Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Roche tomography of cataclysmic variables - VI. Differential rotation of AE Aqr - not tidally locked!

We present Roche tomograms of the K4V secondary star in the cataclysmic variable AE Aqr, reconstructed from two data sets taken 9 d apart, and measure the differential rotation of the stellar surface. The tomograms show many large, cool starspots, including a large high-latitude spot and a prominent appendage down the trailing hemisphere. We find two distinct bands of spots around 22° and 43° latitude, and estimate a spot coverage of 15.4-17 per cent on the Northern hemisphere. Assuming a solar-like differential rotation law, the differential rotation of AE Aqr was measured using two different techniques. The first method yields an equator-pole lap time of 269 d and the second yields a lap time of 262 d. This shows that the star is not fully tidally locked, as was previously assumed for CVs, but has a co-rotation latitude of ˜40°. We discuss the implications that these observations have on stellar dynamo theory, as well as the impact that spot traversal across the L1 point may have on accretion rates in CVs as well as some of their other observed properties. The entropy landscape technique was applied to determine the system parameters of AE Aqr. For the two independent data sets, we find M1 = 1.20 and 1.17 M⊙, M2 = 0.81 and 0.78 M⊙, and orbital inclinations of 50° to 51° at optimal systemic velocities of γ = -64.7 and -62.9 km s-1.

Investigation of influence of process variables on mechanical strength, size and homogeneity of pharmaceutical granules produced by fluidised hot melt granulation

The overall aim of the project was to study the influence of process variables on the distribution of a model active pharmaceutical ingredient (API) during fluidised melt granulation of pharmaceutical granules with a view of optimising product characteristics. Granules were produced using common pharmaceutical excipients; lactose monohydrate using poly ethylene glycol (PEG1500) as a meltable binder. Methylene blue was used as a model API. Empirical models relating the process variables to the granules properties such as granule mean size, product homogeneity and granule strength were developed using the design of experiment approach. Fluidising air velocity and fluidising air temperature were shown to strongly influence the product properties. Optimisation studies showed that strong granules with homogeneous distribution of the active ingredient can be produced at high fluidising air velocity and at high fluidising air temperatures.

On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.

Variables to be considered when assessing the photocatalytic destruction of bacterial pathogens

The current study sought to assess the importance of three common variables on the outcome of TiO₂ photocatalysis experiments with bacteria. Factors considered were (a) ability of test species to withstand osmotic pressure, (b) incubation period of agar plates used for colony counts following photocatalysis and (c) chemical nature of suspension medium used for bacteria and TiO₂. Staphylococcus aureus, Escherichia coli, Salmonella ser. Typhimurium and Pseudomonas aeruginosa were found to vary greatly in their ability to withstand osmotic pressure, raising the possibility that osmotic lysis may be contributing to loss of viability in some photocatalytic disinfection studies. Agar plate incubation time was also found to influence results, as bacteria treated with UV light only grew more slowly than those treated with a combination of UV and TiO_2. The chemical nature of the suspension medium used was found to have a particularly pronounced effect upon results. Greatest antibacterial activity was detected when aqueous sodium chloride solution was utilised, with ∼1 × 10⁶ CFU mL^-1 S. aureus being completely killed after 60 min. Moderate activity was observed when distilled water was employed with bacteria being killed after 2 h and 30 min, and no antibacterial activity at all was detected when aqueous tryptone solution was used. Interestingly, the antibacterial activity of UV light on its own appeared to be very much reduced in experiments where aqueous sodium chloride was employed instead of distilled water.