Over the last 30 years, a number of possible definitions of Sobolev and BV spaces in the metric setting have been proposed by various authors, and a priori it is not known whether they are equivalent. In this monograph, we decided to work with the definition of Newtonian spaces proposed by Shanmugalingam. In this appendix, we present several other approaches present in the literature and comment on their relationship and dependence on the exponent. The first general result concerning the equivalence of the most common definitions of Sobolev spaces was proved by Ambrosio, Gigli, and Savaré in the case p > 1; similar results were subsequently shown for the BV spaces and for the Sobolev space with exponent equal to one. To give a complete historical overview, we present here several variants of definitions and several equivalence results. We also discuss the dependence of the minimal p-weak upper gradient on the exponent. Throughout this appendix, as in the whole monograph, we assume that the metric space is complete, separable, and equipped with a non-negative Borel measure which is finite on bounded subsets.

The introduction begins with the book’s central argument: Egyptian cultural and media institutions have constructed a coherent state project after the 1952 revolution through a praxis of ‘achievement’ (ingāz, pl. ingazāt). Inspired by the anthropology of bureaucracy and the state, the book intervenes in the longstanding historiography on the Nasser era to show how low- and mid-ranking bureaucrats affiliated to the Ministry of Culture and National Guidance have worked to create a unified state-idea after 1952, while constituting a bureaucratic corps on a similar ideological basis. Such bureaucrats, as well as higher-ranking officials and ministers, are central actors in the book’s narrative. The introduction also reviews the book’s main sources and methods, including ethnographic fieldwork, archival visits in institutional repositories and personal libraries, as well as regular dives into the second-hand book market in Cairo.

This chapter introduces the supposed problem of ethnicity: that it undermines national cohesion, or is a colonial hangover with no appropriate place in political life. In contrast, I argue that ethnicity is neither inherently desirable nor undesirable; its political effects depend on how it is known and used, and our understanding of how it is known remains underdeveloped. I establish that there is no definitive list of Kenya’s ethnic groups, and we must stop taking for granted what we think we know about ethnicity. I offer the concept of cultivated vagueness – a widespread aversion to resolving the ambiguity of lists of Kenya’s ethnic groups – to understand how ethnic knowledge works and to contrast it with legibility and governmentality. Cultivated vagueness is the response from bureaucrats, civil society, citizens and the state to the conundrum that ethnic knowledge is both common sense and impossible to settle. It also explains how ethnic classifications serve both projects of division and of pluralism. I suggest that attention to the benefits of cultivated vagueness may facilitate the advancement of the latter over the former. The chapter outlines the book’s methodology and chapters.

Difficult lessons from the Confidential Enquiries into Maternal Deaths remind us that thorough clinical assessment, detailed mental state examination and an appreciation of the dynamic nature of risk and its management are central to the effective treatment of women with perinatal mental illness. This is underpinned by the establishment of a trusting, respectful and honest relationship with the woman, which sees her as a partner in decision-making, and a detailed knowledge of the distinctive presentations and risks associated with illness in pregnancy and after childbirth, and its consequences for the woman and her infant.

What can a premodern narrative of legal change teach us? This brief epilogue raises the more complex question of the totalizing ambitions of states that operate from the assumption that law is a specialized practice, rather than something that emerges from daily life. The existence of a black-letter law urges states towards legislation as legal utopianism: the attempt to remake subjects in an optimal fashion and to exclude those they find problematic. This tendency towards utopianism - a form of state magic - is present in both late antique and modern contexts. Understanding the roots of it urges us towards humility with respect to our own projects of legal transformation.

This chapter considers how Australian theatre responds to, represents and stages floods, and how those representations have changed over the last half-century and more. Beginning with Eunice Hanger’s Flood and Mona Brand’s Flood Tide from the 1950s, the chapter traces how dramatic characters are fashioned in response to increasingly extreme climates. Alana Valentine’s (2008) Watermark, a work of community/verbatim theatre, draws on the oral testimony of survivors of a fast-moving flood that in 1998 swept through the town and surrounding areas of Katherine in the Northern Territory. In Jackie Smith’s (2009) The Flood, rising flood waters have a materiality and agential capacity to provoke fear and anger in the three characters of three dramatic characters trapped inside a run-down farmhouse. Between Two Waves by Ian Meadows (2012) is a politically engaged climate change drama that represents the increasing hysteria of a climate scientist’s warnings as they this to these are distorted and denied by conservative politicians and media.

An important role is played in the most recent developments on gaps between primes by suitable sets of prime k-tuples. Thus before proceeding with this chapter the reader would be well advised to review the contents of §18.5. The principal idea is to use artefacts from sieve theory, especially the Selberg sieve, not directly in the form of a sieve but as a means to increase the likelihood that certain constellations of 𝑘-tuples have relatively few prime factors.

