Poly(4-vinylpyridine) catalyzed hydrolysis of methyl bromide to methanol and dimethyl ether

The hydrolysis of methyl bromide with neutral water is performed in the presence and absence of various amines in a batch reactor at different temperatures (50–125 °C). Screening of poly(4-vinylpyridine) as a potential reusable solid amine catalyst showed maximum efficiency. This significant enhancement in efficiency is due to the capture of HBr by solid PVP and remains phase-separated driving the reaction forward. The major advantage of this process is that the polymer can be easily regenerated and reused without loss of activity making it a very effective catalyst for the conversion of methyl halides to methanol and dimethyl ether.     

Acid-catalyzed isomerization of pivalaldehyde to methyl isopropyl ketone via a reactive protosolvated carboxonium ion intermediate.

Quantitative rearrangement of pivalaldehyde to methyl isopropyl ketone is observed in acids such as trifluoromethanesulfonic acid, anhydrous HF, and trifluoroethyl alcohol-BF3 but not in trifluoroacetic acid. Studies in a mixture of trifluoroacetic acid and trifluoromethanesulfonic acid show that acids with H(o) < or = -11 are able to carry out complete isomerization. These results and density functional theory calculations at the B3LYP/6-31G level suggest that protonated pivalaldehyde undergoes further protosolvation at higher acidities to a reactive superelectrophilic species resulting in rearrangement. A mechanism for the pivalaldehyde rearrangement to methyl isopropyl ketone in strong protic acids involving a reactive protosolvated superelectrophilic intermediate is suggested. Aspects of the related mechanism of the reaction with isobutane with CO in HF/BF3 medium leading to methyl isopropyl ketone are also discussed.     

An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs

Adaptive tensor product wavelet methods are applied for solving Poisson’s equation, as well as anisotropic generalizations, in high space dimensions. It will be demonstrated that the resulting approximations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that we may lose is independent of the space dimension n. The cost of producing these approximations will be proportional to their length with a constant factor that may grow with n, but only linearly.     

Compounds of arsenic,antimony, and tin in mollusc shells

Inorganic arsenic(III) and arsenic(V), methyl-arsenicals, antimony(III), and antimony(V), and butyltin derivatives are present in the shells of molluscs found in the coastal waters of British Columbia.     

A comparison of rigid and flexible crosslinked polymer-supported peptide synthesis

To correlate the coupling difficulty and nature of the support in solid-phase peptide synthesis, a set of difficult peptides were built under identical conditions on rigid and hydrophobic divinyl benzene-crosslinked polystyrene (DVB-PS) and flexible and polar 1,4-butanediol dimethacrylate-crosslinked polystyrene (BDDMA-PS) resins of same functional capacity (∼2 mmol/g). The difficult coupling stages observed on each support were identified by monitoring the acylation time, coupling yield and deprotection efficiency. The yield and purity of the peptides prepared on BDDMA-PS were higher than when DVB-PS support was used.     

Preparation of Enantiomerically Pure β-Silylcarboxyl Derivatives by Asymmetric 1,4-Addition to N-Enoyl-sultams. Preliminary Communication

EtAlCl₂-promoted additions of organocopper reagents to camphor-derived, conjugated N-enoyl-sultams gave saturated and olefinic β-silylcarboxyl derivatives with high diastereodifferentiation. Nondestructive removal of the chiral auxiliary followed by oxidative Si-C bond cleavage furnished enantiomerically pure acetate-derived aldols and propionate-derived ‘anti’ -aldols (via silyl-directed α-methylation).     

Higher Order Mortar Finite Element Methods in 3D with Dual Lagrange Multiplier Bases

Mortar methods with dual Lagrange multiplier bases provide a flexible, efficient and optimal way to couple different discretization schemes or nonmatching triangulations. Here, we generalize the concept of dual Lagrange multiplier bases by relaxing the condition that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the Lagrange multiplier space have the same dimension. We provide a new theoretical framework within this relaxed setting, which opens a new and simpler way to construct dual Lagrange multiplier bases for higher order finite element spaces. As examples, we consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral elements. Numerical results illustrate the performance of our approach. This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12, the Netherlands Organization for Scientific Research and by the European Community's Human Potential Programme under contract HPRN-CT-2002-00286.     

Random Parking, Sequential Adsorption,¶and the Jamming Limit

Identical cars are dropped sequentially from above into a large parking lot. Each car is positioned uniformly at random, subject to non-overlap with its predecessors, until jamming occurs. There have been many studies of the limiting mean coverage as the parking lot becomes large, but no complete proof that such a limit exists, until now. We prove spatial laws of large numbers demonstrating that for various multidimensional random and cooperative sequential adsorption schemes such as the one above, the jamming limit coverage is well-defined. Received: 18 August 2000 / Accepted: 13 November 2000