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A brief outline is given of some of the main historical developments in the theory and practice of conformal mappings. Originating with the science of cartography, conformal mappings has given rise to many highly sophisticated methods. We emphasize the principles of mathematical discovery involved in the development of numerical methods, through several… (More)

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)

- R. Michael Porter
- SIAM J. Scientific Computing
- 2001

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)

- Luis G. Gorostiza, R. Michael Porter, Eliane R. Rodrigues
- Mathematical and Computer Modelling
- 2004

- Robin M Porter, Andreas A Danopoulos, Gillian Reid, Lisa R Titcomb
- Dalton transactions
- 2005

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)

- Robin M Porter, Andreas A Danopoulos, Gillian Reid
- Inorganic chemistry
- 2006

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)

- Robin M Porter, Andreas A Danopoulos
- Dalton transactions
- 2004

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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