查看更多>>摘要：In a graph G , a subset of vertices is a dissociation set if it induces a subgraph with maxi-mum degree at most 1 . A maximal dissociation set of G is a dissociation set which is not a proper subset of any other dissociation sets. A maximum dissociation set is a dissocia-tion set of maximum size. We show that every graph of order n has at most 10 n5 maximal dissociation sets, and that every triangle-free graph of order n has at most 6 n4 maximal dissociation sets. We also characterize the extremal graphs on which these upper bounds are attained. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：To address an economic dispatch issue of multiple microgrids (MGs) in a game-theoretic framework under source-load uncertainties, a robust optimization scheme with geneticpriced mechanism is proposed. This scheme is a nested iterative algorithm with an outer loop calculating the pricing model in a game and an inner loop solving the robust optimization problem. Specifically, in the outer loop, all stakeholders in a grid-connected microgrid cluster (MGC), i.e. one energy trading center (ETC) and several MGs, are in a game where a genetic-priced model is developed. By utilizing this evolutionary pricing model, the ETC can fix electricity prices to maximize its profits and these prices are passed to the inner loop where a two-stage robust optimization approach is introduced to mitigate adverse effects of uncertainties in MGs induced by renewable energy resources (RERs) and loads. All optimization problems of MGs are solved and optimal values of electricity exchanged between ETC and MGs are passed to the outer loop. This optimization scheme can help address the robust economic dispatch problem in a game-theoretic framework. A grid-connected MGC is used as a case to illustrate the effectiveness of the proposed optimization scheme.
查看更多>>摘要：In this study, we propose a new single-step iterative method for solving complex linear systems Az = (W + iT)z = f, where z, f is an element of R-n, W is an element of R-nxn and T is an element of R-nxn are symmetric positive semi-definite matrices such that null(W) & cap;& nbsp; null(T) = { 0 }. The convergence of the new method is analyzed in detail and discussion on the obtaining the optimal parameter is given. From Wang et al. (2017)[36] we can write W = (PDWP)-D-T, T = (PDTP)-D-T, where D-W = Diag(mu(1), . . . , mu(n)) , D-T = Diag(lambda(1) , . . . , lambda(n)), and P is an element of R-nxn is a nonsingular matrix and lambda(k) , mu(k )satisfy mu(k )+ lambda(k) = 1 , 0 <= lambda(k), mu(k) <= 1 , k = 1 , . . . , n. Then we show that under some conditions on mu(max) = max{ mu(k)}(n)(k & nbsp;=1) , the new method has faster convergence rate in comparison with recently introduced methods. Finally, some numerical examples are given to demonstrate the efficiency of the new procedure in actual computation. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
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