Let n be a positive integer. A Latin square of order n is an n × n array whose entries are taken from an alphabet of size n, in such a way that each row or column of the array contains each letter in the alphabet precisely once.

The “letters” in the alphabet could be letters, numbers, colours or indeed any distinguishable symbols. Figure 6.1 gives two examples.

As far as we know, the first person to study Latin squares was the Korean mathematician Choi Seok-jeong (1646–1715), in his book Gusuryak (Fig. 6.2). The name was given by the Swiss mathematician Leonhard Euler (1707–83); we will see why he chose this name later.

Central to religious life in the British Army were the ‘padres’ of the Royal Army Chaplains’ Department (RAChD), whose pre-eminence was enhanced by the demise of the Indian Ecclesiastical Establishment in 1947 and by the slow decline of auxiliary religious welfare agencies. Supported by sending Churches which were also shrinking, and whose approach to Army chaplaincy was often (and for various reasons) ambivalent, the RAChD (like the all-professional Army) generally struggled to find recruits. The duties of chaplains were varied, ranging far beyond the stated requirements of Queen’s Regulations. They were also fulfilled under the umbrella of an organisation that was, until ‘Convergence’ in the early twenty-first century, divided along confessional lines, and whose ethos and training was widely considered archaic and even inadequate. However, the McGill Report of 1999 was a catalyst for change. Its emphasis on efficiency and on chaplaincy’s ethical contribution laid the foundations for an increased and more ubiquitous chaplaincy presence, an improved training regime and for institutional Convergence. The fruits of these changes would quickly become apparent in the War on Terror.

This chapter introduces the theory of lossless transmission lines based on an equivalent circuit. The three key parameters, the velocity of propagation, the characteristic impedance and the reflection coefficient are shown to be linked to the circuit parameters. Using these concepts, there are examples of step waves reflecting from resistances at the end of transmission lines. In some examples, there are also reflections from the source resistance as well. These multiple reflections are analysed to show that they reach a steady state predicted by circuit theory. Pulses on transmission lines are described by taking a positive step wave and then adding a delayed negative step wave. The energy in a pulse is shown to consist of an equal amount of electric and magnetic energy. The chapter ends with examples of reflections from both a capacitor and an inductor.

This chapter explores the progressive development of international biodiversity law, from the 1972 Stockholm Conference on the Human Environment to 2022. It shows that some of the most forward-looking concepts enshrined in the 1972 Stockholm Declaration have guided the progressive development of international biodiversity law for 50 years, notably the need for cosmopolitan cooperation that takes into account distributive justice issues and human rights. Still, the sectoral and largely incremental approach of the Stockholm Declaration no longer fits in addressing the urgent triple planetary crises that we face. Rather, a transformative change is needed. International biodiversity law, in its interactions with human rights, can contribute to such a change, by focusing on environmental and social justice issues, by ensuring that solutions, including climate change response measures, have sustainable impacts at other scales and in other sectors, and by empowering those whose interests are not being met and represent transformative sustainability values.

The historically overlapping discourses of romanticism and aesthetics frequently draw criticism for being mere ideology. “Ideology” here refers to a restricted worldview that misrecognizes itself as universal and suggests why romanticism is crucial to debates about world literature. Insisting on aesthetics as universal, romanticism helps to initiate a Eurocentric conception of world literature. But this criticism ignores the often-conflicted character of romantic writing in which an aesthetic machinery exposes universalism as built on exploitation. To fully grasp the stakes of such breakdowns one must further consider romantic-era texts that are not European. An exemplary instance is Hérard Dumesle’s 1824 political travel narrative Voyage dans le Nord D’Hayti. Drawing on European models, it proves paradoxically revealing in its account of Eurocentric aesthetics. Endorsing and ironizing universalism, it opens onto alternative conceptions of world literature by marking the limits of translatability and refusing to belong to any one world.

The clergy – both Catholic priests and Protestant ministers – are the subject of this chapter. They were both targets for violence and could be among its perpetrators. A core argument here is that Protestant ministers were subjected to violence in large part because of their profession, as against motives such as moneylending that were emphasised in previous scholarship. As leading Protestant figures, they were both symbols of and key actors within Protestant ‘civilising and converting’ that was so central to the decades before the rebellion, helping to explain Irish Catholic hostility towards them. Similarly, violence against Catholic priests drew from longstanding patterns that viewed priests as seditious, troublesome and violent, thus justifying their persecution and even killing. Examining the clergy as symbols as well as people, alongside the study of violence against sacred objects and spaces, reinforces the strong religious character of violence during the rebellion and its continuation in the decade of conflict that followed.

Chapter 8 builds on early understandings and examines how students deepen their conceptual grasp of Number and Algebra in the middle and upper primary years (Years 3 to 6). It clarifies key language and concepts and highlights common misconceptions to support diagnostic teaching. You will explore engaging classroom activities and assessment opportunities to consolidate mathematical reasoning and promote accurate, flexible thinking.

This introduction provides an introduction to the historical and theoretical frameworks for looking at Irish literature in the Romantic period. It considers the place of the Irish language in characterising Irish eloquence, and argues that British critics also linked Irish eloquence to Gothic excess. It introduces some of the main authors that will be looked at in greater depth later, including Maria Edgeworth, Sydney Owenson, Thomas Moore, and Charles Maturin.

This chapter explores the progress of international climate law since the 1972 Stockholm Conference. Climate change threatens the very kind of massive and irreversible harm to the environment that the conference sought to prevent. The chapter shows first that customary international law, while imposing harm prevention obligations on states, has not kept pace with the global, intertemporal, and developmental dimensions of climate change. The chapter then offers a brief account of the evolution of the global climate regime launched by the 1992 UN Framework Convention on Climate Change. As the discussion will illustrate, 30 years later, the regime continues to wrestle with the complexities of the climate challenge, including difficult burden-sharing questions and the fraught relations between North and South. The 2015 Paris Agreement, which introduced a new approach to international climate governance, is a response to these complexities

This chapter looks at the work of Sydney Owenson, focusing on two novels, The Wild Irish Girl and Woman; or Ida of Athens. It considers the way in which Owenson crafted a powerful model of female eloquence in response to the perceived failures of more mainstream political speech. It looks at the legacy of the Volunteer movement of the 1780s as well as the Irish-language background of her work. It also notes the publication of Gilbert Austin’s Chironomia, an important rhetorical treatise, and the links between his work and Owenson.

Drawing together the previous chapters’ discussions of feminine respectability, the Conclusion focuses on the tensions young women experience as they attempt to reconcile personal ambition with societal expectations and as they navigate quotidian life in the city alongside the longer-term objectives of ending their single status. The Conclusion reiterates the book’s two arguments, articulating how feminine youthhood is a period shaped by contingencies, which not only render young women vulnerable but also encourage them to contribute to the uncertainties that shape urban life in contemporary Nigeria. While the previous chapters have discussed how dissimulation, illusion, and concealment shape young women’s lives, and the ambiguous attitudes young women have towards these forms of uncertainty, the Conclusion questions when the fake is categorically immoral. Doing so, young women are inserted into a broader discussion of the means of sustaining, as well as the perceived threats to, social reproduction in urban Nigeria.