Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

How reliably do rheumatologists measure shoulder movement?

Objective: To assess the intrarater and interrater reliability among rheumatologists of a standardised protocol for measurement of shoulder movements using a gravity inclinometer. Methods: After instruction, six rheurnatologists independently assessed eight movements of the shoulder, including total and glenohumeral flexion, total and glenohumeral abduction, external rotation in neutral and in abduction, internal rotation in abduction and hand behind back, in random order in six patients with shoulder pain and stiffness according to a 6x6 Latin square design using a standardised protocol. These assessments were then repeated. Analysis of variance was used to partition total variability into components of variance in order to calculate intraclass correlation coefficients (ICCs). Results: The intrarater and interrater reliability of different shoulder movements varied widely. The movement of hand behind back and total shoulder flexion yielded the highest ICC scores for both intrarater reliability (0.91 and 0.83, respectively) and interrater reliability (0.80 and 0.72, respectively). Low ICC scores were found for the movements of glenohumeral abduction, external rotation in abduction, and internal rotation in abduction (intrarater ICCs 0.35, 0.43, and 0.32, respectively), and external rotation in neutral, external rotation in abduction, and internal rotation in abduction (interrater ICCs 0.29, 0.11, and 0.06, respectively). Conclusions: The measurement of shoulder movements using a standardised protocol by rheumatologists produced variable intrarater and interrater reliability. Reasonable reliability was obtained only for the movement of hand behind back and total shoulder flexion.

Acoustic signature of the normal swallow: Characterization by age, gender, and bolus volume

Despite growing clinical use, cervical auscultation suffers from a lack of research-based data. One of the strongest criticisms of cervical auscultation is that there has been little research to demonstrate how dysphagic swallowing sounds are different from normal swallowing sounds, In order to answer this question, however, one first needs to document the acoustic characteristics of normal, nondysphagic swallowing sounds, This article provides the first normative database of normal swallowing sounds for the adult population. The current investigation documents the acoustic characteristics of normal swallowing sounds for individuals from 18 to more than 60 years of age over a range of thin liquid volumes. Previous research has shown the normal swallow to be a dynamic event. The normal swallow is sensitive to aging of the oropharyngeal system, and also to the volume of bolus swallowed. The current investigation found that the acoustic signals generated during swallowing were sensitive to an individual's age and to the volume of the bolus swallowed. There were also some gender-specific differences in the acoustic profile of the swallowing sound, It is anticipated that the results will provide a catalyst for further research into cervical auscultation.

Relationships of extant lower Brachycera (Diptera): a quantitative synthesis of morphological characters

With over 80 000 described species, Brachycera represent one of the most diverse clades of organisms with a Mesozoic origin. Larvae of the majority of early lineages are detritivores or carnivores. However, Brachycera are ecologically innovative and they now employ a diverse range of feeding strategies. Brachyceran relationships have been the subject of numerous qualitative analyses using morphological characters. These analyses are often based on characters from one or a few character systems and general agreement on relationships has been elusive. In order to understand the evolution of basal brachyceran lineages, 101 discrete morphological characters were scored and compiled into a single data set. Terminals were scored at the family level, and the data set includes characters from larvae, pupae and adults, internal and external morphology, and male and female terminalia. The results show that all infraorders of Brachycera are monophyletic, but there is little evidence for relationships between the infraorders. Stratiomyomorpha, Tabanomorpha, and Xylophagomorpha together form the sister group to Muscomorpha. Xylophagomorpha and Tabanomorpha are sister groups. Within Muscomorpha, the paraphyletic Nemestrinoidea form the two most basal lineages. There is weak evidence for the monophyly of Asiloidea, and Hilarimorphidae appear to be more closely related to Eremoneura than other muscomorphs. Apsilocephalidae, Scenopinidae and Therevidae form a clade of Asiloidea. This phylogenetic evidence is consistent with the contemporaneous differentiation of the main brachyceran lineages in the early Jurassic. The first major radiation of Muscomorpha were asiloids and they may have diversified in response to the radiation of angiosperms in the early Cretaceous.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

