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.

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.

This paper presents part of a study that aimed to make more explicit the pragmatic theories that inform the design of professional development programs with an emphasis on the integration of digital technologies in the practices of mathematics teachers. The analysis carried out was based on a set of projects considered representative and implemented in four countries – Colombia, Italy, Mexico and Portugal. Based on this analysis, we identify relevant elements (e.g., similarities and differences, barriers and opportunities) and develop recommendations to be taken into account in the design of future professional development programs. In this process, we identified a set of aspects and sub-aspects, as well as several interconnections between them, which emerged in relation to five main themes and allowed us to reveal our pragmatic theories. Thus, this work provides a framework to support the design of future projects for the professional development of mathematics teachers regarding the use of digital technology.

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This chapter aims to make more explicit the grounded or ‘pragmatic theories’ that inform the design of mathematics teachers’ professional development (PD) to exploit technological affordances. It uses aspects of some representative projects that took place in four countries (Colombia, Italy, Mexico, and Portugal) to illustrate lessons learned (e.g., similarities and differences, barriers and opportunities) and provide important insights to inform future PD implementations. To do this, we have identified a set of aspects (and sub-aspects) that emerged in relation to five major themes and reveal our ‘pragmatic theories’ alongside a consideration of the interconnections between these aspects. Our contribution offers a methodological frame to support future PD designs for teachers of mathematics concerning digital technology uses.

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In this work, we present a novel application of the full-field energy-dispersive X-ray fluorescence (EDXRF) imaging system based on a MicroPattern Gaseous Detector (2D-THCOBRA) in the cultural heritage field. The detector has an intrinsic imaging capability with spatial resolution of 400μmFWHM, and is energy sensitive, presenting an energy resolution of approximately 1keVFWHM at 5.9keV. The full-field XRF scanner based on the 2D-THCOBRA detector allows mapping the distribution of elements in large area samples with high detection efficiency (75 % at 5.9keV), being a very promising choice for elemental mapping analysis of large area cultural heritage samples. In this work, we have demonstrated the imaging capabilities of the full-field XRF scanner and used it to assess the restoration of a Portuguese faience piece.

After more than one hundred and thirty thousand protein structures determined by X-ray crystallography{,} the challenge of protein crystallization for 3D structure determination remains. In the quest for additives for efficient protein crystallization{,} inorganic materials emerge as an alternative. Magnetic particles (MPs) are versatile inorganic materials{,} easy to use{,} modify and manipulate in a wide range of biological assays. The potential of using functionalised MPs as crystallization chaperones for protein crystallization was shown in this work. MPs with distinct coatings were rationally designed to promote protein crystallization by affinity-triggered heterogeneous nucleation. Hen egg white lysozyme (HEWL) and trypsin{,} were crystallized in the presence of MPs either bare or coated with a polysaccharide (chitin) or a protein (casein){,} respectively. The addition of MPs was characterized in terms of bound protein to the MPs{,} crystal morphology{,} time-lapse of crystal emergence{,} crystallization yield fold change and crystal diffraction quality for structure determination. The MPs additives have shown to bind to the respective target protein{,} and to promote nucleation and crystal growth without compromising crystal morphology. On the other hand{,} MPs addition led to faster detectable crystal emergence and up to 13 times higher crystallization yield{,} addressing some the challenges in protein crystallization{,} the main bottleneck of macromolecular crystallography. Structure determination of the protein crystallized in the presence of MPs revealed that the structural characteristics of the protein remained unchanged{,} as shown by the superposition with PDB annotated proteins. Moreover{,} and unlike most reported cases{,} it was possible to exclude the inhibitor benzamidine during trypsin crystallisation{,} which is a remarkable result opening new prospects in enzyme engineering and drug design. Our results show that MPs coated with affinity ligands to target proteins can be used as controlled and tailor-made crystallization inducers.