Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

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Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

The period function of the generalized Lotka-Volterra centers

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Embedding theorems of function classes, I

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The complexity of random ordered structures

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Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.

Metrics on diagram groups and uniform embeddings in a Hilbert space

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Doctrinas constitucionales y federalismo en España

Tal vez las ideas dominantes no sean exactamente las de las clases dominantes, pero el trabajo parte de la idea de que las ideas dominantes en las clases tienen una gran influencia. Por ello se estudia la versión que se da del federalismo por parte de los autores más influyentes en el derecho público español desde el siglo XIX hasta nuestros días. Se concluye que del rechazo generalizado y del elogio del centralismo, tras la Constitución de 1978 se pasa a proponer el federalismo como la pauta más favorable para la evolución del Estado autonómico. Ahora bien, se propone la versión más centralizadora del federalismo, cual es la del federalismo cooperativo

Transition modes and institutional outcomes in El Salvador and Guatemala

Institutions affect key dimensions of the political process –policy, stability, and conflict. The choice of institutions is thus consequential. I argue that transition modes affect the choice of institutions in predictable and systematic ways. The more balanced power is between the two main bargaining forces –regime elite and opposition– the likelier that the resulting institutions will be pluralistic. Contrarily, the more unbalanced power is in favour of regime elites vis a vis the opposition, the likelier that institutions will be majoritarian. The argument is tested for El Salvador and Guatemala.

Federalismo e forme di governo. L´inopportunità delle differenziazioni di modello

La legge costituzionale 1/1999 per le Regioni ordinarie (e la successiva 2/2001 per le Speciali) ha rappresentato un punto di svolta fondamentale del regionalismo italiano. Essa ha stabilito il principio dell’elezione popolare diretta del Presidente della Regione, a cui si collega un premio di maggioranza nel Consiglio regionale secondo il cosiddetto modello neo-parlamentare. Qualsiasi interruzione del rapporto fiduciario per dimissioni del Presidente o approvazione di una mozione di sfiducia porterebbe a nuove elezioni, cosa che rappresenta un serissimo deterrente alle crisi. La riforma prevedeva anche la possibilità per le Regioni di derogare col proprio Statuto a tali scelte tornando all’elezione consiliare e a sostituzioni della maggioranza. Nonostante alcuni tentativi di sfuggire alla regola del governo di legislatura utilizzando tale deroga in modo esplicito o surrettizio, seguendo vecchi retaggi assemblearisti, l’elezione diretta si è imposta ovunque, garantendo a tutte le Regioni analoghi e inediti standards di governabilità.

Consenso, constitución y partidos políticos: una reflexión crítica 26 años después

Vint-i-sis desprès de la promulgació de la Constitució espanyola, l’autor fa balanç i arriba a un seguit de conclusions. Entre d’altres, que Espanya viu una etapa de clara partitocràcia que, juntament amb el poder desmesurat dels sindicats, lesiona la vida democràtica; que cal reduir la dualitat suposadament legitimadora entre el Parlament i el carrer; i que malgrat les lloances rebudes, la Constitució de 1976 no ha aconseguit una de les funcions essencials de tota constitució: la tasca integradora.

Composition of Greenhouse Gas Emissions in Spain: an Input-Output Analysis

Extending the traditional input-output model to account for the environmental impacts of production processes reveals the channels by which environmental burdens are transmitted throughout the economy. In particular, the environmental input-output approach is a useful technique for quantifying the changes in the levels of greenhouse emissions caused by changes in the final demand for production activities. The inputoutput model can also be used to determine the changes in the relative composition of greenhouse gas emissions due to exogenous inflows. In this paper we describe a method for evaluating how the exogenous changes in sectorial demand, such as changes in private consumption, public consumption, investment and exports, affect the relative contribution of the six major greenhouse gases regulated by the Kyoto Protocol to total greenhouse emissions. The empirical application is for Spain, and the economic and environmental data are for the year 2000. Our results show that there are significant differences in the effects of different sectors on the composition of greenhouse emissions. Therefore, the final impact on the relative contribution of pollutants will basically depend on the activity that receives the exogenous shock in final demand, because there are considerable differences in the way, and the extent to which, individual activities affect the relative composition of greenhouse gas emissions. Keywords: Greenhouse emissions, composition of emissions, sectorial demand, exogenous shock.

A Rembrandt is a Rembrandt

As paintings are assets, we propose to model a painting's price dynamics as a diffusion process, i.e., as the financial literature models share prices, but correcting by size. We show that the influence of size on the artwork price diminishes as the paintings gets older because 1) prices incorporate progressively more noise and 2) for high quality artists, the relative importance of size on price decreases as the artist consolidates and authorship gains importance as explanatory variable. Our theoretical results are consistent with data from a sample of 19th- and 20th-century Catalan painters of similar quality. These findings suggest that an artist's quality and antiquity should be taken into account in order to obtain more efficient estimates of parameters in hedonic art market models.