Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Scripture, style and persuasion in seventeenth-century English theories of preaching

The distinction between a Puritan ‘plain’ and a Laudian ‘metaphysical’ preaching style rests on secular rhetorical theories of persuasion that are relatively unimportant to early Stuart homiletics but are central to later Latitudinarian polemics on preaching. Instead, the ‘English Reformed’ theory and method of sermon composition rests on the didactic function of preaching and the need for the Holy Spirit and hearers to co-operate with the preacher. Although Andrewes and some avant-garde conformists questioned this theory, they developed no alternative method of composition. Arguments made in the 1650s for direct inspiration by the Spirit contributed to the decline of both theory and method

The distribution of London residential property prices and the role of spatial lock-in

Much of mainstream economic analysis assumes that markets adjust smoothly, through prices, to changes in economic conditions. However, this is not necessarily the case for local housing markets, whose spatial structures may exhibit persistence, so that conditions may not be those most suited to the requirements of modern-day living. Persistence can arise from the existence of transaction costs. The paper tests the proposition that housing markets in Inner London exhibit a degree of path dependence, through the construction of a three-equation model, and examines the impact of variables constructed for the 19th and early 20th centuries on modern house prices. These include 19th-century social structures, slum clearance programmes and the 1908 underground network. Each is found to be significant. The tests require the construction of novel historical datasets, which are also described in the paper.