Krull-Schmidt fails for serial modules

We answer a question posed by Warfield in 1975: the Krull-Schmidt Theorem does not hold for serial modules, as we show via an example. Nevertheless we prove a weak form of the Krull-Schmidt Theorem for serial modules (Theorem 1.9). And we show that the Grothendieck group of the class of serial modules of finite Goldie dimension over a fixed ring is a free abelian group.

     

Free differential algebras: Their use in field theory and dual formulation

The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p>1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding gauge transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.     

Kinetic study of nickel(II) complexation by pteroylglutamic acid

The kinetics of the complexation of NiII by pteroylglutamic acid have been studied in the 545 ∘C range, the ionic strength (0.6 M) being regulated with KNO3, in the 5.5–7.0pH range, using the stopped-flow method. Under the experimental conditions two processes were observed. The faster process was detected in the millisecond range and is associated with the reaction between NiII and the ligand. The slower is observed within a few seconds. Complementary equilibrium studies were made at 25 ∘C. The results are consistent with the formation of a 1:1 complex between the reactants, and a mechanism is proposed to account for the observed behaviour. Equilibrium constants for the NiII plus pteroylglutamic acid system, as well as activation parameters, are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

New Hg2+ and Cu2+ selective chromo- and fluoroionophore based on a bichromophoric azine

[graph: see text] A new probe, 1,4-bis(1-pyrenyl)-2,3-diaza-1,3-butadiene, selectively senses Hg2+ and Cu2+ through two different channels: the yellow-deep-pink color change and the enhancement of the fluorescence with the red shift of the excimer emission, which can visually be discernible by a green fluorescence in the presence of Hg2+ and an orange fluorescence in the presence of Cu2+.     

The reactions of some halogenated pyridines with methoxide and methanethiolate ions in dimethylformamide

The reactions of 2,6- and 2,5-dibromopyridines and of 2,3- and 3,5-dichloropyridines with sodium isopropanethiolate and methanethiolate afforded the products of mono- or of bis-substitution depending on the experimental conditions. The same pyridines reacted with sodium methoxide to give good yields of the mono-substituted products; bis-substitution occurred easily only in the case of the 2,6-dibromo- and of the 3,5-dichloropyridine. The syntheses of some methoxy thiomethoxypyridine, starting from the halogeno methoxypyridines or from the halogeno thiomethoxypyhdines are also described. The bis-(alkylthio)pyridines can be fragmented by sodium in HMPA to give the bis(mercapto)pyridines.     

Heme-protein active site models via self-assembly in water

[structure: see text] Water-soluble models of heme-protein active sites are obtained via the self-assembly of cationic porphyrins 1 and tetrasulfonato calix[4]arene 2 (K(1.2)() = 10(5) M(-)(1)). Selective binding of ligands either outside or inside the cavity of assemblies 1.2 via coordination to the zinc center has been observed. Small ligands such as 4-methylpyridine and 1-methylimidazole are encapsulated, while the bulkier caffeine is bound outside. Assemblies Co-1.2, in which the Zn porphyrin moiety has been replaced by a Co(II) porphyrin, can act as O(2) carriers.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.