Open book structures on semi-algebraic manifolds

International audienceGiven a $C^2$ semi-algebraic mapping $F: \mathbb{R}^N \rightarrow \mathbb{R}^p,$ we consider its restriction to $W\hookrightarrow \mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\geq p\geq 2$ and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection $\frac{F}{\Vert F \Vert}:W\setminus F^{-1}(0)\to S^{p-1}$. Moreover, we show that the well known local and global Milnor fibrations, in the real and complex settings, follow as a byproduct by considering $W$ as spheres of small and big radii, respectively. Furthermore, we consider the composition mapping of $F$ with the canonical projection $\pi: \mathbb{R}^{p} \to \mathbb{R}^{p-1}$ and prove that the fibers of $\frac{F}{\Vert F \Vert}$ and $\frac{\pi\circ F}{\Vert \pi\circ F \Vert}$ are homotopy equivalent. We also show several formulae relating the Euler characteristics of the fiber of the projection $\frac{F}{\Vert F \Vert}$ and $W\cap F^{-1}(0).$ Similar formulae are proved for mappings obtained after composition of $F$ with canonical projections

Fibrations structure and degree formulae for Milnor fibers

International audienceIn this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincaré-Hopf type formulae which relates the Euler-Poincaré characteristic of these fibers (also called Milnor's fibers) and indices (topological degree) of appropriated vector fields defined on spheres of radii small or big enough

Fatores contingenciais e as influências para internacionalização das empresas familiares: um estudo no setor industrialContingency factors and the influences for internationalization of family businesses: a study in the industrial sector

Este artigo investigou quais fatores contingenciais são evidenciados como maiores influentes para a internacionalização das empresas familiares do ramo industrial localizadas na região sul brasileira. Para tal, aplicou-se uma survey a 51 empresas cujos dados foram tratados com técnicas de estatística descritiva e ranking médio. Os resultados evidenciaram os seguintes fatores contingenciais nas empresas que possuem iniciativas ou ações consolidadas: estratégia futura da empresa (87,5%); demandas de expansão dos negócios (87,5%), estratégia de fortalecimento da marca (75%); alternativa de crescimento de vendas (87,5%); e influência de processos aduaneiros e portuários (93,75%). De modo geral, os achados estão alinhados com a literatura da Teoria da Contingência, na qual as empresas podem reavaliar suas estratégias de gestão de modo a ampliar sua atuação internacional. Como sugestões de pesquisas futuras recomenda-se a análise de estudos de caso em indústrias que já possuem ações de internacionalização consolidadas para identificar especificidades e dificuldades do processo

A assimetria na relação entre família e escola pública

A relação entre família e escola vem sendo incentivada pelas políticas públicas, apontada como fundamental para uma escolarização bem sucedida. O atual estudo buscou compreender esta relação, tal como vem sendo vivenciada por pais de uma escola pública. Os participantes da pesquisa foram os agentes escolares e 22 responsáveis por alunos de 3ª e 4ª séries do ensino fundamental. Inicialmente foi realizada observação participante na escola e, em seguida, entrevistas semi-estruturadas com os responsáveis pelos alunos, em suas residências, tendo sido abordados três tópicos: a escola, a professora e a escolaridade. Buscou-se ainda resgatar a história das famílias, verificando as diferentes posturas dos pais diante da escola. Os dados foram analisados por meio de uma análise de conteúdo tradicional. Observou-se uma assimetria na relação família-escola, que parece contribuir para a perpetuação da dinâmica de exclusão de parte das camadas populares da escola pública.The incentive to the relationship between families and public school is a target of public politics, seen as something essential for an efficient learning. This research purpose was to investigate parents' experiences vis-à-vis their relationship with the school where their children study. The participants were school members and 22 students tutors attending the 3rd and 4th grades of elementary school. At first was done a participative observation within the school environment, after semi-structured interviews with the children tutors in their homes, focusing three aspects: the school, the teacher and the school education. The families' backgrounds were carefully taken into consideration, and parents showed different postures towards their relationships with their children schools. A traditional analytical approach was adopted to the data collected. As a result, this relationship was proved to be asymmetric, which seems to contribute to the maintenance of mechanisms of exclusion from public school over part of the underprivileged families

Evaluation of oxidative stability, fatty acid profile and quality physico-chemical parameters of Brazil nut, coconut and Palm oils

The aim of this study was to assess the oxidative stability (OS) of oils Brazil nuts, coconut and palm, as well as determine the quality parameters: acid value (AV), humidity, ash content, and fatty acid profile (FA). According to the results the oils of Brazil nuts, coconut and palm oil showed AV of 2.02, 2.49 and 5.92 mg KOH g-1, humidity of 0.060, 0.101 and 0.040% and ash of 0.010, 0.005 and 0.009%, respectively. Considering FA, the Brazil nut oil showed greater amount of linoleic acid (38.61%) and oleic acid (31.95%) in its composition. While in coconut oil the major amounts were lauric acid (35.22%) and myristic (17.43%) and in the palm oil, oleic acid (48.30%) and palmitic (28.67%). The OS analysis showed that there is a relationship between the FA chemical composition of each oil and oxidative stability index (OSI) that relates to the resilience capacity to lipid degradation