The current curricular guidelines for mathematics education in Portugal emphasize the relevance of working with different representations of functions to promote understanding. Given this relevance, we seek understanding about the notion of function held by 37 basic education pre-service teachers in their first year of a master’s course. Data were collected through a task focusing on identifying functions in situations based on different representations. The content analysis technique was then adopted in the search for an understanding of the justifications given by the participants. The results achieved suggest it is easier for the pre-service teachers to identify examples that are not functions than examples that are functions. There is also a tendency for greater accuracy in the identification of examples expressed by tables than by algebraic expressions. The justifications presented show a notion of function as a relation between values of two non-empty sets, but without guaranteeing that this relation is single-valued.

This article focuses the choice and use of examples by two students of the 11th grade to prove or refute a set of statements. The use of representations of sequences and functions is also considered. The study adopts a qualitative approach and data were collected by interviews and documental gathering. The conclusions suggest most of the examples used were well-known sequences or functions. However, the students sought different purposes for the use of examples, such as understanding the conjecture, demonstrate the falsity or truthfulness of the statement and conveying a general argument. The students made a satisfactory articulation between the various types of representations but relied mostly in the cartesian graph.

The mathematical proof is assumed as a central element in the development of Mathematics. However, proof is conceived in different ways and assumed as having different functions in Mathematics. And when we move from mathematics to its teaching, the multiplicity of perspectives becomes even more significant. This diversity can have an impact on the students and on the relationship they establish with Mathematics. In these circumstances, this study seeks knowledge over the perspectives of future teachers regarding the mathematical demonstration. Specifically, it intends to achieve a deeper knowledge over the future teachers’ perspectives about what is a mathematical proof and about its functions. The study adopts a qualitative approach and uses interviews to collect data. The conclusions reached point to a traditional perspective of mathematical proof, closely tied to mathematical formalism and the validation function, where the teaching context introduces some changes, adjusting the formalism to the level of the students and highlighting the understanding function of proof, but maintaining the dominant character of the algebraic language.

Mathematics is present everywhere. However, uncovering the relevance of Mathematics requires, from the teachers, a special kind of knowledge. This study tries to characterize the knowledge used by pre-service teachers when developing a mathematical task intending to promote the students’ exploration of barcodes. The study adopts a qualitative and interpretative methodology and the data were collected using class observation and interviews. The analysis is guided by the Application and Pedagogical Content Knowledge, a model inspired on TPACK (from Mishra and Koehler) and MKT (from Ball and colleagues). The conclusions point to some difficulties to see the potential of the situation to promote mathematical learning. The knowledge on the mathematical content seems to be dominant on the options assumed and operated in a rigid way that prevent the pre-service teachers from exploring the richness of the situation on the tasks they developed.

This volume focuses on the collection of waste and waste streams as an integral aspect of sustainable waste management. The authors take economic models and behavioral studies into account to go beyond just descriptions of waste collections technologies and collection route design. Models and tools for sustainable waste collection are described in detail, and the authors provide a comprehensive, integrated methodology to design waste collection systems that reduce environmental impacts, are economically viable, and achieve buy-in and participation from target populations.
Part I of the book provides fundamentals and context on waste hierarchy, including waste prevention, reduction and reuse, waste collection itself, and steps such as preparation for recycling, recycling, treatment, and landfilling. Background in environmental, social, and economic concerns surrounding waste collection is also provided here. Part II addresses tools for design, operation, and maintenance of waste collection systems. Part III focuses on how the tools presented in Part II can be used to support sustainability assessments and decisions that consider the entire life cycle of waste and the role of waste collection programs in waste prevention, reduction, reuse, recycling, treatment, and disposal. Part IV addresses the challenges of developing sustainable waste management systems and addresses the role of waste collection in sustainable waste management in the future.

