Letter: Models of Relativistic Particle with Curvature and Torsion Revisited

Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and explicitly determined using the Lancret program. The moduli subspaces of closed solitons in the three sphere are also determined.     

Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

A risk model driven by Lévy processes

We present a general risk model where the aggregate claims, as well as the premium function, evolve by jumps. This is achieved by incorporating a Lévy process into the model. This seeks to account for the discrete nature of claims and asset prices. We give several explicit examples of Lévy processes that can be used to drive a risk model. This allows us to incorporate aggregate claims and premium fluctuations in the same process. We discuss important features of such processes and their relevance to risk modeling. We also extend classical results on ruin probabilities to this model. Copyright © 2003 John Wiley & Sons, Ltd.     

Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia

In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant).     

Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Quasi-Hamiltonian structure and Hojman construction

Given a smooth vector field Γ and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that Γ is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.     

Essentially optimal explicit Runge–Kutta methods with application to hyperbolic–parabolic equations

Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL condition even in the presence of viscous fluxes.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Automatic detection and identification of shocks in Gaussian state‐space models: a Bayesian approach

An automatic monitoring and intervention algorithm that permits the supervision of very general aspects in an univariate linear Gaussian state–space model is proposed. The algorithm makes use of a model comparison and selection approach within a Bayesian framework. In addition, this algorithm incorporates the possibility of eliminating earlier interventions when subsequent evidence against them comes to light. Finally, the procedure is illustrated with two empirical examples taken from the literature. Copyright © 2005 John Wiley & Sons, Ltd.