Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses

This paper presents the application of a new constitutive damage model for an epoxy matrix on micromechanical analyses of polymer composite materials. Different representative volume elements (RVEs) are developed with a random distribution of fibres. Upon application of periodic boundary conditions (PBCs) on the RVEs, different loading scenarios are applied and the mechanical response of the composite studied. Focus is given to the influence of the interface between fibre and matrix, as well as to the influence of the epoxy matrix, on the strength properties of the composite, damage initiation and propagation under different loading conditions.     

Analysis of complementary methodologies for the estimation of school value added

This paper analyses the value added (VA) of a sample of Portuguese schools using two methodologies: data envelopment analysis (DEA) and the methodology used presently by the UK Department for Children, Schools and Families (DCSF). The VA estimates obtained by the two methods are substantially different. This reflects their different focus: DEA emphasizes on best-observed performance, whereas the DCSF method reveals average performance. The main advantage of the methodology used by the DCSF is its simplicity, although it confounds pupil effects with school effects in the estimation of school VA. In contrast, the DEA methodology can differentiate these effects, but the complexity may prevent its use in a systematic way. This paper shows that the two methods provide complementary information regarding the VA of schools, and their joint use can improve the understanding of the relative effectiveness of schools regarding the progress that pupils make between educational stages.     

The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs

The most popular weight restrictions are assurance regions (ARs), which impose ratios between weights to be within certain ranges. ARs can be categorized into two types: ARs type I (ARI) and ARs type II (ARII). ARI specify bounds on ratios between input weights or between output weights, whilst ARII specify bounds on ratios that link input to output weights. DEA models with ARI successfully maximize relative efficiency, but in the presence of ARII the DEA models may under-estimate relative efficiency or may become infeasible. In this paper we discuss the problems that can occur in the presence of ARII and propose a new nonlinear model that overcomes the limitations discussed. Also, the dual model is described, which enables the assessment of relative efficiency when trade-offs between inputs and outputs are specified. The application of the model developed is illustrated in the efficiency assessment of Portuguese secondary schools.     

Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I – Constitutive modelling

Micromechanical analyses of unidirectional continuous-fibre reinforced composite materials were performed to study the mechanisms of deformation and fracture of the constituents, and their influence on the mechanical properties of the composite. Special focus was given to the matrix material behaviour as well as to the interface between constituents. The matrix was modelled using a pressure dependent, elasto-plastic thermodynamically consistent damage model. Cohesive elements were used to model the interface between matrix and fibres. Part I of this paper details the continuum model developed for a typical epoxy matrix. Part II will focus on micromechanical analyses of composite materials and the estimation of its elastic and strength properties.     

Performance assessment of secondary schools: the snapshot of a country taken by DEA

This paper describes a performance assessment of Portuguese secondary schools using data envelopment analysis (DEA). The assessment adopts a perspective where schools are viewed as promoting students achievement given their characteristics in terms of academic abilities and socio-economic background. Our sample comprised all secondary schools in Portugal with both basic and secondary education levels. Two types of DEA analysis are performed: one using an output-oriented model that restricts output (exam scores) weights to be linked to the number of students that have done that exam in the school, and the other using a model that restricts factor weights to be equal for all schools. In this model the weight restrictions are linked to the total number of exams done nationally. The first model is well suited for identifying worst performing schools and to assess schools that may specialize in certain subjects, whereas the latter is best suited for improving discrimination between best performing schools when pursuing the identification of benchmarks, as well as to construct performance rankings.     

Predicting partial customer churn using Markov for discrimination for modeling first purchase sequences

Currently, in order to remain competitive companies are adopting customer centered strategies and consequently customer relationship management is gaining increasing importance. In this context, customer retention deserves particular attention. This paper proposes a model for partial churn detection in the retail grocery sector that includes as a predictor the similarity of the products?? first purchase sequence with churner and non-churner sequences. The sequence of first purchase events is modeled using Markov for discrimination. Two classification techniques are used in the empirical study: logistic regression and random forests. A real sample of approximately 95,000 new customers is analyzed taken from the data warehouse of a European retailing company. The empirical results reveal the relevance of the inclusion of a products?? sequence likelihood in partial churn prediction models, as well as the supremacy of logistic regression when compared with random forests.     

On the beam propagation through active media

An analytical iterative procedure has been established to determine the amplitude of a laser beam propagating through an active medium. The treatment is valid for both homogeneous and inhomogeneous broadening, and for arbitrary inhomogeneities of the parameters characterizing the active medium, namely, the refractive index, the small-signal gain and the saturation intensity. After a supplementary approximation, a thin-sheet gain approach is derived from the first iteration. The formalism enables us to provide analytical criteria for evaluating both the accuracy of each iteration and the propagation distances for which the thin-sheet solution can be used. This revised version was published online in November 2006 with corrections to the Cover Date.