Twisted Reidemeister torsion for twist knots

The aim of this paper is to give an explicit formula for the SL2(C)-twisted Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables given approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

Bargaining one-dimensional policies and the efficiency of super majority rules

We consider negotiations selecting one-dimensional policies. Individuals have single-peaked preferences, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. The existence and uniqueness of stationary subgame perfect equilibrium is established, and its explicit characterization provided. We supply an explicit formula to determine the unique alternative that prevails, as impatience vanishes, for each majority. As an application, we examine the efficiency of majority rules. For symmetric distributions of peaks unanimity is the unanimously preferred majority rule. For asymmetric populations rules maximizing social surplus are characterized.

Equations of hyperelliptic Shimura curves

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Estudi de la reformació amb vapor de biocombustibles per a l'obtenció d'hidrogen utilitzant suports estructurats ceràmics funcionalitzats

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Aspectes geomètrics i dinàmics de transformacions racionals planes

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

The Peace Processes in the Basque Country and Northern Ireland (1994-2006): a Comparative Approach

The peace process in Northern Ireland demonstrates that new sovereignty formulas need to be explored in order to meet the demands of the populations and territories in conflict. The profound transformation of the classic symbolic elements of the nation-state within the context of the European Union has greatly contributed to the prospects for a resolution of this old conflict. Today’s discussions are focused on the search for instruments of shared sovereignty that are adapted to a complex and plural social reality. This new approach for finding a solution to the Irish conflict is particularly relevant to the Basque debate about formulating creative and modern solutions to similar conflicts over identity and sovereignty. The notion of shared sovereignty implemented in Northern Ireland –a formula for complex interdependent relations– is of significant relevance to the broader international community and is likely to become an increasingly potent and transcendent model for conflict resolution and peace building.

GREC CLÀSSIC : curs d'autoaprenentatge introductori

GREC CLÀSSIC. Curs d’autoaprenentatge introductori. Dos anys. El curs consta de tretze lliçons i d’una gramàtica estructurada en quatre blocs: 1. Alfabet i diacrítics, fenòmens fonètics. 2. Morfologia nominal. 3. Morfologia verbal. 4. Infinitius i participis. Sintaxi de les oracions. L’estructura de les lliçons, excepte la primera que inclou l’alfabet, combina qüestions de morfologia nominal i verbal o de morfologia i sintaxi, tal com acostumen a fer els mètodes d’aprenentatge de les llengües modernes. Cada lliçó formula els seus objectius específics, desenvolupa la seva part de continguts i conclou amb uns exercicis pràctics d’autocorrecció. La Gramàtica, per la seva banda, està organitzada com un manual elemental de llengua grega on la persona que segueixi el curs pot ampliar la seva formació i consultar els dubtes. Parts complementàries: presentació on es formulen els objectius, la metodologia i les instruccions concretes per a seguir el curs; terminologia on s’ordenen alfabèticament els conceptes gramaticals emprats en el curs; avaluació final per tal que, més enllà dels exercicis de cada lliçó, hom pugui comprovar si ha assolit els coneixements previstos o si, en cas de no arribar-hi, ha de reforçar algunes lliçons o parts de les mateixes abans de tornar a fer l’avaluació; lèxic, ordenat alfabèticament per tal que hom pugui conèixer el significat dels mots emprats en el curs sense necessitat de consultar un diccionari. A la part d’avaluació hi ha també una enquesta per tal que les persones que segueixin el curs en facin una valoració i ens permetin corregir els seus dèficits o mancances. El projecte 2007MQD00178 ha continuat ampliant els dossiers electrònics, els exercicis autoavaluatius del seu web www.ub.edu/filologiagrega/electra i ha dedicat una part important de la seva tasca a elaborar els continguts i els programes de les assignatures dels dos primers cursos del nou grau de Filologia Clàssica.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

How to use the standard model with own data?

In this work discuss the use of the standard model for the calculation of the solvency capital requirement (SCR) when the company aims to use the specific parameters of the model on the basis of the experience of its portfolio. In particular, this analysis focuses on the formula presented in the latest quantitative impact study (2010 CEIOPS) for non-life underwriting premium and reserve risk. One of the keys of the standard model for premium and reserves risk is the correlation matrix between lines of business. In this work we present how the correlation matrix between lines of business could be estimated from a quantitative perspective, as well as the possibility of using a credibility model for the estimation of the matrix of correlation between lines of business that merge qualitative and quantitative perspective.