The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

Species accumulation curves and their applications in parasite ecology

Species accumulation curves (SACs) chart the increase in recovery of new species as a function of some measure of sampling effort. Studies of parasite diversity can benefit from the application of SACs, both as empirical tools to guide sampling efforts and predict richness, and because their properties are informative about community patterns and the structure of parasite diversity. SACs can be used to infer interactivity in parasite infra-communities, to partition species richness into contributions from different spatial scales and different levels of the host hierarchy (individuals, populations and communities) or to identify modes of community assembly (niche versus dispersal). A historical tendency to treat individual hosts as statistically equivalent replicates (quadrats) seemingly satisfies the sample-based subgroup of SACs but care is required in this because of the inequality of hosts as sampling units. Knowledge of the true distribution of parasite richness over multiple host-derived and spatial scales is far from complete but SACs can improve the understanding of diversity patterns in parasite assemblages.

Precision-recall operating characteristic (P-ROC) curves in imprecise environments

Traditionally, machine learning algorithms have been evaluated in applications where assumptions can be reliably made about class priors and/or misclassification costs. In this paper, we consider the case of imprecise environments, where little may be known about these factors and they may well vary significantly when the system is applied. Specifically, the use of precision-recall analysis is investigated and compared to the more well known performance measures such as error-rate and the receiver operating characteristic (ROC). We argue that while ROC analysis is invariant to variations in class priors, this invariance in fact hides an important factor of the evaluation in imprecise environments. Therefore, we develop a generalised precision-recall analysis methodology in which variation due to prior class probabilities is incorporated into a multi-way analysis of variance (ANOVA). The increased sensitivity and reliability of this approach is demonstrated in a remote sensing application.

Compact tiled display with uniform illumination

The demand for more pixels is beginning to be met as manufacturers increase the native resolution of projector chips. Tiling several projectors still offers a solution to augment the pixel capacity of a display. However, problems of color and illumination uniformity across projectors need to be addressed as well as the computer software required to drive such devices. We present the results obtained on a desktop-size tiled projector array of three D-ILA projectors sharing a common illumination source. A short throw lens (0.8:1) on each projector yields a 21-in. diagonal for each image tile; the composite image on a 3×1 array is 3840×1024 pixels with a resolution of about 80 dpi. The system preserves desktop resolution, is compact, and can fit in a normal room or laboratory. The projectors are mounted on precision six-axis positioners, which allow pixel level alignment. A fiber optic beamsplitting system and a single set of red, green, and blue dichroic filters are the key to color and illumination uniformity. The D-ILA chips inside each projector can be adjusted separately to set or change characteristics such as contrast, brightness, or gamma curves. The projectors were then matched carefully: photometric variations were corrected, leading to a seamless image. Photometric measurements were performed to characterize the display and are reported here. This system is driven by a small PC cluster fitted with graphics cards and running Linux. It can be scaled to accommodate an array of 2×3 or 3×3 projectors, thus increasing the number of pixels of the final image. Finally, we present current uses of the display in fields such as astrophysics and archaeology (remote sensing).

Can globalisation result in less efficient and more vulnerable industries?

Growing economic globalisation (a means of market extension) may increase the economic vulnerability of firms in modern industries, especially those in which firms experience substantial economies of scale. The possibility is explored that globalisation activates competitive pressures that forces firms into a situation where their leverage (fixed costs relative to variable costs, or overhead cost relative to operating costs or capital intensity) rises substantially. Consequently, they become increasingly vulnerable to a sudden adverse change in economic conditions, such as a collapse in the demand for their industry’s product. This is explored for monopolistically competitive markets and also for oligopolistic markets of the type considered and modelled by Sweezy using kinked demand curves. In addition, globalisation is hypothesised to induce firms to become more uniformly efficient. While this has static efficiency advantages, this lack of heterogeneity in productive efficiency of firms can make for economic inefficiency in the adjustment of the industry to altered economic conditions. It is shown that lack of variation in the economic efficiency of firms can impede the speed of market adjustment to new equilibria and may destabilise market equilibria.

The anodic dissolution of magnesium in chloride and sulphate solutions

The electrochemical behaviour of magnesium was studied in representative chloride and sulphate solutions including NaCl, Na2SO4, NaOH and their mixed solutions, HCl, and H2SO4: (1) by measuring electrochemical polarisation curves, (2) by using electrochemical impedance spectroscopy (EIS), and (3) by simultaneous measurement of hydrogen gas evolution and measurement of magnesium dissolution rates using inductively coupled plasma atomic emission spectrophotometry (ICPEAS). These experiments showed that a partially protective surface film played an important role in the dissolution of magnesium in chloride and sulphate solutions. Furthermore, the experimental data were consistent with the involvement of the intermediate species Mg+ in magnesium dissolution at film imperfections or on a film-free surface. At such sites, magnesium first oxidised electrochemically to the intermediate species Mg+, and then the intermediate species chemically reacted with water to produce hydrogen and Mg2+. The presence of Cl- ions increased the film free area, and accelerated the electrochemical reaction rate from magnesium metal to Mg+. (C) 1997 Elsevier Science Ltd.

