Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

"Vegeu el resum a l'inici del document del fitxer adjunt."

The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

The Impact of democratization: a preliminary investigation on social policies and political violence in Latin America

The recent strides of democracy in Latin America have been associated to conflicting outcomes. The expectation that democracy would bring about peace and prosperity have been only partly satisfied. While political violence has been by and large eradicated from the sub-continent, poverty and social injustice still prevail and hold sway. Our study argues that democracy matters for inequality through the growing strength of center left and left parties and by making political leaders in general more responsive to the underprivileged. Furthermore, although the pension reforms recently enacted in the region generated overall regressive outcomes on income distribution, democratic countries still benefit from their political past: where democratic tradition was stronger, such outcomes have been milder. Democratic tradition and the specific ideological connotations of the parties in power, on the other hand, did not play an equally crucial role in securing lower levels of political violence: during the last wave of democratizations in Latin America, domestic peace was rather an outcome of political and social concessions to those in distress. In sum, together with other factors and especially economic ones, the reason why recent democratizations have provided domestic peace in most cases, but have been unable so far to solve the problem of poverty and inequality, is that democratic traditions in the subcontinent have been relatively weak and, more specifically, that this weakness has undermined the growth of left and progressive parties, acting as an obstacle to redistribution. Such weakness, on the other hand, has not prevented the drastic reduction of domestic political violence, since what mattered in this case was a combination of symbolic or material concessions and political agreements among powerful élites and counter-élites.

Thyroid hormone enhances transected axonal regeneration and muscle reinnervation following rat sciatic nerve injury.

Improvement of nerve regeneration and functional recovery following nerve injury is a challenging problem in clinical research. We have already shown that following rat sciatic nerve transection, the local administration of triiodothyronine (T3) significantly increased the number and the myelination of regenerated axons. Functional recovery is a sum of the number of regenerated axons and reinnervation of denervated peripheral targets. In the present study, we investigated whether the increased number of regenerated axons by T3-treatment is linked to improved reinnervation of hind limb muscles. After transection of rat sciatic nerves, silicone or biodegradable nerve guides were implanted and filled with either T3 or phosphate buffer solution (PBS). Neuromuscular junctions (NMJs) were analyzed on gastrocnemius and plantar muscle sections stained with rhodamine alpha-bungarotoxin and neurofilament antibody. Four weeks after surgery, most end-plates (EPs) of operated limbs were still denervated and no effect of T3 on muscle reinnervation was detected at this stage of nerve repair. In contrast, after 14 weeks of nerve regeneration, T3 clearly enhanced the reinnervation of gastrocnemius and plantar EPs, demonstrated by significantly higher recovery of size and shape complexity of reinnervated EPs and also by increased acetylcholine receptor (AChRs) density on post synaptic membranes compared to PBS-treated EPs. The stimulating effect of T3 on EP reinnervation is confirmed by a higher index of compound muscle action potentials recorded in gastrocnemius muscles. In conclusion, our results provide for the first time strong evidence that T3 enhances the restoration of NMJ structure and improves synaptic transmission.

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.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Origins and efficiency of the electric industry regulation in Spain, 1910-1936

The aim of this paper is to discover the origins of utility regulation in Spain, and to analyse, from a microeconomic perspective, its characteristics and the impact of regulation on consumers and utilities. Madrid and the Madrilenian utilities are taken as a case study. The electric industry in the period studied was a natural monopoly2. Each of the three phases of production, generation, transmission and distribution, had natural monopoly characteristics. Therefore, the most efficient form to generate, transmit and distribute electricity was the monopoly because one firm can produce a quantity at a lower cost than the sum of costs incurred by two or more firms. A problem arises because when a firm is the single provider it can charge prices above the marginal cost, at monopoly prices. When a monopolist reduces the quantity produced, price increases, causing the consumer to demand less than the economic efficiency level, incurring a loss of consumer surplus. The loss of the consumer surplus is not completely gained by the monopolist, causing a loss of social surplus, a deadweight loss. The main objective of regulation is going to be to reduce to a minimum the deadweight loss. Regulation is also needed because when the monopolist fixes prices at marginal cost equal marginal revenue there would be an incentive for firms to enter the market creating inefficiency. The Madrilenian industry has been chosen because of the availability of statistical information on costs and production. The complex industry structure and the atomised demand add interest to the analysis. This study will also provide some light on the tariff regulation of the period which has been poorly studied and will complement the literature on the US electric utilities regulation where a different type of regulation was implemented.

Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

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.

The problem of the competitiveness of nuclear energy: a biophysical explanation

In this study I try to explain the systemic problem of the low economic competitiveness of nuclear energy for the production of electricity by carrying out a biophysical analysis of its production process. Given the fact that neither econometric approaches nor onedimensional methods of energy analyses are effective, I introduce the concept of biophysical explanation as a quantitative analysis capable of handling the inherent ambiguity associated with the concept of energy. In particular, the quantities of energy, considered as relevant for the assessment, can only be measured and aggregated after having agreed on a pre-analytical definition of a grammar characterizing a given set of finite transformations. Using this grammar it becomes possible to provide a biophysical explanation for the low economic competitiveness of nuclear energy in the production of electricity. When comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. Since the cost of production of fossil energy provides the base line of economic competitiveness of electricity, the (lack of) economic competitiveness of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. In particular, the analysis focuses on fossil-fuel requirements and labor requirements for those phases that both nuclear plants and fossil energy plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. By adopting this approach, it becomes possible to explain the systemic low economic competitiveness of nuclear energy in the production of electricity, because of: (i) its dependence on oil, limiting its possible role as a carbon-free alternative; (ii) the choices made in relation to its fuel cycle, especially whether it includes reprocessing operations or not; (iii) the unavoidable uncertainty in the definition of the characteristics of its process; (iv) its large inertia (lack of flexibility) due to issues of time scale; and (v) its low power level.