A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobiell...A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.展开更多
Many studies have considered the solution of Unit Commitment problems for the management of energy networks. In this field, earlier work addressed the problem in determinist cases and in cases dealing with demand unce...Many studies have considered the solution of Unit Commitment problems for the management of energy networks. In this field, earlier work addressed the problem in determinist cases and in cases dealing with demand uncertainties. In this paper, the authors develop a method to deal with uncertainties related to the cost function. Indeed, such uncertainties often occur in energy networks （waste incinerator with a priori unknown waste amounts, cogeneration plant with uncertainty of the sold electricity price...）. The corresponding optimization problems are large scale stochastic non-linear mixed integer problems. The developed solution method is a recourse based programming one. The main idea is to consider that amounts of energy to produce can be slightly adapted in real time, whereas the on/off statuses of units have to be decided very early in the management procedure. Results show that the proposed approach remains compatible with existing Unit Commitment programming methods and presents an obvious interest with reasonable computing loads.展开更多
基金National Natural Science Foundation of China under Grant Nos 10472063 and 10772110
文摘A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.
文摘Many studies have considered the solution of Unit Commitment problems for the management of energy networks. In this field, earlier work addressed the problem in determinist cases and in cases dealing with demand uncertainties. In this paper, the authors develop a method to deal with uncertainties related to the cost function. Indeed, such uncertainties often occur in energy networks （waste incinerator with a priori unknown waste amounts, cogeneration plant with uncertainty of the sold electricity price...）. The corresponding optimization problems are large scale stochastic non-linear mixed integer problems. The developed solution method is a recourse based programming one. The main idea is to consider that amounts of energy to produce can be slightly adapted in real time, whereas the on/off statuses of units have to be decided very early in the management procedure. Results show that the proposed approach remains compatible with existing Unit Commitment programming methods and presents an obvious interest with reasonable computing loads.
