- A PROCEDURE FOR SHARING RECYCLING COSTS

This paper examines a situation in which the production activities of different agents, in a common geographical location, create waste products that are either of a similar biological or chemical composition or offer commercially compatible combinations. What we propose here, therefore, is a cost-sharing model for the of recycling of their waste products. We concentrate, however, on the specific case in which the agents' activities are heterogeneous. We first examine, from a normative point of view, the cost-sharing rule, which we shall call the multi-commodity serial (MCS) rule. We introduce a property, that we call Cost-Based Equal Treatment, and we demonstrate that the unique rule verifying the Serial Principle and this property is the MCS rule. We then deal with the analysis of the agents' strategic behavior when they are allowed to select their own production levels, in which case the total cost is then split, in accordance with the MCS rule. We show that there is only one Nash equilibrium, which is obtained from an interactive elimination of dominated strategies.Cost Sharing Rules, Serial Cost Sharing, Dominance Solvability.

Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a geodesic sphere or totally geodesic hypersurface in a Riemannian manifold of constant curvature. Using that geodesic spherical curves are normal curves, i.e., they are the image of an Euclidean spherical curve under the exponential map, we are able to characterize geodesic spherical curves in hyperbolic spaces and spheres through a non-homogeneous linear equation. Finally, we also show that curves on totally geodesic hypersurfaces, which play the role of hyperplanes in Riemannian geometry, should be characterized by a homogeneous linear equation. In short, our results give interesting and significant similarities between hyperbolic, spherical, and Euclidean geometries.Comment: 15 pages, 3 figures; comments are welcom

Characterization of manifolds of constant curvature by spherical curves

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, the given manifold has constant sectional curvature. We also furnish two other characterizations in terms of (i) an inequality involving the mean curvature of a geodesic sphere and the curvature function of their curves and (ii) the vanishing of the total torsion of closed spherical curves in the case of three-dimensional manifolds. Finally, we also show that the same results are valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat

A Semi-Lagrangian scheme for a degenerate second order Mean Field Game system

In this paper we study a fully discrete Semi-Lagrangian approximation of a second order Mean Field Game system, which can be degenerate. We prove that the resulting scheme is well posed and, if the state dimension is equals to one, we prove a convergence result. Some numerical simulations are provided, evidencing the convergence of the approximation and also the difference between the numerical results for the degenerate and non-degenerate cases.Comment: 21 pages, 8 figure

Are Voters Rationally Ignorant? An Empirical Study for Portuguese Local Elections

The application of the rational choice postulate to a political context invariably leads to the conclusion that most voters are ill informed when making the decision for whom to vote. In this paper, the authors do an empirical evaluation of the rational ignorance theory, based on the results of the 1997 Portuguese Local Elections. The results only partially sustain the hypothesis of rational ignorance, although it is also possible to identify several limitations that prevent the establishment of definite conclusions in this specific field.JEL Classification: H7 Key words: Voter’s Behaviour; Local Elections; Local Governments; Portugal.

Estimation of component redundancy in optimal age maintenance

The classical Optimal Age-Replacement defines the maintenance strategy based on the equipment failure consequences. For severe consequences an early equipment replacement is recommended. For minor consequences the repair after failure is proposed. One way of reducing the failure consequences is the use of redundancies, especially if the equipment failure rate is decreasing over time, since in this case the preventive replacement does not reduce the risk of failure. The estimation of an active component redundancy degree is very important in order to minimize the life-cycle cost. If it is possible to make these estimations in the early phase of system design, the implementation is easier and the amortization faster. This work proposes an adaptation of the Optimal Age-Replacement method in order to simultaneously optimize the equipment redundancy allocation and the maintenance plan. The main goal is to provide a simple methodology, requiring the fewer data possible. A set of examples are presented illustrating that this methodology covers a wide variety of operating conditions. The optimization of the number of repairs between each replacement, in the cases of imperfect repairs, is another feature of this methodology