K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

A meta-analysis of latitudinal variations in life-history traits of roach, Rutilus rutilus, over its geographical range: linear or non-linear relationships?

1. We collated information from the literature on life history traits of the roach (a generalist freshwater fish), and analysed variation in absolute fecundity, von Bertalanffy parameters, and reproductive lifespan in relation to latitude, using both linear and non-linear regression models. We hypothesized that because most life history traits are dependent on growth rate, and growth rate is non-linearly related with temperature, it was likely that when analysed over the whole distribution range of roach, variation in key life history traits would show non-linear patterns with latitude.

The alteration of the structural properties and photocatalytic activity of TiO2 following exposure to non-linear irradiation sources

When TiO2 powder was irradiated with a laser light (>0.8 MW peak pulse power (PPP) at 355 nm) a visible change in its colour from white to dark blue was observed. The initial rate of change of the total colour difference was related to the laser light intensity and the longer the irradiation time the more substantial the colour change. The result of X-ray diffraction (XRD) studies showed that the crystal structure of the TiO2 developed a more rutile form after laser exposure. ESR studies indicated that the colour change was associated with the generation of Ti(III) species in the photocatalyst. Electron microscopic studies showed that more spherical shaped particles of TiO2 were observed after laser treatment although the average particle size remained largely unchanged. No significant changes in the band gap or the surface area of the laser modified TiO2 were observed. The laser modified photocatalyst showed no enhancement in activity for the destruction of methylene blue, rhodamine B and stearic acids, indicating that the rutile/anatase ratio is unimportant in the destruction of the test pollutants used in this work, via TiO2 photocatalysis

Modification and enhanced photocatalytic activity of TiO2 following exposure to non-linear irradiation sources

The effects of high power pulsed laser light on a TiO2 photocatalyst (powder and 0.1% (w/v) aqueous suspension) are reported. When this material was irradiated with a laser of power over 0.8 MW peak pulse power at 355 nm wavelength a visible change in colour from white to dark blue was observed. The initial rate of change of the total colour difference is related to the laser power; the stronger the laser power the darker the colour change. The result of X-ray diffraction studies indicates that the crystal structure of the TiO2 developed a more rutile form after laser exposure. Electron microscopic studies showed that spherical shaped particles of TiO2 were observed after laser treatment. Preliminary results show enhanced photocatalytic activity for the destruction of methylene blue. (C) 1999 Elsevier Science S.A. All rights reserved.

Poincare Analysis of Non-linear Electromagnetic Modes in Electron-Positron Plasmas

We present an investigation of coupled nonlinear electromagnetic modes in an electron-positron plasma by using the well established technique of Poincaré surface of section plots. A variety of nonlinear solutions corresponding to interesting coupled electrostatic-electromagnetic modes sustainable in electron-positron plasmas is shown on the Poincaré section. A special class of localized solitary wave solution is identified along a separatrix curve and its importance in the context of electromagnetic wave propagation in an electron-positron plasma is discussed.

A simple non-linear global-local finite element methodology for composite structures

A simple non-linear global-local finite element methodology is presented. A global coarse model, using 2-D shell elements, is solved non-linearly and the displacements and rotations around a region of interest are applied, as displacement boundary conditions, to a refined local 3-D model using Kirchhoff plate assumptions. The global elements' shape functions are used to interpolate between nodes. The local model is then solved non-linearly with an incremental scheme independent of that used for the global model.