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We define the generalized equilibrium distribution, that is the equilibrium distribution of a random variable with support in $\mathbb{R}$. This concept allows us to prove a new probabilistic generalization of Taylor’s theorem. Then, the generalized equilibrium distribution of two ordered random variables is considered and a probabilistic analog of the mean value theorem is proved. Results regarding distortion-based models and mean-median-mode relations are illustrated as well. Conditions for the unimodality of such distributions are obtained. We show that various stochastic orders and aging classes are preserved through the proposed equilibrium transformations. Further applications are provided in actuarial science, aiming to employ the new unimodal equilibrium distributions for some risk measures, such as Value-at-Risk and Conditional Tail Expectation.
This chapter gives a detailed and rigorous treatment of Markov decision processes, which are a foundational framework for dynamic programming. Numerous examples are discussed.
Law-making is not a straightforward process in international law. This chapter focuses on the various law-making processes and structures available for creating international law. It first considers the traditional sources of international law as set out in art 38(1) of the Statute of the International Court of Justice generally and the concept of hierarchy of norms and relative norms before considering each of the art 38(1) sources in turn. The chapter concludes by considering alternative sources of international law not covered by art 38(1): 'soft law' including that created by non-State actors, and the role of the UN in creating international law.
This chapter shows how late-antique emperors and bureaucrats looked to the jurists to understand how Classical Roman law worked, and thus built an entirely new legal system in order to put their ideas into practice. I first discuss how post-Severan emperors represented themselves in rescripts as explaining a settled and sovereign law, rather than making new law themselves. I then consider innovations in the indexing of imperial rescripts, which combined rescripts of multiple emperors into new collections organized by subject matter; these collections treated rescripts as legal documents, rather than nonsystematic interventions from an absolute ruler. I then consider how the massive expansions in imperial staffing and bureaucracy that mark the late-antique period, as well as an increase in the frequency and systematicity of legal education, could lead to regularized adjudicative outcomes that better tracked the dictates of juristic law. I finally contrast the treatment of juristic texts and resccripts in the Codex Theodosianus, showing how that text implicitly elevates jurists over emperors and how that elevation flows from broader changes in legal culture of the period.
The Greek model of mental healthcare delivery in rural and remote low-resourced areas is based on Mobile Mental Health Units (MMHUs). MMHUs are low-cost, interdisciplinary, generic community psychiatric services that collaborate closely with the primary healthcare system and local social services. MMHUs may be effective in the treatment of patients with severe and persistent mental illness and cost-effective in the treatment of patients with common mental disorders. The Council of Europe categorised this model as an effective community-based initiative. Major challenges derive from the difficulties MMHUs run by public general hospitals face in recruiting and retaining personnel.
Critics misunderstood Lacan’s thought for decades. They interpreted him as a theorist who reduced subjectivity to its social and linguistic determinations. What they missed was his emphasis, following Kant and Hegel, on subjectivity. This is what both Slavoj Žižek and Joan Copjec provide when they burst onto the Lacanian scene in 1989. Their works place the emphasis in Lacan’s theory on the problem of subjectivity insofar as the subject remains irreducible to the social order. They uncover a radical version of Lacan that subsequent theorists pick up in the fields of queer theory, feminism, anti-racism, and Marxism. This version of Lacan remains vibrant to this day with many adherents in many disciplines.
This chapter explores the challenges faced by the Belgian colonial administration in controlling mobility within and across the borders of Rwanda and the Belgian Congo. After Rwanda had become an official mandated area of Belgium, efforts to regulate movement became integral to economic and labor control. The chapter then sets out to explain the inherent contradictions of this asymmetrical labor system englobing both shores and hinterlands of the Lake Kivu region in which Rwanda came to serve as a labor reserve supporting Belgian economic interests in Kivu, and further away in Katanga. The need for labor in the Belgian Congo became one of the main factors explaining its persistent interconnections with Rwanda during the colonial period; the deep-rooted historical ties between the societies around the Lake another.
These interconnections also amplified and altered pre-existing patterns of mobility. This caused problems for the Belgian administration at both sides of the border as they needed to control mobility without damaging the colonial labor market. The chapter shows that they often prioritized economic benefits over their own rules and regulations, and the interests of the Belgian Congo over those of Rwanda. Here as well, chiefs played ambiguous roles, in regulating the movement of commoners and mobilizing labor. The system fostered competition among chiefs for both people and their labor. It incentivized chiefs to closely monitor their subjects, imposing a heavier burden on ordinary people and prompting them to seek better conditions elsewhere.