On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Sufficiency of Favard's condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, with $U$ being a complex Banach space, the injectivity of all limit operators of $A$ already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of $A$, which, on the other hand, is often equivalent to the Fredholmness of $A$. As a consequence, for operators $A$ in the Wiener algebra, we can characterize the essential spectrum of $A$ on $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.

Biodegradation of the herbicide mecoprop-p with soil depth and its relationship with class III tfdA genes

Mecoprop-p [(R)-2-(4-chloro-2-methylphenoxy) propanoic acid) is widely used in agriculture and poses an environmental concern because of its susceptibility to leach from soil to water. We investigated the effect of soil depth on mecoprop-p biodegradation and its relationship with the number and diversity of tfdA related genes, which are the most widely known genes involved in degradation of the phenoxyalkanoic acid group of herbicides by bacteria. Mecoprop-p half-life (DT50) was approximately 12 days in soil sampled from <30 cm depth, and increased progressively with soil depth, reaching over 84 days at 70–80 cm. In sub-soil there was a lag period of between 23 and 34 days prior to a phase of rapid degradation. No lag phase occurred in top-soil samples prior to the onset of degradation. The maximum degradation rate was the same in top-soil and sub-soil samples. Although diverse tfdAα and tfdA genes were present prior to mecoprop-p degradation, real time PCR revealed that degradation was associated with proliferation of tfdA genes. The number of tfdA genes and the most probable number of mecoprop-p degrading organisms in soil prior to mecoprop-p addition were below the limit of quantification and detection respectively. Melting curves from the real time PCR analysis showed that prior to mecoprop-p degradation both class I and class III tfdA genes were present in top- and sub-soil samples. However at all soil depths only tfdA class III genes proliferated during degradation. Denaturing gradient gel electrophoresis confirmed that class III tfdA genes were associated with mecoprop-p degradation. Degradation was not associated with the induction of novel tfdA genes in top- or sub-soil samples, and there were no apparent differences in tfdA gene diversity with soil depth prior to or following degradation.

"The past is still right here in the present": second-generation Bajan-Brit transnational migrants' views on issues relating to race and colour class

This paper deals with second-generation Barbadians or 'Bajan-Brits', who have decided to,return' to the birthplace of their parents, focusing on their reactions to matters relating to race relations and racialised identities. The importance of race and the operation of the 'colour-class' system in the Caribbean are established at the outset. Based on fifty-two qualitative in-depth interviews, the paper initially considers the positive things that the second-generation migrants report about living in a majority black country and the salience of such racial affirmation as part of their migration process. The paper then presents an analysis of the narratives provided by the Bajan-Brits concerning their reactions to issues relating to race relations in Barbadian society. The impressions of the young returnees provide clear commentaries on what are regarded as (i) the 'acceptance of white hegemony' within Barbadian society, (ii) the occurrence of de facto 'racial segregation, (iii) perceptions of the 'existence of apartheid, and (iv) 'the continuation of slavery'. The account then turns to the contemporary operation of the colour-class system. It is concluded that, despite academic arguments that the colour-class dimension has to be put to one side as the principal dimension of social stratification in the contemporary Caribbean, the second-generation migrants are acutely aware of the continued existence and salience of such gradations within society. Thus, the analysis not only serves to emphasise the continued importance of racial-based stratification in the contemporary Caribbean, but also speaks of the 'hybrid' and 'in-between' racialised identities of the second-generation migrants.

Flavour characterization of fresh and processed pennywort (Centella asiatica L.) juices

The flavour characteristics of fresh and processed pennywort juices treated by pasteurization, sterilization and high pressure processing (HPP) were investigated by using solid-phase micro-extraction combined with gas chromatography-mass spectrometry. Sesquiterpene hydrocarbons comprised the major class of volatile components present and the juices had a characteristic smell due to the presence of volatile compounds including β-caryophyllene, humulene, E-β-farnesene, α-copaene, alloaromadendrene and β-elemene. All processing operations caused a reduction in the total volatile concentration, but HPP caused more volatile acyclic alcohols, aldehydes and oxygenated monoterpenoids to be retained than pasteurization and sterilization. Ketones were not present in fresh pennywort juice, but 2-butanone and 3-nonen-2-one were generated in all processed juices, and 2-nonanone and 2-hexanone were present in pasteurized and sterilized juices. Other chemical changes including isomerization were also reduced by HPP compared to pasteurization, and sterilization.

