Regular Polygonal Complexes of Higher Ranks in E^3

The paper establishes that the rank of a regular polygonal complex in 3-space E^3 cannot exceed 4, and that the only regular polygonal complexes of rank 4 in 3-space are the eight regular 4-apeirotopes

A Central Limit Theorem for the Poisson-Voronoi Approximation

For a compact convex set $K$ and a Poisson point process $\eta$, the union of all Voronoi cells with a nucleus in $K$ is the Poisson-Voronoi approximation of $K$. Lower and upper bounds for the variance and a central limit theorem for the volume of the Poisson-Voronoi approximation are shown. The proofs make use of so called Wiener-It\^o chaos expansions and the central limit theorem is based on a more abstract central limit theorem for Poisson functionals, which is also derived.Comment: 22 pages, modified reference

A Critique of Advertisements for Female Hygiene Products: A Silent Crisis in America

Female hygiene advertisements can be ambiguous due to the intimate nature of menstruation. This can result in a lack of information and invoke the need to hide signals of menstruation. Further, understanding the target audience’s desires and needs is crucial. Just like any other advertisement campaign, the women buying female hygiene products desire to know the benefits of one type over another. Adding an emotive appeal or a creative method to the advertisement is not wrong. This thesis does not suggest for a dull advertisement; however, there is a balance—a campaign designed to care for and inform women while meeting their body’s needs

Chiral polyhedra in ordinary space, II

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean 3-space with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and {6,6}. Part II completes the enumeration of all discrete chiral polyhedra in 3-space. There exist several families of chiral polyhedra with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.Comment: 48 page

Simulation of an Intra-Pulse Interaction Point Feedback for Future Linear Colliders

In future normal-conducting linear colliders, the beams will be delivered in short bursts with a length of the order of 100 ns. The pulses will be separated by several ms. In order to maintain high luminosity, feedback is necessary on a pulse-to-pulse basis. In addition, intra-pulse feedback that can correct beam positions and angles within one pulse seem technically feasible. The likely performances of different feedback options are simulated for the NLC (Next Linear Collider) and CLIC (Compact Linear Collider).Comment: LINAC2000 Conference, Paper ID MOA0

Combinatorial Space Tiling

The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and some old open problems in this area.Comment: 16 pages; to appear in "Symmetry: Culture and Science

Polyhedra, Complexes, Nets and Symmetry

Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zig-zag, or helical. A polyhedron or complex is "regular" if its geometric symmetry group is transitive on the flags (incident vertex-edge-face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well-known to crystallographers, and we identify them explicitly. There also are 6 infinite families of "chiral" apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits.Comment: Acta Crystallographica Section A (to appear

Modelling Phosphorus for Grassland: Agronomically and Environmentally Sustainable Advice

End of project reportIn 2006, the Nitrates Directive (through S.I. 378 (Anon, 2006)) was implemented in Ireland, aimed at reducing nutrient losses from agriculture to water bodies, i.e. surface waters, groundwater and estuarine waters. This legislation introduced strict regulation of nutrient management on Irish farms. Thus far, nutrient management had largely been based on Teagasc advice (Coulter, 2004). However, in the new policy climate, in addition to advice, compliance with legal limits is also required. This significant change in the practicalities surrounding nutrient management led to a review of Teagasc nutrient (phosphorus and nitrogen) advice, based on the following considerations: Traditionally, nutrient advice had largely been based on fertiliser rates for economically optimal productivity, i.e. rates at which further fertiliser applications would not result in higher economic returns. Now, SI 378 of 2006 demands that nutrient application rates do not exceed crop (grass) demand, nor result in nutrient losses that may have a negative impact on water quality. Previous phosphorus (P) advice (Coulter, 2004) was similar for all soil types, and did not account for potentially different P-requirements, or indeed potentially different risks of P-loss to water between soils. Previous P advice was based on returning optimum crop yields. However, grassland management in Ireland is increasingly focussed on maximising the amount of herbage grazed in situ. With extended grazing seasons and an increasing share of the animal diet consisting of grazed herbage, the scope and flexibility of diet supplementation through straights and concentrates is reduced. An increasing proportion of dietary P must be obtained from this grazed herbage as a result. Therefore P fertiliser strategies should no longer be based on yield responses alone, but in addition sustain adequate herbage P-concentrations in order to ensure that the dietary P requirements can be met on a non-supplemented diet of grazed herbage. Against this background, Teagasc, Johnstown Castle Environment Research Centre, undertook a major research programme, reviewing both agronomic and environmental aspects of P-advice for grassland