Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Product form approximations for highly linear loss networks with trunk reservation

Admission controls, such as trunk reservation, are often used in loss networks to optimise their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to finding approximation methods. The Erlang Fixed-Point (EFP) approximation, which is based on an independent blocking assumption, has been used for networks both with and without controls. Several more elaborate approximation methods which account for dependencies in blocking behaviour have been developed for the uncontrolled setting. This paper is an exploratory investigation of extensions and synthesis of these methods to systems with controls, in particular, trunk reservation. In order to isolate the dependency factor, we restrict our attention to a highly linear network. We will compare the performance of the resulting approximations against the benchmark of the EFP approximation extended to the trunk reservation setting. By doing this, we seek to gain insight into the critical factors in constructing an effective approximation. (C) 2003 Elsevier Ltd. All rights reserved.

Eigenvalue computations in the context of data-sparse approximations of integral operators

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Innovation for sustainable urban tourism: some thoughts on best practice

This paper examines a series of strategic initiatives that have been undertaken by Tourism Queensland (TQ), a State Tourism Organization in Australia, to develop tourism and in particular to develop networks in tourism destinations. This paper firstly examines the nature of sustainable urban tourism (SUT) and discusses approaches to defining it. It suggests that developing SUT requires a generic approach to improving sustainable tourism operations amongst all suppliers in an urban area. Further, this approach suggests that best practice in marketing and policy development can be adopted to attract tourists to a SUT destination and examples of this approach are provided.

Research on using the decision tree method in order to select the best alternative for the pharmacies supply

Introduction / Aims: Adopting the important decisions represents a specific task of the manager. An efficient manager takes these decisions during a sistematic process with well-defined elements, each with a precise order. In the pharmaceutical practice and business, in the supply process of the pharmacies, there are situations when the medicine distributors offer a certain discount, but require payment in a shorter period of time. In these cases, the analysis of the offer can be made with the help of the decision tree method, which permits identifying the decision offering the best possible result in a given situation. The aims of the research have been the analysis of the product offers of many different suppliers and the establishing of the most advantageous ways of pharmacy supplying. Material / Methods: There have been studied the general product offers of the following medical stores: A&G Med, Farmanord, Farmexim, Mediplus, Montero and Relad. In the case of medicine offers including a discount, the decision tree method has been applied in order to select the most advantageous offers. The Decision Tree is a management method used in taking the right decisions and it is generally used when one needs to evaluate the decisions that involve a series of stages. The tree diagram is used in order to look for the most efficient means to attain a specific goal. The decision trees are the most probabilistic methods, useful when adopting risk taking decisions. Results: The results of the analysis on the tree diagrams have indicated the fact that purchasing medicines with discount (1%, 10%, 15%) and payment in a shorter time interval (120 days) is more profitable than purchasing without a discount and payment in a longer time interval (160 days). Discussion / Conclusion: Depending on the results of the tree diagram analysis, the pharmacies would purchase from the selected suppliers. The research has shown that the decision tree method represents a valuable work instrument in choosing the best ways for supplying pharmacies and it is very useful to the specialists from the pharmaceutical field, pharmaceutical management, to medicine suppliers, pharmacy practitioners from the community pharmacies and especially to pharmacy managers, chief – pharmacists.

Expert opinion on best practice guidelines and competency framework for visual screening in children

PURPOSE: Screening programs to detect visual abnormalities in children vary among countries. The aim of this study is to describe experts' perception of best practice guidelines and competency framework for visual screening in children. METHODS: A qualitative focus group technique was applied during the Portuguese national orthoptic congress to obtain the perception of an expert panel of 5 orthoptists and 2 ophthalmologists with experience in visual screening for children (mean age 53.43 years, SD ± 9.40). The panel received in advance a script with the description of three tuning competencies dimensions (instrumental, systemic, and interpersonal) for visual screening. The session was recorded in video and audio. Qualitative data were analyzed using a categorical technique. RESULTS: According to experts' views, six tests (35.29%) have to be included in a visual screening: distance visual acuity test, cover test, bi-prism or 4/6(Δ) prism, fusion, ocular movements, and refraction. Screening should be performed according to the child age before and after 3 years of age (17.65%). The expert panel highlighted the influence of the professional experience in the application of a screening protocol (23.53%). They also showed concern about the false negatives control (23.53%). Instrumental competencies were the most cited (54.09%), followed by interpersonal (29.51%) and systemic (16.4%). CONCLUSIONS: Orthoptists should have professional experience before starting to apply a screening protocol. False negative results are a concern that has to be more thoroughly investigated. The proposed framework focuses on core competencies highlighted by the expert panel. Competencies programs could be important do develop better screening programs.

Is the offence the best defense? Influences of childhood experiences and paranoia in the aggression in Azorean youths

A ideação paranoide é um processo cognitivo e social que pode ser considerado normativo (e.g. sentimentos de desconfiança ocasionais) ou disfuncional, constituindo-se, neste ultimo caso, como um sintoma psicopatológico (e.g. delírios paranoides). Mesmo em níveis subclínicos, a ideação paranoide pode constituir um entrave para o bom funcionamento interpessoal, na medida em que o comportamento disruptivo que dela advém pode afetar todas as esferas de funcionamento do indivíduo (e.g. relações familiares, entre pares, profissionais e/ou académicas). O presente estudo explorará a influência dos estilos parentais e o papel mediador da ideação paranoide na agressividade durante a adolescência, bem como as implicações para a prevenção e intervenção em contextos clínicos e educacionais.