A classification, up to hyperbolicity, of groups given by 2 generators and one relator of length 8

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

Social polarization: introducing distances between and within groups

The measurement of social polarization has received little attention from the literature. The only social polarization index that has been used to measure religious or ethnic polarization (the RQ index) has several shortcomings that are critically discussed in the paper. In particular, that index is not taking into account the existing distance between and within different groups. A couple of axiomatically characterized social polarization indices that overcome these limitations are presented. In the empirical section we show that the rankings of countries according to the levels of polarization change to a great extent when we replace the RQ index by the indices presented in this paper.

The Core ideas and axioms of classical fascism (1919-1945)

This article presents and explores the axioms and core ideas, or idées-force, of the Fascist ideologies of the first third of the twentieth century. The aim is to identify the features that define the term “Classical Fascism” as a conceptual category in the study of politics and to uncover the core ideas of its political theory. This analysis requires an appraisal of both the idées-force themselves and the political use that is made of them. If these appreciations are correct, Classical Fascism is characterized by a set of ideological and political aims and methods in which ideas, attitudes and behaviours are determined by an anti-democratic palingenetic ultranationalism underpinned by a sacralized ideology; the quest for a united, indissoluble society as apolitical system and, at the same time, the collective myth that mobilizes and redeems the nation; and third, violence as a political vehicle applied unchecked against internal opposition and against external enemies who challenge the nation´s progression towards the dream of rebirth and the culmination of this progression in the form of an empire.

Musical actions of dihedral groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor triads. We illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

On uniform conjugators in torsion-free hyperbolic groups

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

Structure theorems for subgroups of homeomorphism groups

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

Bounding the residual finiteness of free groups

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

Higher arithmetic Chow groups

We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.

Twisted conjugacy in braid groups

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

Merging the hypothetical extraction method and the classical multiplier approach: a hybrid possibility for identifying key distributive sectors

The two main alternative methods used to identify key sectors within the input-output approach, the Classical Multiplier method (CMM) and the Hypothetical Extraction method (HEM), are formally and empirically compared in this paper. Our findings indicate that the main distinction between the two approaches stems from the role of the internal effects. These internal effects are quantified under the CMM while under the HEM only external impacts are considered. In our comparison, we find, however that CMM backward measures are more influenced by within-block effects than the proposed forward indices under this approach. The conclusions of this comparison allow us to develop a hybrid proposal that combines these two existing approaches. This hybrid model has the advantage of making it possible to distinguish and disaggregate external effects from those that a purely internal. This proposal has also an additional interest in terms of policy implications. Indeed, the hybrid approach may provide useful information for the design of ''second best'' stimulus policies that aim at a more balanced perspective between overall economy-wide impacts and their sectoral distribution.

Educational innovation in large groups. Design of an experimental study implemented at the Polytechnic University of Madrid

The present paper shows de design of an experimental study conducted with large groups using educational innovation methodologies at the Polytechnic University of Madrid. Concretely, we have chosen the course titled "History and Politics of Sports" that belongs to the Physical Activity and Sport Science Degree. The selection of this course is because the syllabus is basically theoretical and there are four large groups of freshmen students who do not have previous experiences in a teaching-learning process based on educational innovation. It is hope that the results of this research can be extrapolated to other courses with similar characteristics.

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies