We are interested in non-trivial bounds for sums of the form where f(x) is a smooth, real-valued function. In this chapter, we develop methods whereby one may show that such a sum is indeed o(N). The quality of the results depends on the finer properties of f.

This chapter focuses on writing medico-legal court reports in the context of being either a) the treating clinician or b) an independent expert, with a focus on reports for child safeguarding and family court processes. It highlights the range of parenting issues that might arise in the context of perinatal mental illness, as well as the roles and duties of writing a report, and areas to include within the report and its structure. The primary objective for family courts is to ensure that children remain with birth parents unless there are overriding risks of significant harm and neglect to the child. Psychiatrists and clinicians therefore have a duty to be able to write high-quality professional witness and expert witness reports which assist courts in the case of maternal/parental mental health conditions and their potential effects on developing infants and children. Whether a baby remains in the care of the birth mother (and family) or not, has profound effects on both, over lifetimes. However, it is ultimately the task of the judge in the family court to weigh up the available evidence submitted by different experts and parties and make the final recommendations.

This chapter explores the scientific connection between sex and sport. It begins by examining the meaning of sex and the criteria used to assign individuals to the male or female category. It ends by exploring the link between sex and sport and identifying the sex-related traits that have the greatest impact on athletic performance.

Characters curse storms, power blackouts and climate change sceptics in twenty-first century drama as the destructive force of climate change is theatrically represented across comic farce, realist tragedy and dystopian horror. While these theatrical forms differ in their affective and emotional impact, they commonly predict ecological disaster in the future. Disaster is broadly understood as the combination of historical and social determinants interacting with natural hazards and forces over time. Climate change disaster is framed in scenarios that range from humorous to terrifying and with a growing dramatic genre of futuristic climate fiction (cli-fi) about ecological collapse and political dystopia. Twenty-first century dramatisation presents both the absurdity of humanity’s inability to reduce carbon emissions and global warming and the tragedy of predicted disaster on a geological scale in the Anthropocene. At the same time, contemporary performance illuminates turning points in time turning points in time including a different outcome within the present including within the present.

José Antonio Saco (1797–1879), a native of Bayamo in Cuba, studied philosophy under the notable Félix Varela and succeeded him in the philosophy chair at the University of Havana. He edited the journals El Mensajero Semanal and the Revista Bimestre Cubana, where his writing against the slave trade caused his exile in 1834 – he only returned to Cuba for a brief period in 1860–1861. He traveled extensively in Europe collecting the documentation for his Historia de la esclavitud (1875–1879). He was elected to the Cortes in Spain but, after 1837, Cuba was excluded from representation there. Saco also became conspicuous for his opposition to the annexation of Cuba to the United States. The current selection was written in the wake of Narciso López’s failed invasion of the island in 1851 and reveals a keen awareness of the international situation and the hard choices facing Cuba in the nineteenth century.

Recent threats to democracy have induced scholars to sound the alarm by employing dramatic terms more broadly, for instance by associating right-wing populism with fascism. From the pragmatic perspective advocated by David Collier and Robert Adcock in their article “Democracy and Dichotomies: A Pragmatic Approach to Choices about Concepts” (1999), this chapter criticizes this attenuation of qualitative differences and pleads for maintaining and reaffirming strict conceptual boundaries. After all, fascism constitutes a syndrome of interlocking components (“bounded whole”) that is distinct from lesser dangers such as right-wing populism and conservative authoritarianism; hybrids are rare and unviable. Careful, circumspect concept usage is crucial for accurately diagnosing democracy’s current predicament and for designing promising, effective remedies.

Disaggregation has been an underappreciated tool for the formation and utilization of concepts. This chapter argues that disaggregating multidimensional concepts can be useful in four ways. It can (1) resolve dilemmas of “awkward fit,” where some empirical cases seem to fit in the categories established by a concept at best awkwardly, at worst inappropriately; (2) address the challenge of “middle cases”; (3) strengthen measurement validity; and (4) avoid a problem of tautology. The use of disaggregation will be examined with respect to important and complex concepts such as corporatism and democracy.

The introduction presents the book’s central argument: that the War of the Spanish Succession inspired an elaborate campaign of ceremonial propaganda in New Spain, portraying the rise of the Bourbon dynasty as both sacred and regenerative, grounded in multivalent corporeal symbolism. It begins with a close reading of Mexico City’s catafalque for Carlos II, a structure saturated with emblems of death, rebirth, and imperial continuity, and then traces how sacred kingship and millenarian rhetoric shaped public representations of Felipe V. Drawing from emblem books, eucharistic imagery, and historical myth, clergy, bureaucrats, and artisans in New Spain recast the monarchy as divinely ordained and capable of restoring a weakened empire. The introduction also sets up the broader stakes of the study, engaging historiographical debates over imperial decline, composite monarchy, and reform. It outlines the book’s methodological commitment to decoding symbolic language and exploring how sacred imagery forged a transatlantic imagined community of empire.