The spread of Angiostrongylus cantonensis in Australia

Until the recent establishment of Angiostrongylus cantonensis in North America. Australia was the only developed region endemic for this parasite. Almost 50 years ago the life cycle was elucidated there, in the city of Brisbane, and the first human infections probably occurred in 1959. From the 1970s, increasing numbers of autochthonous infections have been reported along the central east coast of the continent (southeast Queensland and northern New South Wales), involving humans, rats, dogs, horses, flying foxes and marsupials. Ten years ago, the parasite was discovered in Sydney, almost 1,000 km to the south, in dogs. In that city, it has since been diagnosed as a cause of neurological disease in increasing numbers of dogs, flying foxes, marsupials and zoo primates. Presumably, these infections resulted from the ingestion of snails or slugs, and it seems that virtually all species of native and exotic terrestrial molluscs can serve as intermediate hosts. It is not known how the parasite was introduced to this continent, or how it has spread over such an extensive territory, although eventually its range could encompass the entire east coast, and potentially other regions. It is also not known if the almost identical, native species, A. mackerrasae, is able to infect people (or other non-rodent hosts). All worms recovered to date, from one fatal human case, and from many animal infections, have been confirmed as A. cantonensis.

Predicting plant leaf area production: shoot assimilate accumulation and partitioning, and leaf area ratio, are stable for a wide range of sorghum population densities

Predicting plant leaf area production is required for modelling carbon balance and tiller dynamics in plant canopies. Plant leaf area production can be studied using a framework based on radiation intercepted, radiation use efficiency (RUE) and leaf area ratio (LAR) (ratio of leaf area to net above-ground biomass). The objective of this study was to test this framework for predicting leaf area production of sorghum during vegetative development by examining the stability of the contributing components over a large range of plant density. Four densities, varying from 2 to 16 plants m(-2), were implemented in a field experiment. Plants were either allowed to tiller or were maintained as uniculm by systematic tiller removal. In all cases, intercepted radiation was recorded daily and leaf area and shoot dry matter partitioning were quantified weekly at individual culm level. Up to anthesis, a unique relationship applied between fraction of intercepted radiation and leaf area index, and between shoot dry weight accumulation and amount of intercepted radiation, regardless of plant density. Partitioning of shoot assimilate between leaf, stem and head was also common across treatments up to anthesis, at both plant and culm levels. The relationship with thermal time (TT) from emergence of specific leaf area (SLA) and LAR of tillering plants did not change with plant density. In contrast, SLA of uniculm plants was appreciably lower under low-density conditions at any given TT from emergence. This was interpreted as a consequence of assimilate surplus arising from the inability of the plant to compensate by increasing the leaf area a culm could produce. It is argued that the stability of the extinction coefficient, RUE and plant LAR of tillering plants observed in these conditions provides a reliable way to predict leaf area production regardless of plant density. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Tillering in grain sorghum over a wide range of population densities: Identification of a common hierarchy for tiller emergence, leaf area development and fertility

Most studies of tiller development have not related the physiological and morphological features of each calm to its subsequent fertility. This introduced problems when trying to account for the effects of tillering on yield in crop models. The objective of this study was to detect the most likely early determinants of tiller fertility in sorghum by identifying hierarchies for emergence, fertility and grain number of tillers over a wide range of assimilate availabilities. Emergence, phenology, leaf area development and dry weight partitioning were quantified weekly for individual tillers and main culms of tillering and uniculm plants grown at one of four densities, from two to 16 plants m(-2). For a given plant in any given density, the same tiller hierarchy applied for emergence of tillers, fertility of the emerged tillers and their subsequent grain number. These results were observed over a range of tiller fertility rates (from 7 to 91%), fertile tiller number per plant at maturity (from 0.2 to 4.7), and tiller contribution to grain yield (from 5 to 78%). Tiller emergence was most probably related to assimilate supply and light quality. Development, fertility and contribution to yield of a specific tiller were highly dependent on growing conditions at the time of tiller emergence, particularly via early leaf area development of the tiller, which affected its subsequent leaf area accumulation. Assimilate availability in the main culm at the time of tiller emergence was the most likely early determinant of subsequent tiller fertility in this study. (C) 2002 Annals of Botany Company.

