Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

Taylor v Caldwell (1863)

A Landmark Case is one which stands out from other less remarkable cases. Landmark status is generally accorded because the case marks the beginning or the end of a course of legal development. Taylor v Caldwell is regarded as a landmark case because it marks the beginning of a legal development: the introduction of the doctrine of frustration into English contract law. This chapter explores the legal and historical background to the case to ascertain if it is a genuine landmark. A closer scrutiny reveals that while the legal significance of the case is exaggerated, the historical significance of the cases reveals an unknown irony: the case is a suitable landmark to the frustration of human endeavours. While the existence of the Surrey Music Hall was brief, it brought insanity, imprisonment, bankruptcy and death to its creators.

Do real balance effects invalidate the Taylor principle in closed and open economies?

This paper examines the determinacy implications of forecast-based monetary policy rules that set the interest rate in response to expected future inflation in a Neo-Wicksellian model that incorporates real balance effects. We show that the presence of such effects in closed economies restricts the ability of the Taylor principle to prevent indeterminacy of the rational expectations equilibrium. The problem is exacerbated in open economies, particularly if the policy rule reacts to consumer-price, rather than domestic-price, inflation. However, determinacy can be restored in both closed and open economies with the addition of monetary policy inertia.

The Mystery of Privity: Grand Trunk Railway Company of Canada v Robinson (1915)

This article examines a little known decision of the Judicial Committee of the Privy Council: Grand Trunk Railway Company of Canada v Robinson (1915). The examination is historical and it provides a different insight into the understanding of privity of contract, a doctrine central to contract law. The examination reveals a process of trans-Atlantic legal migration in which English law was applied to resolve an Ontario case. The nature of the resolution is surprising because it appears to conflict with the better known decision of the House of Lords, Dunlop Pneumatic Tyre Company, Limited v Selfridge and Company, Limited, which a similarly constituted panel delivered in the same week. This article argues that there was a greater malleability in the resolution of cases concerned with privity than was thought to have existed. It is also argued that the power of Canadian railway capitalism is a significant factor in understanding the legal resolution of the case. Finally, it the article considers the use of English and American precedents relevant to the case. The application of English precedents to the case led to a resolution not entirely befitting Canadian conditions.

Uniform factorial decay estimate for the remainder of rough Taylor expansion

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.