Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Lattice-dome design using a knowledge-based system approach

In the design of lattice domes, design engineers need expertise in areas such as configuration processing, nonlinear analysis, and optimization. These are extensive numerical, iterative, and lime-consuming processes that are prone to error without an integrated design tool. This article presents the application of a knowledge-based system in solving lattice-dome design problems. An operational prototype knowledge-based system, LADOME, has been developed by employing the combined knowledge representation approach, which uses rules, procedural methods, and an object-oriented blackboard concept. The system's objective is to assist engineers in lattice-dome design by integrating all design tasks into a single computer-aided environment with implementation of the knowledge-based system approach. For system verification, results from design examples are presented.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Considerations in the design of a mixed-method cluster evaluation of a community programme for 'at-risk' young people

This article discusses the design of a comprehensive evaluation of a community development programme for young people 'at-risk' of self-harming behaviour. It outlines considerations in the design of the evaluation and focuses on the complexities and difficulties associated with the evaluation of a community development programme. The challenge was to fulfil the needs of the funding body for a broad, outcome-focused evaluation while remaining close enough to the programme to accurately represent its activities and potential effects at a community level. Specifically, the strengths and limitations of a mixed-method evaluation plan are discussed with recommendations for future evaluation practice.

Distribution of Actinobacillus actinomycetemcomitans, Porphyromonas gingivalis and Prevotella intermedia in an Australian population

Background, aim: The present study describes (i) the natural distribution of the three putative periodontopathogens Porphyromonas gingivalis, Prevotella intermedia and Actinobacillus actinomycetemcomitans in an Australian population and (ii) the relationship between these organisms, pocket depths and supragingival plaque scores. Methods: Subgingival plaque was collected from the shallowest and deepest probing site in each sextant of the dentition. In total, 6030 subgingival plaque samples were collected from 504 subjects. An ELISA utilising pathogen-specific monoclonal antibodies was used to quantitate bacterial numbers. Results:: A. actinomycetemcomitans was the most frequently detected organism (22.8% of subjects) followed by P. gingivalis and P. intermedia (14.7% and 9.5% of subjects respectively). The majority of infected subjects (83%) were colonised by a single species of organism. A. actinomyceteincomitans presence was overrepresented in the youngest age group but under-represented in the older age groups. Conversely, P. gingivalis and P. intermedia presence was under-represented in the youngest age group but over-represented in the older age groups. Differing trends in the distribution of these bacteria were observed between subjects depending upon the site of the infection or whether a single or mixed infection was present; however, these differences did not reach significance. Bacterial presence was strongly associated with pocket depth for both A. actinomyceteincomitans and P. gingivalis. For A. actinomycetemcomitans, the odds of a site containing this bacterium decrease with deeper pockets. In contrast, for P. gingivalis the odds of a site being positive are almost six times greater for pockets >3 ram than for pockets less than or equal to3 nun. These odds increase further to 15.3 for pockets deeper than 5 mm. The odds of a site being P. intermedia positive were marginally greater (1.16) for pockets deeper than 3 mm. Conclusions: This cross-sectional study in a volunteer Australian population, demonstrated recognised periodontal pathogens occur as part of the flora of the subgingival plaque. Prospective longitudinal studies are needed to examine the positive relationship between pocket depth and pathogen presence with periodontal disease initiation and/or progression.

X-ray scattering studies of mixed langmuir monolayers and Langmuir-Blodgett films of a noncentrosymmetric porphyrin with cadmium arachidate

The structures of mixed Langmuir (floating) monolayers and Langmuir-Blodgett (LB) films of a phenanthroline-porphyrin with cadmium arachidate (PhenPor + CdAr) have been investigated by synchrotron X-ray grazing incidence diffraction (GIXD) and specular X-ray reflectivity (SXR). GIXD measurements of the floating monolayers showed only one peak, arising from the CdAr domains in the films, at a scattering angle of 21.5 degrees. This is consistent with a hexagonal structure (alpha = 4.77 Angstrom). The correlation length in these domains is 250 Angstrom. GMD measurements of the LB films, however, show two sets of diffraction features: one arises from CdAr domains with a rectangular in-plane structure (alpha = 7.44 Angstrom and b = 4.90 Angstrom) and a correlation length of 85 Angstrom; the other is from porphyrin domains with an oblique in-plane structure (alpha (p) 15.2 Angstrom, b(p) = 8.86 Angstrom, and gamma (p) = 80 degrees) and a correlation length of 105 Angstrom. These dimensions are consistent with the surface pressure-area isotherm measurements and indicate that the two components are immiscible. The thickness of the bilayer is 57 Angstrom, and there is no correlation between the bilayers. Introduction of a trigger compound does not alter the structure of the films but slightly increases the bilayer thickness. The SXR measurements of the floating monolayers also support the suggested immiscibility of the two components in the films.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

A methodology for analysis of sugarcane productivity trends - I. Analysis across districts

Historically, few articles have addressed the use of district level mill production data for analysing the effect of varietal change on sugarcane productivity trends. This appears to be due to lack of compiled district data sets and appropriate methods by which to analyse these data. Recently, varietal data on tonnes of sugarcane per hectare (TCH), sugar content (CCS), and their product, tonnes of sugar content per hectare (TSH) on a district basis, have been compiled. This study was conducted to develop a methodology for regular analysis of such data from mill districts to assess productivity trends over time, accounting for variety and variety x environment interaction effects for 3 mill districts (Mulgrave, Babinda, and Tully) from 1958 to 1995. Restricted maximum likelihood methodology was used to analyse the district level data and best linear unbiased predictors for random effects, and best linear unbiased estimates for fixed effects were computed in a mixed model analysis. In the combined analysis over districts, Q124 was the top ranking variety for TCH, and Q120 was top ranking for both CCS and TSH. Overall production for TCH increased over the 38-year period investigated. Some of this increase can be attributed to varietal improvement, although the predictors for TCH have shown little progress since the introduction of Q99 in 1976. Although smaller gains have been made in varietal improvement for CCS, overall production for CCS decreased over the 38 years due to non-varietal factors. Varietal improvement in TSH appears to have peaked in the mid-1980s. Overall production for TSH remained stable over time due to the varietal increase in TCH and the non-varietal decrease in CCS.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

On surrogate methods for detecting lateral gene transfer

Surrogate methods for detecting lateral gene transfer are those that do not require inference of phylogenetic trees. Herein I apply four such methods to identify open reading frames (ORFs) in the genome of Escherichia coli K12 that may have arisen by lateral gene transfer. Only two of these methods detect the same ORFs more frequently than expected by chance, whereas several intersections contain many fewer ORFs than expected. Each of the four methods detects a different non-random set of ORFs. The methods may detect lateral ORFs of different relative ages; testing this hypothesis will require rigorous inference of trees. (C) 2001 Federation of European Microbiological Societies. Published by Elsevier Science BN. All rights reserved.

Stickiness in foods: A review of mechanisms and test methods

Problems associated with the stickiness of food in processing and storage practices along with its causative factors are outlined. Fundamental mechanisms that explain why and how food products become sticky are discussed. Methods currently in use for characterizing and overcoming stickiness problems in food processing and storage operations are described. The use of glass transition temperature-based model, which provides a rational basis for understanding and characterizing the stickiness of many food products, is highlighted.