The assignment of credit through bills of exchange and transmission documents in Andalusi Law

The exchange traffic was a practice that suited the modus vivendi of caravanners and traders in the Islamic world. The inclusion of the Iberian.Peninsula into the most important commercial routes of Muslims – such as the silk route through the North Africa – provides a very solid reason to deepen in the study of the sources that have been preserved about the role that certain credit instruments, which represented an alternative to the coin, might have played in trade centres.

A quantitative assessment of students’ experiences of studying music: a Spanish perspective on the European credit transfer system (ECTS)

The purpose of this investigation is to evaluate whether or not the allocation of time proposed in the Music Study Guide, adapted from the European Higher Education Area (EHEA) guidelines, is consistent and adequate for students with minimal musical knowledge. The report takes into account the importance of students’ previous knowledge and the relation this has to the time and effort expended by students in acquiring appropriate knowledge and skills. This is related also to the adequacy of the course specification to meet the demands of university study and the labour market. Results show that those students who enrolled at university without any previous musical knowledge are likely to experience significant difficulty in the acquisition of certain musical and professional competences. This highlights a need to reinforce the music curriculum, or establish zero-level courses, in order to enable such students to succeed in the subject.

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.

Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty

The multiobjective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of our model that are immunized against data uncertainty by way of characterizing corresponding solutions of robust counterpart of the model. Consequently, we present robust duality theorems relating the value of the robust model with the corresponding value of its dual problem.

Three-dimensional planar model estimation using multi-constraint knowledge based on k-means and RANSAC

Plane model extraction from three-dimensional point clouds is a necessary step in many different applications such as planar object reconstruction, indoor mapping and indoor localization. Different RANdom SAmple Consensus (RANSAC)-based methods have been proposed for this purpose in recent years. In this study, we propose a novel method-based on RANSAC called Multiplane Model Estimation, which can estimate multiple plane models simultaneously from a noisy point cloud using the knowledge extracted from a scene (or an object) in order to reconstruct it accurately. This method comprises two steps: first, it clusters the data into planar faces that preserve some constraints defined by knowledge related to the object (e.g., the angles between faces); and second, the models of the planes are estimated based on these data using a novel multi-constraint RANSAC. We performed experiments in the clustering and RANSAC stages, which showed that the proposed method performed better than state-of-the-art methods.

Constraint qualifications in convex vector semi-infinite optimization

Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The results in this paper generalize those obtained by the same authors on linear vector semi-infinite optimization problems.