Abstract
Context-free languages are highly important in computer language processing technology as well as in formal language theory. The Pumping Lemma is a property that is valid for all context-free languages, and is used to show the existence of non context-free languages. This paper presents a formalization, using the Coq proof assistant, of the Pumping Lemma for context-free languages.

Abstract

Abstract
This work presents a new integrated multistage and stochastic mathematical model, which is developed to support the decision-making process related to the expansion planning of distribution network systems for integrating large-scale distributed "clean" energy sources. The developed model, formulated from the distribution system operator's point of view, determines the optimal sizing, time, and placement of distributed energy technologies (renewables, in particular) as well as that of energy storage systems (ESSs) and compensators in distribution networks. The ultimate goal of this optimization work is to maximize the size of distributed generation (DG) power absorbed by the system while maintaining the power quality and stability at the required/standard levels at a minimal cost possible. The model, formulated as a mixed-integer linear programming optimization, employs a linearized alternating current network model that captures well the inherent characteristics of power network systems, and balances accuracy with computational burden. The standard IEEE 41-bus distribution system is used to test the developed model and carry out the required analysis from the standpoint of the objectives set.The results of the case study show that the integration of ESS and compensators helps to significantly increase the size of variable generation (wind and solar) in the system. For the case study, a total of 10. MW demand wind and solar power has been added to the system. One can put this into perspective with the peak load 4.635. MW in the system. This means it has been possible to integrate renewable energy source (RES) power more than twice the peak demand in the base case. It has been demonstrated that the joint planning of DGs, compensators, and ESSs, proposed in this work, bring about significant improvements to the system, such as reduction of losses, cost of electricity and emissions, voltage support, and many more.The expansion planning model proposed here can be considered a major leap forward toward developing controllable grids, which support large-scale integration of RESs (as opposed to the conventional "fit and forget" approach). It can also be a handy tool to speed up the integration of more RESs until smart-grids are materialized in the future.

Abstract
The Official Portuguese curriculum of Mathematics [1] considers that, in the 7th grade classes (12-13 years old students) students begin with the study of the topic "Functions". This algebraic topic is an introduction to the concept of function taking to account the graphical representation of the functions. A special attention is given to the direct proportionality and the particular case of direct proportionality relationship between two quantities be represented by a linear function. Students should understand the relationships between tables, graphs and symbols. As they work with multiple representations of functions such as, numeric, graphic and symbolic, they develop a better understanding of the function concept [2]. The Information and Communications Technology (ICT) is a powerful educational tool for the dissemination of knowledge, as well as for student learning. The software Modellus is addressed to the teaching and learning of mathematics that allows students and teachers to carry out experiments with mathematical models, in particular, to analyse the variation of the function and the respective graphical representation [3]. On the other hand, mathematical modelling as classroom practice is a very current international trend research [4]. This paper explores the Modellus applicability in the linear function learning with twenty students of 7th grade of a Portuguese School. The specific objective is to highlight the contributions of the use of computer simulations with Modellus on student learning, for the study of linear functions. Methodologically, was opted a qualitative and interpretative research approach, based on a case study. Data collection was done through direct observation of a lesson and written productions of students. An activity with an inquiry was drafted and applied in a 7th grade class during a mathematical class of fifty minutes, who answered individually to the data items. The results show that the developed proposal is valid and appropriate for students in 7th grade class. In addition, it was noted that during the study of the linear function, the simulations allowed a better development of the ability to work with various types of representations, promoting the ability to identify the variation and analysis of induced effect by changing the proportionality parameter value into the family of linear functions.

Abstract
INESC TEC is strongly committed to become a center of excellence in maritime technology and, in particular, deep sea technology. The STRONGMAR project aims at creating solid and productive links in the global field of marine science and technology between INESC TEC and established leading research European institutions, capable of enhancing the scientific and technological capacity of INESC TEC and linked institutions, helping raising its staff's research profile and its recognition as a European maritime research center of excellence. The STRONGMAR project seeks complementarity to the TEC4SEA research infrastructure: on the one hand, TEC4SEA promotes the establishment of a unique infrastructure of research and technological development, and on the other, the STRONGMAR project intends to develop the scientific expertise of the research team of INESC TEC.

Abstract
The aim of computer-aided musical orchestration is to find a combination of musical instrument sounds that approximates a target sound. The difficulty arises from the complexity of timbre perception and the combinatorial explosion of all possible instrument mixtures. The estimation of perceptual similarities between sounds requires a model capable of capturing the multidimensional perception of timbre, among other perceptual qualities of sounds. In this work, we use an artificial immune system (AIS) called opt-aiNet to search for combinations of musical instrument sounds that minimize the distance to a target sound encoded in a fitness function. Opt-aiNet is capable of finding multiple solutions in parallel while preserving diversity, proposing alternative orchestrations for the same target sound that are different among themselves. We performed a listening test to evaluate the subjective similarity and diversity of the orchestrations. © Springer International Publishing Switzerland 2016.