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).     

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.     

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.     

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.     

Searching of chemical structure data bases with parallel computer hardware

The use of two types of parallel computer hardware for increasing the efficiency of processing in chemical structure data bases is discussed. The distributed array processor can be used for the clustering of 2-D chemical structure data bases by using the Jarvis—Patrick clustering method and for the ranking of output in an experimental system for substructure searching in the 3-D macromolecules in the Protein Data Bank. The Inmos transputer can be used in the construction of PC-based systems for 2-D substructure searching and in the identification of the maximal substructures common to pairs of 3-D molecules.     

Preparation and Chemical and Biological Studies of the Novel Complex μ-1,4,5-triphenyl-1,3,4-triazole-2-thiolate-bis[dichlorotriethylphosphineplatinum(II)]a

The mesoionic compound, 1,4,5-triazole-2-thiolate, is a versatile ligand, capable of binding metal centres in different ways. The present study shows how it reacts with the bridging platinum(II) complex μ-dichlorobis[(chlorotriethylphosphineplatinum(II)], [Pt₂(PEt₃)₂Cl₄], originating a bimetallic complex. Both the sulphur atom and nitrogen 3 behave as basic sites, coordinating different platinum centres. An interesting isomerization process, shown by ³¹P{¹H} n.m.r. spectroscopy, occurs at the S-bonded platinum moiety, resulting in a fluxional behaviour of the complex. It is also shown to target CT-DNA with moderate binding affinity.To the memory of Dr. Wagner M. Teles (1971–2004).     

X-ray structure of fac-[RuH(1,5-cod)(NH2NMe2)3][PF6]: Stabilization of coordinated substituted hydrazines by hydrogen bonding

The structure of [RuH(cod)(NH₂NMe₂)₃][PF₆] has been solved by X-ray diffraction methods and shows the cation to contain a facial arrangement of N,N-dimethylhydrazine ligands, coordinated via the NH₂ nitrogen atoms, and held together by hydrogen bonds.     

Thermal analysis of PMMA/gel silica glass composites

Thermal analysis of poly-methylmethacrylate (PMMA) impregnated porous gel silica glasses confirms that the PMMA chains form hydrogen bonds with the pore surface silanol groups. The adopted conditions for the insitu polymerisation result in about 4% of residual monomers trapped in the polymer, most of them in the amorphous structure. The polymer and monomer mixture takes up the whole of the free pore volume. Most of the residual monomer polymerises during the DSC scans above the glass transition temperature providing an excellent probe for the weak glass transition. Polymerisation in the gel silica glass medium affects the glass transition temperature, the length of polymer chains, and the degree of polymerisation.