Self-assembled gelation behavior of a hydrophilic polymer bearing a metal-coordination unit with metal ions (PdII or AuIII) was investigated upon addition of a dispersed aqueous solution of the polymer to an aqueous solution of metal ions. Self-assembled gels with different morphologies were formed depending on the metal ions used. Spherical and fibrous gels were formed by gelation with PdII and AuIII ions, respectively. The mechanism for formation of the different gel morphology was examined by measuring cross-linking rates, examining coordination sites, and determining mechanical properties. The PdII self-assembled gels efficiently catalyzed the Mizoroki-Heck cross-coupling reaction of a variety of aryl halides and olefins with a turnover number (TON) and turnover frequency (TOF) of greater than 2,762,000 and 138,100 h–1, respectively. These are the greatest TON and TOF values for heterogeneous polymeric catalysts of the Mizoroki-Heck reaction. The AuIII self-assembled fibrous gels, which had nano-order diameter, contained uniformly dispersed gold nanoparticles and could be synthesized by a facile method, i.e., the dropwise addition of a dispersed aqueous solution of the polymer to an aqueous solution of AuIII ion.

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If a convergent Taylor series f (z) = j 0 a j z j satisfies the condition |a j | M|a k | for some k and all j > k, then one can explicitly determine in terms of M and k the radius of a centred disc containing no more than k roots of f . This problem was solved by Yomdin and Roytwarf using the equivalence of two Bernstein classes of analytic functions and a delicate refinement of the Jensen inequality due to van der Poorten. We give two direct proofs of the above claim: one is more transparent though gives a slightly worse bound for the radius of the circle. The second proof generalizes the simple and popular differentiation-division algorithm and gives the bounds better than the original proof.AMS classification scheme numbers: 34C05, 30C15, 26C10, 34A20 † Home

In the present study, plating films with three-dimensional structures were formed by using a plating bath mixed with Cu sulfate and Ni amidosulfate. Furthermore, the effect of the shape of plating films, which was changed by plating at different potentials, on the adhesive force with epoxy resin was investigated. The results show that when the ratio of the concentration of Ni amidosulfate to that of Cu sulfate was 150:15 (g/L) and the potential was set to ¹1.0 V to ¹2.0 V, dendritic plating films were formed. The average peak shear force of the specimen joined with epoxy resin between two Cu plates with the dendritic plating films formed at the potential of ¹1.5 V, was 180.1 N. The dendritic plating films had higher adhesive force than the smooth plating film through the anchoring effect.

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