Suicide remains a leading cause of maternal death in the UK and in other high-income countries. While there are clear risks in severe mental disorder, those who die have experienced a range of mental illnesses and often come from more deprived communities. The Confidential Enquiries highlight the distinctive patterns of occurrence and progression in perinatal mental illness and the need for improvements in clinical evaluation of risk, effective risk management and the availability of high-quality perinatal mental healthcare as important factors in helping reduce progression to suicide.

This book comes in two parts; the first, consisting of §§1–7, offers an informal axiomatic introduction to the basics of set theory, including a thorough discussion of the axiom of choice and some of its equivalents. The second part, consisting of §§8–14, is written at a somewhat more advanced level, and treats selected topics in transfinite algebra; that is, algebraic themes where the axiom of choice, in one form or another, is useful or even indispensable.

The Riemann zeta function is one of the most profound and extensively studied objects in analytic number theory, with deep connections to the distribution of prime numbers. Initially defined for values of s with real part greater than 1, it can be extended to a meromorphic function on the entire complex plane, except for a simple pole at s = 1.

A central feature of the zeta function is its functional equation, which relates its values at s and 1-s, revealing a deep symmetry. This equation is often written in a symmetric form involving the Gamma function, a fundamental object in complex analysis that generalizes the factorial. The Gamma function plays a key role in the functional equation and links the behavior of the zeta function to complex analytic properties.

Another crucial element in the theory is the Jacobi theta function, whose transformation properties are essential in deriving the functional equation of the zeta function.

Syntactic reconstruction poses a unique set of challenges to comparative philologists, and this has led some authors to go so far as to claim it is impossible. This chapter begins by evaluating these challenges and how troubling they are for the enterprise of syntactic reconstruction. With this baseline established, the author turns to the specific attempts that have been made at reconstructing syntax, in particular with reference to Proto-Indo-European. Although some aspects of syntax were treated as early as the Neo-Grammarians, the earliest concerted efforts to treat Proto-Indo-European syntax on its own terms date to the latter half of the twentieth century. There have been several different approaches to syntactic reconstruction since then, which fall broadly into four categories: Typological reconstruction; Pattern-based approaches; Construction Grammar; and Minimalist reconstruction. This chapter argues that, while it is not the only viable methodology, Minimalist Reconstruction provides the most suitable means for the task of reconstructing relative clause syntax in Proto-Indo-European.

This chapter presents the basic commutative algebra tools for algebraic number theory. It begins with the Chinese Remainder Theorem for arbitrary commutative rings, which decomposes ring elements modulo the intersection of pairwise coprime ideals – illustrating a fundamental local – global principle. This principle is further refined through localization, a technique that isolates the behavior of rings at prime ideals that do not intersect a specified multiplicative subset.

A central class of rings in this study is Noetherian rings, characterized by the ascending chain condition on ideals, which ensures desirable finiteness properties. The Hilbert Basis Theorem guarantees that polynomial rings over Noetherian rings remain Noetherian, extending these finiteness conditions to broader algebraic contexts.

Further structural insights arise from studying fractional ideals and the Picard group, which classify invertible ideals and play a crucial role in the study of rings of Krull dimension 1, particularly Dedekind domains.

The chapter concludes with finite-dimensional commutative algebras over fields, a particular case of rings of Krull dimension 0. Under semisimple and separable conditions, these algebras decompose into direct products of fields, permitting a complete classification.

This book offers a selection of key texts mostly written by leading figures in the history of Spanish American political thought during the first century of independence. Political thinkers in the region had to grapple with rather unique and extraordinary circumstances after three centuries of Spanish colonial rule. The emergence of a significant number of new independent polities that adopted representative institutions in an era when absolutism still prevailed in Western Europe, their general adoption of republicanism (except for Mexico during the brief rule of Agustín de Iturbide in 1822–1823, and Maximilian in 1864–1867), and their complex demographic composition, all posed serious challenges for the formation and consolidation of national states in Spanish America. In dialogue with the major currents of thought in Western Europe and North America, Spanish American thinkers often reflected upon these and other related problems while being politically engaged, either in government or in opposition.

In the 1950s, as one columnist recently pointed out, “the wealthiest people in the U.S. were not corporate executives … Rather, they were entertainers.”2 In 1958, for example, when Arthur B. Homer, the president of Bethlehem Steel, was making $623,336, Frank Sinatra made nearly $4 million.3 Given this reality, when entertainers got together to talk amongst themselves in mid-century America, “the U.S. tax laws [were] deeply involved.”4 It should not be surprising, therefore, that when it came to tax dodging during this period, entertainers were on the cutting edge.

