No abstract

The aim of this paper is to give a classification up to isomorphism of low dimension filiform Lie superalgebras.

Many work was done for filiform Lie algebras defined by M. Vergne [8]. An interesting fact is that this algebras are obtained by deformations of the filiform Lie algebra L n,m . This was used for classifications in [4]. Like filiform Lie algebras, filiform Lie superalgebras are obtained by nilpotent deformations of the Lie superalgebra L n,m . In this paper, we recall this fact and we study even cocycles of the superalgebra L n,m which give this nilpotent deformations. A family of independent bilinear maps will help us to describe this cocycles. At the end an evaluation of the dimension of the space Z 2 0 (L n,m , L n,m ) is established. The description of this cocycles can help us to get some classifications which was done in [2,3].I should like to thank Y. Khakimdjanov and M. Goze for support and numerous discussions.

SummaryWithin ad hoc and wireless sensor networks, communications are accomplished in dynamic environments with a random movement of mobile devices. Thus, routing protocols over these networks are an important concern to offer efficient network scalability, manage topology information, and prolong the network lifetime. Optimized link state routing (OLSR) is one of those routing protocols implemented in ad hoc and wireless sensor networks. Because of its proactive technique, routes between two nodes are established in a very short time, but it can spend a lot of resources for selecting the multipoint relays (MPRs: nodes responsible for routing data) and exchanging topology control information. Thus, nodes playing for a long time a role of MPR within networks implementing such protocol can rapidly exhaust their batteries, which create route failures and affect the network lifetime. Our main approach relies on analyzing this concern by introducing a new criterion that implements a combination between the residual energy of a node and its reachability in order to determine the optimal number of MPRs and sustain the network lifetime. Simulations performed illustrate obviously that our approach is more significant compared with the basic heuristic used by original OLSR to compute the MPR set of a node.

New communication technologies must be provided in order to improve the energy distribution and save electric power. As far as we know, there is not any network protocol designed exclusively for this purpose. In this paper, we present the design and simulation of a group-based protocol to improve the energy distribution in smart grids. We will show the group-based architecture and the protocol operation. Finally, we will show some measurements taken from a test bench in order to show it operation and test its performance.