Time delay in the Einstein-Straus solution

We compute the time delay of strong lensing in the framework of the Einstein-Straus solution in presence of a cosmological constant and restrict ourselves to the case of a spatially flat universe. The calculations are done to first order in the ratio of Schwarzschild radius to peri-lens. We apply our results to the lensed quasar SDSS J1004+4112. Our predictions for the time delay between the images C and D of the quasar range from 6 to 13 years and are compatible with the experimental lower bound.     

Solvent-free synthesis of polyhydroquinoline and 1,8-dioxodecahydroacridine derivatives through the Hantzsch reaction catalyzed by a natural organic acid: A green method

Solvent-free and high yielding one-pot synthesis of 1,8-dioxodecahydroacridine and polyhydroquinoline derivatives have been described through Hantzsch condensation of various aldehydes, ammonium acetate with cyclic 1,3-dicarbonyl compounds and ethyl acetoacetate in a very simple, efficient, and environmentally benign method using ascorbic acid as a nontoxic organocatalyst.     

GC/MS analysis and antimicrobial activity of the essential oil of fresh leaves of Eucalytus globulus, and leaves and stems of Smyrnium olusatrum from Constantine (Algeria)

The essential oils of fresh leaves of Eucalyptus globulus L. (Myrtaceae), and leaves and stems of Smyrnium olusatrum L. (Apiaceae), obtained by hydrodistillation in a Clevenger-type apparatus, were analyzed by GC/MS. Twenty compounds were characterized, representing 98.3% of the essential oil of E. globulus, with 1,8-cineole (48.6%), globulol (10.9%), trans-pinocarveol (10.7%), and alpha-terpineol (6.6%) as main components, while thirty-three compounds were characterized, representing 94.3% of the essential oil of S. olusatrum, with sabinene (27.1%), curzerene (13.7%), methyl-1-benzyl-2-oxocyclooctane carboxylate (12.3%), alpha-pinene (7.2%), cryptone (7.1%) and beta-pinene (5.7%) as the major components. The essential oils of E. globulus and S. olusatrum were tested against a wide range of fungal and bacterial strains. Both oils showed significant antimicrobial activity.     

Harder–Narasimhan reduction for principal bundles over a compact Kähler manifold

Generalizing the Harder–Narasimhan filtration of a vector bundle it is shown that a principal G-bundle over a compact K?hler manifold admits a canonical reduction of its structure group to a parabolic subgroup of G. Here G is a complex connected reductive algebraic group; in the special case where , this reduction is the Harder–Narasimhan filtration of the vector bundle associated to by the standard representation of . The reduction of in question is determined by two conditions. If P denotes the parabolic subgroup, L its Levi factor and the canonical reduction, then the first condition says that the principal L-bundle obtained by extending the structure group of the P-bundle using the natural projection of P to L is semistable. Denoting by the Lie algebra of the unipotent radical of P, the second condition says that for any irreducible P-module V occurring in , the associated vector bundle is of positive degree; here is considered as a P-module using the adjoint action. The second condition has an equivalent reformulation which says that for any nontrivial character of P which can be expressed as a nonnegative integral combination of simple roots (with respect to any Borel subgroup contained in P), the line bundle associated to for is of positive degree. The equivalence of these two conditions is a consequence of a representation theoretic result proved here. Received: 10 November 1999 / Revised version: 31 October 2001 / Published online: 26 April 2002     

Bogomolov inequality for Higgs parabolic bundles

We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank two over smooth projective varieties of dimension ≥ 2 satisfy the “parabolic” 'Bogomolov inequality Received: 1 March 1999 / Revised version: 11 June 1999     

Purification and Biochemical Characterization of a Highly Thermostable Xylanase from <Emphasis Type="Italic">Actinomadura</Emphasis> sp. Strain Cpt20 Isolated from Poultry Compost

An extracellular thermostable xylanase from a newly isolated thermophilic Actinomadura sp. strain Cpt20 was purified and characterized. Based on matrix-assisted laser desorption–ionization time-of-flight mass spectrometry analysis, the purified enzyme is a monomer with a molecular mass of 20,110.13 Da. The 19 residue N-terminal sequence of the enzyme showed 84% homology with those of actinomycete endoxylanases. The optimum pH and temperature values for xylanase activity were pH 10 and 80 °C, respectively. This xylanase was stable within a pH range of 5–10 and up to a temperature of 90 °C. It showed high thermostability at 60 °C for 5 days and half-life times at 90 °C and 100 °C were 2 and 1 h, respectively. The xylanase was specific for xylans, showing higher specific activity on soluble oat-spelt xylan followed by beechwood xylan. This enzyme obeyed the Michaelis–Menten kinetics, with the K _m and k _cat values being 1.55 mg soluble oat-spelt xylan/ml and 388 min⁻¹, respectively. While the xylanase from Actinomadura sp. Cpt20 was activated by Mn²⁺, Ca²⁺, and Cu²⁺, it was, strongly inhibited by Hg²⁺, Zn²⁺, and Ba²⁺. These properties make this enzyme a potential candidate for future use in biotechnological applications particularly in the pulp and paper industry.     

Hydrogen production on iron–magnesium oxide in the high-temperature water-gas shift reaction

The effect of the structure of the achiral primary amine additive on the enantioselective heterogeneous catalytic hydrogenation of (E)-2-methyl-2-butenoic acid over cinchonidine modified Pd/Al₂O₃ was studied. It was found that a variety of amines increase the enantioselectivity, which was always accompanied by decrease in the initial rate of the hydrogenations. Based on these results, the participation of the amine additive in the formation of the intermediate complex responsible for enantioselection was suggested. A decrease in the reaction temperature resulted in further increase in the optical purity of the product up to 67%, the highest value reported in the hydrogenation of unsaturated aliphatic acids in this heterogeneous catalytic system so far.     

Optimized Lower Bounds for Five-Body Hamiltonians

A methodology recently proposed for deriving optimized lower bounds for the energies of the ground states of N-body systems is applied to the five-body case. Such lower bounds result from an optimization process over a certain number of parameters. The so-called universal dynamical constraints, i.e., relations between the values of the parameters corresponding to the optimized lower bound and which have the properties to be of dynamical nature and to be independent of the particular form of the potential, are computed in their totality and great calculational details are given. The optimized lower bound obtained in this way proves to be saturated, i.e., identical to the exact result, in the harmonic oscillator case. Particular mass configurations are considered with the corresponding simplifications in the universal dynamical constraints. In relation to the property of saturability in the case of harmonic interactions, particular attention is devoted to five-body systems with harmonic interactions. Various mass configurations are considered and for each case the corresponding ground state energy is derived.