Let G and H be two vertex disjoint graphs. The join $G+H$ is the graph with $V(G+H)=V(G)+V(H)$ and $E(G+H)=E(G)\cup E(H)\cup \{xy\;|\; x\in V(G), y\in V(H)\}$. A (finite) linear forest is a graph consisting of (finite) vertex disjoint paths. We prove that for any finite linear forest F and any nonnull graph H, if $\{F, H\}$-free graphs have a $\chi $-binding function $f(\omega )$, then $\{F, K_n+H\}$-free graphs have a $\chi $-binding function $kf(\omega )$ for some constant k.

Tens of millions of individuals are displaced due to violence, and most are hosted by other households in their home countries. We ask what motivates people to host the forcibly displaced. We are interested in whether empathy increases the willingness to host but also consider alternative explanations. To explore the correlates of hosting we collected survey data from 1,504 households in the Democratic Republic of the Congo, fielded in-depth interviews, and implemented an experiment. We employ a novel strategy to measure hosting behavior, where household characteristics are measured prior to the arrival of displaced persons. We find that households with higher empathy are more likely to host in the 10-month period following the survey. There is no evidence that ethnicity, religiosity, or wealth affect hosting behavior. Results from the experiment suggest that it is difficult to increase hosting propensity in the longer term (4+ months) through simple interventions.

Recent years have seen a sharp increase in the number of cases being brought before national courts addressing the constitutional rights of children and future generations (FG) in the context of environmental protection. These cases have required courts to devote increasing attention to a wide-ranging and complicated array of constitutional rights claims involving the short- and longer-term impacts of environmental harm on children and FG. This article argues that both litigation and judicial efforts in this area have been hampered by the lack of precision of definitions of ‘future generations’ under comparative constitutional and international human rights law, in particular vis-à-vis children. This lack of precision poses a major challenge to both the delineation and enforcement of rights claims in the context of such litigation. After outlining how these cases are being brought and how courts are addressing (or not) the complexities involved in defining children and FG respectively, the article highlights the lack of authoritative definitions of FG in comparative constitutional law – a lacuna that, the author argues, is exacerbated by the ongoing lack of a clear definition of FG in the international human rights law context. The article concludes by identifying key challenges faced by litigators and courts seeking to engage with the rights of children and FG that result from this definitional gap.

We study the vectorial length compactification of the space of conjugacy classes of maximal representations of the fundamental group $\Gamma$ of a closed hyperbolic surface $\Sigma$ in $\textrm{PSL}(2,{\mathbb{R}})^n$. We identify the boundary with the sphere ${\mathbb{P}}(({\mathcal{ML}})^n)$, where $\mathcal{ML}$ is the space of measured geodesic laminations on $\Sigma$. In the case $n=2$, we give a geometric interpretation of the boundary as the space of homothety classes of ${\mathbb{R}}^2$-mixed structures on $\Sigma$. We associate to such a structure a dual tree-graded space endowed with an ${\mathbb{R}}_+^2$-valued metric, which we show to be universal with respect to actions on products of two $\mathbb{R}$-trees with the given length spectrum.

To enhance the impact resistance capacity and ensure the floatability of aircraft after ditching, the slamming response of three types of aircraft sub-floor structures are investigated including the flat, cylindrical and ellipsoidal under floor. A coupled Finite Element-Smooth Particle Hydrodynamic (FE-SPH) method is employed with focus on non-linear structural collapse in fluid-structure interaction. The material is defined by bilinear elastic plastic law, and the strain rate effect is taken into account. Further, comparison and analyses are performed in terms of acceleration, local pressure and strains at different speeds. Results show that conventional flat sub floor structures perform poorly during ditching due to excessive peak acceleration and pressure. By contrast, the peak acceleration of ellipsoidal under floor is lower at all measured speeds and the pressure on the sides is reduced. Moreover, the ellipsoidal sub-floor with bi-directional curvature generates smaller plastic strain and deflection of skin, demonstrating better mechanical properties in water impact scenarios.

Acute myocarditis leading to severe heart failure in paediatric patients is an uncommon but potentially life-threatening condition. The prompt implant of mechanical circulatory devices such as veno-arterial extra-corporeal membrane oxygenation remains the best treatment option to restore an adequate perfusion and improve patient survival in case of refractory cardiogenic shock cases. While few reports describe the in-hospital course of this dramatic disease, with an in-hospital mortality under veno-arterial extra-corporeal membrane oxygenation support around 30%, our study aims to analyse both short- and long-term outcomes after extra-corporeal membrane oxygenation implant.