Dynamic scaling of bred vectors in spatially extended chaotic systems

We unfold a profound relationship between the dynamics of finite-size perturbations in spatially extended chaotic systems and the universality class of Kardar-Parisi-Zhang (KPZ). We show how this relationship can be exploited to obtain a complete theoretical description of the bred vectors dynamics. The existence of characteristic length/time scales, the spatial extent of spatial correlations and how to time it, and the role of the breeding amplitude are all analyzed in the light of our theory. Implications to weather forecasting based on ensembles of initial conditions are also discussed.

Characteristic magnetic field and speed properties of interplanetary coronal mass ejections and their sheath regions

Prediction of the solar wind conditions in near-Earth space, arising from both quasi-steady and transient structures, is essential for space weather forecasting. To achieve forecast lead times of a day or more, such predictions must be made on the basis of remote solar observations. A number of empirical prediction schemes have been proposed to forecast the transit time and speed of coronal mass ejections (CMEs) at 1 AU. However, the current lack of magnetic field measurements in the corona severely limits our ability to forecast the 1 AU magnetic field strengths resulting from interplanetary CMEs (ICMEs). In this study we investigate the relation between the characteristic magnetic field strengths and speeds of both magnetic cloud and noncloud ICMEs at 1 AU. Correlation between field and speed is found to be significant only in the sheath region ahead of magnetic clouds, not within the clouds themselves. The lack of such a relation in the sheaths ahead of noncloud ICMEs is consistent with such ICMEs being skimming encounters of magnetic clouds, though other explanations are also put forward. Linear fits to the radial speed profiles of ejecta reveal that faster-traveling ICMEs are also expanding more at 1 AU. We combine these empirical relations to form a prediction scheme for the magnetic field strength in the sheaths ahead of magnetic clouds and also suggest a method for predicting the radial speed profile through an ICME on the basis of upstream measurements.

"Racism in a Melting Pot...?" Trinidadian mid-life transnational migrants' views on race and colour-class on return to their homes of descent

This paper deals with second-generation, one-and-a-half generation and ‘‘prolonged sojourner” Trinidadian transnational migrants, who have decided to ‘return’ to the birthplace of their parents. Based on 40 in-depth interviews, the paper considers both the positive and critical things that these youthful transnational migrants report about returning to, and living in, this multi-ethnic plural society and the salience of racial and colour-class stratification as part of their return migration experiences. Our qualitative analysis is based on the narratives provided by these youthful returnees, as relayed ‘‘in their own words”, presenting critical reflections on racism, racial identities and experiences as transnational Trinidadians. It is clear that it is contexts such as contemporary working environments, family and community that act as the reference points for the adaptation ‘‘back home” of this strongly middle-class cohort. We accordingly encounter a diverse, sometimes contesting set of racial issues that emerge as salient concerns for these returnees. The consensus is that matters racial remain as formidable legacies in the hierarchical stratification of Trinidadian society for a sizeable number. Many of our respondents reported the positive aspects of racial affirmation on return. But for another sub-set, the fact that multi-ethnic and multi-cultural mixing are proudly embraced in Trinidad meant that it was felt that return experiences were not overly hindered, or blighted by obstacles of race and colour-class. For these returnees, Trinidad and Tobago is seen as representing a 21st century ‘‘Melting Pot”. But for others the continued existence of racial divisions within society – between ethnic groups and among those of different skin shades – was lamented. In the views of these respondents, too much racial power is still ascribed to ‘near-whiteness’. But for the most part, the returnees felt that where race played a part in their new lives, this generally served to advantage them. However, although the situation in Trinidad appears to have been moderated by assumptions that it remains a racial ‘Melting Pot’, the analysis strongly suggests that the colour-class system of stratification is still playing an essential role, along with racial stereotyping in society at large.