Theatre depicts the way the socio-climate of so it reads Theatre depicts the way the socio-climate of drought intenstified in Australia as settler farmers drought intensified in Australia as settler farmers cleared land to plant imported food crops and, in particular, rain-dependent wheat. Local ecologies were drastically changed by colonial occupation. Dryness and dust increased where there had previously been the biodiverse sources of food depicted in Australian Aboriginal and Torres Strait Islander First Nations (First Nations) performance and drama. Different meanings for meanings for home and homeland exemplify the genocidal conflict between First Nations Country and settler farmsteads. Plays by, for example, Noongar writer Jack Davis and the pre-eminent Dorothy Hewett feature ecologies drastically altered by wheat farming in conjunction with oppressive race and gender relations. Drama about mining similarly shows a combination of ecological damage and social inequity. As Jill Orr performs in a vast monocrop of wheat and amidst gypsum mine waste, her bird-like action evokes in a vast monocrop field of wheat grief over an ecocidal loss of multispecies habitats.

This chapter introduces the three major themes of the book: relative clauses, Proto-Indo-European and syntax.

This chapter is dedicated to the study of the total variation flow on the whole space. In order to use the Anzellotti pairings and the Gauss-Green formula introduced in Chapter 4, we suppose that the metric space is complete, separable, equipped with a doubling measure, and that it supports a weak Poincaré-type inequality. The total variation flow in this setting is understood as the gradient flow of the 1-Cheeger energy, which (as shown by Ambrosio and Di Marino) is convex and lower semicontinuous with respect to L2 convergence; then, the Brezis–Komura theorem guarantees the existence of a unique strong solution. We now provide a characterisation of the subdifferential of the 1-Cheeger energy, introduce the notion of weak solution to the total variation flow based on this characterisation, and prove their existence and uniqueness. We also comment on the asymptotic behaviour of weak solutions and introduce a notion of entropy solutions for initial data in L1 under the assumption that the measure of the space is finite.

This chapter gives an overview of perinatal mental health services in Asia, Africa and South America. These are areas where service delivery, training and funding in perinatal mental health remain a major challenge. Investing in perinatal mental health services is vital for any country to ensure physical and mental well-being of mothers and the upcoming generations.

Mid-century corporate executives received most of their compensation from salaries and cash bonuses, making them highly vulnerable to the top marginal income tax rates. Because executives were also able to negotiate custom pay packages, they adopted policies to dodge those rates. Most importantly, executives were influential in spreading and legitimizing tax dodging not only within their own companies, where they could affect the nature and structure of their own pay packages and those of their employees, but they could influence compensation, benefit and perquisite, and reimbursement policies at thousands more companies in part by lobbying for legislative and regulatory action that officially sanctioned these new policies. Although executive tax dodging was not the only reason corporations partnered with the government in creating the plans that form the backbone of our employer-sponsored retirement and health insurance systems, as well as the stock-based compensation that helped to drive the wealth and pay gap between executives and workers, it was a powerful force in a system that has endured for decades.

The large sieve takes various forms, as a mean square upper bound for a trigonometric polynomial at well-spaced points, as a mean square upper bound for the distribution of a set of integers into arithmetic progressions, and as a mean square upper bound for character sums. We take the trigonometric form to be fundamental and derive the other versions from it.

The distribution of prime numbers, one of the central questions in number theory, is elegantly described by the Prime Number Theorem, which states that the number of primes up to a given value x grows asymptotically like x/log(x). We present a complete proof of this theorem following the approach of Newman and Zagier, using only basic tools from complex analysis.

A deeper refinement is provided by the von Mangoldt exact formula, which expresses the Chebyshev weighted prime-counting function in terms of the zeros of the Riemann zeta function. This formula makes explicit the connection between prime numbers and the non-trivial zeros of the zeta function, showing how each zero contributes to the oscillations in the distribution of primes and to deviations from smooth, regular growth.

The Riemann explicit formula offers an even more direct relationship between the number of primes up to x and the zeros of the zeta function, capturing the deviations from the Prime Number Theorem as a sum over these zeros. Together, these formulas deepen our understanding of prime distribution and highlight the profound connection between analytic and arithmetic structures.

We outline the derivation of both exact formulas, omitting some of the most technical steps.

