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Theoretical research sometimes resembles panning for gold: the first to 'discover' a given subject can take their pick of any bold simplifying assumptions and mine all the good nuggets before the rest of us join in. Still, some beautiful exact results may lie just below the surface. Every now and then, they are uncovered through mathematical tours de force. Short of extraordinary mathematical skills, there is, fortunately, a third way towards successful analytical investigations: Asymptotics – the craft of treating limiting cases. This book is addressed to scientists and engineers from Masters level up who want to enrich their numerical investigations with analytical results. It provides strategies for obtaining approximate results when parameters become small or large. Built round a large number of examples, it demonstrates how the techniques apply to a variety of problems, by considering applications from areas as diverse as quantum mechanics, elasticity, electromagnetism and population dynamics.
This undergraduate textbook carefully introduces the fundamentals of axiomatic set theory; a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One can thus say that set theory is a foundation for mathematics. The proofs are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Topics covered include relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers. Exercises are given at the end of each section in a chapter. The second edition includes a new chapter on set-theoretic constructions of the integers, the rational numbers, and the real numbers; a new chapter on models of set theory. There are also new sections on the hyperreals and applications of stationary sets, club sets, and Fodor's Theorem, as well as additional explanation, examples, and figures. A solutions manual is available for instructors.
This new edition offers a timely and compelling account of how development can be reclaimed as a central purpose of international trade law. Written for scholars, students, policymakers, and practitioners, it explains why a stable rule-based trading system remains essential for economic transformation and poverty reduction. The book provides a comprehensive and accessible guide to the core rules and disciplines of WTO law, while also confronting the systemic crisis facing the World Trade Organization today—marked by dispute settlement paralysis, growing unilateralism, and the resurgence of industrial policy in developed countries that increasingly conflicts with established trade rules. By combining rigorous legal analysis with a development-centered perspective, the book highlights both the challenges and the possibilities for renewing multilateralism. It ultimately proposes realistic pathways for reform, making it an essential resource for understanding the future of the world trading system and its role in global development.
How can we draw reliable conclusions from limited and imperfect data? This textbook offers a clear and accessible guide to the principles behind scientific inference, showing how a unifying framework connects fields as diverse as Earth science, medical imaging, non-destructive testing, meteorology, climate research, and machine learning. It presents both classical and modern methods for solving real-world inference problems, with practical guidance on evaluating the reliability of results and understanding their uncertainties. Designed as both a learning resource and a long-term reference, the book balances depth with clarity. Hands-on computational exercises throughout help readers translate ideas into practice, strengthen their intuition and build confidence in tackling their own data challenges. It is ideal for advanced undergraduate and postgraduate students, as well as researchers and professionals, across many disciplines, from environmental science and medical imaging to climate research, machine learning, and economics.
Digital technologies are reorganizing economies, politics, crime, and international relations faster than existing theories can explain. Rather than treating these changes as separate phenomena, The Digital Revolution and Institutional Change offers a unified framework for understanding how digital innovation reshapes social organization across domains. Drawing on institutional economics, it shows how property rights, transaction costs, and incomplete mental models shape both the adoption of new technologies and society's often flawed responses to them. It argues that international contracting and collective action routinely fails to address the unintended consequences of technological progress and explains why these failures are not accidental but structural. Written by one of the world's foremost experts on New Institutional Economics, this book is the first to analyse the digital revolution from the perspective of the economics of institutions, reframing how we think about technological change in the digital age.
This book explores the ways in which divine and human agency interacted in ancient Greek thought. It offers new interpretations of a wide array of texts and sources, from Homeric epic, Aeschylean tragedy and Herodotus to Neoplatonist thought, emphasising the fascinating diversity, ambiguity and complexity of ancient Greek responses to divine intervention, and asking what these can tell us about how the Greeks related to their gods. At the same time, the volume charts the intellectual history of debates on divine and human agency, from ancient philosophy to twentieth-century scholarship. Most radically, it considers whether commonly used concepts such as 'double motivation' and 'over-determination' have outlived their purpose; and puts forward potential alternative approaches. By engaging with all these questions, the book yields novel insights into how the ancient Greeks responded to the idea of divine intervention, and, by extension, into how they experienced and interpreted the world around them.