Tillering in grain sorghum over a wide range of population densities: Modelling dynamics of tiller fertility

The prediction of tillering is poor or absent in existing sorghum crop models even though fertile tillers contribute significantly to grain yield. The objective of this study was to identify general quantitative relationships underpinning tiller dynamics of sorghum for a broad range of assimilate availabilities. Emergence, phenology, leaf area development and fertility of individual main calms and tillers were quantified weekly in plants grown at one of four plant densities ranging from two to 16 plants m(-2). On any given day, a tiller was considered potentially fertile (a posteriori) if its number of leaves continued to increase thereafter. The dynamics of potentially fertile tiller number per plant varied greatly with plant density, but could generally be described by three determinants, stable across plant densities: tiller emergence rate aligned with leaf ligule appearance rate; cessation of tiller emergence occurred at a stable leaf area index; and rate of decrease in potentially fertile tillers was linearly related to the ratio of realized to potential leaf area growth. Realized leaf area growth is the measured increase in leaf area, whereas potential leaf area growth is the estimated increase in leaf area if all potentially fertile tillers were to continue to develop. Procedures to predict this ratio, by estimating realized leaf area per plant from intercepted radiation and potential leaf area per plant from the number and type of developing axes, are presented. While it is suitable for modelling tiller dynamics in grain sorghum, this general framework needs to be validated by testing it in different environments and for other cultivars. (C) 2002 Annals of Botany Company.

Comparison of lumbar range of movement and lumbar lordosis in back pain patients and matched controls

Inconclusive findings have been shown in previous studies comparing lumbar range of movement (LROM) and lumbar lordosis between back pain patients and healthy subjects. In these studies, confounding variables such as age, gender, height, obesity, and pain level were usually not well controlled. The present study aimed to compare LROM and lumbar lordosis between back pain patients and matched controls. Fifteen male back pain patients and 15 age-, height-, obesity-, and physical activity-matched male controls were investigated. To minimize the effect of pain on the measurements, only patients with minimal or no pain at the time of testing were included in the study. Inclinometer technique was used for the evaluation of LROM in flexion, extension and lateral flexion as well as lumbar lordosis. A lumbar rotameter was used for measuring axial rotation. Pelvic motion was limited by a pelvic restraint device during LROM measurements. Results showed that there were no significant differences between the back pain and control groups in flexion, extension, lateral flexion and axial rotation LROM and also in lumbar lordosis. This may indicate that when a back pain patient is not in pain, LROM and lumbar lordosis may not be the measures that distinguish between back pain patients and subjects without back pain.

Study on diffusion and flow of benzene, n-hexane and CCl4 in activated carbon by a differential permeation method

In this paper the diffusion and flow of carbon tetrachloride, benzene and n-hexane through a commercial activated carbon is studied by a differential permeation method. The range of pressure is covered from very low pressure to a pressure range where significant capillary condensation occurs. Helium as a non-adsorbing gas is used to determine the characteristics of the porous medium. For adsorbing gases and vapors, the motion of adsorbed molecules in small pores gives rise to a sharp increase in permeability at very low pressures. The interplay between a decreasing behavior in permeability due to the saturation of small pores with adsorbed molecules and an increasing behavior due to viscous flow in larger pores with pressure could lead to a minimum in the plot of total permeability versus pressure. This phenomenon is observed for n-hexane at 30degreesC. At relative pressure of 0.1-0.8 where the gaseous viscous flow dominates, the permeability is a linear function of pressure. Since activated carbon has a wide pore size distribution, the mobility mechanism of these adsorbed molecules is different from pore to pore. In very small pores where adsorbate molecules fill the pore the permeability decreases with an increase in pressure, while in intermediate pores the permeability of such transport increases with pressure due to the increasing build-up of layers of adsorbed molecules. For even larger pores, the transport is mostly due to diffusion and flow of free molecules, which gives rise to linear permeability with respect to pressure. (C) 2002 Elsevier Science Ltd. All rights reserved.

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).