Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on M are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries.     

Cellulose nanofibers from white and naturally colored cotton fibers

Suspensions of white and colored nanofibers were obtained by the acid hydrolysis of white and naturally colored cotton fibers. Possible differences among them in morphology and other characteristics were investigated. The original fibers were subjected to chemical analysis (cellulose, lignin and hemicellulose content), X-ray diffraction (XRD) analysis, and scanning electron microscopy (SEM). The nanofibers were analyzed with respect to yield, elemental composition (to assess the presence of sulfur), zeta potential, morphology (by scanning transmission electron microscopy (STEM)) and atomic force microscopy (AFM), crystallinity (XRD) and thermal stability by thermogravimetric analysis in air under dynamic and isothermal temperature conditions. Morphological study of several cotton nanofibers showed a length of 85–225 nm and diameter of 6–18 nm. The micrographs also indicated that there were no significant morphological differences among the nanostructures from different cotton fibers. The main differences found were the slightly higher yield, sulfonation effectiveness and thermal stability under dynamic temperature conditions of the white nanofiber. On the other hand, in isothermal conditions at 180 °C, the colored nanofibers showed a better thermal stability than the white.     

New lipophilic 3-hydroxy-4-pyridinonate iron(III) complexes: synthesis and EXAFS structural characterisation

New tris-iron(III) chelates of 3-hydroxy-4-pyridinone ligands derived from maltol (3-hydroxy-2-methyl-4-pyrone) or ethylmaltol (2-ethyl-3-hydroxy-4-pyrone), including a variety of N-aryl (phenyl, 4'-tolyl, 4'-(n-butyl)phenyl, 4'-(n-hexyl)phenyl) and N-benzyl (4'-methylbenzyl, 4'-fluorobenzyl and 4'-(trifluoromethyl)benzylamine) substituents on the nitrogen atom of the pyridinone ring, have been prepared. Characterization by C,H,N elemental analysis and thermogravimetric measurements indicates that most of the complexes are obtained as hydrates of general formula ML3.xH2O. Structural characterization of these difficult to crystallize lipophilic complexes has been achieved by EXAFS spectroscopy. Solutions of iron(III) complexes of maltol, ethylmaltol, 1,2-dimethyl-3-hydroxy-4-pyridinone and 1-phenyl-2-methyl-3-hydroxy-4-pyridinone in methanol-water mixtures were also examined by EXAFS. Distances from the central atom to ligand atoms, within 6 A of the metal, have been determined in the solid and solution samples and the results show that the structure observed in the powder is maintained in solution. The local structure around the metal centre, bond distances and bond angles, does not change significantly with variable lipophilicity, thus indicating that ligands may be tailored according to specific needs without altering their chelation properties. EXAFS data analysis for this set of tris-iron(III) compounds illustrates the important contribution of both intra-ligand and inter-ligand multiple scattering pathways through the metal centre to a peak observed in the FT spectrum at twice the metal ligand distance (approximately 4 A). The present results demonstrate that EXAFS features at twice the metal-ligand distance are valuable in the assignment of molecular geometry and that location of hydration water molecules, by EXAFS analysis, is limited by the geometry of the complexes, in particular for those in which ligands containing phenyl rings are present.     

Synthesis of niobia nanocrystals with controlled morphology

In this work, TT niobia-phase nanocrystals with controlled morphology were obtained by the hydrothermal treatment of a niobium peroxo complex precursor at very low temperatures. The materials obtained by this route presented a very high surface area (ranging from 79 to 327 m(2)/g), disordered NbO(6), NbO(7), and NbO(8) polyhedra, Nb-O superficial sites, and a superficial OH group, which must have ensured the acidic characteristics of this oxide.     

Resonant Raman scattering characterization of carbon nanotubes grown with different catalysts

Single-walled carbon nanotube samples produced in the presence of different combinations of metal catalysts have been studied by resonant Raman spectroscopy. The diameter distribution of different samples has been determined by analysis of the laser excitation energy dependence of the tangential modes associated with metallic nanotubes. These modes are resonantly enhanced over a narrow range of the exciting energies, which shifts for different samples. The Raman cross-section expression has been used to fit the experimental Raman excitation profiles. This procedure was used to determine the mean value and the width of the distribution of diameters within each sample.     

Low-Loss Photopatternable Hybrid Sol–Gel Materials

Hybrid sol–gel technology has proved its usefulness in the field of micro-optics. Indeed, it makes it possible to manufacture optical microcomponents by processes much simpler than those currently used, particularly when photopatternable materials are employed. However, for wavelengths in the near infrared window (NIR), this process is confronted with a major problem which results from the significant optical absorption of this type of materials, in particular around 1550 nm. The aim of this paper is to describe the origin of the losses of some hybrid sol–gel materials of direct interest in micro-device fabrication in order to propose solutions to achieve a greater transparency in the NIR region. The intrinsic absorption of the precursors was first of all considered since it is crucial to pursue the final goal of decreased losses. Then, the principal parameters of the sol–gel synthesis were studied. Among them, the thermal treatment conditions, the hydrolysis ratio and the controlled addition of transition metal alkoxides allow an improvement of the material transparency, at 1550 nm most particularly. This last point was considered with the highest attention, and NIR and NMR spectroscopies were employed to explain how the addition of zirconium alkoxides at the end of the reaction makes it possible to considerably decrease the losses in the material.     

Er as marker for order–disorder determination in the PbTiO3 system

Er³⁺ ions were added to the PbTiO₃ network using the polymeric precursor method to characterize the order–disorder transformation found in this material by means of experimental and theoretical approach. The disordered and ordered material structures were studied by photoluminescence measurements, X-ray diffraction (XRD) and UV–visible spectroscopy. The Er³⁺ ions served as a marker to identify the structural short-range order beginning in the PbTiO₃ matrix. From photoluminescence results it was concluded that disordered PbTiO₃ powders have a certain short range order in the network that are undetected by XRD measurements. The electronic structures were calculated by the ab initio periodic method in DFT level with the non-local B3LYP hybrid approximation for the Ti atom site interpretation using density of states (DOS) results. This analysis enabled understanding that Ti atom sphere coordination can create possible states for radioactive return and trap of electron–holes pair.     

Ceramic crucibles: a new alternative for melting of PbO-BiO1.5-GaO1.5 glasses

PbO-Bi₂O₃-Ga₂O₃ glasses present interesting properties such as good transmission in the mid-infrared region, high magnetic Verdet constant and non-linear properties. The processing of these heavy-metal-oxide (HMO) glasses is limited by the high corrosive nature of the melt, even in relation to noble metal crucibles. In this work, three kinds of ceramic crucibles (alumina, tin oxide and zirconia) were tested for melting HMO glasses. The main physical properties of the prepared glasses, such as the characteristic temperatures, optical transmission were studied in function of the crucible nature, time/temperature melting parameters. The incorporation of crucible material in the glasses was determined by ICP and atomic absorption. The maximum glass contamination from the crucible was 2.9, 1.6 and 3.6 mol% for Al₂O₃, SnO₂ and ZrO₂ crucibles, respectively, when melting was done at 900 °C/240 min, for zirconia crucibles and at 1000 °C/60 min, for the other two crucibles. The evolution of the physical properties was discussed as a function of contamination degree.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.