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We derive the collisionless Landau damping in a plasma by satisfying the causal requirement that the susceptibility function of the plasma for time t < 0 should be nil. The causality condition should be satisfied by the susceptibility function of a plasma no matter what equations we employ to describe the plasma. Thus we conclude that the fundamental reason of the collisionless damping can be traced to the causality. As an example, we derive the collisionless damping of ion acoustic wave in a plasma by employing fluid equations.
Winner determination is one of the main challenges in combinatorial auctions. However, not much work has been done to solve this problem in the case of reverse auctions using evolutionary techniques. This has motivated us to propose an improvement of a genetic algorithm based method, we have previously proposed, to address two important issues in the context of combinatorial reverse auctions: determining the winner(s) in a reasonable processing time, and reducing the procurement cost. In order to evaluate the performance of our proposed method in practice, we conduct several experiments on combinatorial reverse auctions instances. The results we report in this paper clearly demonstrate the efficiency of our new method in terms of processing time and procurement cost.