Ferrocene derivatives XXVIII. The metallation of phenylazoferrocene and the synthesis of phenylazocyclopentadienyl derivatives of other metals

Phenylazoferrocene undergoes nickelation and palladation exclusively on the phenyl group. Lithium phenylazocyclopentadienide has been converted into derivatives of Mo, Mn, Fe, Ru and Rh.     

Quasipotentials for simple noisy maps with complicated dynamics

The theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems, leading to exponential estimates of invariant probabilities and mean first exit times. In the present article we develop the mathematical foundation of this theory for discrete-time systems, following and extending the work of Freidlin and Wentzell, and Kifer. We discuss strategies for calculating and estimating quasipotentials and show their application to one-dimensionalS-unimodal maps. The method proves to be especially suited for describing the noise scaling behavior of invariant probabilities, e.g., for the map occurring as the limit of the Feigenbaum period-doubling sequence. We show that the method allows statements about the scaling behavior in the case of localized noise, too, which does not originally lie within the scope of the quasipotential formalism.     

A telescope illumination system for a wide-field endoscope

Endoscopic illumination systems conduct light down a built-in fibre-optic bundle to illuminate the object. Many modern endoscopes employ wide-field imaging optical systems and therefore require an illuminating beam of large divergence. This is commonly provided by placing a strong diverging lens at the far end of the fibre bundle, but it results in a poor uniformity of illumination in the object space. This paper describes the design of a telescopic illumination system to overcome this problem.     

Blackett Memorial Lecture: the nuclear option—human factors in safety

The UK nuclear industry is currently undergoing a series of dramatic changes. Important, among many is the establishment of the Nuclear Decommissioning Authority (NDA) with an associated impact on service delivery. At the same time, the debate on the future of our energy supply in the UK is increasingly focused on the question of the nuclear option. Issues of safety and reliability are paramount for the nuclear industry given both the nature of the hazard and the associated public perceptions of the associated risks. This paper explores linked developments in human factors and the management of safety in the nuclear industry in the context of unprecedented change.     

Reliable determination of interpolating polynomials

This paper addresses a fundamental problem in mathematics and numerical analysis, that of determining a polynomial interpolant to specified data. The data is taken as consisting of a set of points (abscissae), at each of which is specified a function value. Additionally, at each point, any number of leading derivative values of the function may be given. Mathematically, this problem is solved. The classical Lagrangian interpolation formula applies in the derivative-free case, and the Newton form of the interpolating polynomial in general.Numerically, few reliable algorithms are available; most published algorithms concentrate on speed of computation. This paper describes an algorithm that delivers the required polynomial in Chebyshev form. It is based on the repeated use of the Newton representation, with a data ordering strategy and iterative refinement to improve accuracy, using a carefully devised merit function to measure success. The algorithm attempts to provide a polynomial that is stable in the sense of backward error analysis, i.e. that is exact for slightly perturbed data.Implementations of the algorithm have been in use since the early 1980s in the NAG Library and NPL's Data Approximation Subroutine Library (DASL). In addition to providing polynomial interpolants in their own right, these implementations are used as computational modules in the NAG and DASL routines for constrained least-squares polynomial data fitting.This paper constitutes the first detailed presentation of the algorithm.     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

A Diepoxide Belonging to the Rare C1 Point Group

2,6- and 2,7-Dimethylanthracenes were reduced seriatim with lithium in liquid ammonia and lithium in methylamine to their 1,4,5,8,9,10-hexahydro derivatives. Two-fold epoxidation of these tetraenes provided the cis and trans diepoxides resulting from electrophilic attack at the inner double bonds. Trans diepoxide 1 has the very unusual characteristic of lacking a σ plane of symmetry but possessing an inversion center. As a consequence, the ¹H NMR spectrum of C₁-symmetric 1 is simplified relative to those of its isomers 5, 9, and 10.