R. Michael Porter

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We study conformal mappings from the unit disk to circular-arc quadrilat-erals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient functions contain the accessory parameters t, λ of the mapping problem. The parameter λ is designed in such(More)
An effective algorithm is presented for solving the Beltrami equation ∂f = µ ∂f in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy , working in concentric rings, is to construct a piecewise linear µ-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are(More)
Reaction of the dilithium salt of 3,3-dimethyl-1,5-diaza-8-oxacyclodecane, [(NLi)2O], with Zr(NEt2)2Cl2(thf)2 gave the formally 20e- complex [Zr(N2O)2]; metallation of the macrocycle [(NH)2O], with Ti(benzyl)4 gave rise to [(N2O)*Ti(benzyl)]2 in which the trianionic diamido (N2O)* was formed by an unprecedented C-H activation of the carbon [small alpha] to(More)
The novel tridentate azaoxa macrocycle [O(NH)2], 3,3-dimethyl-1,5-diaza-8-oxacyclodecane, can be singly or doubly lithiated with (n)BuLi at the secondary amine N atoms, giving [O(NH)N]Li and [O(N)2]Li2, respectively, and further elaborated with introduction of TMS substituents via reaction with (TMS)Cl. Aminolysis of [Ti(NMe2)2Cl2] or [Zr(NR2)2Cl2(THF)2](More)
N-Arylamido complexes of zirconium in which the amido functional group is attached to an o-(alkyliminoethyl) substituted aromatic ring, have been synthesised by salt elimination reactions and characterised by spectroscopic and diffraction methods; they are analogous to the N-silylamido species recently reported (Dalton Trans., 2002, 3290-3299). The ligands(More)
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