A Universal Characterization of the Double Powerlocale

This is a version from 29 Sept 2003 of the paper published under the same name in Theoretical Computer Science 316 (2004) 297{321. The double powerlocale P(X) (found by composing, in either order,the upper and lower powerlocale constructions PU and PL) is shown to be isomorphic in [Locop; Set] to the double exponential SSX where S is the Sierpinski locale. Further PU(X) and PL(X) are shown to be the subobjects P(X) comprising, respectively, the meet semilattice and join semilattice homomorphisms. A key lemma shows that, for any locales X and Y , natural transformations from SX (the presheaf Loc

On the parallel between the suplattice and preframe approaches to locale theory

AbstractThis paper uses the locale theory approach to topology. Two descriptions are given of all locale limits, the first description using suplattice constructions and the second preframe constructions. The symmetries between these two approaches to locale theory are explored. Given an informal assumption that open locale maps are parallel to proper maps (an assumption hinted at by the underlying finitary symmetry of the lattice theory but not formally proved) we argue that various pairs of locale theory results are ‘parallel’, that is, identical in structure but prove facts about proper maps on one side of the pair and about open maps on the other. The pairs of results are: pullback stability of proper/open maps, regularity of the category of compact Hausdorff/discrete locales, and theorems on information systems. Some remarks are included on a possible formalization of this parallel as a duality

Local law-of-the-wall in complex topography: a confirmation from wind tunnel experiments

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface, the variation of the mean velocity with respect to the distance from the surface obeys the logarithmic law (the so-called ``law-of-the-wall''). More recently, the same logarithmic law has been found also in the presence of non flat surfaces. It governs the dynamics of the mean velocity (i.e. all the smaller scales are averaged out) and involves renormalized effective parameters. Recent numerical simulations analyzed by the authors of the present Letter show that a more intrinsic logarithmic shape actually takes place also at smaller scales. Such a generalized law-of-the-wall involves effective parameters smoothly depending on the position along the underlying topography. Here, we present wind tunnel experimental evidence confirming and corroborating this new-found property. New results and their physical interpretation are also presented and discussed.Comment: 9 pages, (Latex), 4 figure

Near-zero humidities on Ben Nevis, Scotland, revealed by pioneering 19th-century observers and modern volunteers

The weather on Ben Nevis – the highest mountain in the British Isles, 1345 m AMSL – sometimes shows episodes of remarkably low relative humidity (RH) with few precedents anywhere else in the British Isles. We are able to quantify this for the first time using a high-quality series of hourly dry- and wet-bulb observations, made on the summit. These observations were made between 1883 and 1904, but have only just become available to modern science, thanks to thousands of volunteers who worked to rescue this unique and exemplary dataset from published volumes. Careful examination and analysis of the original observations using modern psychrometric theory revealed several occasions where we are confident that the summit RH fell close to zero as a result of anticyclonic subsidence. Three case histories are examined in some detail. The nineteenth-century Ben Nevis humidity records are also compared with contemporary automatic weather station (AWS) data from two high-altitude Scottish mountain sites

Preframe techniques in constructive locale theory

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN018027 / BLDSC - British Library Document Supply CentreGBUnited Kingdo