Moving beyond familiar discussions of ethnic conflict, this Handbook presents a bold rethinking of how language shapes identity, power, and violence. With contributions from leading scholars in linguistics, political science, and public policy, it presents global case studies alongside new analytic tools for the study of language and global politics. It introduces “language conflict” as a clearer and more useful framework-one that brings linguistic structure, institutional policy, and communicative inequality into focus. Split into four sections, chapters cover topics such as hate speech, language rights, transitional justice, education policy, and postcolonial literature, spanning contexts from Cameroon to Catalonia, and from Guatemala to Sri Lanka. Together, these chapters show how language is not simply a cultural marker, but a political force that shapes collective identities, nationalism, and resistance. It is essential reading for anyone interested in language policy, multilingual governance, and the deep entanglement of language with political life.
Charles Rivera's study offers the first substantive comparison of the theologies of Origen of Alexandria and Ephrem of Nisibis, two towering figures of early Christian literature. Tracing the distinct approaches to grace in Origen and Ephrem, he argues that Origen uses grace (Greek charis) as a technical term for the gifts of the Spirit, whereas Ephrem uses grace (Syriac taybuta) to encompass divine attributes like goodness, mercy, and generosity. Tracing these different ideas of grace across topics from providence to divinization to the last judgment, Rivera demonstrates that Origen and Ephrem do not merely have different understandings of a shared concept. Rather, they use a shared key term to refer to two distinct theological ideas. Rivera's comparison of Origen and Ephrem thus suggests a re-evaluation of the diversity of views of grace not only in the Patristic period but in the Christian tradition more broadly, prompting a reconsideration of long-held assumptions of Christian theology.
Roman Satire and the Fall of Rome reveals the involvement of the satirist Juvenal in composing the history of Roman decline. He was perhaps the most fashionable classical author in England in the eighteenth century, when Edward Gibbon wrote The History of the Decline and Fall of the Roman Empire (1776–88). Juvenal's satires enjoyed a similar level of notoriety among the Roman writers of late antiquity, who furnished Gibbon with the materials for his history. This book traces the reverberations of Juvenal's satirical rhetoric between these different periods. Ian Fielding offers detailed new readings of the responses to the satires in the works of Ammianus Marcellinus and Claudian, while also examining the responses to those responses in Gibbon's Decline and Fall. The complex case of Juvenal's reception shows how satire, the quintessentially Roman genre, has represented the problems of the Roman past as a warning for modern times.
This book offers a broad-ranging study of the Athenian stratēgoi in the fifth and fourth centuries BCE, combining an institutional approach with close analysis of command in practice. The commanders' numerous responsibilities at every stage of a campaign, from mustering troops to managing finances, point to considerable autonomy and authority exercised within the often loose boundaries of mandates issued by the Assembly. The analysis of extra-legal authority is shown to be consistent with this interpretation: personal authority shaped how individual stratēgoi exercised power and helps explain discrepancies in independence, attitude, and performance. The result is a fresh perspective on the stratēgoi that rethinks established scholarly interpretations, including their progressive professionalisation, the significance of individual agency, and the role of unmet expectations in their accountability. The volume situates Athenian commanders within broader contemporary debates on military leadership and the widely recognised non-institutional dynamics that regulated public life in Athens.
This book presents an accessible approach to an emerging theory of picture groups. Intended for graduate students and researchers, it explains the connections between several branches of algebra and topology, and demonstrates how they interact. It begins with foundational material on modulated quivers and their representations, cluster categories, and semi-invariants. The text then develops virtual analogues of classical results, allowing dimension vectors with negative coordinates. Finally, it defines the notion of a picture group associated to a semi-invariant picture, also introducing picture spaces which are CW-complexes constructed from semi-invariant pictures. For quivers of type $A_n$ the key theorem draws on K-theory and states that the associated picture space is a $K(G(A_n) , 1)$ connected CW-complex for the corresponding group $G(A_n)$ associated with the same quiver.
This Handbook provides the first comprehensive examination of the legal strategies around the world shaping sustainability in global value chains. Bringing together leading scholars, it maps how diverse legal disciplines (including corporate law, labour law, tax law, tort law, private law, environmental law, international law and more) conceptualise and regulate the complex architectures of cross-border production. Through a unifying analytical framework, the book reveals how fragmented regulatory approaches can complement one another, and how legal tools may address the environmental, social, and economic challenges that global production networks create and sustain. Covering jurisdictions across the globe and engaging with emerging regulatory instruments such as due diligence laws, sustainability reporting obligations, climate transition plans, and international taxation initiatives, this Handbook offers an indispensable resource for academics, policymakers, practitioners, and students concerned with responsible business conduct and sustainable development. This title is also available as open access on Cambridge Core.
