This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of tableaux, we present Robinson--Schensted--Knuth-type correspondences (that is, bijective correspondences between word arrays and certain pairs of semistandard tableaux of the same shape), generalizing two known correspondences: a bijective correspondence between standard words and certain pairs of standard tableaux, and an injective correspondence between words and pairs of tableaux.

We also exhibit formulas to count both the number of each type of tableaux with given evaluations (that is, containing a given number of each symbol). Observing that for any natural number $n$, the $n$-th Bell number is given by the number of standard tableaux containing $n$ symbols, we restrict the previous formulas to standard words and extract a formula for the Bell numbers. Finally, we present a `hook length formula' that gives the number of standard tableaux of a given shape and deduce some consequences.

In this paper we characterize the monoids of endomorphisms of the semigroups PO_n and POI_n of all order-preserving partial transformations and of all order-preserving partial permutations, respectively, of a finite n-chain.

This chapter provides an overview of the alpha paleobiodiversity of Angola based on the available fossil record that is limited to the sedimentary rocks, ranging in age from Precambrian to the present. The geological period with the highest paleobiodiversity in the Angolan fossil record is the Cretaceous, with more than 80{%} of the total known fossil taxa, especially marine molluscs, including ammonites as a majority among them. The vertebrates represent about 15{%} of the known fauna and about one tenth of them are species firstly described based on specimens from Angola.

Late Jurassic theropod tracks are very common both in North Africa and Europe. Two recently described ichnotaxa Megalosauripus transjuranicus and Jurabrontes curtedulensis from the Kimmeridgian of Switzerland show the coexistence of two apex predators in the same palaeoenvironment. Similar tracks can be found in tracksites from the Iberian Peninsula and from Morocco. Here, we further explore the similarities among the Swiss ichnotaxa and the other tracks from Germany (Kimmeridgian), Spain (Tithonian-Berriasian), Portugal (Oxfordian-Tithonian) and Morocco (Kimmeridgian) through novel three-dimensional data comparisons. Specimens were grouped in two morphotypes: 1) large and gracile (30 < Foot Length<50 cm) and 2) giant and robust (FL > 50 cm). The analyses show a great morphological overlap among these two morphotypes and the Swiss ichnotaxa (Megalosauripus transjuranicus and Jurabrontes curtedulensis, respectively), even despite the differences in sedimentary environment and age. This suggests a widespread occurrence of similar ichnotaxa along the western margin of Tethys during the Late Jurassic. The new data support the hypothesis of a Gondwana-Laurasia faunal exchange during the Middle or early Late Jurassic, and the presence of migratory routes around the Tethys.

The left patience sorting (lPS) monoid, also known in the literature as the Bell monoid, and the right patient sorting (rPS) monoid are introduced by defining certain congruences on words. Such congruences are constructed using insertion algorithms based on the concept of decreasing subsequences.
Presentations for these monoids are given.

Each finite-rank rPS monoid is shown to have polynomial growth and to satisfy a non-trivial identity (dependent on its rank), while the infinite rank rPS monoid does not satisfy a non-trivial identity. The lPS monoids of finite rank have exponential growth and thus do not satisfy non-trivial identities. The
complexity of the insertion algorithms is discussed.

rPS monoids of finite rank are shown to be automatic and to have recursive complete presentations. When the rank is $1$ or $2$, they are also biautomatic. lPS monoids of finite rank are shown to have finite complete presentations and to be biautomatic.

Este capítulo apresenta uma visão geral da paleobiodiversidade alfa de Angola com base no registo fóssil disponível, o qual se limita às rochas sedimentares, a sua idade variando entre o Pré‑Câmbrico e o pre‑
sente. O período geológico com a maior paleobiodiversidade no registo fóssil angolano é o Cretácico, com mais de 80% do total dos táxones fósseis conhecidos, especialmente moluscos marinhos, sendo estes na sua maioria
amonites. Os vertebrados representam cerca de 15% da fauna conhecida e cerca de um décimo destes são espécies descritas pela primeira vez com base em espécimes de Angola.

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The degradation mechanisms of bonded joints between CFRP laminates and steel substrates under severe environmental conditions require more durability data and studies to increase the database and better understand their causes. Studies on bond properties of double-strap CFRP-to-steel bonded joints with two different composite materials as well as adhesive coupons subjected to freeze-thaw cycles for 10,000 h were conducted to reduce that gap. In addition, the equivalent to the number of thermal cycles and their slips induced in the CFRP laminates was replicated by an equivalent (mechanical) loading-unloading history condition imposed by a static tensile machine. The mechanical properties of the adhesive coupons and the strength capacity of the bonded joints were only slightly changed by the artificial aging. It was confirmed that the interfacial bond strength between CFRP and adhesive is critically related to the maximum shear stress and failure mode. The interfacial bond strength between adhesive and steel degraded with the aging. However, the equivalent thermal cyclic bond stress caused no detectable damage on the bond because only the interfacial elastic regime was actually mobilized, which confirmed that pure thermal cycles aging, per se, at the level imposed, have a low impact on the degradation of CFRP-to-steel bonded joints. © 2019 Elsevier Ltd

We report on measurements of the Kβ diagram, valence-to-core (VtC), and hypersatellite X-ray spectra induced in metallic Cr by photon single and double K-shell ionization. The experiment was carried out at the Stanford Synchrotron Radiation Lightsource using the seven-crystal Johann-type hard X-ray spectrometer of the beamline 6-2. For the Kβ diagram and VtC transitions, the present study confirms the line shape features observed in previous works, whereas the K h β hypersatellite transition was found to exhibit a complex spectral line shape and a characteristic low-energy shoulder. The energy shift of the hypersatellite relative to the parent diagram line was deduced from the measurements and compared with the result of extensive multiconfiguration Dirac–Fock (MCDF) calculations. A very good agreement between experiment and theory was found. The MCDF calculations were also used to compute the theoretical line shape of the hypersatellite. A satisfactory agreement was obtained between the overall shapes of the experimental and theoretical spectra, but deviations were observed on the low- and high-energy flanks of the hypersatellite line. The discrepancies were explained by chemical effects, which were not considered in the MCDF calculations performed for isolated atoms.