Economic and environmental impacts of pollution control in a system of environment and economic interdependence

The importance of the rate of change of the pollution stock in determining the damage to the environment has been an issue of increasing concern in the literature. This paper uses a three-sector (economy, population and environment), non-linear, discrete time, calibrated model to examine pollution control. The model explicitly links economic growth to the health of the environment. The stock of natural resources is affected by the rate of pollution flows, through their impact on the regenerative capacity of the natural resource stock. This can shed useful insights into pollution control strategies, particularly in developing countries where environmental resources are crucial for production in many sectors of the economy. Simulation exercises suggested that, under plausible assumptions, it is possible to reverse undesirable transient dynamics through pollution control expenditure, but this is dependent upon the strategies used for control. The best strategy is to spend money fostering the development of production technologies that reduce pollution rather than spending money dealing with the effects of the pollution flow into the environment. (C) 2001 Elsevier Science Ltd. All rights reserved.

Use of confocal microscopy to follow the development of penetrative hyphae during growth of Rhizopus oligosporus in an artificial solid-state fermentation system

Two methods were compared for determining the concentration of penetrative biomass during growth of Rhizopus oligosporus on an artificial solid substrate consisting of an inert gel and starch as the sole source of carbon and energy. The first method was based on the use of a hand microtome to make sections of approximately 0.2- to 0.4-mm thickness parallel to the substrate surface and the determination of the glucosamine content in each slice. Use of glucosamine measurements to estimate biomass concentrations was shown to be problematic due to the large variations in glucosamine content with mycelial age. The second method was a novel method based on the use of confocal scanning laser microscopy to estimate the fractional volume occupied by the biomass. Although it is not simple to translate fractional volumes into dry weights of hyphae due to the lack of experimentally determined conversion factors, measurement of the fractional volumes in themselves is useful for characterizing fungal penetration into the substrate. Growth of penetrative biomass in the artificial model substrate showed two forms of growth with an indistinct mass in the region close to the substrate surface and a few hyphae penetrating perpendicularly to the surface in regions further away from the substrate surface. The biomass profiles against depth obtained from the confocal microscopy showed two linear regions on log-linear plots, which are possibly related to different oxygen availability at different depths within the substrate. Confocal microscopy has the potential to be a powerful tool in the investigation of fungal growth mechanisms in solid-state fermentation. (C) 2003 Wiley Periodicals, Inc.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.