Natural maps between CAT(0) boundaries

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(-1) space can fail to be either injective or surjective.Comment: 8 page

Rough CAT(0) spaces

We investigate various notions of rough CAT(0). These conditions define classes of spaces that strictly include the union of all Gromov hyperbolic length spaces and all CAT(0) spaces.Comment: Corrected typos and updated Corollaries 3.22 and 3.2

The Catalan simplicial set

The Catalan numbers are well-known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a simplicial set. We show how the low-dimensional parts of this simplicial set classify, in a precise sense, the structures of monoid and of monoidal category. This involves aspects of combinatorics, algebraic topology, quantum groups, logic, and category theory.Comment: 15 pages. Replaces and expands upon parts of arXiv:1307.0265; remaining parts of arXiv:1307.0265 will be incorporated into a sequel. Version 2: minor revision; to appear in Math. Proc. Camb. Phil. So

Simultaneous optical polarimetry and X-ray observations of the magnetic CV CP Tuc (AX J2315--592)

CP Tuc (AX J2315--592) shows a dip in X-rays which lasts for approximately half the binary orbit and is deeper in soft X-rays compared with hard X-rays. It has been proposed that this dip is due to the accretion stream obscuring the accretion region from view. If CP Tuc was a polar, as has been suggested, then the length of such a dip would make it unique amongst polars since in those polars in which a dip is seen in hard X-rays the dip lasts for only 0.1 of the orbit. We present optical polarimetry and RXTE observations of CP Tuc which show circular polarisation levels of ~10 per cent and find evidence for only one photometric period. These data confirm CP Tuc as a polar. Our modelling of the polarisation data imply that the X-ray dip is due to the bulk of the primary accretion region being self-eclipsed by the white dwarf. The energy dependence of the dip is due to a combination of this self-eclipse and also the presence of an X-ray temperature gradient over the primary accretion region.Comment: 6 pages, accepted for publication in MNRA

Recreational Pursuits on Marginal Farm Land: A Discrete-Choice Model of Irish Farm Commonage Recreation

In the last decade the demand for rural recreation has increased in Ireland as the population has become increasingly urbanised. Increased affluence, mobility and changing values have also brought new demands with respect to landscape, conservation, heritage and recreation, with a greater emphasis on consumption demands for goods and services in rural areas. This paper’s contribution to the understanding of outdoor recreational pursuits in Ireland is based on the estimation of the first farmland recreation demand function. We use this empirical work to investigate the more general conflict between countryside recreational pursuits and farming activity. Through the estimation of a travel cost model, the study derives the mean willingness to pay of the average outdoors enthusiast using a farm commonage site in Co. Galway, Ireland and an estimate of the gross economic value of the site as a recreational resource. The result indicates the high value of Irish farmland from a recreational amenity perspective.

Sobolev spaces: a short course

Notes for a course in Sobolev spaces given to the Department of Mathematical Analysis, University of La Laguna, Tenerife in May 2000

Pointwise multipliers for reverse Hölder spaces II

We classify weights which map strong reverse Hölder weight classes to weak reverse Hölder weight spaces under pointwise multiplication