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.

The island and the world: kinship, friendship and living together in selected writings of Sam Selvon

This article argues that the ethical force of Trinidadian Sam Selvon’s creative writings comes from the particular configuration of living together that he is interested in, both in his Trinidadian novels and his London ones. It reads examples of this living together alongside and in difference that emerges through his focus on the relations between neighbours, friends and lovers, rather than the kinship relations of family. It argues that his works thereby map horizontal zones of attachment and possible solidarities across groupings that reconfigure vertically inscribed genealogical paradigms of belonging to place and each other based on models of historical continuity and inheritance.

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.

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.

Fast and slow responses of Southern Ocean sea surface temperature to SAM in coupled climate models

We investigate how sea surface temperatures (SSTs) around Antarctica respond to the Southern An- nular Mode (SAM) on multiple timescales. To that end we examine the relationship between SAM and SST within unperturbed preindustrial control simulations of coupled general circulation models (GCMs) included in the Climate Modeling Intercomparison Project phase 5 (CMIP5). We develop a technique to extract the re- sponse of the Southern Ocean SST (55◦S−70◦S) to a hypothetical step increase in the SAM index. We demonstrate that in many GCMs, the expected SST step re- sponse function is nonmonotonic in time. Following a shift to a positive SAM anomaly, an initial cooling regime can transition into surface warming around Antarctica. However, there are large differences across the CMIP5 ensemble. In some models the step response function never changes sign and cooling persists, while in other GCMs the SST anomaly crosses over from negative to positive values only three years after a step increase in the SAM. This intermodel diversity can be related to differences in the models’ climatological thermal ocean stratification in the region of seasonal sea ice around Antarctica. Exploiting this relationship, we use obser- vational data for the time-mean meridional and vertical temperature gradients to constrain the real Southern Ocean response to SAM on fast and slow timescales.