The mean dehn functions of Abelian groups

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Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Traverso's isogeny conjecture for p-divisible groups

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Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

Parametric analysis of different compact tension specimens for fracture toughness characterisation in woven composite materials

Estudi elaborat a partir d’una estada a l’ Imperial College London, entre juliol i novembre de 2006. En aquest treball s’ha investigat la geometria més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. L’objectiu és assegurar la propagació de l’esquerda sense que la proveta falli abans per cap altre mecanisme de dany per tal de permetre la caracterització experimental de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. Amb aquesta fi, s’ha dut a terme l’anàlisi paramètrica de diferents tipus de provetes mitjançant el mètode dels elements finits (FE) combinat amb la virtual crack closure technique (VCCT). Les geometries de les provetes analitzades corresponen a la proveta de l’assaig compact tension (CT) i diferents variacions com la extended compact tension (ECT), la proveta widened compact tension (WCT), tapered compact tension (TCT) i doubly-tapered compact tension (2TCT). Com a resultat d’aquestes anàlisis s’han derivat diferents conclusions per obtenir la geometria de proveta més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. A més, també s’han dut a terme una sèrie d’assaigs experimentals per tal de validar els resultats de les anàlisis paramètriques. La concordança trobada entre els resultats numèrics i experimentals és bona tot i la presència d’efectes no previstos durant els assaigs experimentals.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

Discriminating groups: a comprehensive overview

Discriminating groups were introduced by G.Baumslag, A.Myasnikov and V.Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. However they have taken on a life of their own and have been an object of a considerable amount of study. In this paper we survey the large array results concerning the class of discriminating groups that have been developed over the past decade.

The equation xpyq=zr and groups that act freely on Λ-trees

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Orbit decidability and the conjugacy problem for some extensions of groups

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Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Metric properties of the braided Thompson's groups

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On the intersection of free subgroups in free products of groups

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

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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.