Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

On the intersection of free subgroups in free products of groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

"Vegeu el resum a l'inici del document del fitxer adjunt."

Large gypsum nodules in the Paleogene and Neogene evaporites of Spain: distribution and palaeogeographic significance

Sabkha and deep burial set tings are the most com mon sites where diagenetic anhydrite forms. In a sabkha setting, displacive facies (iso lated nodules, bed ded nodules, enterolithic levels) of early diagenetic or primary anhydrite are generated (Shearman, 1966; Hardie, 1967). These anhydrite facies are commonly foundat the top of shoal ing cycles representing the evolution from subaqueous depositional conditions at the base (carbonates, lutites) to exposure conditions at the top where in ter stitially-grown gypsum/anhydrite de velops ( sabkha cy cles). In a deep burial setting, gypsum transforms to tally to anhydrite with in creas ing temperature and lithostatic pressure (Murray, 1964). Al though this mineral transformation usually preserves the depositional gypsum facies, a significant textural change is in volved in other cases, resulting in replacive anhydrite with a nodular-mosaic or"chicken-wire" fabric (Warren, 2006). In the two settings, how ever, the size of the individual anhydrite nodules is relatively small, rarely reaching some tens of centimetres across. More over, bedding is preserved or little disturbed, al though minor de formation is caused by the displacive sabkha nodules.

Prehospital ticagrelor in ST-segment elevation myocardial infarction

Background:The direct-acting platelet P2Y receptor antagonist ticagrelor can reduce the incidence of major adverse cardiovascular events when administered at hospital admission to patients with ST-segment elevation myocardial infarction (STEMI). Whether prehospital administration of ticagrelor can improve coronary reperfusion and the clinical outcome is unknown. Methods: We conducted an international, multicenter, randomized, double-blind study involving 1862 patients with ongoing STEMI of less than 6 hours' duration, comparing prehospital (in the ambulance) versus in-hospital (in the catheterization laboratory) treatment with ticagrelor. The coprimary end points were the proportion of patients who did not have a 70% or greater resolution of ST-segment elevation before percutaneous coronary intervention (PCI) and the proportion of patients who did not have Thrombolysis in Myocardial Infarction flow grade 3 in the infarct-related artery at initial angiography. Secondary end points included the rates of major adverse cardiovascular events and definite stent thrombosis at 30 days. Results: The median time from randomization to angiography was 48 minutes, and the median time difference between the two treatment strategies was 31 minutes. The two coprimary end points did not differ significantly between the prehospital and in-hospital groups. The absence of ST-segment elevation resolution of 70% or greater after PCI (a secondary end point) was reported for 42.5% and 47.5% of the patients, respectively. The rates of major adverse cardiovascular events did not differ significantly between the two study groups. The rates of definite stent thrombosis were lower in the prehospital group than in the in-hospital group (0% vs. 0.8% in the first 24 hours; 0.2% vs. 1.2% at 30 days). Rates of major bleeding events were low and virtually identical in the two groups, regardless of the bleeding definition used