Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Violations of Bell's inequality for Gaussian states with homodyne detection and nonlinear interactions

We show that homodyne measurements can be used to demonstrate violations of Bell's inequality with Gaussian states, when the local rotations used for these types of tests are implemented using nonlinear unitary operations. We reveal that the local structure of the Gaussian state under scrutiny is crucial in the performance of the test. The effects of finite detection efficiency are thoroughly studied and shown to only mildly affect the revelation of Bell violations. We speculate that our approach may be extended to other applications such as entanglement distillation where local operations are necessary elements besides quantum entanglement.

Promoting mental health in Northern Ireland: addressing division, inequality and stigma

This article provides an overview of the literature on the impact of ‘the Troubles’ on mental health in Nor thern Ireland. It identifies three main phases of professional and policy response from concerns about the effects of the violence in the early 1970s, through many years of collective denial and neglect, until acknowledgment, following the Good Friday Agreement in 1998 (Nor thern Ireland Office, 1998), of high levels of trauma and unmet need. The issues of inequality and stigma are also considered and it is argued that peace is necessary but insufficient for promoting mental health. The development of mental health services in Nor thern Ireland and the relatively recent focus on promoting mental health are also outlined and examined. It is suggested that attempts to address the needs arising as a result of ‘the Troubles’ and more general mental health promotion strategies have, to some extent, developed in parallel and that it may be impor tant to integrate these effor ts. The relative under-development of mental health services, the comprehensive Bamford Review of Mental Health and Learning Disability (2005; 2006) and the positive approach of the Public Health Agency mean that, even in the current economic climate, there are great oppor tunities for progress. Routine screening, in primary care and mental health services for trauma, including Troubles-related trauma, is recommended to identify and address these issues on an individual level. It is also argued, however, that more substantial political change is needed to effectively address societal division, inequality and stigma to the benefit of all.

An Introduction to the Special issue - Housing in Hard Times: Marginality, Inequality and Class, with Kim McKee

‘Housing in Hard Times’ was the theme of the Housing Studies Association annual conference in April 2011. The papers featured in this special issue are drawn from that conference. They examine the uneven impact of economic change on housing policy and related areas, with reference to conceptual ideas pertaining to urban marginality, inequality and class. Whilst the empirical focus of the papers is the UK, their intellectual contribution represents an attempt to ‘bring class back in’ to the housing studies literature and encourage more critical, theoretically informed scholarship.

Work-life Conflict and Social Inequality in Western Europe

Recent debates on time-use suggest that there is an inverse relationship between time poverty and income poverty (Aguiar and Hurst in Q J Econ C(3):969-1006, 2007), with Hammermesh and Lee (Rev Econ Stat 89(2):374-383, 2007) suggesting much time poverty is 'yuppie kvetch' or 'complaining'. Gershuny (Soc Res Int Q Soc Sci 72(2):287-314, 2005) argues that busyness is the 'badge of honour': being busy is now a positive, privileged position and it is high status people who work long hours and feel busy. Is this also true of work-life conflict? This paper explores the relationship between work-life tension and social inequality, as measured by social class, drawing on evidence from the European Social Survey. To what extent is work-life conflict a problem of the (comparatively) rich and privileged professional/managerial classes, and is this true across European countries? The countries selected offer a range of institutional and policy configurations to maximise variation. Using regression modelling of an index of subjective work-life conflict, we find that in all the countries under study, work-life conflict is higher among professionals than non-professionals. Part of this is explained by the fact that professionals work longer hours and experience more work pressure than other social classes, though the effect remains even after accounting for these factors. While levels of work-life conflict vary across the countries studied, country variation in class differences is modest. We consider other explanations of why professionals report higher work-life conflict and the implications of our findings for debates on social inequality.