The amniote eggshell functions as a respiratory structure adapted for the optimal transmission of respiratory gasses to and from the embryo according to its physiological requirements. Therefore amniotes with higher oxygen requirements, such as those that sustain higher metabolic rates, can be expected to have eggshells that can maintain a greater gas flux to and from the egg. Studies of extant amniotes have found that eggshells of reduced porosity impose a limit on the metabolic rate of the offspring. Here we show a highly significant relationship between metabolic rates and eggshell porosity in extant amniotes that predicts highly endothermic metabolic rates in dinosaurs. This study finds the eggshell porosity of extant endotherms to be significantly higher than that of extant ectotherms. Eggshell porosity values of dinosaurs are found to be significantly higherthan that of extant ectotherms, but not extant endotherms. Dinosaur eggshells are commonly preserved in the fossil record, and porosity may be readily identified and measured. This provides a simple tool to identify metabolic rates in extinct egg-laying tetrapods whose eggs possessed a mineralized shell

We present the δ13C and paleomagnetic stratigraphy for marine strata at the coast of southern Angola, anchored by an intercalated basalt with a whole rock 40Ar/39Ar radiometric age of 84.6 ± 1.5 Ma, being consistent with both invertebrate and vertebrate biostratigraphy. This is the first African stable carbon isotope record correlated to significant events in the global carbon cycle spanning the Late Cenomanian to Early Maastrichtian. A positive ∼ 3‰ excursion seen in bivalve shells below the basalt indicates the Cenomanian-Turonian Boundary Event at 93.9 Ma, during Oceanic Anoxic Event 2. Additional excursions above the basalt are correlated to patterns globally, including a negative ∼ 3‰ excursion near the top of the section interpreted as part of the Campanian-Maastrichtian Boundary Events. The age of the basalt ties the studied Bentiaba section to a pulse of Late Cretaceous magmatic activity around the South Atlantic and significant tectonic activity, including rotation, of the African continent.

Let \(p:\mathbb{R}\to(1,\infty)\) be a globally log-Hölder continuous variable exponent and \(w:\mathbb{R}\to[0,\infty]\) be a weight. We prove that the Cauchy singular integral operator \(S\) is bounded on the weighted variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R},w)=\{f:fw\in L^{p(\cdot)}(\mathbb{R})\}\) if and only if the weight \(w\) satisfies $$ \sup_{-\infty < a < b < \infty} \frac{1}{b-a} \|w\chi_{(a,b)}\|_{p(\cdot)} \|w^{-1}\chi_{(a,b)}\|_{p'(\cdot)}<\infty \quad (1/p(x)+1/p'(x)=1). $$

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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.