Attempts to register and control the populations of the east left a documentary record that was often extremely local. Provincial subjects proved astute readers and compilers of local documentation, which they rearranged in order to make claims of right. These claims can be mined for their underlying legal ideologies. Provincial subjects imagined law not as an abstract system, but as a running list of privileges and disabilities. Rights emerged from having the most correct or most persuasive hermeneutic for making sense of collections of documents in dialogue with officials, through the process of generating legal paperwork. Archives were not merely repositories of external facts about the world: they were collections of arguments that could be made. Law emerged from the collaborative process of claiming such rights.

This chapter examines how achievement books produced by Egyptian state institutions have narrated and re-narrated the 1952 revolution. These books were centrally published by the Information Department, a crucial yet seldom studied organ in the emerging Ministry of Culture and National Guidance, as well as public relations units across different ministries. After a brief institutional history of the Ministry of Culture and National Guidance as a whole, in which I demonstrate how ‘culture’ and ‘media’ were originally intertwined in administrative terms, I argue that the state’s achievements were narrated according to a changing conception of the revolution between 1954 and 1970. This rhetoric cemented a distinctive version of history among Egyptian bureaucrats, in which long lists of achievements came to articulate the bureaucratic corps’ contributions to the revolution. Moreover, it aimed to counter colonial propaganda via a systematic presentation of ‘the true Egypt’ in numerous European languages. In short, achievement books recorded, disseminated, and embodied the revolution’s accomplishments for a domestic and an international audience.

Pregnancies among individuals with schizophrenia spectrum disorders have increased in recent years. In the perinatal period, individuals with schizophrenia spectrum disorders are faced with managing the unique effects of their symptoms on pregnancy and parenting, which fluctuate through the perinatal period with the early postpartum being a high-risk time for relapse. Their pregnancies are also associated with a range of adverse pregnancy, neonatal and long-term child outcomes, the risk for which may be related in part to modifiable factors. Prejudice, discrimination and subsequent isolation of perinatal individuals with schizophrenia spectrum disorders may limit health care and social support opportunities in this group, further exacerbating the risk for negative outcomes. These issues underscore the need for comprehensive management approaches including attention to pre-conception health, medication management during pregnancy and postpartum, and multifaceted support for the parent and family. This chapter is an overview of schizophrenia spectrum disorders in the perinatal period, including a summary of the epidemiology, clinical presentation, course, outcomes and management.

Esteban Echeverría (1805–1851) was born in Buenos Aires before the May 25, 1810, revolution, but was educated in the liberal environment of Bernardino Rivadavia’s government, which sent him to Paris to further his education. Upon return in 1830, he saw the rise of Juan Manuel de Rosas and became an opponent of his regime in both a literary and a political sense. He along with others founded the Asociación de Mayo in 1837, which caused his exile in Montevideo, where he wrote the compelling ‘El matadero’ (The Slaughterhouse) and published the Dogma socialista, from which the current selection is taken. The “socialism” of the title might be somewhat deceptive, in that Echeverría’s program contained the standard tenets of liberal democracy. His thoughts on the rule of law, while not entirely original, became a powerful weapon against dictatorship, one that was seen as applicable well beyond his native land and became a classic of Spanish American political thought.

Juan Francisco Manzano (1797/8?–1853) was born and grew up as an enslaved person in the province of Matanzas, Cuba. He taught himself to write despite being forbidden to do so by his masters: “when everybody went to bed, I used to light a piece of candle, and then at my leisure I copied the best verses, thinking that if I could imitate these, I would become a poet.” He published a first selection of his poems in 1821, still under slavery. His work attracted the attention of literary circles in Havana, and the favour of Domingo del Monte (1804–1853), “a wealthy intellectual, leader, and patriot who … mentored a generation of young writers.” It was thanks to Del Monte’s efforts that Manzano was able to buy his freedom in 1836. Del Monte also persuaded Manzano to write his autobiography narrating his sufferings under slavery, which he started to write in 1835.

In this appendix, we outline some of the results of the theory of convex analysis that we need throughout the book; two principal examples of such tools are the Brezis–Komura theorem and the Fenchel–Rockafellar duality theorem.

As climate awareness intensifies in the first decades of the twenty-first century, theatre and performance studies continues to reflect on and revise the depth of its engagement with ecology, understood broadly as the interrelationships between organisms and their environments. ‘From Ecology to Ecocriticism’ covers the rise of ecology first as a science then its gradual shift to the humanities and onto theatre and performance studies. The question of the relationship between humans and nature now animates much of the scholarship on ecology, theatre and performance. Hence, if ecology is the study of the interrelations between organisms and environments, then ecology in theatre studies focuses on the interrelations of the theatrical and its referents in the politics of sentence at climate change. The chapter concludes by arguing that ecocriticism in Australia expands to encompass the impact of settler colonialism and the continuing dependence on fossil fuel consumption and exports.