Kinetic analysis of vascular marker distribution in perfused rat livers after regeneration following partial hepatectomy

Background/Aims: Liver clearance models are based on information (or assumptions) on solute distribution kinetics within the microvasculatory system, The aim was to study albumin distribution kinetics in regenerated livers and in livers of normal adult rats, Methods: A novel mathematical model was used to evaluate the distribution space and the transit time dispersion of albumin in livers following regeneration after a two-thirds hepatectomy compared to livers of normal adult rats. Outflow curves of albumin measured after bolus injection in single-pass perfused rat livers were analyzed by correcting for the influence of catheters and fitting a long-tailed function to the data. Results: The curves were well described by the proposed model. The distribution volume and the transit time dispersion of albumin observed in the partial hepatectomy group were not significantly different from livers of normal adult rats. Conclusions: These findings suggest that the distribution space and the transit time dispersion of albumin (CV2) is relatively constant irrespective of the presence of rapid and extensive repair. This invariance of CV2 implies, as a first approximation, a similar degree of intrasinusoidal mixing, The finding that a sum of two (instead of one) inverse Gaussian densities is an appropriate empirical function to describe the outflow curve of vascular indicators has consequences for an improved prediction of hepatic solute extraction.

Corrosion behaviour of AZ21, AZ501 and AZ91 in sodium chloride

The corrosion behaviour of AZ21, AZ501 and AZ91 was studied in 1 N NaCl at pH 11 by measuring electrochemical polarization curves, electrochemical AC impedance spectroscopy (EIS) and simultaneously measuring the hydrogen evolution rate and the: magnesium dissolution rate. The corrosion rates increased in the following order: AZ501 < AZ21 < AZ91. The: corrosion behaviour was related to alloy microstructure as revealed by optical and electron microscopy. The beta phase was very stable in the test solution and was an effective cathode. The beta phase served two roles, as a barrier and as a galvanic cathode. If the beta phase is present in the alpha matrix as intergranular precipitates with a small volume fraction, then the beta phase mainly serves as a galvanic cathode, and accelerates the corrosion of the alpha matrix. If the beta Fraction is high, then the beta phase may mainly act as an anodic barrier to inhibit the overall corrosion of the alloy. The composition and compositional distribution in the alpha phase is also crucial to the overall corrosion performance of dual phase alloys. Increasing the aluminum concentration in the alpha phase increases the anodic dissolution rate and also increases the cathodic hydrogen evolution rate. Increasing the zinc concentration in the alpha phase may have the opposite effect. (C) 1998 Elsevier Science Ltd. All rights reserved.

Influence of microstructure on the corrosion of diecast AZ91D

The corrosion of die cast AZ91D was studied and related to its microstructure. For comparison and to more fully understand the behaviour of die cast AZ91D, corrosion studies and microstructural examinations were also carried out using slowly solidified high purity AZ91, Mg-2%Al, Mg-9%Al, low purity magnesium and high purity magnesium. Corrosion was studied in 1N NaCl at pH 11 by (1) observing the corrosion morphology, (2) measuring electrochemical polarisation curves and (3) simultaneously measuring both the hydrogen evolution rate and the magnesium dissolution rate. The skin of die cast AZ91D showed better corrosion resistance than the interior. This is attributed to a combination of(1) a higher volume fraction of the beta phase, (2) a more continuous beta phase distribution around finer alpha grains, and (3) lower porosity in the skin layer than in the interior of the die casting. This study showed that the casting method can influence the corrosion performance by its influence on the alloy microstructure. (C) 1999 Elsevier Science Ltd. All rights reserved.

A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

A six-year longitudinal study of the relationship of physical activity to bone mineral accrual in growing children: The University of Saskatchewan bone mineral accrual study

To investigate the influence of physical activity on bone mineral accrual during the adolescent years, we analyzed 6 years of data from 53 girls and 60 boys. Physical activity, dietary intakes, and anthropometry were measured every 6 months and dual-energy X-ray absorptiometry scans of the total body (TB), lumbar spine (LS), and proximal femur (Hologic 2000, array mode) were collected annually. Distance and velocity curves for height and bone mineral content (BMC) were fitted for each child at several skeletal sites using a cubic spline procedure, from which ages at peak height velocity (PHV) and peak BMC velocity (PBMCV) were identified. A mean age- and gender-specific standardized activity (Z) score was calculated for each subject based on multiple yearly activity assessments collected up until age of PHV. This score was used to identify active (top quartile), average (middle 2 quartiles), or inactive (bottom quartile) groups. Two-way analysis of covariance, with height and weight at PHV controlled for, demonstrated significant physical activity and gender main effects (but no interaction) for PBMCV, for BMC accrued for 2 years around peak velocity, and for BMC at 1 year post-PBMCV for the TB and femoral neck and for physical activity but not gender at the LS (all p < 0.05). Controlling for maturational and size differences between groups, we noted a 9% and 17% greater TB BMC for active boys and girls, respectively, over their inactive peers 1 year after the age of PBMCV. We also estimated that, on average, 26% of adult TB bone mineral was accrued during the 2 years around PBMCV.