Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

An Analysis of black-box optimization problems in reinsurance: evolutionary-based approaches

Black-box optimization problems (BBOP) are de ned as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the eld of insurance, and more speci cally in reinsurance problems. In this area, the complexity of the models and assumptions considered to de ne the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, nding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

Immigrant Families and the School in Spain: Dynamics and Factors that Influence their Relations

In Spain, academic debate and school administrations have evolved to the extent that relations between the school, the family and the surrounding environment are now considered as crucial to student achievement at school and to the good functioning of the educational system as a whole. Despite this development, change is slow in practice and often complicated due to the emerging resistance of families and schools, given that they have always maintained relations marked by an imbalance of power. Our theoretical and especially our empirical work has focused on the relations between immigrant families and the school system in Spain. In view of the above, the creation of what we call positive relational dynamics and communication in schools is conditioned by the attitudes and behaviour of the school administration, professionals and families. However, the physical space in which these relations take place must also be taken into consideration. Regarding school organisation, we have emphasised the role of the school’s administration. By differentiating the range of management models, we note the ones that facilitate more relations and communication with and among families (especially the one we have called the horizontal participative model) and those that discourage them. However, the multiple and complex range of attitudes among teachers and families must always be taken into account.

Problems of the randomization test for AB designs

N = 1 designs imply repeated registrations of the behaviour of the same experimental unit and the measurements obtained are often few due to time limitations, while they are also likely to be sequentially dependent. The analytical techniques needed to enhance statistical and clinical decision making have to deal with these problems. Different procedures for analysing data from single-case AB designs are discussed, presenting their main features and revising the results reported by previous studies. Randomization tests represent one of the statistical methods that seemed to perform well in terms of controlling false alarm rates. In the experimental part of the study a new simulation approach is used to test the performance of randomization tests and the results suggest that the technique is not always robust against the violation of the independence assumption. Moreover, sensitivity proved to be generally unacceptably low for series lengths equal to 30 and 40. Considering the evidence available, there does not seem to be an optimal technique for single-case data analysis

Measuring school demand in the presence of spatial dependence. A conditional approach

Improving educational quality is an important public policy goal. However, its success requires identifying factors associated with student achievement. At the core of these proposals lies the principle that increased public school quality can make school system more efficient, resulting in correspondingly stronger performance by students. Nevertheless, the public educational system is not devoid of competition which arises, among other factors, through the efficiency of management and the geographical location of schools. Moreover, families in Spain appear to choose a school on the grounds of location. In this environment, the objective of this paper is to analyze whether geographical space has an impact on the relationship between the level of technical quality of public schools (measured by the efficiency score) and the school demand index. To do this, an empirical application is performed on a sample of 1,695 public schools in the region of Catalonia (Spain). This application shows the effects of spatial autocorrelation on the estimation of the parameters and how these problems are addressed through spatial econometrics models. The results confirm that space has a moderating effect on the relationship between efficiency and school demand, although only in urban municipalities.

¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students