The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.

A Matemática é uma das áreas que integra o plano curricular dos Cursos de Educação e Formação (CEF), pelo contributo para o exercício da cidadania em sociedades democráticas e tecnologicamente avançadas, mas esta é, também, frequentemente fonte de exclusão. O programa reconhece-o e enfatiza uma aprendizagem mais ligada ao concreto e à realidade. Mas reconhece também que é ao professor que compete gerir a sua implementação, dando forma às situações de aprendizagem e integrando-as de forma coerente e articulada no curso específico que os alunos frequentam. O estudo que aqui se apresenta teve como principal objectivo analisar e compreender as opções efectuadas pelo professor no decorrer das diferentes etapas da sua prática, dando atenção aos dilemas que enfrentou e às razões que valorizou na tomada de decisões. A abordagem metodológica adoptada é de natureza qualitativa e interpretativa, com a realização dum estudo de caso do professor de Matemática Aplicada dum CEF de Decoração e Pintura Cerâmica. A recolha de dados foi concretizada através de entrevistas, observação de aulas e recolha documental, sendo a análise de dados orientada pelo quadro teórico, conciliado com a interpretação destes. Nas conclusões do estudo a redução dos pré-requisitos, a preocupação em partir dos interesses dos alunos e a intenção de alargar a cultura dos alunos surgem como centrais na selecção das tarefas; enquanto o envolvimento activo dos alunos caracteriza a implementação das aulas. Os dilemas centram-se fundamentalmente na valorização relativa e aprofundamento a atribuir a cada conteúdo e na articulação entre formal e intuitivo.

We here present fossil Crocodylomorpha eggshells from the Upper Jurassic Lourinhã Formation of Portugal, recovered from five sites: one nest from Cambelas with 13 eggs, and three partial eggs and various fragments from, Paimogo N (I), Paimogo S (II), Casal da Rola, and Peralta. All specimens but the nest were found in association with dinosaur egg material. Our research reveals that on a micro- and ultrastructural analysis, all samples present the typical characters consistent with crocodiloid eggshell morphotype, such as the shell unit shape, the organization of the eggshell layers, and the triangular blocky extinction observed with crossed nicols. We assign the material from the Lourinhã Formation to the oofamily Krokolithidae, making it the oldest crocodylomorph eggs known so far, as well as the best record for eggs of non- crocodylian crocodylomorphs. Furthermore, our study indicates that the basic structure of crocodiloid eggshells has remained stable since at least the Upper Jurassic.

The color sensing ability of a data acquisition prototype system integrating a 32 linear array of 1D amorphous silicon position sensitive detectors (PSD) was analyzed. Besides being used to reproduce a 3D profile of highly reflective surfaces, here we show that it can also differentiate primary red, green, blue (RGB) and derived colors. This was realized by using an incident beam with a RGB color combination and adequate integration times taking into account that a color surface mostly reflects its corresponding color. A mean colorimetric error of 25.7 was obtained. Overall, we show that color detection is possible via the use of this sensor array system, composed by a simpler amorphous silicon pin junction. © 2013 Elsevier B.V. All rights reserved.

We here present fossil Crocodylomorpha eggshells from the Upper Jurassic Lourinhã Formation of Portugal, recovered from five sites: one nest from Cambelas with 13 eggs, and three partial eggs and various fragments from, Paimogo N (I), Paimogo S (II), Casal da Rola, and Peralta. All specimens but the nest were found in association with dinosaur egg material. Our research reveals that on a micro- and ultrastructural analysis, all samples present the typical characters consistent with crocodiloid eggshell morphotype, such as the shell unit shape, the organization of the eggshell layers, and the triangular blocky extinction observed with crossed nicols. We assign the material from the Lourinhã Formation to the oofamily Krokolithidae, making it the oldest crocodylomorph eggs known so far, as well as the best record for eggs of non- crocodylian crocodylomorphs. Furthermore, our study indicates that the basic structure of crocodiloid eggshells has remained stable since at least the Upper Jurassic.

A transparent Eu3 +-doped lithium aluminophosphate glass was prepared by melt-quenching technique. The thermal behavior of the glass was investigated by differential thermal analysis (DTA), the structure was studied by X-ray diffraction (XRD) and the morphology was observed by optical polarization microscopy and scanning electron microscopy (SEM). The activation energy of glass transition and the activation energy of crystallization and Avrami exponent have been evaluated under non-isothermal conditions from the data obtained by DTA at different heating rates. DTA curves exhibited an endothermic peak associated with the glass transition and two exothermic peaks. The mean value calculated for the activation energy of glass transition was 545 kJ mol- 1. The activation energy of crystallization was   400 kJ mol- 1 for the first exothermic peak and   170 kJ mol- 1 for the second peak. The Avrami exponent was   1 for both peaks indicating surface crystallization. XRD results showed that the main crystalline phase, aluminum metaphosphate, Al(PO3)3, and aluminum phosphate, AlPO4, were formed together with lithium barium phosphate, Li 3Ba(PO3)7, during the first exothermic peak and together with barium pyrophosphate, Ba2P2O7, during the second peak. Morphological study of heat-treated glass samples revealed microstructural features that confirmed a surface crystallization process. © 2014 Elsevier B.V.