Approximation on Simplices with Respect to Weighted Sobolev Norms

Inequalities of Jackson and Bernstein type are derived for polynomial approximation on simplices with respect to Sobolev norms. Although we cannot use orthogonal polynomials, sharp estimates are obtained from a decomposition into orthogonal subspaces. The formulas reflect the symmetries of simplices, but analogous estimates on rectangles show that we cannot expect rotational invariance of the terms with derivatives.     

Electrodeposition of nanocrystalline aluminium from a chloroaluminate ionic liquid

In this letter we show that nanocrystalline aluminium can be electrodeposited in the Lewis acidic ionic liquid based on AlCl₃ (60 mol%) and 1-(2-methoxyethyl)-3-methylimidazolium chloride ([MoeMIm]Cl) (40 mol%). The study comprised cyclic voltammetry, potentiostatic polarization, and SEM and XRD measurements. The methoxy group in the side chain of the imidazolium cation significantly influences the electrodeposition pathway of Al in comparison to [EMIm]Cl/AlCl₃. Cyclic voltammetry shows a significant current loop attributed to nucleation. Shiny Al layers are obtained with an average crystallite size of about 40 nm.     

On the electronic structure of the hydrogenase H-cluster

X-ray absorption spectroscopic measurements and density functional calculations suggest that the hydrogenase H-cluster is best described as an electronically inseparable 6Fe-cluster due to extensive delocalization of frontier molecular orbitals of the iron centres, sulfide and the non-innocent dithiolate ligands.     

Muonium dynamics in doped Si above room temperature studied by longitudinal field — μSR

We report longitudinal fieldSR 1/T ₁ measurements in Si from room temperature to 850 K. The data in pure Si and SiB (p-type) can be explained in a two-state model where muonium cycles between its positive and neutral charge states. Within this model, the average muon-electron hyperfine parameter in the neutral state is consistent with muonium at the tetrahedral interstitial site, indicating that at the highest temperatures measured, neutral muonium spends a significant amount of time away from the bond centered site, the calculated potential minimum. Although this is also true for SiP (n-type) at high temperatures, the data in the region between 300–450 K indicates that at least one other state is involved in the dynamics.This work is partially supported by the Natural Sciences and Engineering Research Council of Canada, the Welch Foundation (C-1048 [TLE], D-1053 [RLL] and the U.S. National Science Foundation (DMR-8917639 [TLE,BH]).     

The Synthesis and Some Reactions of N-Alkyl-4-Quinolone-3-Carboxylic Acids

A modification of the Gould-Jacobs reaction, particularly useful for the preparation of N-alkyl-4-quinolone-3-carboxylic acids, is described. Decarboxylation of these acids leads to N-alkyl-4-quinolones or, in the case of N-ethyl-benzo[h]-4-quinolone-3-carboxylic acid, to 4-ethoxy-benzo[h]quinoline. Evidence for the structure of the products is presented and the synthesis of relevant compounds is described.     

Application of atmospheric pressure ionization HPLC-MS-MS for the analysis of natural products

Summary The development of techniques utilizing atmospheric pressure ionization, namely atmospheric pressure chemical ionization (APCI) and electrospray ionization (ESI), has pioneered the coupling of liquid chromatography (HPLC) with mass spectrometry in recent years. Both ESI and APCI generate ions from polar and labile biomaterials with remarkable ease and efficiency. In particular, the use of HPLC with tandem mass spectrometry (MS-MS) opens further dimensions in the field of bioorganic analysis. Thus, HPLC-MS-MS provides the tools for direct elucidation of the structure and variety of polar natural compounds in complex matrices. In order to develop efficient and straightforward strategies for the analysis of polar natural products, the potential and the limitations of these hyphenated analytical techniques are discussed using heterocyclic aromatic amines, fumonisins, acylated glycoconjugates and regioisomeric fatty acid hydroperoxides as examples. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

The bridging function of an apparently nonbridging ligand: dinuclear rhodium complexes with Rh(mu-SbR3)Rh as a molecular unit

Novel dinuclear rhodium complexes of the general composition [Rh2Cl2(mu-CRR')2(mu-SbiPr3)] (4-6) were prepared by thermolysis of the mononuclear precursors trans-[RhCl(=CRR')(SbiPr3)2] in excellent yield. The X-ray crystal structure analysis of 4 (R = R' = Ph) confirms the symmetrical bridging position of the stibane ligand. Related compounds [Rh2Cl2(mu-CPh2)(mu-CRR')(mu-SbiPr3)] (7, 8) with two different carbene units were obtained either from trans-[RhCl(=CPh2)(SbiPr3)2] (1) and RR'CN2 or by a conproportionation of 4 and 5 (R = R' = p-Tol) or 4 and 6 (R= Ph, R' = p-Tol), respectively. While CO reacts with 4 to give the polymeric product [[RhCl(CPh2)(CO)]n] (9), tert-butyl isocyanide replaces the bridging stibane and yields [Rh2Cl2(mu-CPh2)2(mu-CNtBu)] (10). The reaction of 4 with tertiary phosphanes PR3 leads to complete bridge cleavage and affords the mononuclear compounds trans-[RhCl(=CPh2)(PR3)2] (11-15). In contrast, treatment of 4 with SbMe3 and SbEt3 yields the related triply bridged complexes [Rh2Cl2(mu-CPh2)2(mu-SbR3)] (16, 17) by substitution of SbiPr3 for the smaller stibanes. The displacement of the chloro ligands in 4-6 and 10 by n5-cyclopentadienyl gives the dinuclear complexes [(n5-C5H5)2Rh2(mu-CRR')2] (18-20) and [(n5-C5H5)2Rh2(mu-CPh2)2(mu-CNtBu)] (21), of which 18 (R = R' = Ph) was characterized crystallographically.