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Research has highlighted the potential of technology to transform the teaching of Mathematics, but also the relevance of teachers and their professional knowledge. In this article, a qualitative methodology is adopted and two episodes of the practice of one teacher are analyzed in the scope of the study of functions in the 10th grade, based on the model of Knowledge for Teaching Mathematics with Technology (KTMT). The goal is to characterize the teacher's knowledge from her practice, simultaneously understanding how this contributes to promoting the development of the teacher's knowledge. The conclusions reached show the importance of including in the KTMT conception aspects highlighted by the research on technology integration. These aspects are determinant to characterize the teacher's knowledge. They also show the relevance of the practice for the development of the teacher's knowledge and the dynamic character of the vision of knowledge offered by KTMT.

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A new plesiosaur partial skeleton, comprising most of the trunk and including axial, limb, and girdle bones, was collected in the lower Sinemurian (Coimbra Formation) of Praia da Concha, near São Pedro de Moel in central west Portugal. The specimen represents a new genus and species, Plesiopharos moelensis gen. et sp. nov. Phylogenetic analysis places this taxon at the base of Plesiosauroidea. Its position is based on this exclusive combination of characters: presence of a straight preaxial margin of the radius; transverse processes of mid-dorsal vertebrae horizontally oriented; ilium with sub-circular cross section of the shaft and subequal anteroposterior expansion of the dorsal blade; straight proximal end of the humerus; and ventral surface of the humerus with an anteroposteriorly long shallow groove between the epipodial facets. In addition, the new taxon has the following autapomorphies: iliac blade with less expanded, rounded and convex anterior flank; highly developed ischial facet of the ilium; apex of the neural spine of the first pectoral vertebra inclined posterodorsally with a small rounded tip. This taxon represents the most complete and the oldest plesiosaur species in the Iberian Peninsula. It is also the most complete, best preserved, and oldest marine vertebrate in the region and testifies to the incursion of marine reptiles in the newly formed proto-Atlantic sea, prior to the Atlantic Ocean floor spreading in the Early Cretaceous.

The Kap Stewart Group (Rhaetian-Sinemurian, Triassic–Early Jurassic) of the Jameson Land Basin in central East Greenland has traditionally been regarded as a strictly continental unit with delta and perennial lake sediments. New finds of plesiosaur bone remain in a thin storm deposited sandstone bed in the middle part of the Rhætelv Formation of the Kap Stewart Group, however, indicates a likely period of marine influence. At the study area at the eastern margin of the basin, the Rhætelv Formation is 300-m thick and overlies unconformably the Norian Fleming Fjord Group. The bone-bearing sandstone occurs 190 m above the base of the group and is closely associated with black laminated mudstones; palynological investigation of three samples from these mudstones indicates that they are of a younger Hettangian age. The Hettangian was a relatively short stage (201.3–199.5 Ma) and elsewhere characterized by two episodes of sea-level highstands. Assuming that the marine incursion in the Jameson land Basin evidenced by the plesiosaur fossil remains took place during the youngest of these sea-level highstands, the bone-bearing bed of the Rhætelv Formation can be dated to 200 Ma and thereby gives the first numerical age constraint of this hitherto poorly dated succession.

We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.

We propose and study a simple model for microcredit using two sums, with a random number of terms, of identically distributed random variables, the number of terms being Poisson distributed; the first sum accounts for the payments { the payables{ made to the collective vault by the participants and the second sum, subtracted to the first, accounts for the loans received by the participants, the receivables.
Under a global independence hypothesis we define, by mean of moment generating functions, an easily
implementable condition for the sustainability of the collective vault. That is, if, for all the participants and at any time, on average, the sum of the loans is strictly less than the sum of the payments to the collective vault then the probability of the collective vault failing can be made arbitrarily small, provided the loans only start to be accepted after a sufficiently large delay. We present numerical illustrations of collective vaults for exponential and chi-squared distributed random terms. For the practical management of such a collective vault it may be advisable to have loan granting rules that destroy independence of the random terms. We present a first simulation study that shows the effect of such a breaking dependence loan granting rule on maintaining the stability of the collective vault.

In this paper we introduce the notion of an orientation-preserving transformation on an arbitrary chain, as
a natural extension for infinite chains of the well known concept for finite chains introduced in 1998 by McAlister and, independently, in 1999 by Catarino and Higgins.
We consider the monoid POP(X) of all orientation-preserving partial transformations on a finite or infinite chain X and its submonoids OP(X) and POPI(X) of all orientation-preserving full transformations and of all orientation-preserving partial permutations on X, respectively.
The monoid PO(X) of all order-preserving partial transformations on X and its injective counterpart POI(X) are also considered.
We study the regularity and give descriptions of the Green's relations of the monoids POP(X), PO(X), OP(X), POPI(X) and POI(X).

We formulate an optimization stochastic algorithm convergence theorem, of Solis and Wets type, and we show several instances of its application to concrete algorithms. In this convergence theorem the algorithm is a sequence of random variables and, in order to describe the increasing flow of information associated to this sequence we define a filtration – or flow of σ -algebras – on the probability space, depending on the sequence of random variables and on the function being optimized. We compare the flow of information of two convergent algorithms by comparing the associated filtrations by means of the Cotter distance of σ-algebras. The main result is that two convergent optimization algorithms have the same information content if both their limit minimization functions generate the full σ-algebra of the probability space.

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Studying the dynamics of deposits is important for three reasons: first, it serves as an important component of liquidity stress testing; second, it is crucial to asset-liability management exercises and the allocation between liquid and illiquid assets; third, it is the support for a liquidity at risk (LaR) methodology.

Current models are based on AR(1) processes that often underestimate liquidity risk. Thus a bank relying on those models may face failure in an event of crisis. We propose a novel approach for modeling deposits, using panel data and a momentum term.

The model enables the simulation of a variety of deposit trajectories, including episodes of financial distress, showing much higher drawdowns and realistic liquidity at risk estimates, as well as density plots that present a wide range of possible values, corresponding to booms and financial crises.

Therefore, this methodology is more suitable for liquidity management at banks, as well as for conducting liquidity stress tests.

In this paper, we study partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of the monoids IEnd(P_n) and PAut(P_n) of all injective partial endomorphisms and of all partial automorphisms of the undirected path P_n with n vertices. We also describe Green's relations of PAut(P_n) and IEnd(P_n) and calculate their cardinals.

A large, well-preserved vertebrate coprolite was found in a lacustrine sediment in the Malmros Klint Formation of the Late Triassic Fleming Fjord Group in the Jameson Land Basin, central East Greenland. The size and internal and external morphology of the coprolite is consistent with that of crocodilian coprolites and one end of the coprolite exhibits evidence of post-egestion trampling. As the associated vertebrate fauna of the Fleming Fjord Group contains abundant remains of pseudosuchian phytosaurs, the coprolite is interpreted as being from a large phytosaur.