The Late Ramesside Letters comprise over seventy surviving texts from the end of Egypt's New Kingdom, created by a community living around the Medinet Habu temple complex in western Thebes. These letters reveal how individuals negotiated varied social relationships and communicative norms, including interactions with the divine. By applying frameworks from (Im)politeness Research – such as Discernment Politeness, Facework, Politic Behaviour, Frame Theory, and Ritual – it is possible to reconstruct the underlying (im)politeness system that shaped all communication within this community. This approach highlights how specific linguistic patterns supported social harmony, managed tensions, and facilitated obligations to both people and gods. The analysis also identifies emerging phenomena that require new theoretical directions, such as the unique strategies used to maintain relationships with deities. Ultimately, the letters demonstrate that Power permeated every level of interaction, and its centrality within this linguaculture challenges modern assumptions about how Power operates in contemporary societies.
What is the moral foundation of human rights, justice, and the rule of law? In a time of deep cultural and political division, this volume charts the rich history of one of the most enduring ideas in Western thought: that moral and legal norms are rooted in human nature and accessible to reason. Spanning ancient, medieval, early modern, and contemporary traditions-including Islamic and African-American perspectives-the volume shows how Natural Law has evolved and how it continues to shape debates in ethics, politics, and jurisprudence. With chapters on Aristotle, Aquinas, Grotius, Locke, and the American Founders, as well as modern voices like Jacques Maritain and Martin Luther King, it offers both historical depth and philosophical clarity. Essential reading for students and scholars in philosophy, law, theology, and political theory, it invites readers to rediscover a tradition that speaks urgently to the moral challenges of our time.
Aquinas argues that, abstracting from divine revelation, God's existence can be argued for successfully, and that God is the source of the existence of all that is not divine for as long as it exists. His philosophical thought about God has been seminal for later thinkers, but can be hard to grasp as it is scattered across a broad range of his writings. This book provides a comprehensive and accessible single-volume account of Aquinas's philosophy of God which also evaluates it in the light both of various criticisms that have been made of it, and of philosophical thought more generally. It situates Aquinas's thinking about God in relation to major philosophers of the past and a number of important philosophers writing today, which will enable readers to understand Aquinas's philosophy of God in the context of centuries of philosophical thought.
In The Wealth of Nations, Adam Smith set out a system for understanding why some societies prosper and others do not, and in the process founded the discipline of economics. In the 250 years since its publication, the world has transformed beyond recognition. Smith has also been reduced in the collective imagination to little more than a byword for the free market. The Wealth of Nations at 250 brings together today's most influential economists and economic historians to ask where Smith's system still holds, and where it needs new machinery. The task of rethinking what causes prosperity demands a return to the breadth of Smith's original vision, incorporating the cultural, institutional, and political foundations as well as the economic. Written in the spirit of Smith's own clarity, the book speaks to anyone interested in how and why nations prosper. This title is also available as Open Access on Cambridge Core.
Like blame, praise has historically been considered one of the defining aspects of morality. Yet unlike blame, praise has received comparatively little dedicated attention in the philosophical canon. Does this emphasis on the negative tell us something about the nature of morality, or is it an accidental feature of the history of philosophy? This volume is the first collection of its kind to include state of the art discussions of the morality of praise as that topic relates to central issues in moral and political theory. Topics addressed in the volume include how the morality of praise relates to the morality of blame; how the apt praise of agents relates to their praiseworthiness; whether agents can be praiseworthy for their beliefs; how the morality of praise is affected by questions about autonomy, identity and luck, and the relationship between praise and distributive justice. The essays in this collection will be of interest to students and researchers in philosophy as well as to the general reader with an interest in questions of moral responsibility.
The linguistic landscape has shifted considerably over the last twenty years, making it increasingly less clear how the key components of language (phonology, syntax, and semantics) communicate and interact with one another. With contributions from a team of renowned scholars, this volume addresses this gap by offering an interdisciplinary account of the current state of knowledge on linguistic interfaces. Chapters are split into five parts, and provide detailed, cutting-edge overviews of the main theoretical approaches to how grammatical components interact. The volume also includes in-depth descriptions of the empirical domains and individual phenomena in which the interface between syntax, semantics, and phonology becomes more informative, along with their psycholinguistic implications for processing and acquisition. Combining empirical data with theoretical analysis, it enables readers to assess and compare linguistic phenomena from multiple perspectives. It is essential reading for researchers and advanced students in syntax, morphology, semantics, pragmatics, phonetics and phonology.