n/a

The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. For certain monoids connected with combinatorics, such as the plactic monoid (the monoid of Young tableaux) and the sylvester monoid (the monoid of binary search trees), connected components consist of elements that have the same evaluation (that is, contain the same number of each generating symbol). This paper discusses new results on the diameters of connected components of the cyclic shift graphs of the finite-rank analogues of these monoids, showing that the maximum diameter of a connected component is dependent only on the rank. The proof techniques are explained in the case of the sylvester monoid.

Apesar da escrita ter, habitualmente, uma maior expressão no ensino da Matemática que a própria oralidade, os alunos não estão habituados a explicitar raciocínios e a utilizar linguagem matemática apropriada. A comunicação matemática escrita tem algumas particularidades que podem ser diretamente trabalhadas com os alunos. Por exemplo, a escrita ajuda os alunos a dar sentido à Matemática e a melhorar o próprio discurso. As produções dos alunos transportam informações para o professor contribuindo para a planificação e concretização da sua prática profissional. Assim, e apesar de frequentemente ser descurada, a escrita matemática pode ser trabalhada na sala de aula, em particular, com futuros professores. Este artigo reporta parte de uma experiência realizada com uma turma da Licenciatura em Educação Básica, tendo por base a resolução em grupo de um problema de Geometria e o registo escrito do processo de resolução elaborado pelos alunos. Pretendeu-se desta forma caraterizar a comunicação escrita dos alunos e identificar contributos desta para a compreensão por parte do professor dos conhecimentos dos alunos. A análise da escrita matemática dos alunos, tendo por base um conjunto de critérios previamente definidos, permitiu identificar a preferência destes pelo recurso à representação verbal, dificuldades em fundamentar adequadamente as respostas apresentadas e uma forte tendência para desvalorizar as abordagens prévias que não conduziram à resposta ao problema. Permitiu ainda identificar uma tendência para não explicitar o entendimento das questões que lhes eram colocadas. A forma como os conceitos matemáticos surgem nas repostas escritas permite identificar aspetos relevantes do conhecimento dos alunos.

Precast concrete sandwich panels started being used as cladding for buildings, together with the rise of industrial prefabrication, during the mid-20th century. Since then, society and industry have become increasingly aware of energy efficiency in all fields, for both affordability and sustainability consciousness. As such, buildings have been subject to increasingly stringent requirements with the technology of sandwich panels kept continually at the forefront.
Nowadays, sandwich panels have reached the highest standards of functional performance as structural efficiency, flexibility in use, the speed as well as of aesthetic appeal. These combine in building construction with the well-known advantages of prefabrication; such as construction, quality consciousness, durability and sustainability. Sandwich panels have gained more and more important in their field, thus representing quite a significant application within the industry of prefabrication and an important share of the market.
The Commission ‘Prefabrication’ is keen to promote the development of all precast structural concrete products and to transfer the knowledge to practical design and construction. Now filling a strategic gap, by issuing this Guide to Good Practice, which includes design considerations, structural analysis, building physics, use of materials, manufacturing methods, equipment, field performance, and provides a comprehensive overview of the information currently available worldwide. The Commission is particularly proud that this document is a result of close cooperation with PCI and that it will be published by both fib and PCI. This cooperation started six years ago, first with comparing the different approaches to several issues, then progressively integrating up to producing common documents, like this one, that wasn’t yet treated in a specific Guide by either body.

AbstractThe behaviour of standard boltedsteel connections submitted to monotonic loads, through the use of numerical models, is presented in the current paper.The bolted connections allow speed up constructive processes in an increasingly competitive and globalized world in which the costs are a decisive factor in the development of a project. The use of computational tools in the analysis of bolted connections becomes determinant, mainly for new solutions or solutions less explored in terms of design codes.Throughout the years, bolted connections have been suffering transformations resulting from research activities performed by many authors. Rivets have been replaced by bolts, the main achievement being the pre-stressed bolts. Methodologies based on finite element analyses were proposed for double shear bolted connection. The non-linear behaviour of these connections is investigated and their performances are compared. In the numerical modelling of the bolted connection, linear elastic and elastoplastic analyzes reveal that there are two slip levels associated with local non-linearities caused by the contact pairs, which vary with clamping stresses.

The teacher's knowledge of the mathematical fidelity of technology and the impact it has on the teacher’s practice is the focus of this article. Based on the conceptualization of Knowledge for Teaching Mathematics with Technology (KTMT), and involving the teaching of Functions at the 10th grade, we analyze: the situations of lack of mathematical fidelity considered by the teacher in the classes, the way how the teacher manages students' contact with this kind of situations, and how the teacher supports students when they are faced with a lack of mathematical fidelity. The conclusions reached point to: some devaluation of the situations of lack of mathematical fidelity, with only one type of situation being explicitly addressed; a careful selection of tasks, in order to ensure that these situations do not occur too soon; a focus on the identification by the students of this type of situation, suggesting what they can do to confirm the suspicion but without effective implementation of the process. As a consequence, knowledge of mathematical fidelity does not necessarily have a relevant impact on teacher’s practice and it is not easily transformed into a deep teacher’s KTMT.

n/a

The development of meaningful learning becomes possible when students are actively involved in solving real problems. Thus, this study intends to investigate how students of the 11th grade of a vocational course solve problems of Linear Programming, using the graphing calculator. The conclusions reached indicate that: the interpretation of the conditions of the problems is the most delicate point; the graphical approach using technology is dominant; and the difficulties raised by the problem as well as the need to discuss the results achieved are the basis for the interactions both among the students and between them and the teacher.

n/a

Abstract The current chromatographic approaches used in protein purification are not keeping pace with the increasing biopharmaceutical market demand. With the upstream improvements, the bottleneck shifted towards the downstream process. New approaches rely in Anything But Chromatography methodologies and revisiting former techniques with a bioprocess perspective. Protein crystallization and precipitation methods are already implemented in the downstream process of diverse therapeutic biological macromolecules, overcoming the current chromatographic bottlenecks. Promising work is being developed in order to implement crystallization and precipitation in the purification pipeline of high value therapeutic molecules. This review focuses in the role of these two methodologies in current industrial purification processes, and highlights their potential implementation in the purification pipeline of high value therapeutic molecules, overcoming chromatographic holdups.