On the vanishing of negative K-groups

We show that for a d-dimensional scheme X essentially of finite type over an infinite perfect field k of characteristic p > 0, the negative K-groups K _q (X) vanish for q < ?d provided that strong resolution of singularities holds over the field k.     

Proficiency testing in occupational and environmental health – Current practice and international initiatives for harmonisation

An increasing number of proficiency testing schemes (PT schemes) related to occupational and environmental health have been organised. Most schemes emphasise the importance of the validation of analytical results. With regards to harmonisation of the schemes, there are many differences between the schemes at many levels. These include factors concerning their relationship with legislation, national status, type and quality of proficiency testing material, analytical range and priorities for future development. Since differences between PT schemes have been recognised at the European level by organisers of PT schemes and external quality assessment schemes (EQASs) it seems appropriate to reinforce collaboration between scheme organisers in order to improve the quality of analytical performance in occupational and environmental health.     

Dirac operators and spectral triples for some fractal sets built on curves

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension log3/log2.     

Programmable interferometry

The advent of automatic data-processing for interferometry greatly reduced the complexity of interferometric testing, thereby significantly increasing its usage both within and outside the optics community. A great many of these new applications require special data-processing and output data not normally used for testing lenses. To address these new measurement problems, many data-analysis programs were written, ranging from advanced analysis of wavefronts (i.e., Zernike polynominals, point-spread function, modulation-transfer function) to analysis of mechanical surfaces, such as Winchester-disk read/write heads. Some of these programs were very specific to a particular application, and some tried to be general and as such became cumbersome. Even with much of this software available for sale to the general public, most applications other than simple surface and lens measurements usually cannot be solved directly by using the available programs. In an attempt to solve this problem, we have developed software for interferometry that allows users to easily develop their own measurement routines. The solution was to take a version of the BASIC programming language and add the commands necessary to do interferometry. This software is resident in a processor that can easily be adapted to a large number of interferometry applications. By using this processor and its associated software with an appropriate interferometer, it is possible for the user to tailor the measurement to a particular application. This can be very useful in an optical-production shop, where each different testing application can have its own program. If the program is written properly, the operator will not have to set up any default conditions or format the output; the operation of the program can be reduced to the pushing of a single button, and the output will be formatted properly for that particular test. Examples of this system in actual optical shop-testing situations will be discussed.     

Adsorption of polyallylamine to lignocellulosic fibres: effect of adsorption conditions on localisation of adsorbed polyelectrolyte and mechanical properties of resulting paper sheets

Cationic polyallylamine (PAH), was adsorbed onto lignocellulosic fibres, and a fluorescent label on the polyelectrolyte enabled its location to be shown by confocal fluorescence microscopy. The adsorption time and ionic strength were varied to study their effect on the localisation of the adsorbed PAH. The microscopy showed that a long adsorption time, 24 h, and a high ionic strength, 10⁻¹ M NaCl + 5 × 10⁻³ M NaHCO₃ or higher, resulted in the adsorption of polyallylamine throughout the fibre walls. Shorter adsorption times and/or lower ionic strength resulted in adsorption only to the fibre exterior. By preparing sheets from fibres with polyelectrolyte adsorbed either to the exterior parts or into the fibre cell wall and testing their mechanical behaviour, a link was established between the localisation of adsorbed polyelectrolyte and the mechanical properties. Adsorption to the fibre exterior led to an increase in tensile strength and strain at break. The creep deformation at 90%RH was also slightly reduced by the adsorption of low molecular weight PAH (15 kDa). When polyallylamine was adsorbed throughout the wall of the lignocellulosic fibres, the mechanical properties were not however improved and the creep deformation at 90%RH actually increased somewhat.     

A Uniform Exponential Spectrum for Linear Flows on Vector Bundles

For linear flows on vector bundles we define a uniform exponential spectrum. For a compact invariant set for the projected flow we obtain this spectrum by taking all accumulation points for the time tending to infinity of the union over the finite time exponential growth rates for all initial values in this set. Using direct arguments we show that for a connected compact invariant set this spectrum is a closed interval whose boundary points are Lyapunov exponents. For a compact invariant set on which the flow is chain transitive we show that this spectrum coincides with the Morse spectrum. In particular, this approach admits a straightforward analytic proof for the regularity and continuity properties of the Morse spectrum without using cohomology or ergodicity results.     

2,2′,6,6′-Tetrachloro-4,4′-propane-2,2-diyldiphenol, 2,2′,6-tribromo-4,4′-propane-2,2-diyldiphenol and 2,2′,6,6′-tetrabromo-4,4′-propane-2,2-diyldiphenol

Three flame retardants with very similar molecular structures showing three different packing patterns have been studied. The crystal structure of 2,2′,6,6′-tetrachloro-4,4′-propane-2,2-diyldiphenol, C₁₅H₁₂Cl₄O₂, can be described as a packing of sheets. The packing shows a very short intermolecular Cl⋯Cl contact distance of 3.094 (2) Å between pairs of mol­ecules inside each sheet. The crystal structure of 2,2′,6-tribromo-4,4′-propane-2,2-diyldiphenol, C₁₅H₁₃Br₃O₂, can be described as a packing of doubly stranded helical square tubes. These square helices are interconnected through Br⋯Br contacts between different helices. Finally, a previously known structure, 2,2′,6,6′-tetrabromo-4,4′-propane-2,2-diyldiphenol [Simonov, Cheban, Rotaru & Bels'skii (1986). Kristallografiya, 31 , 397–399], C₁₅H₁₂Br₄O₂, which is the most commonly used flame retardant and which has twofold rotational symmetry, has been refined in the correct absolute configuration. The structure shows large differences from the chloro analogue with regard to packing, van der Waals distances and hydrogen-bond distances.