Hölder exponents and box dimension for self-affine fractal functions

We consider some self-affine fractal functions previously studied by Barnsleyet al. The graphs of these functions are invariant under certain affine scalings, and we extend their definition to allow the use of nonlinear scalings. The Hölder exponent,h, for these fractal functions is calculated and we show that there is a larger Hölder exponent,h , defined at almost every point (with respect to Lebesgue measure). For a class of such functions defined using linear affinities these exponents are related to the box dimensionD _B of the graph byh2–D _Bh .Communicated by Michael F. Barnsley.     

Iron(III) salen-type catalysts for the cross-coupling of aryl Grignards with alkyl halides bearing beta-hydrogens

Iron(III) salen and related complexes are active catalysts for the coupling, under mild and simple reaction conditions, of aryl Grignard reagents with primary and secondary alkyl halide substrates bearing beta-hydrogens.     

Palladacyclic catalysts in C-C and C-heteroatom bond-forming reactions

Palladacycles are amongst the most active catalysts in Heck-type carbon-carbon bond formation and related carbon-heteroatom bond forming reactions. For instance they have recently emerged as showing the highest activity in the Suzuki coupling of electronically challenging aryl chloride substrates. In addition to the high activity they display, their ease of synthesis, facile modification and comparative stability all act to enhance their appeal.     

The Structure of the Antibiotic Hedamycin. I. Chemical,Physical and Spectral Properties

Interpretation of the chemical and spectral (IR., UV., ¹H- and ¹³C-NMR.) properties of the antitumor antibiotic hedamycin (C₄₁H₅₀N₂O₁₁) suggests that the molecule contains a methyl substituted 1-hydroxyanthraquinone nucleus, an α, β-unsaturated ketone, two sugar-like tetrahydropyran rings ( 4 and 8 ) and an aliphatic chain 2 , presumably with an epoxy group (see the Scheme).     

Simple tricyclohexylphosphine-palladium complexes as efficient catalysts for the Stille coupling of deactivated aryl chlorides

Simple, inexpensive tricyclohexylphosphine adducts of palladium show the highest activity yet observed in the Stille coupling of non-activated and deactivated aryl chlorides.     

The Suzuki coupling of aryl chlorides in TBAB-water mixtures

Palladium acetate in a mixture of TBAB and water can be used as an effective catalyst for the Suzuki coupling of deactivated aryl chloride substrates.