This article examines how carbon dioxide (CO2) removal credits can be integrated into the European Union (EU) Emissions Trading System (ETS), focusing on questions of permanence and climate liability. It identifies challenges within the integration process and analyzes approaches from practice and literature to cultivate learning. These approaches apply different strategies to address the issue of permanence, including temporary credit issuance, granting credits once a certain number of carbon tonne-years have been accumulated, or issuing credits at the beginning of the project period and relying on liability instead. Drawing from the findings of this research, the article presents legal considerations that may inform a proposal for an EU legislative act on the integration of carbon removal credits into the EU ETS. It suggests that only credits issued for permanent CO2 removal should be integrated to ensure the environmental integrity of the system. Furthermore, the liability of the project operator should transfer to the Member State under certain conditions to make liability risks more predictable.

This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental noise. After setting up the problem, the existence and uniqueness of solutions of the underlying SPDEs are examined. Then, definitions of permanence and extinction are given, and certain sufficient conditions are provided for permanence and extinction. Our hope is that this paper will open up windows for investigation of epidemic models from a new angle.

Drawing on the findings of a Churchill Fellowship study tour, this article discusses the need to expand our understanding of family engagement and, in particular, to implement Family Inclusive practice in Australian child welfare, both to increase reunification and to improve outcomes for children who do not return home. I argue for this expansion through the integration of six key elements of Family Inclusive practice drawing on examples of practice and innovation from my study tour. This article commences with a discussion of the literature in support of family engagement and Family Inclusive practice. It is argued that we need to embrace an approach to Family Inclusive practice that acknowledges and addresses power imbalances, is contextualised and goes beyond relationships between workers and families. An exploration of the six elements of Family Inclusive practice follows, contributing to the understanding and practical application of Family Inclusive practice, with reference to initiatives in several countries visited during my study tour as well as to the literature more broadly. If these elements are integrated into child welfare practice and policy, they will contribute to Family Inclusive practice in the interests of children in Australia.

We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics, which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.

In this paper we derive sufficient conditions for the permanence and ergodicity of a stochastic predator–prey model with a Beddington–DeAngelis functional response. The conditions obtained are in fact very close to the necessary conditions. Both nondegenerate and degenerate diffusions are considered. One of the distinctive features of our results is that they enable the characterization of the support of a unique invariant probability measure. It proves the convergence in total variation norm of the transition probability to the invariant measure. Comparisons to the existing literature and matters related to other stochastic predator–prey models are also given.

This article seeks to demonstrate the permanent character of at least parts of the marketplace in Ribe (Denmark) from the first decades of its existence at the beginning of the eighth century. As with other early medieval emporia in northern Europe, it has been debated whether the marketplace was a permanent or seasonal site, the conclusion generally being that it would not have become permanently occupied until the AD 780s–790s. Although other markers of ‘urbanness’ can be found in the archaeological evidence from eighth-century Ribe, permanency is here considered as a decisive argument for its definition. Indeed, it is believed that it is through year-round, long-lasting occupation that a distinctively un-rural daily life could take shape. The material from the excavations conducted in 1985–1986 at Sct Nicolajgade 8 forms the empirical basis for this reassessment. By integrating artefacts in the contextual interpretation of the well-stratified deposits that characterize the archaeology of the marketplace, it is possible to identify several markers of permanency (site foundation, domestic life, and houses). Among them, particular focus is put on houses, whose presence at the site has been the object of controversy in previous research. By reconsidering the evidence and by comparing it to house finds from contemporary urban sites in northwestern Europe, former statements about the presence of houses at the marketplace in Ribe are challenged.

In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDSepidemic model with an imperfect HIV vaccine, varying total population size anddistributed time delay to become infectious due to intracellular delay between initialinfection of a cell by HIV and the release of new virions. Here, we have established somesufficient conditions on the permanence and extinction of the disease by using inequalityanalytical technique. We have obtained the explicit formula of the eventual lower boundsof infected persons. We have introduced some new threshold valuesR 0 and R ∗ and further obtainedthat the disease will be permanent when R 0 > 1 and thedisease will be going to extinct when R ∗ < 1. ByLyapunov functional method, we have also obtained some sufficient conditions for globalasymptotic stability of this model. The aim of the analysis of this model is to trace theparameters of interest for further study, with a view to informing and assistingpolicy-maker in targeting prevention and treatment resources for maximumeffectiveness.

A disease transmission model of SEIR type with exponential demographic structure is formulated, with a natural death rate constant and an excess death rate constant for infective individuals. The latent period is assumed to be constant, and the force of the infection is assumed to be of the standard form, namely, proportional to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The infected individuals are assumed not to be able to give birth and when an individual is removed fromthe I-class, it recovers, acquiring permanent immunity with probability f (0 ≤ f ≤ 1) and dies from the disease with probability 1 − f. The global attractiveness of the disease-free equilibrium, existence of the endemic equilibrium as well as the permanence criteria are investigated. Further, it is shown that for the special case of the model with zero latent period, R0 > 1 leads to the global stability of the endemic equilibrium, which completely answers the conjecture proposed by Diekmann and Heesterbeek.

A Volterra model with mutual interferenceconcerning integrated pest management is proposed and analyzed. Byusing Floquet theorem and small amplitude perturbation method andcomparison theorem, we show the existence of a globallyasymptotically stable pest-eradication periodic solution. Further,we prove that when the stability of pest-eradication periodicsolution is lost, the system is permanent and there exists alocally stable positive periodic solution which arises from thepest-eradication periodic solution by bifurcation theory. When theunique positive periodic solution loses its stability, numericalsimulation shows there is a characteristic sequence ofbifurcations, leading to a chaotic dynamics. Finally, we comparethe validity of integrated pest management (IPM) strategy withclassical methods and conclude IPM strategy is more effective thanclassical methods.