This chapter focuses on the derivation and interpretation of functional relations among commuting transfer matrices, which underpin a wide range of powerful techniques in quantum integrable systems. These include spectral equations, Baxter’s TQ-relations, and the analytic Bethe ansatz, as well as methods based on wronskian Bethe equations. Rather than isolated tools, these structures are intricately connected and reveal deep algebraic insights with significant implications, including quantum–classical duality and the completeness problem.

Further emphasis is placed on the group-theoretic structure underlying these functional relations. Connections are drawn with the classical theory of characters, where objects such as Schur polynomials and Jacobi–Trudi formulae lead to bilinear relations naturally interpreted as Hirota equations in the context of transfer matrices. This perspective offers a conceptual bridge between quantum integrable models and classical representation theory, highlighting the unifying role of functional relations in both structure and application. Special attention is given to Q-functions governed by Baxter’s TQ-relations and, more broadly, by determinant identities from the wronskian formalism. These functions encode the transfer matrix eigenvalues and serve as fundamental algebraic objects. Functional methods thus offer powerful tools for exploring integrable models, especially when conventional Bethe ansatz techniques become impractical.

There has been unbroken Anglophone settlement of the Falkland Islands, a British Overseas Territory in the South Atlantic, since 1833. The current chapter begins with an overview of the islands’ settlement and socio-economic history, taking into consideration migration from the English South-West and the Scottish Highlands, contact in the nineteenth century with Spanish-speaking gauchos, twentieth century population decline and the aftermath of the brief 1982 conflict with Argentina, since which both the population and the economy of the islands have picked up in sociolinguistically consequential ways. The chapter then provides a detailed overview of the phonology, morphosyntax and lexis of contemporary Falkland Island English, based on a near-million word corpus of spoken conversational data collected by Andrea Sudbury in the late 1990s and Hannah Hedegard in early 2020. This description represents, therefore, an update from earlier accounts (e.g. Britain and Sudbury 2010, 2013; Sudbury 2000, 2001, 2004), given our analysis of a very recently collected new corpus.

Before his rehabilitation got under way in the late 1970s, had Emerson really been the object of “repression” by the American philosophical establishment? The validity of the historical claim put forward by Stanley Cavell has always seemed doubtful. In point of fact, Emerson turns out to have, from his day to ours, a largely unbroken chain of legitimate heirs among American philosophers. This chapter, which builds on previous scholarly efforts to correct and complete the record, notably by historians of pragmatism, continues the work of recovering the Emersonian legacy in American philosophy. The multiform nature of that legacy, which extends to pedagogical theory and classroom practice in American schools, raises important questions for historiographers as they deal with changes in cultural and institutional reception over time. Of particular importance is the question raised by Cavell’s own contribution to Emerson studies: what is philosophy’s relation to the broader literary culture?

Bethe ansatz is a fascinating device in the theory of quantum integrable models. It enables the exact determination of the energy spectrum of dynamical systems ranging from integrable spin chains of magnetism to integrable models in high energy physics. It is particularly valuable for computing critical exponents in solvable models of statistical mechanics and plays a significant role in bootstrapping correlation functions in integrable gauge and string theories. Originally introduced in 1931 by Hans Bethe for solving the Heisenberg model of magnetism, the Bethe ansatz has since been extensively generalized and expanded. It now appears in various forms — the algebraic, analytic, functional, and thermodynamic — and has evolved into a universal framework for understanding integrability in quantum many-body systems. This book offers a comprehensive introduction to the Bethe ansatz techniques. It covers the factorized scattering theory and coordinate and algebraic versions of the Bethe ansatz, including the case of nested structures. Advanced methods based on functional relations among commuting transfer matrices and separation of variables are also addressed. A wealth of detailed calculations is included to facilitate the reader's swift engagement with the original literature.

The concluding chapter provides a summary of the findings and arguments developed in the previous chapters. It also provides a reflection on the policy implications of the study for reforming the international governance of the Amazon and other international rainforests, such as the Congo rainforest. Finally, it provides some reflections on how the proposed framework can be applied to global commons, such as the high seas and seabed beyond national jurisdictions, and outer space.

This chapter focuses on what race is and what race is not by looking at the interplay of race and human variation. It notes that while race is not biologically real, the invention of race as a social construct is real in cultural, social, and economic terms, often with deleterious biological consequences.

This chapter considers Lewis Carroll’s Alice’s Adventures in Wonderland (1865) and William Morris’s New from Nowhere (1890) through the lens of the commons and what counts as “common sense.” Taking its cue from a question Morris poses about art’s role in radical social transformation, the chapter asks if the recent environmental turn in Victorian studies is interested in piecemeal or systemic change. Considering both modes of change, the chapter proposes a “poetry of the commons,” grounded in Carroll’s and Morris’s very different approaches to both the commons and common sense, as an alternative to the market economy and as more accurate approximation of how the commons traditionally worked. Accordingly, Alice and News can be seen as laying the foundations for something like “commons sense” and a practice and poetry of the commons adequate to the demands of the climate crisis.

‘Elizabeth Maconchy (1907–94): A Chronology’ provides a timeline of the key events in Maconchy’s lifetime.

This chapter provides an account of the types of contact and spread associated with the growth of English beyond the United Kingdom. It describes the main linguistic outcomes of these contacts, including pidgins, creoles, English as a second language (ESL), English as a Foreign Language (EFL), English as Lingua Franca (ELF), Immigrant Englishes and hybridities arising from code-switching and electronic and social media. It also gives an account of how different scholars have tried to make sense of the immense variety within ‘the English language complex’. Particular attention is paid to Kachru’s Three Circles model, Schneider’s Dynamic Model and its current refinements, Mair’s World System for Englishes, Mesthrie’s Contact-Contingency model, and insights from Corpus Linguistics, Language Contact and Language Ecology.

Located across a large swath of land in the north of Australia, the Gulf Country has a history encompassing lives where race has featured predominantly. In the context of European colonization from around the mid nineteenth century, relations between people who have become known colloquially as Whitefellas and Blackfellas have been central to the region’s society, cultural mix, and economy. As understood in everyday language, Whitefellas are known to have no Aboriginal ancestry, while Blackfellas are descended from forebears belonging to one or more of the Indigenous language groups connected to traditional lands.

This poses the question as to why the American air arm began World War II with excellent offensive bombers but mediocre defense fighter planes, which was seemingly in contradiction to a national policy of isolationism and defense. The standard explanation for this dichotomy is that doctrine shaped force structure. I disagree and believe it was a combination of technology, economics, the Army procurement system, and personalities that played the determinant role.

Like Europeans all over the Global South, settlers and administrators in East Africa used the concept of race as a weapon to oppress, elevating themselves and for decades enjoying the luxury of immunity from having their “race” used against them. However, in the context of post-independence, whites came under an uncomfortable spotlight as many Kenyans of African descent questioned their entitlement to belong to the nation in light of their enduring and extreme privilege. The typification of whiteness in the Kenyan discourses traced here thus emerges as a backlash against a history of colonial theft and frames whites as outsiders, conspicuously Other. Time is folded and flattened in these formulations; even whites born long after independence, or who bought their land from Africans, become “white settlers” or “land-grabbers,” and decidedly not “Kenyan.”