than 50 nm were produced by electrochemical decoration of step edge sites on the surface of highly ordered pyrolytic graphite via the following three steps. First an electrochemical activation step was used to oxidize the edge plane sites on highly ordered pyrolytic graphite surfaces in 0.5 M Na(2)SO(4). Second, a potential cycling step in a 1 mM PdCl(2) solution in 0.1 M H(2)SO(4) was used to form palladium oxide (s) and/or complexes of Pd on the step edges. Third, Pd nanowires were formed by electroreduction after transfer of the graphite to 0.1 M H(2)SO(4). The resulting wires showed a high degree of uniformity. A merit of this approach is that it allowed metal nanowires to be fabricated without the simultaneous formation of nanoparticles on the basal plane terraces, in contrast to other studies of this type. The mesoscopic palladium wires are shown to be useful for the electrochemical sensing of hydrazine.     

A general approach to porous crystalline TiO2, SrTiO3, and BaTiO3 spheres

Monodispersed porous crystalline TiO(2), SrTiO(3), and BaTiO(3) spheres were produced through a one-step hydrothermal process from amorphous TiO(2) spheres. The resulting samples were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), and nitrogen sorption measurements. On the basis of the characterization results, we proposed a formation process of these porous spheres according to a mechanism analogous to the Kirkendall effect. This study provides a general way to synthesize porous titania-based spheres.     

Mg-catalyzed autoclave synthesis of aligned silicon carbide nanostructures

In this article, a novel magnesium-catalyzed co-reduction route was developed for the large-scale synthesis of aligned beta-SiC one-dimensional (1D) nanostructures at relative lower temperature (600 degrees C). By carefully controlling the reagent concentrations, we could synthesize beta-SiC rodlike and needlelike nanostructures. The possible growth mechanism of the as-synthesized beta-SiC 1D nanostructures has been investigated. The structure and morphology of the as-synthesized beta-SiC nanostructures are characterized using X-ray diffraction, Fourier transform infrared absorption, and scanning and transmission electron microscopes. Raman and photoluminescence properties are also investigated at room temperature. The as-synthesized beta-SiC nanostructures exhibit strong shape-dependent field emission properties. Corresponding to their shapes, the as-synthesized nanorods and nanoneedles display the turn-on fields of 12, 8.4, and 1.8 V/microm, respectively.     

Experimental and computational studies of alkali-metal coinage-metal clusters

Coinage and alkali metal mixed clusters, M4Na- (M = Cu, Au) have been investigated experimentally using photoelectron spectroscopy and computationally at correlated ab initio levels. The related Cu4Li-, Ag4Li-, Ag4Na-, and Au4Li- clusters as well as the neutral Cu4Li2 and Cu4Na2 clusters have also been studied computationally. The calculations show that the two lowest isomers of the negatively charged clusters include a pyramidal C4v structure and a planar C2v species. For Cu4Li- and Cu4Na-, the C4v structure is calculated at correlated ab initio level to be 30.9 and 16.9 kJ/mol below the planar C2v isomer, whereas the planar isomers of Au4Li- and Au4Na- are found to be 29.7 and 49.4 kJ/mol below the pyramidal ones. For Ag4Li- and Ag4Na-, the pyramidal isomers are the lowest ones. Comparison of the calculated and measured photoelectron spectra of Cu4Na- and Au4Na- shows that the pyramidal Cu4Na- cluster of C4v symmetry and the planar Au4Na- of C2v symmetry are detected experimentally. Calculations of the magnetically induced current density in Cu4Li- and Cu4Li2 using the Gauge-Including Magnetically Induced Current (GIMIC) method show that strong ring currents are sustained mainly by the highest-occupied molecular orbital primarily derived from the Cu 4s. The GIMIC calculations thus show that the Cu4(2-) ring is -aromatic and that the d orbitals do not play any significant role for the electron delocalization effects. The present study does not support the notion that the square-planar Cu4(2-) is the first example of d-orbital aromatic molecules.     

Structural evolution of anionic silicon clusters SiN (20 <or= N <or= 45)

Results of a combined photoelectron spectroscopy and first-principles density-functional study of SiN- clusters in the size range 20 or= 20. For 28 相似文献   

Dipole-bound anions of beta-alanine: canonical and zwitterionic conformers

The remarkable stabilities of the dipole-bound anions of the canonical and zwitterionic conformers of beta-alanine are predicted at the high level of theories, in which the former is the global minimum and the latter, the anti zwitterionic anion, is the local minimum. In contrast to the dipole-bound anions of glycine, the gauche zwitterionic anion of beta-alanine is an unstable conformer. The vertical electron detachment energies for the canonical and anti zwitterionic anions are 58 and 1145 meV, respectively. The photodetachment electron spectrum of the canonical anion is theoretically simulated on the basis of the Franck-Condon factor calculations.     

Reactions of cerium atoms and dicerium molecules with CO: formation of cerium carbonyls and photoconversion to CO-activated insertion molecules

Reactions of cerium with carbon monoxide molecules in solid argon have been studied using matrix isolation infrared absorption spectroscopy. The cerium carbonyls CeCO and Ce2CO are produced spontaneously on annealing and they are photochemically rearranged to the CCeO and c-Ce2(mu-C)(mu-O) isomers, where Ce and Ce2 are inserted into the CO triple bond. Theoretical calculations indicate that CeCO is an end-on-bonded carbonyl with a quintet ground state, whereas Ce2CO is a rare dinuclear lanthanide carbonyl complex with CO serving as an asymmetrically bridged, side-on ligand. The CCeO molecule was theoretically characterized to have a linear structure with a singlet ground state. Evidence is also presented for the CeCO- anion and other cerium carbonyls with higher coordination numbers.