Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Novel colloidal materials for high-throughput screening applications in drug discovery and genomics

Tracking the reaction history is the means of choice to identify bioactive compounds in large combinatorial libraries. The authors describe two approaches to synthesis on silica beads: a) addition of a reporter dye tag during each synthesis step (see Figure), which attaches itself to the bead by colloidal forces, and b) encapsulating arrays of fluorescent dyes into the beads to encode them uniquely, for recognition with a flow cytometer after each reaction step.

Colorectal cancer screening - what the guidelines don't tell you - letter

The author discusses the recommendation by the NH and MRC for faecal occult blood testing in bowel cancer screening.