Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

Why all counter-evidence to the critical period hypothesis in second language acquisition is not equal or problematic

That adult and child language acquisitions differ in route and outcome is observable. Notwithstanding, there is controversy as to what this observation means for the Critical Period Hypothesis’ (CPH) application to adult second language acquisition (SLA). As most versions of the CPH applied to SLA claim that differences result from maturational effects on in-born linguistic mechanisms, the CPH has many implications that are amendable to empirical investigation. To date, there is no shortage of literature claiming that the CPH applies or does not apply to normal adult SLA. Herein, I provide an epistemological discussion on the conceptual usefulness of the CPH in SLA (cf. Singleton 2005) coupled with a review of Long's (2005) evaluation of much available relevant research. Crucially, I review studies that Long did not consider and conclude differently that there is no critical/sensitive period for L2 syntactic and semantic acquisition.

Variation, asymmetry and working memory in the process of second language acquisition

Calls for understanding the interface between L2 linguistic knowledge and development (Gregg 1996; Carroll 2001; Towell 2003) provide a context for analysing the role of memory (Paradis 2004), specifically working memory (Baddeley 1986, 2003) in L2 development. Miyake and Friedman (1998) have claimed that Working Memory (WM) may be the key to L2 acquisition, especially in explaining individual variation in L2 acquisition. Recent findings found a robust connection between greater working memory (WM) capacity and rapid, successful acquisition of L2 vocabulary, reading and oral fluency (Service 1992; Harrington and Sawyer 1992; Fortkamp 1999). This study adds to the growing body of research by investigating correlations between WM and variation in grammatical development, focusing on asymmetries in processing L2 English wh-constructions in an immersion setting.

An evolutionary innovation perspective on the selection of low and zero carbon technologies in new housing

The Code for Sustainable Homes (the Code) will require new homes in the United Kingdom to be ‘zero carbon’ from 2016. Drawing upon an evolutionary innovation perspective, this paper contributes to a gap in the literature by investigating which low and zero carbon technologies are actually being used by house builders, rather than the prevailing emphasis on the potentiality of these technologies. Using the results from a questionnaire three empirical contributions are made. First, house builders are selecting a narrow range of technologies. Second, these choices are made to minimise the disruption to their standard design and production templates (SDPTs). Finally, the coalescence around a small group of technologies is expected to intensify with solar-based technologies predicted to become more important. This paper challenges the dominant technical rationality in the literature that technical efficiency and cost benefits are the primary drivers for technology selection. These drivers play an important role but one which is mediated by the logic of maintaining the SDPTs of the house builders. This emphasises the need for construction diffusion of innovation theory to be problematized and developed within the context of business and market regimes constrained and reproduced by resilient technological trajectories.

Effects of second language on cognition in English users of L2 Japanese

It is now established that certain cognitive processes such as categorisation are tightly linked to the concepts encoded in language. Recent studies have shown that bilinguals with languages that differ in their concepts may show a shift in their cognition towards the L2 pattern primarily as a function of their L2 proficiency. This research has so far focused predominantly on L2 users who started learning the L2 in childhood or early puberty. The current study asks whether similar effects can be found in adult L2 learners. English speakers of L2 Japanese were given an object classification task involving real physical objects, and an online classification task involving artificial novel objects. Results showed a shift towards the L2 pattern, indicating that some degree of cognitive plasticity exists even when a second language is acquired later in life. These results have implications for theories of L2 acquisition and bilingualism, and contribute towards our understanding of the nature of the relationship between language and cognition in the L2 user’s mind.

A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.