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The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content.
In recent years, the United States has witnessed a resurgence in mainstream acceptance of overt, racist rhetoric from politicians. This increased tolerance arises despite previous evidence suggesting that white Americans reject racist appeals when they are explicit. Destabilized examines this shift and points to a perception of threat to white dominance as the root cause. The book finds that when white Americans feel their dominance in the racial hierarchy is unstable, their prejudice activates, and they seek to 'restabilize' the racial hierarchy by accepting negative, explicit racial appeals. Analyses of survey experiments, observational survey data, and political media demonstrate this phenomenon. Finding that this link exists among both white Republicans and white Democrats, Destabilized speaks broadly to the nature of whiteness as a racial identity rooted in the desire for dominance.
The appeal of the Seven Wonders of the Ancient World led many authors to attempt reconstructing them on paper, thus giving rise to an exercise in speculation whose results would soon be published as engravings. These, in turn, would later provide models for series of paintings, which reflect not only a historical interest in the scholarly reconstructions but also a recognition of their aesthetic value.1 In this regard, one of the pioneers of a pictorial appropriation of the Wonders was Maarten van Heemskerck (1498–1574), who developed a fascination for the architecture of Antiquity during his long stay in Rome, a period that witnessed the discovery and assessment of many ancient remains and monuments.2 His endeavour led to the establishment of the canonical series of the Seven Wonders,3 defining not only the list of works but also the iconography for each monument, which would later become fully integrated within a collective worldview.
Scholars have long recognized John's dual focus on Jesus's relationship to God's presence and his impending physical absence. Yet attention to Jesus's absence is often restricted to the Farewell Discourse. Josiah D. Hall here provides an innovative reading of John's Gospel, arguing that tension between Jesus's presence and absence develops throughout the narrative and is integral to the Gospel's plot. Drawing on sources from across the ancient Mediterranean basin, Hall contends that John leverages conceptions of how deities would manifest their presence to clarify that Jesus is the enfleshed divine presence. Likewise, John depicts Jesus's absence by drawing on motifs of divine departure, especially those which understand a deity's absence as judgment. Attending closely to the paradoxical import of Jesus's presence and absence in John, Hall provides insights on classic Johannine riddles, including John's perspectives on the temple, the characters he labels as 'the Jews', and the Spirit-Paraclete's relationship to Jesus.
Chapter 2 develops the theoretical framework that underpins the book. It argues that politicians in developing democracies face a dual incentive: they need competent bureaucrats who can implement programs effectively, yet they also desire control over those bureaucrats to secure loyalty and political advantage. As a result, politicians often recruit based on merit but retain formal or informal levers of influence, such as control over promotions or geographic transfers. The chapter distinguishes between programmatic and non-programmatic distribution, emphasizing that politicians often require bureaucratic loyalty to engage in non-programmatic distribution. Further, politicians have greater incentives to engage in non-programmatic distribution when local elections are highly competitive. Accordingly, I expect that intense local electoral competition will result in worse governance outcomes, including higher levels of corruption and partisan allocation of public goods. This framework provides the theoretical lens to interpret the empirical evidence presented in subsequent chapters and situates the book’s contribution within broader debates on state capacity, bureaucratic autonomy, clientelism, and democratic accountability.
How can we reconfigure our way of understanding all that is, what Heidegger calls 'being' – so that we can live differently and more fittingly, together? How can we get a sense of different possibilities for being and doing, that allow for hope and change? How can things show themselves so that we heed them and feel a kind of grateful receptivity to them? To all of these questions, Heidegger's answer is 'art.' This Element aims to make sense of the incredible importance Heidegger affords art, on the one hand, and his pessimistic reflections on the possibilities for both art and life in late modernity, on the other. The author proposes that thinking of the artwork as a measure – opaque, basic, and with a regulative normative force – helps make sense of Heidegger's thinking and the promise and peril of art.
Most people not only believe in free will but assume that if we didn't have it society would fall apart. Gregg Caruso challenges this assumption and argues that belief in free will, rather than being a good thing, actually has a dark side and we would be better off without it. His book develops an ethically defensible and practically workable account of how we can live well—indeed, live better—without belief in free will. The book discusses the moral psychology of blame and anger, the intricacies of our moral responsibility practices, and how we can preserve love, morality, creativity, friendship, and criminal and social justice without free will. He also develops an account of virtue ethics and argues not only that it is consistent with free will skepticism, but that adopting the skeptical perspective can better help us achieve the virtues most important to human flourishing and wellbeing.
Is the Arctic destined for conflict, or can cooperation prevail? This timely book explores the complex interplay of security, geography, and regions in the Arctic. Moving beyond simplistic narratives of geopolitical rivalry, it offers a nuanced, multilevel analysis of state security practices, foreign policies, and regional cooperation across distinct subregions. Challenging conventional notions of 'regions' and re-evaluating the role of geographic proximity, it provides fresh insights into how states engage with their neighbours. It also explores the enduring relevance of geography in international relations, demonstrating how the concept of an 'Arctic region' can be a powerful framework but also rests on some false assumptions. Essential for scholars, students, and policymakers, Arctic Geopolitics reshapes our understanding of security dynamics in the Arctic and beyond. This title is also available as Open Access on Cambridge Core.
Protection at the Margins is a ground-breaking account of how and why religious actors protect local communities from state-driven populist violence. Focusing on Philippine president Rodrigo Duterte's notorious 'Drug War,' the book provides an intricate view of how religion, populism, and political violence interact on the ground. Drawing on original surveys of Catholic clergy, experiments with members of the Philippine National Police, spatial data on thousands of drug killings, and dozens of field interviews in these neighborhoods, the book shows how Catholic elites used moral commitment and institutional capacity to influence street-level bureaucrats with discretion over violence, work with secular partners, and challenge populist dehumanization. It also highlights obstacles to protection, in the Philippines as well as Brazil and the United States. Amidst rising global concern about populism and violence, Protection at the Margins generates new insights into how religious actors shielded communities in one of the world's largest mega-cities.
In this chapter, we first provide an overview of health and mental health outcomes across the different types of street segments studied to assess whether residents of crime hot spots have more adverse health issues compared with residents living on street segments with little or no crime. We find that there are strong relationships between mental and physical health and living in crime hot spots as opposed to non-hot spots. We then examine whether negative health outcomes are a consequence of living in a crime hot spot. We find that hot spots of crime are not simply places with high crime rates; they are also places with strong physical and mental health deficits. After accounting for selection, several physical and mental health problems are found to result from living in a crime hot spot.
This chapter analyses the Marxian problem of transforming values into prices of production in light of Sraffa’s price system. It begins by introducing an ‘ideal’ price system where workers receive the entire net product. This system, based on ‘values’ or embodied labor, is contrasted with the ‘prices-of-production system’ where profits are distributed in proportion to total capital. The chapter then delves into the differences between these systems, highlighting Marx’s three propositions about the relationship between the rate of surplus value and the rate of profit.
It examines the special case of Sraffa’s Standard system where income distribution is independent of the price system and explores the concept of a linear operator that transforms values into prices. The chapter also discusses Marx’s simplification of uniform ‘organic composition of capital,’ where values and prices coincide. Finally, it demonstrates that the rate of surplus value is inherent in the prices-of-production system when expressed in terms of the per-capita net product.