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.     

Magnetostrictive Polarization Compensation on SOI Rib Waveguide

We proposed a novel application of magnetostriction for tuning differential -group- delay (DGD)and polarization- dependent-loss (PDL) of silicon- on -insulator waveguide. A magnetic-field induced change inPDL of over 4dB and a change in DGD by 1ps was demonstrated.     

Polarization-Insensitive All-Optical Time-Division Demultiplexer Constructed with a Nonlinear Loop Interferometer

A polarization-insensitive 40-Gb/s time-division demultiplexer was demonstrated in a polarization-diversity loop configuration. The power penalty was measured to be 2.3 dB at a bit error rates of 10-9 for 10 Gb/s output signals.     

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.