The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Forum theorizing in the context of professional practice: The case for middle-range theories

This commentary seeks to complement the contribution of the Building Research & Information special issue on 'Developing Theories for the Built Environment' (2008) by highlighting the important role of middle-range theories within the context of professional practice. Middle-range theories provide a form of theorizing that lies between abstract grand theorizing and atheoretical local descriptions. They are also characterized by the way in which they directly engage with the concerns of practitioners. In the context of professional practice, any commitment to theorizing should habitually be combined with an equivalent commitment to empirical research; rarely is it appropriate to neglect one in favour of the other. Any understanding of the role that theory plays in professional practice must further be informed by Schon's seminal ideas on reflective practice. Practitioners are seen to utilize theories as inputs to a process of continuous reflection, thereby guarding against complacency and routinization. The authors would challenge any assumption that academics alone are responsible for generating theories, thereby limiting the role of practitioners to their application. Such a dichotomized view is contrary to established ideas on Mode 2 knowledge production and current trends towards co-production research in the context of the built environment.

An experimental comparison between rival theories of rapid automatized naming performance and its relationship to reading

Two studies investigated the degree to which the relationship between rapid automatized naming (RAN) performance and reading development is driven by shared phonological processes. Study 1 assessed RAN, phonological awareness, and reading performance in 1010 7- to -10 year-olds. Results showed that RAN deficits occurred in the absence of phonological awareness deficits. These were accompanied by modest reading delays. In structural equation modeling, solutions where RAN was subsumed within a phonological processing factor did not provide a good fit to the data, suggesting that processes outside phonology may drive RAN performance and its association with reading. Study 2 investigated Kail’s proposal that speed of processing underlies this relationship. Children with single RAN deficits showed slower speed of processing than did closely matched controls performing normally on RAN. However, regression analysis revealed that RAN made a unique contribution to reading even after accounting for processing speed. Theoretical implications are discussed.

An examination of the complementary volume–volatility information theories

The volume–volatility relationship during the dissemination stages of information flow is examined by analyzing various theories relating volume and volatility as complementary rather than competing models. The mixture of distributions hypothesis, sequential arrival of information hypothesis, the dispersion of beliefs hypothesis, and the noise trader hypothesis all add to the understanding of how volume and volatility interact for different types of futures traders. An integrated picture of the volume–volatility relationship is provided by investigating the dynamic linear and nonlinear associations between volatility and the volume of informed (institutional) and uninformed (the general public) traders. In particular, the trading behavior explanation for the persistence of futures volatility, the effect of the timing of private information arrival, and the response of institutional traders to excess noise trading risk is examined