n/a

We report a new chelonioid turtle on the basis of a nearly complete skull collected in lower Paleocene, shallow marine deposits, equivalent to the offshore Landana Formation, near the town of Landana in Cabinda Province, Angola. Chelonioid material previously reported from this locality is likely referable to this new taxon. The well-preserved skull is missing the left quadrate, squamosal, and prootic, both opisthotics, and the mandible. The skull possesses a rod-like basisphenoid rostrum, which is a synapomorphy of Chelonioidea, but it differs from other chelonioid skulls in that the contact between the parietal and squamosal is absent, and the posterior palatine foramen is present. Phylogenetic analysis recovers the new taxon as a basal chelonioid. The Paleocene– Eocene strata near Landana have produced a wealth of turtle fossils, including the holotype of the pleurodire Taphrosphys congolensis. A turtle humerus collected from the Landana locality differs morphologically from the humeri of chelonioids and Taphrosphys, indicating the presence of a third taxon. Chelonioid fossil material in the Landana assemblage is rare compared to the abundant fragmentary remains of Taphrosphys that are found throughout the stratigraphic section. This disparity in abundance suggests the new chelonioid taxon preferred open marine habitats, whereas Taphrosphys frequented nearshore environments.

In this note we consider the monoid $PODI_n$ of all monotone partial permutations on $\{1,\ldots,n\}$ and its submonoids $DP_n$, $POI_n$ and $ODP_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $POI_n$ and $ODP_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $PODI_n$ is a quotient of a semidirect product of $POI_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $DP_n$ is a quotient of a semidirect product of $ODP_n$ and $\mathcal{C}_2$.

Games are commonly appointed as a methodological tool capable of promoting students’ effective learning. In this context, this study intends to analyze the impact of mathematical discussions developed while
playing a polynomial game. Namely it intends to analyze the impact on the consolidation of mathematical concepts previously worked in the classroom and on the communications skills. Two case studies where developed involving 10th grade students. Data gathering was based on direct observation and an inquiry. The main conclusions suggest that the game encouraged the discussion about the mathematical contents and therefore promoted the development of the mathematical discourse. Besides that, it allowed a deeper apprehension of mathematical concepts, and the overcome of some difficulties.

Deductive reasoning, being central in mathematics, is also usually a source of difficulties for students, more used to the empirical approaches. In this study we focus on mathematical proof and we try to give attention to how this kind of reasoning is envisaged by the students, to the options they assume when asked to develop a deductive reasoning and to the factors affecting the implementation of this kind of reasoning. The study follows a qualitative and interpretative methodological approach, including the completion of two case studies of students of the 10th grade. Data were collected in work sessions and through interviews. The main findings point to a devaluation of mathematical proof and a strong preference for empirical approaches. Yet students show ability to develop different approaches. The preference for the mathematical subject and the attention given in class to the deduction work, appears to be relevant factors when considering the students' ability to develop a deductive reasoning when involved on a mathematical proof.

The design of timber beams has strict limits when it comes to the Serviceability Limit States (SLS) either in short-term or in long-term deflections. In order to face this aspect efficiently, the increase of the cross section of the beams might be considered as a solution. However, the prohibitive increase of the costs associated to this solution or the change of the initial architecturedesign of the building, opens the opportunity to find new and more efficient solutions. In that way, the use of additional reinforcements to the timber beams may be seen as a promising solution because either new or old structures would keep always their original aesthetical aspect with no significant self-weight increase and improving their behaviour to short and long-term actions.Therefore, the current study is dedicated to the analysis of composite timber beams where Fiber Reinforcement Polymers (FRP), steel or stainless steel are used to improve the stiffness, strength and deflection behaviour of old suspended timber floors. An experimental program was conducted where old suspended timber floors reinforced with CFRP strips were subjected to 4-point bending tests. A simplify nonlinear numerical model was developed to simulate the bending behaviour of the specimens and several other cases with other reinforcement configurations and different structural materials were assumed. The numerical analysis herein presented also takes into account both Ultimate and Serviceability Limit States of the reinforced specimens.

Let \(\alpha,\beta\) be orientation-preserving diffeomorphism (shifts) of \(\mathbb{R}_+=(0,\infty)\) onto itself with the only fixed points \(0\) and \(\infty\) and \(U_\alpha,U_\beta\) be the isometric shift operators on \(L^p(\mathbb{R}_+)\) given by \(U_\alpha f=(\alpha')^{1/p}(f\circ\alpha)\), \(U_\beta f=(\beta')^{1/p}(f\circ\beta)\), and \(P_2^\pm=(I\pm S_2)/2\) where \[ (S_2 f)(t):=\frac{1}{\pi i}\int\limits_0^\infty \left(\frac{t}{\tau}\right)^{1/2-1/p}\frac{f(\tau)}{\tau-t}\,d\tau, \quad t\in\mathbb{R}_+, \]
is the weighted Cauchy singular integral operator. We prove that if \(\alpha',\beta'\) and \(c,d\) are continuous on \(\mathbb{R}_+\) and slowly oscillating at \(0\) and \(\ infty\), and \[ \limsup_{t\to s}|c(t)|<1,\quad \limsup_{t\to s}|d(t)|<1, \quad s\in\{0,\infty\}, \] then the operator \((I-cU_\alpha)P_2^++(I-dU_\beta)P_2^-\) is Fredholm on \(L^p(\mathbb{R}_+)\) and its index is equal to zero. Moreover, its regularizers are described.

Let $X_n$ be a chain with n elements ($n\in\N$) and let $\OP_n$ be the monoid of all orientation-preserving transformations of $X_n$. In this paper, for any nonempty subset $Y$ of $X_n$, we consider the subsemigroup $\OP_n(Y)$ of $\OP_n$ of all transformations with range contained in $Y$: we describe the largest regular subsemigroup of $\OP_n(Y)$, which actually coincides with its subset of all regular elements, and Green's relations on $\OP_n(Y)$. Also, we determine when two semigroups of the type $\OP_n(Y)$ are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid $\OR_n$ of all either orientation-preserving or orientation-reversing transformations of $X_n$.