Oriented local entropies for expansive actions by commuting automorphisms

Given an expansive action α of ?² by automorphisms of a compact connected metrizable abelian groupX, we show how the entropy of the action may be decomposed into local contributions, 1 $$h(\alpha ) = \sum\limits_{p \leqslant \infty } {h_p^{(a,b)} } (\alpha )$$ in which the summandh _p ^(a,b) (α) represents thep-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a, b). We recognize thep-adic contribution as an integral over thep-adic unit circle, in analogy with the global counterpart. As (a, b) changes, the decomposition (1) changes only when the line through (a, b) passes through one of a finite collection of critical directions, which are explicitly identified.     

Towards slow μ− production via muon catalyzed fusion

Slow ^– production via dd-CF using a two-layer arrangement is investigated. To determine its feasibility, experimental measurements are now in progress using the muonic X-ray detection method. The following experimental steps are being considered: (1) measurement of the number of ^– stopped inside a solid H₂/D₂ layer by detecting p K X-rays, (2) hot d emission detection by placing a secondary target at a distance of 10–30 mm from the layer and by detecting specific delayed X-rays, (3) measurement of the disappearance of d emission as the added D₂ layer is increased, (4) dd-CF measurement by detecting fusion protons, and (5) slow ^– emission detection. Results of the initial test experiment are presented.     

Unprecedented reversible migration of amide to schiff base ligands attached to tin: latent single-site initiators for lactide polymerization

In an unprecedented transformation, amide ligands are found to attack the imine carbon centers of tridentate Schiff base ligands attached to tin. The process is reversible, and the resultant (masked) amide species can be exploited as latent single-site initiators for the controlled polymerization of rac-lactide.     

Reactivity patterns of thermally stable, terminal, electrophilic phosphinidene complexes towards diazoalkanes: oxidation at the phosphorus centre and formation of P-bound eta1-phosphaazine, eta1-phosphaalkene and eta3-diazaphosphaallene complexes

The thermally stable, terminal phosphinidene complexes [CpM(CO)2(eta1-PNiPr2)]AlCl4(Cp= Cp, Cp*; M = Fe) and [Cp*M(CO)3(eta1-PNiPr2)]AlCl4 (M = Cr, Mo, W) react with Ph2C=N=N to form terminal P-coordinated eta1-phosphaazine and eta3-diazaphosphaallene ligands, respectively, whereas [CpFe(CO)2(eta1-PNiPr2)]AlCl4 reacts with Me3SiCHN2 affording a terminal phosphorus bound eta1-phosphaalkene complex.     

Selective modification of the 2-position of pyridoxol

Pyridoxol, protected by acetylation of the hydroxyl groups, has been converted to its N-oxide which upon reaction with perfluoroacetie anhydride yields a 2-nor-2-hydroxymethylpyridoxol derivative as an intermediate. This compound undergoes acyl migration from the 3-position. Protection of the pyridoxol hydroxyls by benzylalion followed by the same treatment yields the unrearranged α²-hydroxy derivative. This compound has been converted to a series of α²-substituted pyridoxols (X = -Cl, -Br, -OCOCH₃, -OCH₃, -OC₂H₅).