Quantum algebras for maximal motion groups ofN-dimensional flat spaces

An embedding method to getq-deformations for the nonsemisimple algebras generating the motion groups ofN-dimensional flat spaces is presented. This method gives a global and simultaneous scheme ofq-deformation for all iso(p, q) algebras and for those obtained from them by some Inönü-Wigner contractions, such as theN-dimensional Euclidean, Poincaré, and Galilei algebras.     

Discrete coulomb potential

Physics of Atomic Nuclei - In this work we present a discretization of the Schrödinger equation with the Coulomb potential in a discrete space—time making use of the Umbral Calculus.     

Simple algebras and Drinfeld doubles

The Drinfeld double structure underlying all the Cartan series of simple Lie algebras is discussed. The two solvable algebras that allow its definition are constructed enlarging each simple algebra of rank n with a central Abelian algebra of dimension n. In these solvable algebras, isomorphic to the two Borel subalgebras, a pairing can be built. The complete machinery of Drinfeld doubles is described in all details. This offers a new approach to the explicit construction of canonical quantum deformation of simple algebras and fixes uniquely, independently and differently from known conventions, canonical bases for all of them. The Drinfeld doubles for A _n and C _n are explicitly written. The full quantization of su(3) is discussed in terms of standard commutators as the A ₂ Drinfeld double requires. The text was submitted by the authors in English.     

The crystal structure of biatractylolide,an 8,8' (C-C) linked dimeric 12,8-eudesmanolide from the resin of Trattinickia rhoifolia WILLD

A symmetrical dimeric sesquiterpenoid, biatractylolide (1), was isolated from the resin of Trattinickia rhoifolia WILLD. The structure of compound 1 was elucidated by one- and two-dimensional NMR techniques and electron impact-mass spectra (EI-MS) data, and confirmed by X-ray crystallographic analysis.     

Development of Methodologies for Different Degrees of Resolution of Linear Alkylbenzene Sulfonates in Groundwater and Wastewater by Liquid Chromatography Using Sodium Dodecyl Sulphate

Linear alkylbenzenesulfonates (LAS) are used extensively as surfactants in consumer formulations as a complex mixture of homologues and isomers. Separation of homologues and isomers of LAS is important in industrial and environmental samples in order to establish their behaviour. Here we present a HPLC methodology with fluorescent detection (FD) for the determination of the homologues and isomers as well as the sum of LAS present. The quantification of total LAS was achieved without a column, using the liquid chromatograph as a FIA system. The different homologues were separated using a Lichrospher-100 RP-8 column of 125 × 4 mm using a linear gradient of methanol and 30.0 mM sodium dodecyl sulphate (SDS), increasing the methanol content linearly from 55% to 70% in 16 min. The resolution of isomers was carried out by using two coupled Lichrospher-100 RP-18 columns of 250 × 4 mm. Elution of isomers was done with a gradient of flow rate from 1.0 to 0.25 mL min^–1 using a linear gradient of acetonitrile and 5.0 mM SDS increasing the acetonitrile content linearly from 20% to 40% in 160 min. The methods were validated and applied satisfactorily to the determination of LAS in urban wastewater and ground water.     

Analysis of human histone H4 by capillary electrophoresis in a pullulan-coated capillary,LC-ESI-MS and MALDI-TOF-MS

The object of the present study was the analysis of the human histone H4 (a core histone) in order to evaluate the state of its acetylation. Capillary electrophoresis (CE) using a pullulan-coated capillary provides a rapid and efficient approach to the separation of monoacetylated, diacetylated and triacetylated H4 isoforms from human cells. By using a simple running buffer of 100 mM triethanolamine-phosphate solution at pH 2.5 and exploiting the effectiveness of pullulan-based coverage in preventing adsorptive phenomena, the separation of the differently acetylated isoforms was achieved in less than 15 min with high efficiency and reproducibility. The proposed method was for the first time applied in the analysis of histone H4 fractions obtained from cell lines treated with different histone deacetylase (HDAC) inhibitors, used as potential anticancer drugs. Matrix-assisted laser desorption ionisation time-of-flight mass spectrometry (MALDI-TOF-MS) analysis demonstrated that the acetylation occurred in the histone H4 tail, whereas the CE separation allowed for a fast determination of the percentages of H4 acetylated isoforms in real samples; the results were in agreement with those obtained from liquid chromatography electrospray ionisation mass spectrometry (LC-ESI-MS) analysis. Therefore, the proposed CE method is a useful complementary support to the hyphenated techniques for the rapid monitoring of the activity of HDAC inhibitors.     

Large volume sample stacking in capillary zone electrophoresis for the monitoring of the degradation products of metribuzin in environmental samples

A capillary zone electrophoresis (CZE) method with UV-vis detection has been developed for the simultaneous monitoring of the major degradation products of metribuzin, i.e. deaminometribuzin (DA), deaminodiketometribuzin (DADK) and diketometribuzin (DK). The dissociation acid constants have also been estimated by CE and no significant differences have been observed with the values obtained by applying other techniques. Optimum separation has been achieved in less than 9 min in 40 mM sodium tetraborate buffer, pH 9.5 by applying a voltage of 15kV at 25 degrees C and using p-aminobenzoic acid as internal standard. In order to increase sensitivity, large volume sample stacking (LVSS) with polarity switching has been applied as on-line pre-concentration methodology. Detection limits of 10, 10 and 20 ng/mL for DA, DADK and DK, respectively were obtained. The method has been applied to soil samples, after pressurized liquid extraction (PLE). Samples were extracted at high temperature (103 degrees C and 1500 psi) using methanol as extraction solvent and sodium sulphate as drying agent. This PLE procedure was followed by an off-line pre-concentration and sample clean-up procedure by solid-phase extraction (SPE) using a LiChrolut EN sorbent column. These last two procedures were also suitable for the direct treatment of groundwater samples before CE analysis. The combination of both off-line and on-line pre-concentration procedures provided a significant improvement in sensitivity. LVSS provided pre-concentration factors of 4, 36 and 28 for DK, DA and DADK, respectively and with SPE a pre-concentration of 500-fold for the case of water samples and of 2.5-fold in the case of soil samples was obtained. The method is suitable for the monitoring of these residues in environmental samples with high sensitivity, precision and satisfactory recoveries.     

From <Emphasis Type="Italic">osp</Emphasis>(1|32)⊕<Emphasis Type="Italic">osp</Emphasis>(1|32) to the M-theory superalgebra: a contraction procedure

We show the impossibility to obtain the D’auria–Fré-type superalgebras that allow for an underlying gauge theoretical structure of D = 11 supergravity from the superalgebra osp(1|32)⊕osp(1|32)?, by means of aWeimar-Woods contraction.     

The Conformal Group SU(2, 2) and Integrable Systems on a Lorentzian Hyperboloid

Eleven different types of “maximally superintegrable” Hamiltonian systems on the real hyperboloid (s⁰)² – (s¹)² + (s²)² – (s³)² = 1 are obtained. All of them correspond to a free Hamiltonian system on the homogeneous space SU(2, 2)/U(2, 1), but to reductions by different maximal abelian subgroups of SU(2, 2). Each of the obtained systems allows 5 functionally independent integrals of motion, from which it is possible to form two or more triplets in involution (each of them includes the hamiltonian). The corresponding classical and quantum equations of motion can be solved by separation of variables on the O(2, 2) space.