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     

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 alkaline polymer electrochemical interface: a breakthrough in application of alkaline anion-exchange membranes in fuel cells

A novel alkaline polymer has been developed as an interfacial material for use in the preparation of metal-cation-free alkaline membrane electrode assemblies (MEAs) for all-solid-state alkaline fuel cells (AFCs) with long-term performance stability.     

Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on . In dimensions d > 6, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is , and thereby prove a version of the Alexander–Orbach conjecture in this setting. The proof divides into two parts. One part establishes general estimates for simple random walk on an arbitrary infinite random graph, given suitable bounds on volume and effective resistance for the random graph. A second part then provides these bounds on volume and effective resistance for the incipient infinite cluster in dimensions d > 6, by extending results about critical oriented percolation obtained previously via the lace expansion.     

GUIDELINES FOR WHOLE-BODY VIBRATION HEALTH SURVEILLANCE

There is strong epidemiological evidence that occupational exposure to WBV is associated with an increased risk of low back pain (LBP), sciatic pain, and degenerative changes in the spinal system, including lumbar intervertebral disc disorders. A prototype health surveillance scheme for WBV is presented in this paper. Surveillance is the collection, analysis, and dissemination of data for the purpose of prevention. The aims are to assess health status and diagnose vibration-induced disorders at an early stage, to inform the workers on the potential risk associated with vibration exposure, to give preventive advice to employers and employees and to control whether preventive measures which have been taken, were successful. It is suggested that a pre-placement health examination should be offered to each worker who will be exposed to WBV so as to make the worker aware of the hazards, to obtain baseline health data, and to identify medical conditions that may increase the risk due to WBV. The case history should focus on personal history, work history, and leisure activities involving driving of vehicles. The personal medical history should detail back pain complaints, disorders in the spine, any injuries or surgery to the musculoskeletal system. A physical examination on the lower back should be performed on workers who have experienced LBP symptoms over the past 12 months. The preplacement examination should be followed by periodic health reassessment with a regular interval according to the legislation of the country. It is suggested that periodic medical examination should be made available at least every 2 years to all workers who are exposed to WBV. Any change in vibration exposure at the workplace should be reported by the employer. If an increase in vibration exposure or a change in health status have occurred, the medical re-examination should be offered at shorter intervals at the discretion of the attending physician. There should be a periodic medical examination, which includes recording any change in exposure to WBV. The findings for the individual should be compared with previous examinations. Group data should also be compiled periodically. Medical removal may be considered along with re-placement in working practices without exposure to WBV. This paper presents opinions on health surveillance for whole-body vibration developed within a working group of partners funded on a European Community Network (BIOMED2 concerted action BMH4-CT98-3251: Research network on detection and prevention of injuries due to occupational vibration exposures). The health surveillance protocol and the draft questionnaire with explanation comments are presented for wider consideration by the science community and others before being considered appropriate for implementation.