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.     

Restricted rotation about the boron---nitrogen bond in aminoboranes

The application of variable temperature ¹³C NMR to the study of a series of chlorodialkylaminophenylboranes has enabled G values for the rotational barrier, about the boron---nitrogen bond, to be determined.     

Properties of ITO films prepared by reactive magnetron sputtering

Indium tin oxide (ITO) thin films were deposited by mid frequency pulsed dual magnetron sputtering using a metallic alloy target with 10 wt.% tin in an atmosphere of argon and oxygen. The aim of the work was to study the interdependence of structural, electrical and optical properties of ITO films deposited in the reactive and transition target mode, respectively. The deposition rate in the transition mode exceeds the deposition rate in the reactive mode by a factor of six, a maximum value of 100 nm·m min⁻¹ could be achieved. This corresponds to a static deposition rate of 200 nm min⁻¹. The lowest electrical resistivity of 1.1·10⁻³ Ω cm was measured at samples deposited in the high oxygen flow range in the transition mode. The samples show a good transparency in the visible range corresponding to extinction coefficients being below 10⁻². X-ray diffraction was used to characterise crystalline structure as well as film stress. ITO films prepared in the transition mode show a slightly preferred orientation in (211) direction, whereas films deposited in the reactive mode are strongly (222) oriented. Compared to undoped In₂O₃ all samples have an enlarged lattice. The lattice strain perpendicular to the surface is about 0.8% and 2.0% for films grown in the transition and the reactive mode, respectively. Deposition in the transition mode introduces a biaxial film stress in the range of −300 MPa, while stress in reactive mode samples is −1500 MPa.     

Synthesis of substituted 5-aminomethyl tetrahydro-isoquinolines and dihydro-isoindoles

The synthesis of ten substituted aminomethylene tetrahydro-isoquinolines is described, proceeding in eight steps from 5-hydroxyisoquinoline via reductive amination of N-Boc tetrahydro-isoquinoline 5-carboxaldehyde. Likewise, reductive amination was used to prepare four substituted dihydro-isoindoles from the corresponding aldehyde. The dihydro-isoindole ring system was conveniently accessed via a 2+2+2 cycloaddition reaction.     

N-heterocyclic carbenes as ligands in high-valent molybdenum and tungsten complexes

Oxometal complexes of molybdenum and tungsten in high oxidation states from stable adducts with 1,3-dimethylimidazoline-2-ylidene (L) 1. The first ‘carbene’ complexes of molybdenum(VI) [MoO₂Cl(L)₃]Cl (3a) and tungsten(VI) WO₂Cl₂(L)₂ (4b) are reported.     

Link concordance invariants and homotopy theory

Summary We show that each of a sequence of concordance invariants for codimension-two links of spheres inS ⁿ⁺² , defined by Kent Orr, is identically zero forn>1. For classical links (n=1), the same proof shows that these invariants vanish if and only if Milnor's vanish (a result obtained independently and earlier by Orr himself). We offer sufficient conditions for the vanishing of Orr's -invariant (not covered by the above). We discuss how this relates to positive results.Supported by a National Science Foundation Postdoctoral Fellowship and the hospitality of Univ. Calif. San Diego Math. Dept.