Rates of superlinear convergence for classical quasi-Newton methods

Mathematical Programming - We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these...     

Size‐Dependence of the Melting Temperature of Individual Au Nanoparticles

Nanoparticles have an immense importance in various fields, such as medicine, catalysis, and various technological applications. Nanoparticles exhibit a significant depression in melting point as their size goes below ≈10 nm. However, nanoparticles are frequently used in high temperature applications such as catalysis where temperatures often exceed several 100 degrees which makes it interesting to study not only the melting temperature depression, but also how the melting progresses through the particle. Using high‐resolution transmission electron microscopy, the melting process of gold nanoparticles in the size range of 2–20 nm Au nanoparticles combined with molecular dynamics studies is investigated. A linear dependence of the melting temperature on the inverse particle size is confirmed; electron microscopy imaging reveals that the particles start melting at the surface and the liquid shell formed then rapidly expands to the particle core.     

Separation technique based on electrophoresis,chromatography and magnetism phenomena: the migration time and peak broadening

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Alkyne hydrogenation using Pd–Ag hybrid nanocatalysts in surface‐immobilized dendrimers

A series of Pd–Ag mixed‐metal nanocatalysts were prepared by reduction of Pd–Ag salts in the presence of poly(propylene imine) dendrimers, which were covalently bound to the surface of a silica polyamine composite, BP‐1 (polyallylamine covalently bound to a silanized amorphous silica gel). Three different Pd‐to‐Ag ratios were evaluated (50:50, catalyst 1 ; 40:60, catalyst 2 ; 60:40, catalyst 3 ) with the goal of determining how the amount of Ag effects selectivity, rate and conversion in the selective reduction of alkynes, such as phenylacetylene and 1‐ or 4‐octyne, to the corresponding alkenes. Conditions for the catalysis are reported where there is improved selectivity without a serious reduction in rate when compared with the analogous Pd‐only catalysts. Catalyst 2 worked best for phenylacetylene and catalyst 3 worked best for the octynes. The catalysts could be reused seven times without loss of activity. Copyright © 2015 John Wiley & Sons, Ltd.     

An Isolable Gallium-Substituted Nitrilimine and its Reactivity with B−H,Si−H and B−B Bonds

Reaction of the Ga(I) compound NacNacGa ( 9 ) with the diazo compound N₂CHSiMe₃ affords the nitrilimine compound NacNacGa(N-NCSiMe₃)(CH₂SiMe₃) ( 10 ). Carrying out this reaction in the presence of pyridine does not lead to C−H activation on the transient alkylidene NacNacGa=CHSiMe₃ but generates a metallated diazo species NacNacGa(NHN=CHSiMe₃)(CN₂SiMe₃) ( 13 ) that further rearranges into the isonitrile compound NacNacGa(NHN=CHSiMe₃)(N(NC)SiMe₃) ( 15 ). Reactions of 10 with the silane H₃SiPh and the borane HBcat furnished products of 1,3 addition to the nitrilimine moiety NacNacGa{N(ER_n)NCSiMe₃}(CH₂SiMe₃), whereas reaction with the diborane B₂cat₂ gave the product of formal nitrene insertion into the B−B bond. DFT calculations suggest that the interaction of 9 with N₂CHSiMe₃ proceeds through intermediate formation of an alkylidene compound that undergoes CH activation with a second molecule of N₂CHSiMe₃. Insertion into the B−B bond likely proceeds through an initial 1,3-addition of the diborane, followed by boryl migration to the former nitrene center.