This chapter is a survey of the legal languages used to govern territory, sovereignty and the right of a ruler within a polity. Debates were heavily dominated by feudal and private law-concepts. Sovereigns maintained the diversity of privileges in the territories ruled in the setting of a composite monarchy. Claims and titles could or could not entail consequences for sovereignty. Reservations and exceptions to full internal sovereignty were not uncommon. Succession quarrels (often causes of war), could be solved by treaty, often in conflict with domestic constitutional rules and principles. Mixed polities (Poland-Lithuania, Holy Roman Empire) offered a broad range of argumentative topoi to either confirm or combat overlordship. Internal German questions could quickly escalate to the field of the law of nations through the game of alliances and guarantees. Although republican forms of monarchy and republican oligarchies were on the decline in the seventeenth and eighteenth centuries, their legal agency was not contested. In extra-European dominions of European sovereigns, the chain of reasoning was significantly lighter, as feudal arguments rarely came into play. Conversely, the agency of subaltern actors in establishing boundaries, or the treatment of native Americans as either allies or subjects provide original avenues of research.

This chapter examines Thomas Pringle’s and Susanna Strickland’s literary relationship and their contributions to anti-slavery print culture in the years surrounding their work on The History of Mary Prince. Each brought a different set of interests and strengths to the production of The History. Pringle was an established voice in abolitionist writing, having published anti-slavery poems and essays in venues ranging from the Oriental Herald to the Penny Magazine. Strickland had not previously written about slavery, but she was practiced in writing for the fashionable and ornamental publications that targeted one of the anti-slavery movement’s primary audiences, middle-class white women. In the years immediately surrounding the publication of Prince’s History, Pringle and Strickland brought anti-slavery discourse into ornamental and ostensibly apolitical forms of print culture such as literary annuals; conversely, by foregrounding the first-person testimony of enslaved people, they brought novelistic discourse into overtly political and polemical publications such as the Anti-Slavery Reporter.

This text on general relativity and its modern applications is suitable for an intensive one-semester course on general relativity, at the level of a PhD student in physics. Assuming knowledge of classical mechanics and electromagnetism at an advanced undergraduate level, basic concepts are introduced quickly, with greater emphasis on their applications. Standard topics are covered, such as the Schwarzschild solution, classical tests of general relativity, gravitational waves, Arnowitt, Deser, Misner parametrization, relativistic stars, and cosmology, as well as more advanced standard topics such as vielbein–spin connection formulation, trapped surfaces, the Raychaudhuri equation, energy conditions, the Petrov and Bianchi classifications, and gravitational instantons. More modern topics, including black hole thermodynamics, gravitational entropy, effective field theory for gravity, the parametrized post- Newtonian expansion, the double copy, and fluid-gravity correspondence are also introduced using the language understood by physicists, without mathematics that is too abstract mathematics, proven theorems, or the language of pure mathematics.

In Chapter 8 we consider a recurrent Markov chain possessing an invariant measure which is either probabilistic in the case of positive recurrence or σ-finite in the case of null recurrence. Our main aim here is to describe the asymptotic behaviour of the invariant distribution tail for a class of Markov chains with asymptotically zero drift proportional to 1/x. We start with a result which states that a typical stationary Markov chain with asymptotically zero drift always generates a heavy-tailed invariant distribution, which is very different from the case of Markov chains with asymptotically negative drift bounded away from zero. Then we develop techniques needed for deriving precise tail asymptotics of power type.

Progesterone is an endogenous hormone which is derived from cholesterol steroids. It is secreted in women principally by the corpus luteum in the ovaries during normal menstrual cycles. Progesterone exerts a number of essential effects vital for the support and maintenance of a pregnancy. The role of progesterone in threatened and recurrent miscarriage was a matter of debate for many decades, until the findings of the PROMISE and PRISM trials. Vaginal micronized progesterone may increase the live birth rate for women with a history of one or more previous miscarriages and early pregnancy bleeding, with likely no difference in adverse events. There remains an uncertainty over the effectiveness and safety of alternative progestogen treatments for threatened and recurrent miscarriage.