A recursive process related to a partisan variation of Wythoff

Wythoff Queens is a classical combinatorial game related to very interesting mathematical results. An amazing one is the fact that the P-positions are given by (⌊├ φn⌋┤┤,├ ├ ⌊φ┤^2 n⌋) and (⌊├ φ^2 n⌋┤┤,├ ├ ⌊φ┤n⌋) where φ=(1+√5)/2. In this paper, we analyze a different version where one player (Left) plays with a chess bishop and the other (Right) plays with a chess knight. The new game (call it Chessfights) lacks a Beatty sequence structure in the P-positions as in Wythoff Queens. However, it is possible to formulate and prove some general results of a general recursive law which is a particular case of a Partizan Subtraction game.

Percolation of colloids with distinct interaction sites

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.

Écriture, stéréotypes et créativité

Notre objectif consiste à interroger les effets de dispositifs d’enseignement apprentissage de l’écriture narrative, en prenant pour analyseur l’usage du stéréotype par des élèves de la fin de l’école élémentaire. Le stéréotype, considéré comme le lieu commun de l’expression (Dufays & Kervin, 2010) est potentiellement générateur de ressources (Marin & Crinon, 2014, à paraître) par les contraintes mêmes qu’il induit (Plane, 2006). En prise sur l’appréhension des critères de genre, la reconnaissance des stéréotypes renvoie à une forme particulièrement discriminante de capital symbolique (Tardy et Swales, 2008) dont il convient d’envisager les effets sur la régulation des inégalités entre élèves (Rochex & Crinon, 2011). Nous présentons en complémentarité deux recherches, dans lesquelles les élèves bénéficient de ressources de nature différente : l’aide apportée y assumant pour la première le statut d’outil technique (Crinon, Legros & Marin, 2002-2003), alors qu’elle relève pour la seconde d’un instrument psychologique (Marin, 2011). Les résultats de ces recherches montrent comment la focalisation sur les critères de genre constitue une ressource utile aux élèves, la seconde mettant en exergue le rôle des tuteurs dans la critique des textes de leurs pairs et son effet récursif sur la conscientisation des invariants génériques du texte de fiction.

Biomass production of four Cynara cardunculus clones and lignin composition analysis

Four Cynara cardunculus clones, two from Portugal and two from Spain were studied for biomass production and their lignin was characterized. The clones differed in biomass partitioning: Spanish clones produced more capitula (54.5% vs. 43.9%), and Portuguese clones more stalks (37.2% vs. 25.6%). The heating values (HHV0) of the stalks were similar, ranging from 17.1 to 18.4 MJ/kg. Lignin was studied by analytical pyrolysis (Py-GC/MS(FID)), separately in depithed stalks (stalksDP) and pith. StalksDP had in average higher relative proportions of lignin derived compounds than pith (23.9% vs. 21.8%) with slightly different lignin monomeric composition: pith samples were richer in syringyl units as compared to stalksDP (64% vs. 53%), with S/G ratios of 2.1 and 1.3, respectively. The H:G:S composition was 7:40:53 in stalksDP and 7:29:64 in pith. The lignin content ranged from 18.8% to 25.5%, enabling a differentiation between clones and provenances. © 2015 Elsevier Ltd. All rights reserved.