Chapter 1 introduces the War of the Spanish Succession as it unfolded in both Europe and Spanish America, emphasizing its profound impact on the social and political fabric of New Spain. It argues that persistent fears of foreign invasion and economic instability generated heightened anxieties across racial, class, and regional lines. The chapter examines how viceregal authorities mobilized mixed-race militias, co-opted Creole elites, and engaged municipal governments to defend the viceroyalty. These efforts were not only reactive but also instrumental in reinforcing loyalty to the Bourbon cause. At the same time, the war imposed economic burdens on broad sectors of society, even as it created opportunities for advancement among Creole families with access to patronage networks. Through sermons, official correspondence, and public rituals, the chapter highlights how political uncertainty intensified the stakes of dynastic legitimacy and fueled a sense of urgency surrounding the future of the empire.

This chapter examines the key principles of applying mental health and capacity legislation in the perinatal period. The four nations of the United Kingdom have different legislative frameworks. England and Wales are governed by the same legislation – the Mental Health Act 1983 (MHA) and the Mental Capacity Act 2005 (MCA), although with some minor variations. Scotland has an entirely different framework – the Mental Health (Care and Treatment) Act 2003 and the Adults with Incapacity Act 2000. Northern Ireland is in a (slow) transition from having mental health legislation (the Mental Health (Northern Ireland) Order 1986) sitting alongside, in effect, no formal framework for thinking about capacity, to ‘fused’ legislation (the Mental Capacity Act (Northern Ireland) 2016) with no stand-alone mental health legislation. This chapter focuses on the position in England and Wales, primarily because it has the largest body of case law to help understand how to think through the dilemmas covered; for those in other parts of the United Kingdom grappling with those dilemmas, the most useful resource is the BMA’s Ethics Toolkit which has specific sections for each of the nations.

For many people the journey to becoming a parent is not a straightforward one. The following chapter examines how experiences with infertility, assisted conception and perinatal loss can impact on an individual’s mental health, relationships with others and future children. The chapter is divided into two sections: the first examining infertility and assisted conception, and the second focusing on perinatal loss. Each section will briefly define key concepts, definitions and prevalence before describing the psychosocial impact of these difficulties and treatment options.

Although this chapter is divided into two sections, it should be noted that women who experience infertility and utilise artificial reproductive techniques (ART) are also highly likely to have experienced some form of perinatal loss. The experience of infertility alone is its own form of loss and individuals who experience it may have a grief response and share similar psychological difficulties to those who experience pregnancy loss or baby loss. The aim of this chapter is to increase awareness around the often complex and lengthy journey to parenthood, and to support clinicians in understanding the experiences of those they come across at various stages of this journey and how they can best support them.

This chapter begins with the study of Dedekind domains: integrally closed Noetherian integral domains of Krull dimension one. Dedekind domains are the natural framework for studying rings of integers in number fields.

A key feature of Dedekind domains is that every fractional ideal is invertible, and the set of fractional ideals forms a group under multiplication – in fact, a free abelian group with basis given by the set of prime ideals. This recovers unique factorization, but for ideals rather than elements.

The theory of modules over Dedekind domains is particularly elegant: finitely generated torsion-free modules decompose into direct sums of ideals and are classified up to isomorphism by their rank and Steinitz invariant. Finitely generated torsion modules are classified by their invariant factors, similarly to the case of PIDs.

In arithmetic applications, ramification in field extensions describes how prime ideals factor when extended to larger rings. The explicit factorization of a prime ideal is governed by the factorization of the minimal polynomial of a primitive element modulo that prime.

José María Samper (1828-1888) was born in the provincial town of Honda, Colombia. A prolific author, he combined his writing activities with politics, journalism, and teaching. In his earlier career, Samper became prominent within a young generation of radical liberals who advocated universal and direct suffrage, the separation of church and state, and the abolition of the standing army. In 1855, In what was perhaps one of the first usages of the expression “Latin American,” Samper proposed the formation of a federation of Spanish American republics to defend their emerging “democracies” and their interests from the ambitions of the European monarchies, the Brazilian Empire, and US expansionism (Reflexiones sobre la federación colombiana, 1855). “Colombia” was the name Samper gave to his proposed union. Later in his life, however, Samper tempered the radicalism of his youth and moved closer to the Conservative Party. Yet in the convention that adopted the 1886 centralist, “conservative” constitution, Samper’s interventions revealed that he continued defending key liberal principles. Samper’s selected passages in our volume come from his earlier liberal phase.