The role of social networks in business, and entrepreneurship, in particular, is widely acknowledged. Chapter 2 explores the ways in which business persons relate to networks and how networks impact the circumstances of entrepreneurs. The enabling and constraining properties of networks, their effects on participants, and their subsequent social consequences have all been extensively explored in a large and growing literature. A feature of social network analysis lies in its tendency to deploy structural perspectives in explaining social outcomes. Chapter 2 highlights the ways in which social networks operate as a context in which individual initiative and engagement lead to the making and remaking of network attributes. An empirical examination of business networks in Chinese cities reveals the way in which the formation and maintenance of networks require the conscious contributions of their members, how network norms are produced by the expressed preferences of individual members, and finally how network membership involves management of network participants.

Chapter 5: Many abstract concepts that make linear algebra a powerful mathematical tool have their roots in plane geometry, so we begin the study of inner product spaces with a review of basic properties of lengths and angles in the real two-dimensional plane. Guided by these geometrical properties, we formulate axioms for inner products and norms, which provide generalized notions of length (norm) and perpendicularity (orthogonality) in abstract vector spaces.

The sixth chapter examines the relationship between coutumiers as texts that describe custom, and custom in practice. The difficulty with discussing this is that the coutumiers only begin to be cited in court records at the very end of the thirteenth century and very rarely even then. This was not unusual for the lay courts of northern France in this period, which cited ‘custom’ and not lawbooks or specific precedents. I discuss the relationship between the coutumiers and representations of practice – as filtered through its documentary record-keeping – in two ways. On one level, this chapter shows how at least some people were thinking about court cases that they presided over, took part in, witnessed or heard about. On another, this chapter demonstrates how the coutumier represents practice differently from other remaining records and how coutumier authors used what they saw in practice to extract principles and articulate general rules. Through the coutumiers, we can see how individual actors reshaped specific cases and transactions into general principles, and those general principles into a body of customary law.

In this appendix we review some essential concepts regarding finite dimensional vector spaces, their bases, norms, and inner products that are essential for the reader and appear repeatedly throughout the text.

The recognition of naturally occurring radioactive material (NORM) associated with oil and gas fields started nearly at the same time as the discovery of radioactivity itself. Radium in produced water is typically the source of the majority of the NORM. Four processes within oil and gas formations, solubility, alpha recoil, cation exchange, and coprecipitation lead to high radium activity in pore fluids. These processes occur regardless of the type of reservoir (conventional high permeability oil and gas reservoirs or unconventional low permeability organic-rich shale source rocks). Following well stimulation via hydraulic fracturing fluids and some solids that return to the surface contain elevated radium. The data on radium from oil and gas wells across the USA is severely lacking relative to the volumes of produced water, especially considering that large volumes are beneficially used or disposed of to surface waters. Novel treatment and accurate measurements of radium are necessary prior to beneficially reuse or dispose produced water in order to protect human and environmental health. More measurements of radium in produced water should be obtained and made publicly available.

In algebraic number theory the determinant plays a bigger role than in a typical undergraduate linear algebra course. In particular, its relationship to trace, norm, and characteristic polynomial is important. For this reason, we develop determinant theory from scratch in this chapter, using an axiomatic characterization of determinant due to Artin. Among other things, this quickly gives basis-independence of the characteristic polynomial, trace, and norm. With these foundations we can introduce the discriminant, which tests whether an n-tuple of vectors form a basis, and paves the way for integral bases studied in the next chapter.

Diophantine equations are polynomial equations for which integer (or sometimes rational) solutions are sought. The oldest examples date from ancient Greek times, and Diophantus in particular solved many such equations. His methods and the questions they raised inspired much of modern number theory, beginning with the work of Fermat and Euler. Euler, and later Gauss, introduced algebraic integers to solve Diophantine equations, implicitly or explicitly using "unique prime factorization" to do so.

In Chapter 2, we explain some of the basics of algebraic number theory, which we will need in Chapter 3 to introduce the theory of heights and to give a proof of the Mordell-Weil theorem. We begin by introducing the trace and the norm of an element of a finite extention field. We show the existence of an integral basis for a ring of integers and define the discriminant of a number field. After showing the existence of a prime factorization of a fractional ideal of a ring of integers (Theorems 2.5 and 2.6), we prove Minkowski's convex body theorem (Theorem 2.9) and Minkowski's discriminant theorem (Theorem 2.13). Finally, we introduce the notions of the ramification index and the residue degree at a prime ideal of an extension field. We define the difference of a number field, and explain several results relating the discriminant, the difference, and the ramifications of prime ideals (Lemma 2.17 and Theorem 2.18).

Context, plot, character and theme have dominated modern critical understandings of Wilkie Collins’s fiction, and there are relatively few discussions of his idiom, tone or voice. Collins himself seems to have encouraged this approach to his work, and repeatedly downgraded the question of literary style. But the topic takes us to the heart of his work, and helps us both to understand the nature and quality of his achievement and to see the relationship within it between questions of language and signification and those of identity and the sense of self.  Collins is fascinated in many of his fictions by what it means to have a troubled, false or non-existent identity, to have bodies and sensations that are not properly one’s own; the most revelatory texts and inscriptions in his work are often anonymous or unstylised. This chapter is about how Collins’s work explores and exposes the vulnerability of style, as it stages style’s appearances and disappearances.

Chapter 2 describes the theoretical approach to the concept of obscenity by examining what counts as “horrifically graphic,” a term drawn from the coverage of American soldiers burning dead bodies in Fallujah, Iraq, and the release of these images by the entertainment website TMZ. Drawing on a variety of theorists, it uses the framing of the taboo to articulate the idea of an obscenity norm that functions towards a particular politics. It situates the contributions of this work more substantively in terms of how it speaks to constructivist work on norms, the growing literature on emotions in global politics, and the visual politics literature. Specifically, this chapters theorizes three main ideas related to the obscenity norm and its functioning: (1) the existence of the taboo itself as something that plays with our perception of whether images depict the real, (2) the functioning of regulations on images such as trigger warnings or image bans, and (3) the relationship between the obscenity norm and the larger dynamics of security and securitization.

The first chapter of the book outlines the status of the right to life under international law. It concludes that the right to life is both a customary rule and a general principle of law while the prohibition on arbitrary deprivation of life is a peremptory norm of international law (jus cogens).

Caesar was no aspiring autocrat seeking to realize the imperial future but a republican political leader whose success was based on a combination of patrician pedigree with a popular persona built on an extraordinary record of military achievement. He was no anti-senatorial, populist revolutionary but followed in the tracks of Roman heroes of the past such as the Scipios. His astonishing success hardened his enemies' determination to stop him, even at the price of forcing a civil war. His assassination on the eve of his departure for a great war of vengeance against Parthia precluded whatever plans for consolidation he may have had, but also propelled the violence of civil war into the next phase of what would become a decisively destructive cycle. If Gruen was correct to emphasize that civil war destroyed the Republic, not its preexisting institutional weaknesses, then human choices, especially those that brought about the Civil War, provide the most satisfactory explanation for the collapse of the Republic.