Our best unconditional bounds for ψ(x, χ), such as Theorem 11.16, are not very good owing to our rather limited knowledge of the zero-free region of L(s, χ). It is possible to extend the range for the modulus q of χ at the expense of the error term or by including zeros close to 1. See Corollary 11.20 or the chapter on Vinogradov’s mean value theorem in the forthcoming Volume III. If we assume GRH, then we have a much better estimate (cf. Theorem 13.7). However, in some situations, a good bound for an average of |ψ (x, χ) | is all that is required, and such bounds can be obtained unconditionally by combining our methods of Chapter 17 with the large sieve.

This book comes in two parts; the first, consisting of §§1–7, offers an informal axiomatic introduction to the basics of set theory, including a thorough discussion of the axiom of choice and some of its equivalents. The second part, consisting of §§8–14, is written at a somewhat more advanced level, and treats selected topics in transfinite algebra; that is, algebraic themes where the axiom of choice, in one form or another, is useful or even indispensable.

Fear-inducing tragedy encompasses the deadly consequences of contaminating the atmosphere, including through nuclear radiation. Theatrical works juxtapose the threat of extinction with the benefits of energy obtained from nuclear, coal and oil power sources as they indicate that the earth’s atmosphere can no longer be regarded as an exploitable resource. The degradation of breathable air is life-threatening for human and nonhuman species alike. The depiction of human-induced contamination from mid twentieth-century theatre encompasses life-threatening atmospheric nuclear bomb testing in the Pacific Ocean region and on mainland Australia. First Nations theatrical performance about nuclear-damaged ecological systems broadens the emotional commons of climate change theatre in which characters confront atmospheric contamination and the threat of annihilation.

Based on extensive in-depth interviews and primary documents, Chapter 5 presents a case study of a middle-performing county in central China to illustrate the core arguments of the book. It shows how the local state reassigns rural land rights in an effort to drive urbanization and industrialization. It provides data on how local officials respond to performance targets by using land to attract investment in both real estate and industry. The chapter also provides data on the county’s debt-fueled infrastructural development employing land-backed LGFVs and presents data on economic activity and fiscal revenue. The chapter illustrates the nature of popular dissatisfaction over the reassignment of land rights and how local officials use law to deflect discontent and conflict away from the state itself, while exacerbating conflict between villagers and village collectives and among neighbors. It shows how villagers, unable to effectively challenge the state, seek to exclude others from sharing in land-taking compensation funds by using contested ideas about household registration (hukou), marriage, village charters, and land contracts. Villagers manifest legal consciousness, including awareness of legal aid, and engage in legal mobilization, including negotiation, mediation, petition, litigation, and protest.

Sexual harassment in the medical workplace is a complex, multifaceted problem that needs evidence-based solutions. Medicine is, of course, not unique in having to manage this. For decades, consciousness-raising groups have created spaces to find ways to speak the unspeakable, raising awareness of gender-based violence at work and at home, in order for survivors to begin to heal. Hashtags such as such as #MeToo, #MeoQueridoProfesor, and #UtanTystnadsplikt perform this function in a digital landscape, exposing entrenched toxicity across a range of workplaces, and agitating for legislative and political reform in a number of global contexts.

What is a legal culture, and how do we understand and describe it? Historians have done a good job, over the past century, of describing legal institutions. They have been less successful at understanding legal cultures. Yet the eastern Roman Empire is suffused with attempts to articulate understandings of state power and capacity in the language of law. The current "institutional" approach does very little to explain why law was meaningful to subjects of empire: it merely attempts to explain "how it worked," hypothesizing that decent functioning incentivizes the use of the system. This is problematic: it relies anachronistically on a positivist understanding of law. Instead, law is shown to be implicated in multiple acts of community self-definition, in public rituals, and in popular consciousness. This raises the questions: why did legality play such an important role in the provincial imagination? And with what effects on the state itself?

David Collier and Steven Levitsky’s original “Democracy with Adjectives” article (1997) offered a useful corrective to Sartorian thinking about conceptualization, and the new revised version further clarifies its contribution. There is a crucial difference between identifying a diminished subtype (moving from democracy as attributes “A and B and C” to “A and B and not C”) and moving up the ladder of abstraction (from democracy as attributes “A and B and C” to “A and B and either C or not C”). Diminished subtypes are more precise and do not necessarily increase the extension of a concept. This chapter offers a critique of both examples of conceptual innovation, which are grounded in categorical thinking, from the conceptual approach used by the Varieties of Democracy (V-Dem) project, which conceives of democracy as an aggregate of multiple continuous dimensions. Examples using V-Dem data suggest that it is possible to create measurements of specific concepts that are both qualitatively rich and quantitatively precise. However, the measurement of very general concepts such as democracy comes at the cost of some quantitative information and conceptual clarity.

Generalizations of LDPC codes: In Chapter 9, we present code ensembles that may be regarded as special instances, generalization, or modifications of LDPC code ensembles introduced in Chapter 4. This chapter starts with spatially coupled LDPC codes, introduced within a protograph-based framework, then addresses generalized LDPC codes, where some of the CNs impose multiple linear constraints, and finally describes low-density generator matrix codes. Erasure decoding algorithms are described for all code classes.

The pre-birth planning meeting is an essential aspect of the care of any pregnant woman who has a current or previous severe or complex mental illness. It brings together the pregnant woman, her partner and/or other family members and all the professionals involved. The meeting ensures that relevant information is shared so that everyone has a good understanding of the concerns, risks and strengths. At the meeting a perinatal mental health care plan is devised collaboratively. This outlines the woman’s care for the remainder of her pregnancy, her maternity admission for the birth of her baby and for the early postnatal period. It also includes a crisis plan. This process helps all the professionals to work in partnership with the woman and her family and to ensure she and her family have the best possible care and outcomes.

No figure did more to promote the myth of blood and soil than Richard Darré, the Nazi minister of agriculture. Darré’s environmental legacy is disputed; current scholarship recognizes his racial obsessions while typically denying any substantive ecological orientation. This chapter takes a different perspective, arguing that Darré’s views on race and on care for the soil were inseparable ideologically as well as in practice. Moreover, his environmental allegiances shifted significantly over time, reflecting a series of fierce debates about the politics of nature that involved competing Nazi factions. Peering below the level of famous Nazis, the core of the chapter presents a detailed appraisal of often neglected mid-level officials in interaction with conservationists, organic adherents, and life reform activists, with particular attention to the increasingly influential biodynamic representatives on Darré’s staff. The resulting profile of blood and soil principles in action casts Nazi environmental efforts in a new light: never fully at the center of power but never entirely marginalized, ecological politics played out in tandem with conflicting economic priorities and overarching racial objectives.

This book comes in two parts; the first, consisting of §§1–7, offers an informal axiomatic introduction to the basics of set theory, including a thorough discussion of the axiom of choice and some of its equivalents. The second part, consisting of §§8–14, is written at a somewhat more advanced level, and treats selected topics in transfinite algebra; that is, algebraic themes where the axiom of choice, in one form or another, is useful or even indispensable.

This chapter explores the complexities of pushing for cultural change from a leadership position. After examining the barriers leaders may face in changing their workplace culture, we provide practical actions and key considerations to inform a strategy that improves workplace accountability and eradicates sexual misconduct. By outlining a framework for change and including examples of the framework in action, we look at how leaders can implement measures that are person-centred, collaborative, integrated and measurable. Our recommendations focus on the prevention of sexual harm as well as creating a culture where impacted people feel safe to report inappropriate behaviour because they trust their organisation to take swift, fair and decisive action.