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.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high T-c cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu3O8+delta, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high T-c cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high T-c cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.

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.

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.

Memory awareness and schematization: Learning in the university context

Following the application of the remember/know paradigm to student learning by Conway et al. (1997), this study examined changes in learning and memory awareness of university students in a lecture course and a research methods course. The proposed shift from a dominance of 'remember' awareness in early learning to a dominance of 'know' awareness as learning progresses and schematization occurs was evident for the methods course but not for the lecture course. The patterns of remember and know awareness and proposed associated levels of schematization were supported by a separate measure of the quality of student learning using the SOLO (Structure of Observed Learning Outcomes) Taxonomy. As found by previous research, the remember-to-know shift and schematization of knowledge is dependent upon type of course and level of achievement. Findings are discussed in terms of the utility of the methodology used, the theoretical implications and the applications to educational practice. Copyright (C) 2001 John Wiley & Sons, Ltd.

Introducing ethnomethodological analysis to the field of music education

In recent years qualitative research methods have been adopted within in the field of music education and have received widespread acceptance. However, the theoretical framework provided by ethnomethodology (Garfinkel, 1974, in R. Turner, Ethnomethodology , Penguin, Middlesex, UK) and the tools of conversational analysis (Sacks, 1992, Lectures on Conversation , edited by Gail Jefferson, Blackwell, Oxford, UK) have, to this point, been overlooked by researchers in the field of music education. In this paper I argue that the application of ethnomethodological and conversation analytical approaches in the field of research in music education can provide fresh insights into the work of music teachers and how this work is accomplished in institutional settings. Here I demonstrate how a conversation analytical perspective drawing on an ethnomethodological framework might be used to investigate transcripts of audio-recorded interview talk. This type of analysis can illuminate aspects of members' roles in relation to, and perceptions about music education in school settings that might be overlooked in other types of analysis. A conversation analytical approach to the examination of talk-in-interaction explicates in fine-grained detail how members orient to matters at hand in the context of research settings, as well as revealing features of the cultural world of music teaching. Further application of the approach to research problems in other school settings, I argue, will inform the field of music education in ways yet to be realised.

Clinical supervision in four mental health professions: A review of the evidence

This paper examines a range of theoretical issues and the empirical evidence relating to clinical supervision in four mental health professions, namely clinical psychology, occupational therapy, social work, and speech pathology. Despite the widespread acceptance of the value of supervision among practitioners and the large quantity of literature on the topic, there is very little empirical evidence in this area. It is not clear whether supervision actually produces a change in clinician behaviour, nor whether it produces benefits in terms of client outcomes. To date, there is insufficient evidence to demonstrate which styles of supervision are most beneficial for particular types of staff, in terms of their level of experience or learning style. The data suggest that directive forms of supervision, rather than unstructured approaches, are preferred by relatively inexperienced practitioners, and that experienced clinicians also value direct supervision methods when learning new skills or dealing with complex or crisis situations. The available evidence suggests that supervisors typically receive little training in supervision methods. However, to date, we have little information to guide us as to the most effective ways of training supervisors. While acknowledging the urgent need for research, the paper concludes that supervision is likely to form a valuable component of professional development for mental health professionals.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.