Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

On the (un)-ambiguity of adjectival modification in Spanish determiner phrases: informing debates on the mental representations of L2 syntax.

This study contributes to a central debate within contemporary generative second language (L2) theorizing: the extent to which adult learners are (un)able to acquire new functional features that result in a L2 grammar that is mentally structured like the native target (see White, 2003). The adult acquisition of L2 nominal phi-features is explored, with focus on the syntactic and semantic reflexes in the related domain of adjective placement in two experimental groups: English-speaking intermediate (n = 21) and advanced (n = 24) learners of Spanish, as compared to a native-speaker control group (n = 15). Results show that, on some of the tasks, the intermediate L2 learners appear to have acquired the syntactic properties of the Spanish determiner phrase but, on other tasks, to show some delay with the semantic reflexes of prenominal and postnominal adjectives. Crucially, however, our data demonstrate full convergence by all advanced learners and thus provide evidence in contra the predictions of representational deficit accounts (e.g., Hawkins & Chan, 1997; Hawkins & Franceschina, 2004; Hawkins & Hattori, 2006).

Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.

Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

Mg/Ca partitioning between aqueous solution and aragonite mineral: a molecular dynamics study

We have calculated the concentrations of Mg in the bulk and surfaces of aragonite CaCO3 in equilibrium with aqueous solution, based on molecular dynamics simulations and grand-canonical statistical mechanics. Mg is incorporated in the surfaces, in particular in the (001) terraces, rather than in the bulk of aragonite particles. However, the total Mg content in the bulk and surface of aragonite particles was found to be too small to account for the measured Mg/Ca ratios in corals. We therefore argue that most Mg in corals is either highly metastable in the aragonite lattice, or is located outside the aragonite phase of the coral skeleton, and we discuss the implications of this finding for Mg/Ca paleothermometry.

Human monstrosity: rape, ambiguity and performance in Rosemary’s Baby (Roman Polanski, 1968)

The narrative of Rosemary’s Baby hinges on a central hesitation between pregnancy induced madness and the existence of Satanism. Accordingly, the monstrous element is embodied in both the real and the supernatural: Rosemary’s husband Guy (John Cassavetes) is responsible for her victimisation through rape in either explanation. However, I will argue that the inherent ambiguity of the plot makes it difficult to place him as such a figure typical to the archetypal horror binaries of normality/monster, human/inhuman. By displacing generic convention the film complicates the issue of monstrosity, whilst simultaneously offering the possibility for the depiction of female experience of marriage to be at the centre of the narrative, for the real to be possibly of more significance than the supernatural. Previous writing has tended to concentrate on Rosemary and her pregnancy, so through detailed consideration of Cassavetes’ performance and its placement in the mise-en-scène this focus on Guy aims to demonstrate that he changes almost as much as Rosemary does. The chapter will focus on the film’s depiction of rape, during Rosemary’s nightmare and after it, in order to demonstrate how the notion of performance reveals Guy’s monstrousness and the difficulties this represents in our engagement with him.

Neocuproine-functionalized silica-coated magnetic nanoparticles for extraction of copper(II) from aqueous solution

Neocuproine has been covalently bound to silica-coated maghemite(c-Fe2O3) magnetic nanoparticles (MNPs) by a phenyl ether linkage. The resulting MNPs are able to remove Cu(II) from 12 ppm aqueous solution with an extraction efficiency of up to 99% at pH 2.

Solution calorimetry as a tool for investigating drug interaction with intestinal fluid

Solution calorimetry offers a reproducible technique for measuring the enthalpy of solution (ΔsolH) of a solute dissolving into a solvent. The ΔsolH of two solutes, propranolol HCl and mannitol were determined in simulated intestinal fluid (SIF) solutions designed to model the fed and fasted states within the gut, and in Hanks’ balanced salt solution (HBSS) of varying pH. The bile salt and lipid within the SIF solutions formed mixed micelles. Both solutes exhibited endothermic reactions in all solvents. The ΔsolH for propranolol HCl in the SIF solutions differed from those in the HBSS and was lower in the fed state than the fasted state SIF solution, revealing an interaction between propranolol and the micellar phase in both SIF solutions. In contrast, for mannitol the ΔsolH was constant in all solutions indicating minimal interaction between mannitol and the micellar phases of the SIF solutions. In this study, solution calorimetry proved to be a simple method for measuring the enthalpy associated with the dissolution of model drugs in complex biological media such as SIF solutions. In addition, the derived power–time curves allowed the time taken for the powdered solutes to form solutions to be estimated.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

