Left, right, and inner socles of associative systems

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Simulation of a monolayer adsorbed on a heterogeneous surface: effect of the size and shape of the adsorbate on the structure of the interface and the distribution of the adsorption energies

At the low temperature limit, the effect on the size and shape factors of the adsorbate molecule is shown in a simulation of a monomolecular phase adsorbed on a heterogeneous surface. This factor is reflected both in the theoretical distribution of the adsorption energies and the packing of the adsorbed phase.     

Vibronic intensities in centrosymmetric lanthanide complex ions. I

Summary A theoretical model to calculate the vibronic intensities induced by the odd vibrational modes in centrosymmetric lanthanide complexes is developed and applied to octahedral complex ions, LnX ₆ ^3– , such as occur in the hexachloroelpasolites Cs₂NaLnCl₆. Both the crystal field and the ligand polarisation contributions are evaluated using a standard set of symmetry coordinates. For the crystal field term a truncated expansion of the intermediates states is employed rather than the more conventional closure approximation. Special care is necessary to ensure that the phases of the contributions are correctly determined since the cross-term between the ligand polarisation and crystal field contributions is signed. General equations applicable to anyf ⁿ complex ion are derived and an example of their application to the PrCl ₆ ^3– ion is given The agreement with experiment is satisfactory.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

Uranyl-salophen based ditopic receptors for the recognition of quaternary ammonium halides

Uranyl-salophen complexes endowed with aromatic side arms behave as very efficient ditopic receptors towards tetralkylammonium halides as a result of a combination of Lewis acid-base and cation-pi interactions.     

Unprecedented detection of inherent chirality in uranyl-salophen complexes

In complexes with the uranyl dication salophen ligands are highly puckered. This implies that non-symmetrically substituted uranyl-salophen derivatives exist in principle as a pair of enantiomers. However, due to easy disrotations about the bonds connecting the phenoxide units to the imine carbons, the rate of interconversion between enantiomeric forms of simple, sterically unhindered compounds is extremely fast. Bulky substituents in appropriate positions decrease the interconversion rate and make this novel type of inherent chirality detectable by 1H and 13C NMR.     

A study of some trace elements in infant foods

Seven trace elements were determined in milk formulas, powder milk and infant food. Instrumental neutron activation analysis was used for the analysis of Fe, Zn, Co, Cr and Rb, while As and Cu content was determined using radiochemical neutron activation analysis. Differences were found in the trace element content of foods of the same type. Milk formulas are comparable with human milk according to the results obtained for the elements analyzed. The samples of powder cow's milk presented similar concentrations of the elements studied. Liver with vegetables was found to have the highest Cu content. A meal prepared at home, made of beef and fresh vegetables showed a higher trace element content than its similar commercial one. An estimation of the daily intake of the elements analyzed was made and compared with minimum recommended daily ingestion.     

Monitoring multi-class pesticide residues in fresh fruits and vegetables by liquid chromatography with tandem mass spectrometry

A new analytical method was developed using liquid chromatography with tandem mass spectrometry for the routine analysis of 31 multi-class pesticide residues and applied to approximately 50 fresh fruit and vegetable samples (green bean, cucumber, pepper, tomato, eggplant, watermelon, melon and zucchini). Extraction of the pesticides with ethyl acetate was carried out. The optimal ionisation conditions were selected for each pesticide in the same run. The procedure was validated and the values of some merit figures, such as recovery, precision, linear range, detection limit and quantification limit for each pesticide were calculated together with its calculated expanded uncertainty (U). The average recoveries in cucumber obtained for each pesticide ranged between 74 and 105% at two different fortification levels (n = 10 each) that ranged between 9 and 250 ng g(-1) (depending on the pesticide). The uncertainty associated to the analytical method was lower than 23% for all compounds tested. The calculated limits of detection and quantitation were typically <1 ng g(-1) that were much lower than the maximum residue levels established by European legislation.     

Influence of synthesis methods on tungsten dispersion, structural deformation, and surface acidity in binary WO3-ZrO2 system

WO3-ZrO2 catalysts were synthesized by precipitating the aqueous solutions of zirconium oxynitrate and ammonium metatungstate with ammonium hydroxide. The white slurry precipitate was treated under three different conditions. In the as-made materials, the amorphous phase was formed in the aged and refluxed samples, while well-crystallized tetragonal and monoclinic phases were obtained in the hydrothermally treated sample. The real amount of tungsten loaded in the samples was similar for the three samples, independently of the treatments; however, the tungsten surface atomic density in the annealed WO3-ZrO2 samples varied between 6 and 9 W atoms/nm2. Two different contrast types of aggregates were determined by scanning electron microscopy, the white particles which are rich in W, and the gray ones which are rich in zirconium; both of them were formed in the calcined solids prepared under aging or reflux condition. A very high dispersion of tungsten species on the zirconia surface was achieved in the hydrothermally treated sample. The degree of the interaction between WO(x) and ZrO2 surface strongly modified the Zr-O bond lengths and bond angles in the structure of tetragonal zirconia as proved by X-ray diffraction analysis and the Rietveld refinement. The catalyst obtained under hydrothermal condition exhibited the highest dispersion of tungsten species in the zirconia, which in turn causes strong structural deformation of the tetragonal ZrO2 phase responsible of the strongest surface acidity and, consequently, the optimum catalytic activity for n-hexane isomerization.