Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Polarization, fractionalization and conflict

A recent upsurge of empirical studies on the causes of conflict attempts to connect various features of the distribution of the relevant characteristic (typically ethnicity or religion) to conflict. The distributional indices differ (polarization, fractionalization or Lorenz-domination) and so do the various specifications of "conflict" (onset, incidence or intensity). Overall, the results are far from clear, and combined with the mixture of alternative indices and notions of "conflict" it is not surprising that the reader may come away thoroughly perplexed. The aim of this paper is to provide a theoretical framework that permits us to distinguish between the occurrence of conflict and its severity and that clarifies the role of polarization and fractionalization in each of these cases.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

The Measurement of social polarization in a multi-group context

Polarization indices presented up to now have only focused their attention on the distribution of income/wealth. However, in many circumstances income is not the only relevant dimension that might be the cause of social conflict, so it is very important to have a social polarization index able to cope with alternative dimensions. In this paper we present an axiomatic characterization of one of such indices: it has been obtained as an extension of the (income) polarization measure introduced in Duclos, Esteban and Ray (2004) to a wider domain. It turns out that the axiomatic structure introduced in that paper alone is not appropriate to obtain a fully satisfactory characterization of our measure, so additional axioms are proposed. As a byproduct, we present an alternative axiomatization of the aforementioned income polarization measure.

Metric properties of the braided Thompson's groups

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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.

Link between microstructure and properties in new metallurgical concepts for very low loss non-oriented electrical steel

The influence of chemistry and soaking temperature (maximal temperature of the continuous annealing) on the final properties of non-oriented electrical steels has been studied. With this objective two different studies have been performed. First the Mn, Ni and Cr content of a low loss electrical steel composition has been modified. An intermediate content and a high content of each element has been added in order to study the influence of this components on the magnetic looses, grain size and texture. Secondly the influence of the soaking temperature on magnetic properties, grain size and oxidation in four grades of non-oriented electrical steels (Steel A, B, C and D) was studied.

Portal web inmobiliario Luxury Properties con posicionamiento SEO

Este documento explica la metodología de trabajo utilizada durante el desarrollo de este proyecto. El resultado obtenido ha sido un producto que forma parte del portal web Luxury Porperties. Luxury Properties es una marca comercial, creada por la compañía Luxury Dreams, para identificar un portal web especializado en las propiedades de lujo. Para desarrollar este concepto, la empresa compró el dominio luxuryproperties.es con el objetivo de crear un sistema que implemente toda la lógica de negocio necesaria para la publicidad y mercadeo de sus productos. Al final del documento se encuentran las recomendaciones y las futuras valoraciones a tener en cuenta por el cliente en futuras ampliaciones del portal.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Leading indicator properties of US high-yield credit spreads

In this paper we examine the out-of-sample forecast performance of high-yield credit spreads regarding real-time and revised data on employment and industrial production in the US. We evaluate models using both a point forecast and a probability forecast exercise. Our main findings suggest the use of few factors obtained by pooling information from a number of sector-specific high-yield credit spreads. This can be justified by observing that, especially for employment, there is a gain from using a principal components model fitted to high-yield credit spreads compared to the prediction produced by benchmarks, such as an AR, and ARDL models that use either the term spread or the aggregate high-yield spread as exogenous regressor. Moreover, forecasts based on real-time data are generally comparable to forecasts based on revised data. JEL Classification: C22; C53; E32 Keywords: Credit spreads; Principal components; Forecasting; Real-time data.

Linking conflict to inequality and polarization

In this paper we study a behavioral model of conflict that provides a basis for choosing certain indices of dispersion as indicators for conflict. We show that the (equilibrium) level of conflict can be expressed as an (approximate) linear function of the Gini coefficient, the Herfindahl-Hirschman fractionalization index, and a specific measure of polarization due to Esteban and Ray

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Estudi dinàmic i manipulació de fluxos en monocapes de Langmuir de molècules fotosensibles

Durant el període de gaudiment de la beca, des del dia 9 de març del 2007 fins el dia 8 de març del 2010, s’han dut a terme diferents tipus d’experiments amb sistemes bidimensionals com són les monocapes de Langmuir. Inicialment es va començar per l’estudi i la caracterització d’aquests sistemes experimentals, tant en repòs com en dinàmic, com és l’estudi de la reposta col•lectiva molecular de dominis d’un azoderivat fotosensible al rotar el pla de polarització mentre es mante sota il•luminació constant i els estudis de sistemes bidimensionals al collapse que es poden relacionar a les propietats viscoplàstiques dels sòlids. Una altra via d’estudi és la reologia d’aquests sistemes bidimensionals quan flueixen a través de canals. Arrel del sistema experimental més simple, una monocapa fluint per un canal, s’ha observat i estudiat l’efecte coll d’ampolla. Un cop assolit i estudiat el sistema més senzill, s’han aplicat tècniques més complexes de fabricació per fotolitografia per fer fluir monocapes de Langmuir per circuits on hi ha un gran contrast de mullat. Un cop aquests circuits es van implementar satisfactòriament en un sistema pel control de fluxos bidimensionals, es posen de manifest les possibles aplicacions futures d’aquests sistemes per l’estudi i el desenvolupament de la microfluídica bidimensional.

Ethnic and religious polarization and social conflict

In this paper we examine the link between ethnic and religious polarization and conflict using interpersonal distances for ethnic and religious attitudes obtained from the World Values Survey. We use the Duclos et al (2004) polarization index. We measure conflict by means on an index of social unrest, as well as by the standard conflict onset or incidence based on a threshold number of deaths. Our results show that taking distances into account significantly improves the quality of the fit. Our measure of polarization outperforms the measure used by Montalvo and Reynal-Querol (2005) and the fractionalization index. We also obtain that both ethnic and religious polarization are significant in explaining conflict. The results improve when we use an indicator of social unrest as the dependent variable.