This paper presents a study of the behaviour and load capacity of steel-fibre-reinforced concrete (SFRC) flat slabs under monotonically increased concentrated vertical loads. The SFRC was used only in the local region of the slab–column connection, as the rest of the slab was cast using normal concrete without fibres. The six experimental test specimens had a thickness of 150 mm with different longitudinal reinforcement ratios, using a non-uniform distribution over the slab width. The concretes used were made with different Dramix 4D 65/60 BG steel fibre contents (0, 0·5, 0·75 and 1·0% volume content). The slab tests were complemented by flexural tests on notched beams. This made it possible to determine the tension behaviour of the different concretes used, through a linear post-cracking behaviour and inverse analysis. The inverse analysis made it possible to define the stress–crack opening relationship that characterises the tension behaviour of SFRC and to relate it to the observed behaviour and load capacity of the tested slabs. The tests results show that the tensile behaviour of the SFRC plays an important role in the behavioural and load capacity of the slabs and that it can be considered relevant to physically based models.

This paper presents an experimental study of four flat slab specimens subjected to combined vertical and horizontal cyclic loading. Steel fibre-reinforced concrete (SFRC) was used only in the local region of the slab–column connection, while the rest of the slabs were cast using normal concrete. The specimens measured 4·15 m × 1·85 m × 0·15 m and were connected to two steel half columns by 0·25 m × 0·25 m rigid steel plates, prestressed against the slab using steel bolts, to ensure monolithic behaviour. The specimens were tested using an innovative test setup system that accounted for important factors, such as the ability of bending moment redistribution, line of inflection mobility and assured equal vertical displacements at the opposite slab borders, and symmetrical shear forces. Results show that the presence of SFRC in the slab–column connection region is effective in increasing the deformation capacity of slab–column connections, allowing the increase of horizontal drift ratios.

The current research aims to study the behavior of thin reinforced concrete (RC) slabs under concentrated loads as well as to investigate the application of Critical Shear Crack Theory (CSCT) to such slabs. For this purpose, four square 100-mm-thick slabs were cast and subjected to concentrated punching monotonic loading. The experimental parameters were the flexural reinforcement ratio, 0.38% and 1.00%, and the presence or absence of shear headed stud reinforcement. It is shown that the failure criteria of CSCT describe reasonably well the observed failure modes and the ultimate loads of the specimens. However, attention is brought to some peculiarities in the analytical derivation of the load-rotation curve for thin lightly reinforced flat slabs, in which large deformations are experienced. Results showed that in such slabs, the behavior can be highly influenced by the post-yield stress-strain curve of the flexural steel reinforcement. As a result, the constitutive law of steel reinforcement should be explicitly taken into account in such cases. The versatility of CSCT to adapt to these conditions is demonstrated.

This chapter focuses on mid-range wireless power transfer (WPT) systems applied to electric vehicle (EV) battery chargers. The WPT is recently considered as an efficient electric energy transfer process between two or more points in space, without wiring. The technology associated with each specific process of WPT differs from case to case depending on the distance between those points and the power to be transferred between them. The widely adopted distance categories are named short-range, mid-range, and long-range. The short-range is normally defined as up to a few millimeters range. The mid-range is between a few millimeters and a few meters. The long-range distance is defined as a longer than that of the previous category, stretching up to a few kilometers.

The focus of this chapter is the electromagnetic interference (EMI) and the electromagnetic compatibility (EMC) that the wireless power transfer (WPT) systems reveal as problems. The wireless power transfer (WPT) was introduced by Nikola Tesla more than one hundred years ago, and only recently it attracted the attention of specialists, due to the improved technical means. The WPT technology now has many applications, especially for charging of various electronic devices (i.e., mobile phones, laptops, implants, and home appliances), informatics, and electronics equipment. The high-power equipment and installations (e.g., intelligent machining systems, robots, forklift trucks, and electric cars) are also getting wireless. Moreover, much attention has been focused on the electric transportation system for improving the safe and convenient charging of electric vehicle (EV) batteries.

This chapter provides an overview of the alpha paleobiodiversity of Angola based on the available fossil record that is limited to the sedimentary rocks, ranging in age from Precambrian to the present. The geological period with the highest paleobiodiversity in the Angolan fossil record is the Cretaceous, with more than 80{%} of the total known fossil taxa, especially marine molluscs, including ammonites as a majority among them. The vertebrates represent about 15{%} of the known fauna and about one tenth of them are species firstly described based on specimens from Angola.