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.     

Benzo[d]-1,2-oxaphospholes as precursors of stabilized C-centered radicals

[reaction: see text] Several benzo[d]-1,2-oxaphosphole 2-oxides were examined as potential precursors of stabilized C-centered radicals. The transient absorption spectra obtained after laser flash photolysis in the presence of di-tert-butyl peroxide showed the features of benzylic radicals with formation and decay kinetics not significantly influenced by the presence of oxygen. In the case of compounds with two possible diastereomeric forms, the C-H bond of the trans-isomers [corrected] is more reactive toward hydrogen abstraction.     

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.     

On the convergence of isolated neutral oxygen vacancy and divacancy properties in metal oxides using supercell models

The properties of isolated neutral oxygen vacancies and divacancies of metal oxides of increasing complexity (MgO, CaO, alpha-Al2O3, and ZnO) have been studied by means of density-functional theory within a supercell periodic approach. Vacancy formation energies, vacancy-vacancy interactions, and geometry rearrangements around these point defects have been investigated in detail. The characterization of the electronic structure of these point defects has been established by analysis of the density of states and of the topology of the electron density and of electron localization function. It is found that the chemical character of the oxide determines the properties of the oxygen vacancies. For the covalent ZnO oxide, a more complex scheme arises in which the relaxation around the oxygen vacancy is much larger leading to the formation of Zn4-like almost metallic particles in the crystal. The relationship of these structures with the crystal shear planes is discussed. The present study shows that supercells containing approximately 200-300 atoms provide converged values for the geometric and electronic structure of oxygen vacancies of these metal oxides in the point defect low concentration limit.     

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.     

Development and validation of an analytical methodology for the determination of p,p′-DDT, p,p′-DDE and p,p′-DDD in fish oil pills

An analytical methodology was proposed and validated to be applied to the determination of p,p′-DDT and its metabolites p,p′-DDE and p,p′-DDD in fish oil. The analytical procedure presented in this paper involves a single-step clean up process prior to the analysis. A solution of 1,2,3,4-tetrachloronaphtalene was used as internal standard.The analytical technique used was gas chromatography coupled to an electron capture detector. Details on the validation process are provided.The limits of detection ranged from 2.6 to 4.7 pg μL^− 1. The BCR 598 standard reference material (cod liver oil) was used to evaluate the performance of the methodology with satisfactory recoveries for all the compounds.The analytes were determined in three different fish oil pills sold in Spain as a supplementary vitamin support. The sum of p,p′-DDT and metabolites was from 13.2 to 51.3 ng g^− 1, the dominant compound being p,p′-DDE.     

Solid-phase synthesis of the cyclic lipononadepsipeptide [N-Mst(Ser1), d-Ser4, L-Thr6, L-Asp8, L-Thr9]syringotoxin

An optimized solid-phase strategy for the preparation of the cyclic lipononadepsipeptide [N-Mst(L-Ser1), D-Ser4, L-Thr6, L-Asp8, L-Thr9]syringotoxin is reported. The strategy is based on the use of a mild orthogonal protection scheme and the incorporation of the nonproteinogenic amino acid (Z)-Dhb into the peptide chain as the dipeptide Fmoc-Thr(tBu)-(Z)-Dhb-OH. The didehydrodipeptide was synthesized by a water-soluble carbodiimide-induced beta-elimination of a protected dipeptide containing a residue of Thr with its free hydroxy side chain unprotected.     

Stereoselective synthesis of trans-2,3-disubstituted pyrrolidines via addition to N-acyliminium ions

An efficient and stereoselective synthesis of trans-2,3-disubstituted pyrrolidines is described. The intermolecular alkylation of racemic N-acyliminium ions generated in situ from the corresponding 3-substituted lactams proceeds stereoselectively and in high yield.     

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).