The land now called Australia was settled by humans between 50,000 and 65,000 years ago, and the lands and waterways sustained balanced life until 1788 when a fleet of British soldiers, settlers and convicts landed on the central east coast. This chapter traces the ways theatrical works stage ‘land’ that has been transformed and depleted by the interrelated actions of colonialism, deforestation and pastoralism. It features the ecological content and staging of three works: Yanagai! Yanagai! by Yorta Yorta and Gunaikurnai woman Andrea James (2003), Louis Nowra’s (1985) The Golden Age and The White Earth by Andrew McGahan and Shaun Charles (2009). These depict violent land-grabs violent land-grabs, massacres, stubborn farming practices and ignorance of the environment as an ecosystem with a long history of human habitation. This chapter looks at the problem of ongoing ecological damage and struggles to develop sustainable land practices.

Chapter 3 turns to one of the best known but most controversial instances of ecological practice under Nazi auspices. It centers on the coterie of “advocates for the landscape” responsible for environmental planning on a series of major Nazi public works projects, most famously the building of the Autobahn system. The group was led by Alwin Seifert, whose title was Reich Advocate for the Landscape. Seifert was a pivotal figure in the development of the post-war environmental movement in Germany, and the work of his landscape advocates on the Autobahn has been the subject of several important previous studies. The focus of the chapter extends far beyond the Autobahn project to include many other fields in which the landscape advocates took an active part, styling themselves “the conscience of the German countryside.” The chapter shows that Seifert and the landscape advocates consistently applied ecological techniques even in the face of concerted resistance from other branches of the Nazi bureaucracy, with the support of a surprising range of high-level party and state functionaries. Though their achievements were limited in significant ways, through a modernized version of blood and soil ideology they conjoined Nazi ideals with environmentally sustainable policies.

This chapter discusses relative clauses in some theoretical detail. It begins by establishing a working definition of relative clauses appropriate for the purposes of the book, providing an overview of the different semantic and syntactic types. It then moves on to the way in which these clauses are analysed within Minimalist linguistic theory, weighing up the Head-External, Head-Raising and Matching analyses; this is followed by a more detailed look at the left periphery as a vital part of this structure. The chapter concludes with a discussion of the ways in which these formal approaches have been applied to ancient Indo-European languages, isolating the points of identity and divergence between them. These establish the relevant points of comparison, which inform the reconstructive program pursued in subsequent chapters.

Quadratic fields are the simplest examples of number fields, yet they already exhibit the full richness of the theory of class groups and class numbers. Their study originated with Gauss’s binary quadratic forms, later linked to quadratic fields via Dedekind’s correspondence between narrow ideal classes and proper equivalence classes of forms.

A significant portion of this chapter is devoted to the reduction theory of binary quadratic forms, which, among other applications, enables the algorithmic computation of class numbers via Dedekind’s correspondence.

For definite forms, reduction yields unique representatives for proper equivalence classes. The modular group acts via linear substitution, inducing Möbius transformations on principal roots in the upper half-plane. Each orbit intersects the fundamental domain at a unique point, corresponding to a canonical reduced form.

Indefinite forms are more intricate. Though the modular group similarly acts on principal roots, no natural fundamental domain exists to select unique orbit representatives. Instead, Zagier’s notion of reduction – distinct from Gauss’s – establishes a bijection between reduced indefinite forms and purely periodic negative regular continued fractions. Remarkably, cyclic permutations of the period generate all reduced forms within a proper equivalence class.

Chapter 5 analyzes the symbolic and political meanings ascribed to the birth of Spain’s first Bourbon crown prince, Luis I, and the broader theme of dynastic succession. It explores how pro-Bourbon orators and visual artists celebrated the royal birth as a miraculous sign of divine favor, emphasizing fertility, continuity, and providence. Sermons of thanksgiving and ceremonial oaths of allegiance to Luis I presented him as a flower blooming from sacred roots, a living promise of future abundance. This chapter further examines the role of Queen María Luisa Gabriela de Saboya, who emerged as a symbol of both fecundity and pious maternity. Using floral imagery, Marian symbolism, and genealogical metaphors, propagandists portrayed the Bourbon line as physically vigorous and spiritually blessed. In doing so, they addressed lingering anxieties about Habsburg infertility and cast the Bourbons as restorers of imperial health and sacred monarchy.

Chapter 2 uses official data and primary documents to examine land as a factor of production and the legal status of land in China’s political economy. It highlights how insecure property rights and incomplete markets for land diverge from the liberal economic model. As codified in law, the state generates rents through its ability to take land from the rural sector at below-market prices to sell into the urban real estate and industrial sectors at higher and lower prices, respectively. This pattern is reminiscent of the planned economy and enacts urban bias. Local governments rely on land for revenue, as a tool of industry policy, and for capital mobilization through local government financing vehicles (LGFVs). Informality persists in the form of illegal land conversion and “small property rights” in urban villages and elsewhere. Beyond the analysis of land law at the rural-urban interface, the chapter also analyzes land rights within the rural and urban sectors, respectively. Within the agricultural sector, reforms have improved the property rights of rural households to arable land, but limits on rights and sources of insecurity remain. Urban households have been the beneficiaries of housing reforms, giving them a vested interest in resisting property taxes.