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.     

Resistant starches and health

It was initially hypothesized that resistant starches, i.e., starch that enters the colon, would have protective effects on chronic colonic diseases, including reduction of colon cancer risk and in the treatment of ulcerative colitis. Recent studies have confirmed the ability of resistant starch to increase fecal bulk, increase the molar ratio of butyrate in relation to other short-chain fatty acids, and dilute fecal bile acids. However the ability of resistant starch to reduce luminal concentrations of compounds that are damaging to the colonic mucosa, including fecal ammonia, phenols, and N-nitroso compounds, still requires clear demonstration. As such, the effectiveness of resistant starch in preventing or treating colonic diseases remains to be assessed. Nevertheless, there is a fraction of what has been termed resistant (RS1) starch, which enters the colon and acts as slowly digested or lente carbohydrate in the small intestine. Foods in this class are low glycemic index and have been shown to reduce the risk of chronic disease. They have been associated with systemic physiological effects such as reduced postprandial insulin levels and higher HDL cholesterol levels. Consumption of low glycemic index foods has been shown to be related to reductions in risk of coronary heart disease and Type 2 diabetes. Type 2 diabetes has in turn been related to a higher risk of colon cancer. If carbohydrates have a protective role in colon cancer prevention this may lie partly in the systemic effects of low glycemic index foods. The colonic advantages of different carbohydrates, varying in their glycemic index and resistant starch content, therefore, remain to be determined. However, as recent positive research findings continue to mount, there is reason for optimism over the possible health advantages of those resistant starches, which are slowly digested in the small intestine.     

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).     

The crystal structure of tetrakis[trimethylthiomethyl-platinum(IV)], [Pt(CH3)3(SCH3)4

The crystal structure of trimethyl(thiomethyl)platmum(IV), [Pt(CH₃)₃(SCH₃)]₄, has been determined using X-ray diffraction. The compound has three independent but isostructural tetrameric units in the asymmetric unit. The four metal atoms in each tetramer are linked by bridging thiomethyl sulphurs, with three methyl groups completing the octahedral coordination around each platinum. Mean interatomic distances within the tetramer are PtS, 2.48(2), PtC, 2.00(4), PtPt, 3.80(2) Å, with a mean bridge angle SPtS, 79.1(7)°.     

Hydrolysis of substituted 8-acetoxyquinolines

In the absence of metal ions, the hydrolysis of 2-methyl-8-acetoxyquinoline and of 5-chloro-8-acetoxyquinoline follow the same reaction paths as those of the parent ester 8-acetoxyquinoline, including an intramolecular catalysis by the quinoline nitrogen. Unlike the hydrolysis of the other esters, that of the 2-methyl compound appears not to be catalysed by metal ions, and this is consistent with the view that catalysis by a metal ion involves the formation of a 7-membered chelate structure.