Multilinear interpolation between adjoint operators

Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L^q estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak L^q estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak L^q has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).     

Synthesis and addition polymerization of vinylbenzyl transition metal compounds

Summary The synthesis of three vinylbenzyl complexes (n⁵-C₅H₅)-M(CO)_n(CH₂C₆H₄CH=CH₂), [1), M=Mo, n=3; (2), M=W, n=3; (3), M=Fe, n=2] is reported. Complexes (1) and (2) have been copolymerized with monomers, such as styrene, methyl methacrylate, andN-vinyl-2-pyrrolidone, in benzene using azoisobutyronitrile as initiator. The rates of incorporation of (2) into copolymers with styrene and methyl methacrylate were the same as the rate of incorporation of the organic monomer. The homopolymerization of (2) was also carried out. Polymerizations occurred satisfactorily except for the copolymerization of (1) with styrene, where little incorporation of the organometallic monomer occurred.     

Output dynamics and stabilisation of a multi-mode double-clad Yb-doped silica fibre laser

The intensity dynamics of the double-clad Yb fibre laser have been characterised. Stabilisation of the fibre laser intensity by using uniform bi-directional pumping is demonstrated. For the single-end-pumped Yb fibre laser, the output becomes more stable for the shorter fibre length due to the higher threshold of stimulated Brillouin scattering, SBS, and Kerr effects and the reduction of saturated absorber effects caused by any unpumped fibre section. By additional pumping in a double-end-pumped configuration, the output power can be scaled higher before detecting high intensity pulses initiated by SBS in the Yb fibre laser due to the reduction of saturable absorption effect. It is confirmed that uniform pumping enhances the stability of the laser output.     

Photo-stabilising action of metal chelates in polypropylene—Part IV: Influence of metal stearates in an exchange mechanism

The effect of calcium and nickel stearates on the photo-stabilising action and photo-decomposition of one calcium and two nickel metal chelates in polypropylene has been examined using infra-red and ultraviolet derivative spectroscopy. Whereas the presence of calcium stearate antagonises the photo-stabilising action of one nickel chelate, Irgastab 2002, it strongly synergises with the other, Cyasorb UV 1084. The presence of nickel stearate synergises with the calcium chelate, Irganox 1425, in unprocessed polymer whereas, in processed polymer, it exhibits antagonism. Rates of photo-decomposition of the metal chelates are also affected by metal stearates. The data suggests that, with these nickel chelates, there might be some degree of metal exchange with certain metal stearates.     

Dynamic light scattering studies of poly(ethylene oxide) adsorbed on Laponite: layer conformation and its effect on particle stability

Dynamic light scattering has been used to determine the hydrodynamic thickness of poly(ethylene oxide) (PEO) adsorbed on synthetic anisotropic clay particles (Laponite) as a function of molecular weight. The layer thicknesses, and their increase with molecular weight, indicate that the conformation of the adsorbed layer is very compact and is much smaller than those normally observed for polymer adsorption on flat interfaces. The aggregation kinetics of the polymer coated particles in 5 mM NaCl was analyzed in a quantitative manner, revealing that the potential barrier to aggregation is strongly enhanced when polymer is present.     

Regioselective supramolecular catalysis. Exploiting multiple binding motifs in propanediurea molecular clips

Molecular clips derived from 2,4,6,8-tetraazabicyclo[3.3.1]nonane-3,7-dione promote increased regioselectivity in the SO₂Cl₂-mediated electrophilic aromatic chlorination of ortho-cresol leading to para/ortho ratios (R_p/o) <25; approximately six times larger than in the absence of the clip. Specific recognition events involving hydrogen-bond, π-π and dative covalent interactions are implicated.     

Synthesis and anticonvulsant activity of some novel 3-aminoquinazolines

A number of novel 3-aminoquinazolines were obtained via two synthetic pathways. In the first method o-aminobenzoylhydrazines were prepared either by reacting an isatoic anhydride and a hydrazine or by reacting o-nitrobenzoic acid with a hydrazine, followed by catalytic reduction. Subsequent cyclization with an appropriate orthoester provided 3-aminoquinazolines and 2-methyl-3-aminoquinazolines. The second pathway involved condensation of o-aminoacetophenone with a hydrazine to form hydrazones which were reduced to aminohydrazines and cyclized as above to yield 4-methyl-3-aminoquinazolines and 2,4-dimethyl-3-aminoquinazolines. The title compounds were evaluated in mice in MES and sc Met seizure models for anticonvulsant activity, and in the rotorod test for neurotoxicity. They were generally toxic. However, 4-methyl-3-(N-piperidino)-3,4-dihydroquinazoline hydrochloride exhibited activity comparable to that of methaqualone.     

Thin layer distillation for matrix isolation in flow analysis

Analyte transfer from the matrix in a thin layer distillation (TLD) cell and its subsequent measurement were investigated in a flow injection configuration. We designed the cell such that the donor and acceptor streams flowed in parallel channels separated by a thin dividing wall. The matrix transfer process involved room-temperature distillation of the analyte into the headspace of the TLD cell and its subsequent condensation/uptake by a concurrently flowing acceptor stream. There are no membranes; hence there are no membrane-related problems. The TLD system design was optimized with respect to its dimensions and operational parameters. Throughput and sensitivity were compared with a conventional pervaporation flow injection (PFI) system for ammonia and five different amines. For the higher molecular mass amines, the TLD approach provided comparable or superior performance. The TLD technique should be an attractive approach for online analysis of volatile chemical species in ‘dirty’ samples, especially for volatile analytes of higher molecular mass.     

Interactions between terminally substituted amino acids in an aqueous and a non-aqueous environment. Enthalpic interaction coefficients in water and in N,N-dimethylformamide at 25°C

Enthalpies of dilution of the N-acetyl amides of glycine, L-alanine, L-valine, L-leucine, and L-phenylalanine, dissolved in N,N-dimethylformamide (DMF) as a solvent have been measured at 25°C. The results obtained have been analyzed to give the enthalpic interaction (or virial) coefficients of the solutes and these are compared with information previously obtained in aqueous systems. There are marked differences in the interaction properties in the two solvents and, while the additivity approach of Savage and Wood is applicable to the solutes in water it is not suitable for representing the interactions in DMF. A correlation is presented between the enthalpic second virial coefficients in DMF and the propensity of side-chains to be in proximity in globular proteins.