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We give a combinatorial characterization of conjugacy in the sylvester monoid, showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids.

Theropod teeth are particularly abundant in the fossil record and frequently reported in the literature. Yet, the dentition of many theropods has not been described comprehensively, omitting details on the denticle shape, crown ornamentation and enamel texture. This paucity of information has been particularly striking in basal clades, thus making identification of isolated teeth difficult, and taxonomic assignments uncertain. We here provide a detailed description of the dentition of Megalosauridae, and a comparison to and distinction from superficially similar teeth of all major theropod clades. Megalosaurid dinosaurs are characterized by a mesial carina facing mesiolabially in most mesial teeth, centrally positioned carinae on both most mesial and lateral crowns, a mesial carina terminating above the cervix, and short to well-developed interdenticular sulci between distal denticles. A discriminant analysis performed on a dataset of numerical data collected on the teeth of 62 theropod taxa reveals that megalosaurid teeth are hardly distinguishable from other theropod clades with ziphodont dentition. This study highlights the importance of detailing anatomical descriptions and providing additional morphometric data on teeth with the purpose of helping to identify isolated theropod teeth in the future.

Neste texto apresentamos os jogos no ensino da matemática como uma forma de aprendizagem de conteúdos e não apenas como um recurso que cada professor pode usar nas suas aulas para tornar a aula diferente. Analisamos dois jogos desenvolvidos por nós e que utilizámos com alunos dos 7.º e 10.º anos de escolaridade, procurando não só apresentar os jogos, mas também aspetos da sua implementação em sala de aula, ponderando o contributo que trouxeram à aprendizagem dos alunos.
Aprender matemática depende de um grande número de variáveis, o que torna o ensino um processo complexo, pois é necessário que se desenvolva o raciocínio lógico, além de estimular o desenvolvimento das mais variadas capacidades transversais, tais como o pensamento autónomo, a criatividade, o sentido de estratégia e a capacidade de resolver problemas.
Duas das dificuldades frequentemente encontradas pelos professores passam pela falta de motivação para a aprendizagem e pelo desinteresse pela Matemática. A solução para estes problemas pode passar pela utilização de jogos para complementar o estudo, mas também para a aquisição de novos conteúdos. No entanto, apenas a implementação dos jogos não basta. O papel do professor é de extrema importância e a planificação e orientação da aula são fundamentais para que se alcancem os objetivos pretendidos.

Multi-threaded programs allow one to achieve better performance by doing a lot of work in parallel using multiple threads. Such parallel programs often contain code blocks that a thread must execute atomically, i.e., with no interference from the other threads of the program. Failing to execute these code blocks atomically leads to errors known as atomicity violations. However, frequently it not obvious to tell when a piece of code should be executed atomically, especially when that piece of code contains calls to some third-party library functions, about which the programmer has little or no knowledge at all. One solution to this problem is to associate a contract with such a library, telling the programmer how the library functions should be used, and then check whether the contract is indeed respected. For contract validation, static approaches have been proposed, with known limitations on precision and scalability. In this paper, we propose a dynamic method for contract validation, which is more precise and scalable than static approaches.

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This paper shows that every Plactic algebra of finite rank admits a finite Gröbner--Shirshov basis. The result is proved by using the combinatorial properties of Young tableaux to construct a finite complete rewriting system for the corresponding Plactic monoid, which also yields the corollaries that Plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right $\mathrm{FP}_\infty$. Also, answering a question of Zelmanov, we apply this rewriting system and other techniques to show that Plactic monoids of finite rank are biautomatic.

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Abstract Direct identification of cohesive laws in modes I and İI\} of wood bonded joints is addressed by the double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively. Moreover, the development and extension of fracture process zone (FPZ) ahead of the initial crack tip, is analysed by means of digital image correlation (DIC) and embedded fibre Bragg grating (FBG) sensors. From \{FBG\} spectral response, the spectrum geometric mean is determined and the strain induced by wavelength variation employed to identify the initial and final stages of the FPZ. These stages are used to consistently define the cohesive laws in both modes I and II. Resistance-curves are determined from the compliance-based beam method (CBBM). Besides, the crack tip opening displacements (CTOD) are determined by post-processing displacement field provided by \{DIC\} around the initial crack tip. The strain energy release rate as a function of the \{CTOD\} are then determined for both mode I and mode II. The respective cohesive laws are reconstructed by numerical approximation and differentiation. It is concluded that the proposed data reduction scheme is effective to determine both the \{FPZ\} development phase and the corresponding cohesive laws of wood bonded joints in both mode I and mode II.

The Bench 19 Bonebed at Bentiaba, Angola, is a unique concentration of marine vertebrates preserving six species of mosasaurs in sediments best correlated by magnetostratigraphy to chron C32n.1n between 71.4 and 71.64 Ma. The bonebed formed at a paleolatitude near 24°S, with an Atlantic width at that latitude approximating 2700 km, roughly half that of the current width. The locality lies on an uncharacteristically narrow continental shelf near transform faults that controlled the coastal outline of Africa in the formation of the South Atlantic Ocean. Biostratigraphic change through the Bentiaba section indicates that the accumulation occurred in an ecological time dimension within the 240 ky bin delimited by chron 32n.1n. The fauna occurs in a 10 m sand unit in the Mocuio Formation with bones and partial skeletons concentrated in, but not limited to, the basal 1–2 m. The sediment entombing the fossils is an immature feldspathic sand shown by detrital zircon ages to be derived from nearby granitic shield rocks. Specimens do not appear to have a strong preferred orientation and they are not concentrated in a strand line. Stable oxygen isotope analysis of associated bivalve shells indicates a water temperature of 18.5°C. The bonebed is clearly mixed with scattered dinosaur and pterosaur elements in a marine assemblage. Gut contents, scavenging marks and associated shed shark teeth in the Bench 19 Fauna indicate biological association and attrition due to feeding activities. The ecological diversity of mosasaur species is shown by tooth and body-size disparity and by δ13C analysis of tooth enamel, which indicate a variety of foraging areas and dietary niches. The Bench 19 Fauna was formed in arid latitudes along a coastal desert similar to that of modern Namibia on a narrow, tectonically controlled continental shelf, in shallow waters below wave base. The area was used as a foraging ground for diverse species, including molluscivorus Globidens phosphaticus, small species expected near the coast, abundant Prognathodon kianda, which fed on other mosasaurs at Bench 19, and species that may have been transient and opportunistic feeders in the area.