Periodic homogenization of non-local operators with a convolution type kernel

The paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled operators converges to a second order elliptic operator with constant coefficients. We also prove the convergence of the corresponding semigroups both in $L^2$ space and the space of continuous functions, and show that for the related family of Markov processes the invariance principle holds

Fish Wars: Cooperative and Non-Cooperative Approaches

Mirman (1979) and Levhari and Mirman (1980) suggested a simple two person multistage game-theoretical model which sheds some light on the economic implications inherent in the fishing conflicts where the decisions of the competitors have an effect on the evolution of the fish population and so, on the future expected profit of the competitors. In this paper we consider a generalization of the Levhari and Mirman Fish War Game for the case of n participants of the conflict for different scenarios of hierarchical and coalition structures of countries. We derive the equilibrium and its steady-state behavior for all these scenarios and analyze the impact which the hierarchical and coalition structures can have on fishery and ecology.Nash equilibrium, multistage game, fish war game, cooperative behavior

Gluon dominance model and cluster production

Gluon dominance model (GDM) studies multiparticle production in lepton and hadron processes. It is based on the QCD and phenomenological scheme of hadronization. The model describes well multiplicity distributions and their moments. It has revealed an active role of gluons in multiparticle production, it also has confirmed the fragmentation mechanism of hadronization in e+e- annihilation and its change to recombination mechanism in hadron and nucleus interactions. The GDM explains the shoulder structure of multiplicity distributions. The agreement with Au+Au peripheral collisions data for hadron-pion ratio has been also obtained with this model. Development of GDM allows one to research the multiplicity behavior of ppbar annihilation at tens of GeV. The mechanism of soft photons production and estimates of their emission region have been offered. The experimental data (project "Thermalization", U-70, IHEP) have confirmed a cluster nature of multiparticle production.Comment: 4 pages, 4 figures, Proceedings of the ISMD06 conference, Paraty, Brazil, 2-9 Sep 2006, to appear in Brazilian Journal of Physic