The Golden Dawn's 'nationalist solution': explaining the rise of the far right in Greece

The book is concerned with the rise of the Greek Golden Dawn. Although most literature focuses on demand and supply-side explanations, this book progresses beyond the state of the art by examining the Golden Dawn as an outlier and focusing on political culture as an explanation for its dramatic rise.

Role conflict and role ambiguity in construction projects

Role conflict happens when a person faces different and incompatible expectations regarding a particular social status which they occupy. The literature on role conflict is reviewed for a better understanding of project dynamics in construction teams. The discussion focuses on issues surrounding the miscommunication of role expectations and tensions owing to differences in expectations of the same role. This ongoing doctoral study involves a qualitative research design, based on interviews with practicing professionals. Analysis will focus on the relation between formal expectations, as evidenced in contracts and other types of written communication, and informal expectations as observed from the interviews. Insights from the literature review suggest: 1. that the differences between formal and informal expectations is a major sources of role conflict in construction teams and 2. that this effect is exacerbated by the failure of team members to recognise it and take it into account.

Child anxiety and the processing and ambiguity

An association between interpretation of ambiguity and anxiety may exist in children, but findings have been equivocal. The present research utilized the Interpretation Generation Questionnaire for Children (IGQ-C), a novel measure that breaks down the processing of ambiguity into three steps: the generation of possible interpretations, the selection of the most likely interpretation and the anticipated emotional response to the ambiguous situation. The IGQ-C was completed by 103 children aged 11–12 years, 28 of whom had a clinical anxiety disorder. There was some evidence for an association between anxiety and: (1) the generation of initial negative interpretations; (2) the generation of a greater number of negative interpretations overall; and (3) the selection of negative responses. These findings were not consistent across measures of anxiety. A more convincing association was found between child anxiety and anticipated emotional response to the ambiguous scenarios, with anxious children anticipating more negative emotion.

Interpretation of ambiguity: differences between children and adolescents with and without an anxiety disorder

Background: Theory and treatment of anxiety disorders in young people are commonly based on the premise that interpretation biases found in anxious adults are also found in children and adolescents. Although there is some evidence that this may be the case, studies have not typically taken age into account, which is surprising given the normative changes in cognition that occur throughout childhood. The aim of the current study was to identify whether associations between anxiety disorder status and interpretation biases differed in children and adolescents. Methods: The responses of children (7-10 years) and adolescents (13-16 years) with and without anxiety disorders (n = 120) were compared on an ambiguous scenarios task. Results: Children and adolescents with an anxiety disorder showed significantly higher levels of threat interpretation and avoidant strategies than non-anxious children and adolescents. However, age significantly moderated the effect of anxiety disorder status on interpretation of ambiguity, in that adolescents with anxiety disorders showed significantly higher levels of threat interpretation and associated negative emotion than non-anxious adolescents, but a similar relationship was not observed among children. Conclusions: The findings suggest that theoretical accounts of interpretation biases in anxiety disorders in children and adolescents should distinguish between different developmental periods. For both ages, treatment that targets behavioral avoidance appears warranted. However, while adolescents are likely to benefit from treatment that addresses interpretation biases, there may be limited benefit for children under the age of ten.

A semantic solution to the problem with aesthetic testimony

There is something peculiar about aesthetic testimony. It seems more difficult to gain knowledge of aesthetic properties based solely upon testimony than it is in the case of other types of property. In this paper, I argue that we can provide an adequate explanation at the level of the semantics of aesthetic language, without defending any substantive thesis in epistemology or about aesthetic value/judgement. If aesthetic predicates are given a non-invariantist semantics, we can explain the supposed peculiar difficulty with aesthetic testimony.