Gorenstein curves and symmetry of the semigroup of values

LetO be the local ring of a irreducible algebroid curve and S its semigroup of values, Kunz in [7] proves thatO is a Gorenstein ring if and only if S is symmetrical. In this paper we give a generalization of this fact for the case of reduced curves with an arbitrary number of branches, d. For it we introduce a concept of symmetry for the semigroup of values S₊ ^d which generalizes the well known symmetry for d=1 (i.e. the irreducible case). This concept of symmetry is also closely related to the symmetry introduced by García in [4] (for the d=2 case) and the author in [3] (for arbitrary d) with the main goal of the explicit determination of S (in the case of plane curves).     

The modulating possibilities of dicarbollide clusters: optimizing the Kharasch catalysts

exo-Cluster dicarbollides substitution has allowed tuning of the E degrees (Ru(II)/Ru(III)) potential to obtain the best-performing Kharasch catalyst. We postulate that this is possible through the to-and-fro electron movement between the boron cluster and the sulfonium moieties.     

Shaping Solid-State Supramolecular Cavities: Chemically Induced Accordionlike Movement of gamma-Zirconium Phosphate Containing Polyethylenoxide Pillars

The hydrophilic oxygen atoms of polyethylenoxide chains inserted as pillars in gamma-zirconium phosphate form hydrogen bonds with the acid groups of the host. As a result the pillars are almost perpendicular to the gamma layers. Upon changing the pH level of the supernatant solution the hydrogen bonds are broken and the pillars become almost perpendicular to the layers (shown schematically). Thus there is a reversible enlargement-shortening of the interlayer space.     

Optimization of culture medium and conditions for penicillin acylase production by Streptomyces lavendulae ATCC 13664

The culture medium for Streptomyces lavendulae ATCC 13664 was optimized on a shake-flask scale by using a statistical factorial design for enhanced production of penicillin acylase. This extracellular enzyme recently has been reported to be a penicillin K acylase, presenting also high hydrolytic activity against penicillin V and other natural aliphatic penicillins such as penicillin K, penicillin F, and penicillin dihydroF. The factorial design indicated that the main factors that positively affect penicillin acylase production by S. lavendulae were the concentration of yeast extract and the presence of oligoelements in the fermentation medium, whereas the presence of olive oil in the medium had no effect on enzyme production. An initial concentration of 2.5% (w/v) yeast extract and 3 microg/mL of CuSO4 x 5H2O was found to be best for acylase production. In such optimized culture medium, fermentation of the microorganism yielded 289 IU/L of enzyme in 72 h when employing a volume medium/volume flask ratio of 0.4 and a 300-rpm shaking speed. The presence of copper, alone and in combination with other metals, stimulated biomass as well as penicillin acylase production. The time course of penicillin acylase production was also studied in the optimized medium and conditions. Enzyme production showed catabolite repression by different carbon sources such as glucose, lactose, citrate, glycerol, and glycine.     

Latex Fractionation by Sedimentation and Colloidal Crystallization: The Case of Poly(styrene-co-acrylamide)

Poly(styrene-co-acrylamide) (PS-AAM) latex was prepared, fractionated by sedimentation under gravity, and characterized by PCS, infrared spectra, secondary and backscattered electron imaging in the scanning electron microscope, and electron spectroscopy imaging in an analytical transmission electron microscope. Three latex fractions were obtained. The lower fraction was opalescent and its particles were the more uniform, concerning size, chemical composition, and topochemical features. This lower fraction was still further fractionated by zonal centrifugation in a density gradient, yielding two fractions with similar macrocrystal-forming abilities but different sizes and chemical compositions. These results confirm those previously obtained for the PS-HEMA latex. Copyright 2000 Academic Press.