Transreal limits and elementary functions

We extend all elementary functions from the real to the transreal domain so that they are defined on division by zero. Our method applies to a much wider class of functions so may be of general interest.

Half-remembered quotations from mostly forgotten speeches: the limits of Labour’s European policy discourse

This article uses discourse analysis to study the continuities in British foreign policy thinking within the Labour party from the 1960s to the present day. Using representative extracts from speeches by Hugh Gaitskell, Harold Wilson, Tony Blair and Gordon Brown, it identifies the ideational consis- tencies in the leaders’ attitudes to: Empire; federalism in the EEC/EU; and laying down conditions that have to be met before any constructive engagement with ‘Europe’ can be countenanced. We argue that these consistencies, spanning a 50-year period, exemplify a certain stagnation both within Labour’s European discourses and within British foreign policy thinking more widely. We develop the idea that Labour party thinking has been crucially framed by both small ‘c’ conser- vative and upper-case Conservative ideology, popularised by Winston Churchill in his ‘three circles’ model of British foreign policy.

Identifying the generic limits of the Cheilanthoid genus Doryopteris

Morphology-based delimitation of genera in the Cheilanthoid ferns has proved to be problematic and understanding of the phylogeny and relationships amongst Cheilanthoid ferns based on morphological characters has posed even further difficulties, owing perhaps in large part to adaptation by many taxa to xeric habitats, as well as convergent evolution. It is only now with the application of DNA sequence data that relationships of species and genera are becoming clear. Here, we present results of cpDNA sequence data from species that have been traditionally placed in the genus Doryopteris and, based on both these results, and morphological and distribution data, this study helps clarify the concept of the genus Doryopteris its position within the Cheilanthoid ferns and the status of Lytoneuron. As a result, three genera are redefined: Doryopteris, Lytoneuron and Ormopteris.

Impact of a Fram Strait cyclone on ice edge, drift, divergence, and concentration: Possibilities and limits of an observational analysis

This study aims at the determination of a Fram Strait cyclone track and of the cyclone’s impact on ice edge, drift, divergence, and concentration. A 24 h period on 13–14 March 2002 framed by two RADARSAT images is analyzed. Data are included from autonomous ice buoys, a research vessel, Special Sensor Microwave Imager (SSM/I) and QuikSCAT satellite, and the operational European Centre for Medium-Range Weather Forecasts (ECMWF) model. During this 24 h period the cyclone moved northward along the western ice edge in the Fram Strait, crossed the northern ice edge, made a left-turn loop with 150 km diameter over the sea ice, and returned to the northern ice edge. The ECMWF analysis places the cyclone track 100 km too far west over the sea ice, a deviation which is too large for representative sea ice simulations. On the east side of the northward moving cyclone, the ice edge was pushed northward by 55 km because of strong winds. On the rear side, the ice edge advanced toward the open water but by a smaller distance because of weaker winds there. The ice drift pattern as calculated from the ice buoys and the two RADARSAT images is cyclonically curved around the center of the cyclone loop. Ice drift divergence shows a spatial pattern with divergence in the loop center and a zone of convergence around. Ice concentration changes as retrieved from SSM/I data follow the divergence pattern such that sea ice concentration increased in areas of divergence and decreased in areas of convergence.