This chapter introduces the reader to the political environment of Archaic Greece (seventh through early fifth centuries BCE) on the eve of the emergence of the first democracies. Archaic city-states had already taken important steps combatting tyranny, working toward the rule of law, and providing outlets for popular participation. The first instances of dēmokratia in the late sixth and early fifth centuries BCE represented both an expansion of these tendencies and a revolutionary shattering of the status quo. Poets and intellectuals of the time register democracy’s radical empowerment of lower-class male citizens. Oligarchy or the rule of the wealthy few begins to emerge as a reactionary, countervailing constitutional force.

Basic definitions and tools for error correction: In Chapter 2, we provide the basic elements of classical error correcting codes, how to perform operations in finite fields, the decision rules, the structure and properties of classical block codes, and finally a description of the Reed–Solomon codes which are particularly important for the erasure channel.

Juan Bautista Alberdi (1810–1884), was originally from the province of Tucumán, in today’s western Argentina. Alberdi was part of the Generation of 1837, a literary salon highly influenced by European Romanticism. The increasingly dictatorial rule of Juan Manuel de Rosas forced the group to go underground and eventually to exile in neighboring Uruguay. After the siege of Montevideo in 1843, Alberdi went to Europe and settled subsequently in Chile. As a writer and political commentator, Alberdi was instrumental in the overthrow of Rosas and in the promulgation of the Constitution of 1853. Under the rule of Justo José Urquiza as head of the Argentine Confederation, Alberdi became a diplomatic representative in Europe. His most important work is Bases y puntos de partida para la organización política de la república Argentina, which as the title indicates became the leading draft of the Constitution of 1853. Due to his experience in Europe, he was also a keen observer of international affairs. The selection included in this volume represents a strong argument in favor of a community of nations whose principal aim was the eradication of war, which he considered as a crime against humanity.

The rise in rates and drop in the exemption, not increased interest in tax advice among the wealthy, but among the new generation of middle class taxpayers. Tax advisors spring up to fill this new demand, not only in the form of tax lawyers and accountants for the well-off, which existed, albeit in smaller numbers, before World War II, but in the emergence of retail tax help, such as H&R Block, self-help advice books, tax advice columns in newspapers and magazines, and fly-by-night advice for people with far less ability to pay. Some of these were focused on tax return preparation, but because of the pressures to attract customers in the low margin retail tax industry, there were substantial incentives to promise high refunds. The growth of the tax advice industry sensitized the average person to common tax dodging techniques and to the practice of planning, rather than merely reacting, to taxes. The growth of tax advice also created a space for tax dodging school and tax protester movements, who spread information on tax dodging methods and justifications for non-filing in this pre-internet era by distributing pamphlets, organizing small group meetings and giving lectures.

While Donald Trump's ruthless, reckless, aggressive, multi-pronged assaults are threatening American democracy in unprecedented ways, India nevertheless stands out when viewed against broader trends of democratic backsliding (Haggard and Kaufman 2021). Since 2014, liberal democracy in India has come under increasing pressure from Hindu nationalism. Commentators and scholars who are sympathetic to liberal democracy express grave concern, if not alarm, about the state of Indian democracy: ‘The blaze is at our door’ (A. Roy 2022) and ‘The Hindu Rashtra [Hindu Nation] is … indeed underway’ (Jaffrelot 2019a, p. 64). One writes that ‘India's Democracy Is Dying’ and notes that democracy watch organizations now classify India as a ‘hybrid regime’, an ‘electoral autocracy’ or a ‘flawed democracy’ (Tudor 2023).

Electoral democracy remains intact in India, but civil freedoms, minority rights, and institutional constraints on executive power have been substantially weakened (Varshney 2022), and ‘India's standing as an inclusive, diverse nation with an independent judiciary, rule of law and free media was degraded’ (Patel 2021, p. 460).

During the past decade, prime minister Narendra Modi's Bharatiya Janata Party (BJP) government has ‘tethered religious nationalism to right-wing populism’ (Basu 2021, p. 278) and prioritized Hindu nationalism over the Indian constitution, as ‘an ideology that promotes the idea that Hinduism is the authentic religious and cultural identity of the Indian people’ (Yilmaz and Morieson 2023, p. 185). ‘The BJP has thus moved Hindutva beyond right-wing nationalism and toward a civilisational struggle between Hindus and “others”’ (ibid., p. 198).