Asymptotic expansions in n−1 for percolation critical values on the n‐Cube and ℤn

We use the lace expansion to prove that the critical values for nearest‐neighbor bond percolation on the n‐cube {0, 1}ⁿ and on the integer lattice ?ⁿ have asymptotic expansions, with rational coefficients, to all orders in powers of n^?1. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Ruthenium complexes that incorporate a chiro-inositol derived diphosphinite ligand as catalysts for asymmetric hydrogenation reactions

The diol, 1d-1,2,5,6-tetra-O-methyl-chiro-inositol (D-9), can be conveniently prepared from 1d-chiro-inositol using a series of standard protection/deprotection steps. Treatment of D-9 with Ph₂PCl gives the chiral diphosphinite, 1d-3,4-bis(O-diphenylphosphino)-1,2,5,6-tetra-O-methyl-chiro-inositol (D-10). The structure of D-10 has been determined by X-ray crystallography. Using 1l-chiro-inositol as starting material and following the same synthetic sequence used to produce D-10, the other enantiomer of this diphosphinite, 1l-3,4-bis(O-diphenylphosphino)-1,2,5,6-tetra-O-methyl-chiro-inositol (L-10) can also be obtained. Ruthenium complexes of these diphosphinite ligands can be conveniently prepared through ligand substitution reactions with appropriate substrate complexes. Thus, treatment of [RuCl₂(COD)]_n with D-10 in the presence of triethylamine produces the bis(diphosphinite) complex, RuHCl{κ²(P,P)-1d-3,4-bis(O-diphenylphosphino)-1,2,5,6-tetra-O-methyl-chiro-inositol}₂ (11). In addition, reaction between RuCl₂(PPh₃)₃, D-10 and (1R,2R)-(+)-1,2-diphenylethylenediamine gives the mono(diphosphinite) complex, RuCl₂{κ²(P,P)-1d-3,4-bis(O-diphenylphosphino)-1,2,5,6-tetra-O-methyl-chiro-inositol}{κ²(N,N)-(1R,2R)-(+)-1,2-diphenylethylenediamine} (12). The closely related complex RuCl₂{κ²(P,P)-1d-3,4-bis(O-diphenylphosphino)-1,2,5,6-tetra-O-methyl-chiro-inositol}{κ²(N,N)-(1S,2S)-(−)-1,2-diphenylethylenediamine} (13) can be obtained in a similar manner using (1S,2S)-(−)-1,2-diphenylethylenediamine in place of the corresponding (+)-isomer. These new chiral, diphosphinite complexes catalyse the hydrogenation of the ketones acetophenone and 3-quinuclidinone to give the corresponding alcohols with low to moderate enantiomeric excesses. The complexes are not catalytically active for the hydrogenation of the olefin dimethylitaconate or the α-ketoester methyl benzoylformate.     

Logarithmic Correction for the Susceptibility of the 4-Dimensional Weakly Self-Avoiding Walk: A Renormalisation Group Analysis

We prove that the susceptibility of the continuous-time weakly self-avoiding walk on \({\mathbb{Z}^d}\), in the critical dimension d = 4, has a logarithmic correction to mean-field scaling behaviour as the critical point is approached, with exponent \({\frac{1}{4}}\) for the logarithm. The susceptibility has been well understood previously for dimensions d ≥ 5 using the lace expansion, but the lace expansion does not apply when d = 4. The proof begins by rewriting the walk two-point function as the two-point function of a supersymmetric field theory. The field theory is then analysed via a rigorous renormalisation group method developed in a companion series of papers. By providing a setting where the methods of the companion papers are applied together, the proof also serves as an example of how to assemble the various ingredients of the general renormalisation group method in a coordinated manner.     

The diffusion of self-avoiding random walk in high dimensions

We use the Brydges-Spencer lace expansion to prove that the mean square displacement of aT step strictly self-avoiding random walk in thed dimensional square lattice is asymptotically of the formDT asT approaches infinity, ifd is sufficiently large. The diffusion constantD is greater than one.     

A generalised inductive approach to the lace expansion

 The lace expansion is a powerful tool for analysing the critical behaviour of self-avoiding walks and percolation. It gives rise to a recursion relation which we abstract and study using an adaptation of the inductive method introduced by den Hollander and the authors. We give conditions under which the solution to the recursion relation behaves as a Gaussian, both in Fourier space and in terms of a local central limit theorem. These conditions are shown elsewhere to hold for sufficiently spread-out models of networks of self-avoiding walks in dimensions d > 4, and for sufficiently spread-out models of critical oriented percolation in dimensions d + 1 > 5, providing a unified approach and an essential ingredient for a detailed analysis of the branching behaviour of these models. Received: 13 September 2000 / Revised version: 16 May 2001 / Published online: 20 December 2001     

Regeneration of ketones from semicarbazones by lead tetra-acetate: A novel preparation of 18-hydroxycorticosterone

Lead tetra-acetate in acetic acid has been used to cleave a 3-semi-carbazone in a novel preparation of 18-hydroxycorticosterone, designed to avoid strongly acidic conditions.     

High field MAS NMR,with simulations of the effects of disorder on lineshape,applied to thermal transformations of alumina hydrates

Applied Magnetic Resonance - Samples of gibbsite, boehmite, pseudoboehmite and bayerite, calcined at temperatures up to 1000°C, were studied using27Al MAS NMR with spinning speeds up to 15 kHz...     

An optimised glucose oxidase bioelectrode exhibiting high performance direct electron transfer

A glucose oxidase (GOd) bioelectrode exhibiting high performance, direct electron transfer (DET) has been prepared. Unprecedented redox peak current densities of 1 mA cm(-2) were observed alongside a clear electrochemical response to glucose. This system shows potential as a low cost, high performance enzymatic bioelectrode.