Thyreophoran dinosaurs have spike- and club-shaped osteoderms probably used for defensive weapons. The structural and histological variations have been little known. Here, we provide the comparisons of the internal structures in defensive weapons of ankylosaurs and stegosaurs, using spikes of a polacanthid (Gastonia) and a nodosaurid (Edmontonia), clubs of ankylosaurids (Saichania and Ankylosauridae indet. from Canada), and spikes of stegosaurids (Stegosaurus and Dacentrurus), which sheds light on understandings of evolutionary history and functional implications of defensive weapons in thyreophorans. In ankylosaurs, the structural and histological features of spikes and clubs are similar with those of small osteoderms in having thin compact bones, thick cancellous bones with large vascular canals, and abundant collagen fibers. A previous study demonstrated that each of three groups of ankylosaurs (polacanthid, nodosaurid, and ankylosaurid) has distinct characteristic arrangements of collagen fibers in small osteoderms. This study shows that spikes and clubs of ankylosaurs maintain the same characteristic features for each group despite of the differences in shapes and sizes. Conversely, the spike-shaped osteoderms in primitive (Dacentrurus) and derived (Stegosaurus) stegosaurids have similar structure to each other and are significantly different from the other types of stegosaur osteoderms (throat bony ossicles and plates) in having thick compact bones with a medullary cavity. These lack abundant collagen fibers unlike ankylosaur osteoderms. The spikes of ankylosaurs and stegosaurs are similar in shape, but their structural and histological features are different in having unique structures of collagen fibers for ankylosaurs and thick compact bones for stegosaurs, providing enough strength to have large spikes and to use them as defensive weapons. Although the shapes of ankylosaur clubs are different from spikes, the internal structures are similar, suggesting that ankylosaurs maintain similar structures despite of different shapes in osteoderms. These results indicate that ankylosaurs and stegosaurs used different strategies independently to evolve defensive weapons.

An European directive established that all EU countries must have, until the end of 2006, a recovery network for the electric and electronic equipment waste (WEEE). In Portugal, a group of producers formed a non-profit organization to design and manage this waste now. In this work, a model developed previously by the authors to design and plan a generic WEEE network is presented and applied to the Portuguese case. The results obtained are discussed and compared with the network that is currently operating.

We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to Hölder-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refines previous asymptotic trace formulas by Szegő and Widom and complement higher order asymptotic formulas for determinants of finite block Toeplitz matrices due to Böttcher and Silbermann.

We prove higher-order asymptotic formulas for determinants and traces of finite block Toeplitz matrices generated by matrix functions belonging to generalized Hölder spaces with characteristic functions from the Bari-Stechkin class. We follow the approach of Böttcher and Silbermann and generalize their results for symbols in standard Hölder spaces.

n/a

n/a

In this work, the design of supply chains with reverse flows is studied in a multi-objective context. A MILP model is developed for the optimization of the supply chain structures where both environmental impacts and costs are considered. An optimal Pareto front is obtained that plays an important role in evaluating the best locations of all the entities in the supply chain while accounting for the global supply chain environmental impacts. A study based on a Portuguese glass industry is presented to corroborate both the applicability and the adequacy of the model.

n/a

n/a