Implicit Solution of Hyperbolic Equations with Space-Time Adaptivity

Adaptivity in space and time is introduced to control the error in the numerical solution of hyperbolic partial differential equations. The equations are discretised by a finite volume method in space and an implicit linear multistep method in time. The computational grid is refined in blocks. At the boundaries of the blocks, there may be jumps in the step size. Special treatment is needed there to ensure second order accuracy and stability. The local truncation error of the discretisation is estimated and is controlled by changing the step size and the time step. The global error is obtained by integration of the error equations. In the implicit scheme, the system of linear equations at each time step is solved iteratively by the GMRES method. Numerical examples executed on a parallel computer illustrate the method.     

A multigrid preconditioner for an adaptive Black-Scholes solver

This paper is concerned with the efficient solution of the linear systems of equations that arise from an adaptive space-implicit time discretisation of the Black-Scholes equation. These nonsymmetric systems are very large and sparse, so an iterative method will usually be the method of choice. However, such a method may require a large number of iterations to converge, particularly when the timestep used is large (which is often the case towards the end of a simulation which uses adaptive timestepping). An appropriate preconditioner is therefore desirable. In this paper we show that a very simple multigrid algorithm with standard components works well as a preconditioner for these problems. We analyse the eigenvalue spectrum of the multigrid iteration matrix for uniform grid problems and illustrate the method’s efficiency in practice by considering the results of numerical experiments on both uniform grids and those which use adaptivity in space.     

THE IMPACT OF THE NATIONAL NUMERACY STRATEGY IN YEAR 4 (II): TEACHING

The Nuffield Year 4 project set out to examine selected aspects of the impact of the National Numeracy Strategy (NNS) in primary schools by using comparable data on Year 4 pupil attainment and teaching collected in 1997/98 and 2001/02, two years before and two years after the introduction of the Numeracy Strategy. In this second paper we address the following questions:

• How and to what extent has numeracy teaching in Year 4 changed?

• Why have these changes occurred?

• How can we improve future implementation of reforms?

• How can we inform continuing professional development?

     

Demonstration of the importance of oxygenated species at the ends of carbon nanotubes for their favourable electrochemical properties

Definitive evidence is presented for the favourable electrochemical properties of carbon nanotube modified electrodes arising from the ends of SWNTs due to oxygenated carbon species in general, and carboxylic acid moieties in particular, produced during acid purification.     

Investigation and optimisation of the use of micellar electrokinetic chromatography for the analysis of six cardiovascular drugs

A micellar electrokinetic chromatography method was optimised for the separation of the six cardiovascular drugs atenolol, nicardipine, nifedipine, diltiazem, verapamil, and amlodipine by investigating the effects of pH, sodium dodecyl sulphate (SDS) concentration, selection and concentration of organic modifier. An electrophoresis buffer of 100 mM borate pH 8.1 containing 50 mM SDS and 15% (v/v) acetone was found to provide the optimum separation with respect to resolution and migration time.     

Vanadium haloperoxidase-catalyzed bromination and cyclization of terpenes

Marine red algae (Rhodophyta) are a rich source of bioactive halogenated natural products, including cyclic terpenes. The biogenesis of certain cyclic halogenated marine natural products is thought to involve marine haloperoxidase enzymes. Evidence is presented that vanadium bromoperoxidase (V-BrPO) isolated and cloned from marine red algae that produce halogenated compounds (e.g., Plocamium cartilagineum, Laurencia pacifica, Corallina officinalis) can catalyze the bromination and cyclization of terpenes and terpene analogues. The V-BrPO-catalyzed reaction with the monoterpene nerol in the presence of bromide ion and hydrogen peroxide produces a monobromo eight-membered cyclic ether similar to laurencin, a brominated C15 acetogenin, from Laurencia glandulifera, along with noncyclic bromohydrin, epoxide, and dibromoproducts; however, reaction of aqueous bromine with nerol produced only noncyclic bromohydrin, epoxide, and dibromoproducts. The V-BrPO-catalyzed reaction with geraniol in the presence of bromide ion and hydrogen peroxide produces two singly brominated six-membered cyclic products, analogous to the ring structures of alpha and beta snyderols, brominated sesquiterpenes from Laurencia, spp., along with noncyclic bromohydrin, epoxide, and dibromoproducts; again, reaction of geraniol with aqueous bromine produces only noncyclic bromohydrin, epoxide, and dibromoproducts. Thus, V-BrPO can direct the electrophilic bromination and cyclization of terpenes.     

Separation, recovery and recycling of a fluorous-tagged nickel catalyst using fluorous solid-phase extraction

Highly efficient separation, recovery and recycling of the fluorous-tagged catalyst, [Ni[F13C6C(O)CHC(O)C6F13]2], can be achieved with fluorous solid-phase extraction, after the Lewis acid catalysed synthesis of enaminodiones in conventional organic solvents.     

Synthetic anisomycin analogues activating the JNK/SAPK1 and p38/SAPK2 pathways

The synthesis of C(4)H and C(4)Me analogues of the JNK/p38 pathway activator anisomycin, based upon an aldol or Claisen construction of the C(3)-C(4) bond, has been demonstrated. The relative activation of the JNK/SAPK1 and p38/SAPK2 pathways in RAW macrophages by these analogues, and their synthetic precursors, has been assessed using immunoblot assays against phosphorylated c-Jun and MAPKAP-K2. These studies demonstrate that some of the synthetic C(4) analogues are also potent activators of these stress kinase pathways.     

Syntheses and oxygenation of iron(II) “strapped” porphyrin complexes

A general route to ‘strapped’ porphyrins which are bridged between diagonally opposite meso-positions is described. Studies on the oxygenation and carbonylation of their iron(II) complexes have shown that they are inferior to ‘capped’ porphyrins as models for the oxygen-carrying haemoproteins. The results reported herein suggest that strapping structures which do not enforce well-defined and rigid cavities for oxygen binding afford little protection against irreversible oxidation of (dioxygen) (porphyrin) iron(II) complexes.