On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Normalisation et dimension culturelle des délocalisations de services : les cas du Maroc et de l'Inde

Cette thèse explore le rôle de la normalisation technique dans les délocalisations de services en Inde et au Maroc. La recherche appréhende le phénomène en opposant explicitement ou implicitement deux modèles. Un modèle serviciel dans lequel les activités de services sont difficilement délocalisables parce que non-mesurables ; un modèle industriel qui articule des activités de services mesurables par les normes techniques et susceptibles d'être délocalisés dans les pays du Sud à bas salaires. Notre thèse s'interroge sur la manière dont les relations Nord-Sud peuvent s'appréhender au sein de cette dichotomie et propose une réflexion épistémologique sur les représentations culturelles induites au sein de ce cadrage. A partir d'une perspective qui combine les apports de l'économie politique culturelle, la sociologie économique et les études postcoloniales au sein de l'économie politique internationale, elle mobilise trois catégories (la normalisation technique, l'imaginaire économique, la qualité). Ces catégories nous permettent de suggérer la centralité des enjeux de pouvoirs dans la définition de ce que sont les activités de services. L'analyse empirique suggère que les délocalisations de services au Maroc et en Inde expriment des réalités plus poreuses et plus dynamiques que la dichotomie entre modèle serviciel et modèle industriel laisse entendre. Elle met en évidence la capacité d'agir des acteurs des pays du Sud et suggère que les normes techniques ont une fonction politique à travers leurs fonctions de mesure. Abstract This thesis explores the role of technical standards in offshore outsourcing in India and Morocco. Current research captures the phenomenon while opposing explicitly or implicitly two models of production. A service-based model in which service activities are difficult to relocate because they are non-measurable; an industrial model that articulates service activities measured with technical standards and that may be outsourced to developing countries with low wages. Our thesis questions how North-South relations can be grasped within this dichotomy and offers an epistemologica! reflection on cultural representations induced within this framework. From a perspective that combines the contributions of cultural political economy, economic sociology and postcolonial studies in international political economy, it mobilizes three categories (technical standardization, the economic imaginary and quality). These categories allow us to suggest the centrality of power issues in the definition of service activities. The empirical analysis suggests that offshoring of services in Morocco and India express more porous and dynamic realities than the dichotomy suggested between a service model and an industrial model. It highlights the ability of the actors to act in the South and suggests that technical standards have a political function through their measurement functions.