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.     

Total Synthesis of Callyspongiolide,Part 2: The Ynoate Metathesis/cis-Reduction Strategy

The macrocyclic core of the cytotoxic marine natural product callyspongiolide ( 1 ) was forged by ring-closing alkyne metathesis (RCAM) of an ynoate precursor using a molybdenum alkylidyne complex endowed with triarylsilanolate ligands as the catalyst. This result is remarkable in view of the failed attempts documented in the literature at converting electron deficient alkynes with the aid of more classical catalysts. The subsequent Z-selective semi-reduction of the resulting cycloalkyne by hydrogenation over nickel boride required careful optimization in order to minimize overreduction and competing dehalogenation of the compound's alkenyl iodide terminus as needed for final attachment of the side chain of 1 by Sonogashira coupling. The required cyclization precursor itself was prepared via Kocienski olefination.     

Synthesis and Cation-Binding Properties of (1→6)-2,5-Anhydro-D-glucitol with 3,4-Di-O-Pentyl and Decyl Groups by Cyclopolymerization of 1,2:5,6-Dianhydro-D-mannitols

Abstract

The cyclopolymerizations of 1,2:5,6-dianhydro-3,4-di-O-pentyl-D-mannitol (1b) and 1,2:5,6-dianhydro-3,4-di-O-decyl-D-mannitol (1c) were carried out using BF₃OEt₂ and t-BuOK. All the resulting polymers consisted of cyclic constitutional units, i.e., the extent of cyclization was 100%. The polymer structures for the polymerization with t-BuOK were (1→6)-2,5-anhydro-3,4-di-O-pentyl-D-glucitol (2b) and (1→6)-2,5-anhydro-3,4-di-O-decyl-D-glucitol (2c), whereas those with BF₃O-decyl₂ comprised 2,5-anhydro-D-glucitols as major units along with other cyclic ones. These polymers were soluble in n-hexane, CHCl₃, and THF, but insoluble in water, which differs from the amphiphilic solubility of (1→6)-2,5-anhydro-3,4-di-O-methyl-D-glucitol (2a). The cation-binding properties of 2b and 2c were examined using alkali-metal picrates in order to compare them with those of 2a. The extraction yields for each cation decreased in the order of 2c < 2b < 2a. Every polymer exhibited a similar cation-binding selectivity in the order Cs⁺ > Rb⁺ > K⁺ ? Na⁺ > Li⁺. The ratio of K⁺ and Na⁺, K⁺/Na⁺, was 4.6 for 2a, 5.1 for 2b, and 7.1 for 2c in the increasing order 2a < 2b > 2c.     

Conductometry and Thermodynamics Study of Metal Dodecyl Sulfates in Aqueous Solution

The aggregation behavior of metal dodecyl sulfates (MDS), [Na¹⁺, Mg²⁺, Mn²⁺, Co²⁺, and Ni²⁺] in water has been studied by electrical conductivity (at 293.15–333.15 K) and surface tension methods (at 303.15 K). Critical micelle concentrations (CMCs), degree of counterion dissociation (β) evaluated from conductivity data. Using law of mass action model, the thermodynamic parameters viz. Gibbs energy (ΔG_m ⁰), enthalpy (ΔH_m ⁰), and entropy (ΔS_m ⁰) were evaluated. The enthalpy of micellization decreases strongly with increasing temperature. ΔG is always negative (thermodynamically favored process) and slightly temperature and counterion dependent. Gibbs energy and entropy exploit micellization as thermodynamic favorable process. The electrostatic repulsions between ionic head groups, which prevent the aggregation, are progressively screened as the ionic character decreases with the size of the counterion. The plots of differential conductivity, (dk/dc) _T,P , versus the total surfactant concentration enables us to determine the CMC values more precisely than the conventional method. Surfactants with strong condense counterion are adapted to rodlike micelle better than to a spherical micelle. The data are explained in terms of molecular characteristics of surfactants viz. degree of dissociation, polar head group size and counterion.