Contrary to what modern observers might have you believe, tax dodging during the 1950s and 1960s was more about tax cuts than tax increases. Faced with a high tax rate it did not support, but, for political reasons, it could not lower, Congress did the next best thing. It riddled the tax laws with “leaks, loopholes, exemptions, and preferences,” while looking the other way at much of the widespread “income-tax chiseling” in American society and only occasionally passing watered down legislation targeting the more high-profile tax dodging schemes.1 In effect, it cut the tax rates implicitly, rather than explicitly, which amounted to a tax cut of the worst kind. It was not transparent, it was not evenly distributed among the taxpayers or even targeted to achieve any policy objective in some cases, and, because it was too unpredictable for taxpayers to rely upon for planning purposes, it was inefficient.

In this chapter we return to the topic of Chapter 3, (small) sieves, which we now treat, at least initially, in some generality. However our objective is to give nothing more than an introduction and some applications to what has become a vast and complex subject. Readers who wish to see the many aspects of the subject in more detail are advised to consult the standard reference on the subject, Friedlander & Iwaniec (2010).

With the rise of the Bharatiya Janata Party (BJP) to power in India in 2014, and over the following years, questions around the nature of this regime and its increasingly close links to large Indian corporates have drawn attention. That these links exist is beyond dispute. However, their specific nature and what they can tell us about the RSS (Rashtriya Swayamsevak Sangh)–BJP combine, the Sangh Parivar (the family of organizations led by the RSS, including the BJP), is less clear, as in what they might mean for its future trajectory and for the future trajectory of Indian politics.

This chapter, a preliminary exploration of these questions, is largely confined to specific aspects of this government's economic policies. In this context, it will argue that these links are embedded within a specific political trajectory and that this trajectory may lead to eventual possibilities that are neither easy to predict nor necessarily in line with intuitive expectations. Indeed, I will argue that, instead of the apparent stability and supposed strength of the corporate–BJP–state nexus that currently exists, the years to come are likely to see more challenges to this nexus than are usually expected— and a key reason for this is the dynamic produced by this nexus itself.

The historical relationship between the Sangh Parivar and Indian big capital

The relationship between Indian big business and the Sangh Parivar is not a recent one, but arguably such a relationship also did not characterize the RSS's history for most of its existence.

Minkowski’s convex body theorem provides a fundamental bridge between algebraic number theory and Euclidean geometry. The theorem asserts that any sufficiently large, centrally symmetric, convex set in n-dimensional real space must contain a nonzero lattice point.

Classical applications include representing integers as sums of two or four squares, where the existence of lattice points in two- and four-dimensional balls yields concrete arithmetic solutions.

The theorem’s deeper significance appears in the context of number fields, which are finite extensions of the rational numbers. These fields can be embedded into Euclidean space, turning arithmetic problems into geometric ones. The ring of integers and its ideals can be regarded as lattices, making Minkowski’s theorem directly applicable.

This geometric viewpoint leads to central results in algebraic number theory, such as the finiteness of the class group and explicit bounds on its size.

Likewise, the group of units can be regarded as a lattice in Euclidean space via the logarithmic embedding, and Minkowski’s theorem is instrumental in determining its structure (Dirichlet’s unit theorem).

These ideas come together in the analytic class number formula, which relates the size of the class group to the residue of the Dedekind zeta function at s = 1 and to the regulator.

The challenge of finding appropriate tools for measurement validation is an abiding concern in political science. This chapter considers four traditions of validation, using examples from cross-national research on democracy: the levels-of-measurement approach, structural-equation modeling with latent variables, the pragmatic tradition, and the case-based method. Methodologists have sharply disputed the merits of alternative traditions. The chapter encourages scholars – and certainly analysts of democracy – to pay more attention to these disputes and to consider strengths and weaknesses in the validation tools they adopt. An appendix summarizes the evaluation of six democracy data sets from the perspective of alternative approaches to validation.

This chapter concludes the volume by reflecting on the ongoing value of concept analysis in the social sciences. It revisits the tension between hyperfactualism – obsessive attention to granular detail – and the necessary abstraction that enables generalization. Conceptualization, the authors argue, helps scholars not only communicate more clearly but also observe and describe phenomena more effectively. Far from being a distraction, conceptual work sharpens empirical inquiry. The chapter highlights the interplay between conceptualization and measurement, especially in validity assessment, and underscores how concepts represent and structure knowledge. Attention to concepts also facilitates integration and translation across time, space, and disciplines, as seen in such examples as the V-Dem project. Issues of conceptual boundedness, typologies, and traveling are revisited, drawing on contributions from cognitive linguistics and classic debates between lumpers and splitters. The authors also reflect on how digital tools and formal modeling offer new avenues for concept innovation. Finally, they affirm the importance of teaching concept analysis as a way to clarify students’ thinking, research design, and disciplinary communication. In sum, the chapter defends the overconscious scholar: one who sees in concepts not distraction, but a path toward cumulative, communicable, and intellectually satisfying scholarship.

The introduction in this chapter has been written by Josephine Canceri, a newly graduated doctor in Sydney, Australia. She gives an overview of the experience of International Medical graduates (IMGs) across the globe. International Medical Graduates are at higher risk of harm from sexual harassment, and are less familiar with their options for reporting. Women are at higher risk.

Valeria Chua writes from her lived experience as a doctor from Brunei who trained and worked in England and Australia. As a young, Asian female practicing and training in these countries, she was already disadvantaged in the medical world. She experienced sexual harm from a relative and from several male doctors. She describes the ways her upbringing, past experiences and circumstances as a foreign-trained doctor which is likely to have increased her risk of harm. She hopes that her contribution to this book will prevent others from falling victim to sexual assault by doctors and will raise awareness of this little-known subject.

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.

Talking with women in the pre-conception or perinatal periods about psychotropic medication is an essential, sometimes difficult, part of the work of the perinatal psychiatrist. Understanding the current evidence base; knowing how and when to acknowledge the uncertainty inherent in current knowledge and how that translates to the individual woman; balancing risks of medication with risks of not treating and benefits of treating; sharing decision-making while not putting all of the responsibility on the woman; communicating with the woman, her partner, other professionals, services and agencies; and knowing when and how to seek further help or advice, are all essential components of good practice when prescribing in pregnancy and breastfeeding.

The expansion of the Roman Empire into the Mediterranean in the early second century BCE represented a gradual diminution of the independence and autonomy of the Greek cities. At the same time, processes internal to the poleis were moving them in a more elitist direction, as the “big benefactors,” ultrawealthy men who bestowed ever-greater favors on their cities, moved toward monopolizing participation in civic magistracies. The council and other political bodies became off-limits to citizens who were not among the euergetistic elite. Still, democratic institutions and ideas of the previous period persisted, especially in the popular assembly. Christianity, the centralization of administrative power in the Roman Empire under Constantine, and various crises combined to deprive the cities of the last vestiges of dēmokratia in the fourth century CE, when popular assemblies largely disappear from the poleis.