On the graded quantum Yang-Baxter and reflection equations

We clarify the extra signs appearing in the graded quantum Yang-Baxter reflection equations, when they are written in a matrix form. We find the boundary K-matrix for the Perk-Schultz six-vertex model, thus give a general solution to the graded reflection equation associated with it.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.

Reflection of structural waves at a solid/liquid interface

This paper investigates the reflection characteristics of structural or guided waves in rods at a solid/liquid interface. Structural waves, whose wavelengths are much larger than the diameter of the rod, are described in a first approximation by classical one-dimensional wave theory. The reflection characteristics of such waves at a solid/liquid (melting) interface has been reported by two different ultrasonic measurement techniques: first, measuring the fast regression rate of a melting interface during the burning of metal rod samples in an oxygen-enriched environment, and second, monitoring the propagation of the solid/liquid interface during the slow melting and solidification of a rod sample in a furnace. The second work clearly shows that the major reflection occurs from the solid/liquid interface and not the liquid/gas interface as predicted by plane longitudinal wave reflectivity theory. The present work confirms this observation by reporting on the results of some specially designed experiments to identify the main interface of reflection for structural waves in rods. Hence, it helps in explaining the fundamental discrepancy between the reflection characteristics at a solid/liquid interface between low frequency structural waves and high frequency bulk waves, and confirms that the detected echo within a burning metallic rod clearly represents a reflection from the solid/liquid interface. (C) 2003 Elsevier Science B.V. All rights reserved.

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Reflective analysis: Techniques for facilitating reflection

This paper describes a number of techniques for facilitating reflective critical analysis as a means of eliciting in-depth reflections on practice. The authors have previously used similar techniques in the research context, to assist practitioners to identify and analyse the basis of their work with clients. The techniques presented in this paper have been adapted for use in social work education, including in class-based and field education contexts, and to professional supervision.

Multimodal affective interaction: a comment on musical origins

THE RIGORS OF ESTABLISHING INNATENESS and domain specificity pose challenges to adaptationist models of music evolution. In articulating a series of constraints, the authors of the target articles provide strategies for investigating the potential origins of music. We propose additional approaches for exploring theories based on exaptation. We discuss a view of music as a multimodal system of engaging with affect, enabled by capacities of symbolism and a theory of mind.

The multimodal world of medical monitoring displays

A vision of the future of intraoperative monitoring for anesthesia is presented-a multimodal world based on advanced sensing capabilities. I explore progress towards this vision, outlining the general nature of the anesthetist's monitoring task and the dangers of attentional capture. Research in attention indicates different kinds of attentional control, such as endogenous and exogenous orienting, which are critical to how awareness of patient state is maintained, but which may work differently across different modalities. Four kinds of medical monitoring displays are surveyed: (1) integrated visual displays, (2) head-mounted displays, (3) advanced auditory displays and (4) auditory alarms. Achievements and challenges in each area are outlined. In future research, we should focus more clearly on identifying anesthetists' information needs and we should develop models of attention in different modalities and across different modalities that are more capable of guiding design. (c) 2006 Elsevier Ltd. All rights reserved.