Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the d...Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.展开更多
By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A...By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A method to construct the Lax representations for both x- and t(n)- constrained flows via reduction of the adjoint representations of the auxiliary linear problems is developed.展开更多
By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all con...By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is presented.The Darboux transformation for these FDIHSs is derived.展开更多
Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear prob...Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.展开更多
Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has...Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has also increased as more devices are being connected to the network. To understand the physical laws governing the operation of the network, techniques such as optimal power flow (OPF), Economic dispatch (ED) and Security constrained optimal power flow (SCOPF) were developed. These techniques have been used extensively in network operation, planning and so on. However, an in-depth presentation showcasing the merits and demerits of these techniques is still lacking in the literature. Hence, this paper intends to fill this gap. In this paper, Economic dispatch, optimal power flow and security-constrained optimal power flow are applied to a 3-bus test system using a linear programming approach. The results of the ED, OPF and SC-OPF are compared and presented.展开更多
This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progre...This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progress payment （PP） and the payment at an equal time interval （ETI）. The objective of each model is to maximize the net present value （NPV） for all cash flows in the project, subject to the related operational constraints. The models are characterized as NP-hard. A heuristic algorithm, coupled with two upper bound solutions, is proposed to efficiently solve the models and evaluate the heuristic algorithm performance which was not performed in past studies. The results show that the performance of proposed models and heuristic algorithm is good.展开更多
The airspace congestion is becoming more and more severe.Although there are traffic flow management（TFM）initiatives based on CDM widely applied,how to reschedule these disrupted flights of different airlines integra...The airspace congestion is becoming more and more severe.Although there are traffic flow management（TFM）initiatives based on CDM widely applied,how to reschedule these disrupted flights of different airlines integrating TFM initiatives and allocate the limited airspace resources to these airlines equitably and efficiently is still a problem.The air traffic management（ATM）authority aims to minimizing the systemic costs of congested airspaces.And the airlines are self-interested and profit-oriented.Being incorporated into the collaborative decision making（CDM）process,the airlines can influence the rescheduling decisions to profit themselves.The airlines maybe hide the flight information that is disadvantageous to them,but is necessary to the optimal system decision.To realize the coincidence goal between the ATM authority and airlines for the efficient,and equitable allocation of airspace resources,this paper provides an auction-based market method to solve the congestion airspace problem under the pre-tactic and tactic stage of air traffic flow management.Through a simulation experiment,the rationing results show that the auction method can decrease the total delay costs of flights in the congested airspace compared with both the first schedule first service（FSFS）tactic and the ration by schedule（RBS）tactic.Finally,the analysis results indicate that if reallocate the charges from the auction to the airlines according to the proportion of their disrupted flights,the auction mechanism can allocate the airspace resource in economy equitably and decrease the delay losses of the airlines compared with the results of the FSFS tactic.展开更多
Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy wi...Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy withself-consistent sources,of the TD hierarchy with self-consistent sources,and of the Jaulent Miodek hierarchy with self-consistentsources,together with their Lax representations are presented.展开更多
A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The...A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The zero-curvature representation for the （γn, σk ）-CKPH is derived. The reduction and constrained flows of （γn, σk ）-CKPH are studied.展开更多
In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many method...In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many methods of computing TS-IRPFL have been proposed.However,in practice,the method widely used to determine TS-IRPFL is based on selection and analysis of typical scenarios as well as scenario matching.First,typical scenarios are selected and analyzed to obtain accurate limits,then the scenario to be analyzed is matched with a certain typical scenario,whose limit is adopted as the forecast limit.In this paper,following the steps described above,a pragmatic method to determine TS-IRPFL is proposed.The proposed method utilizes data-driven tools to improve the steps of scenario selection and matching.First of all,we formulate a clear model of power system scenario similarity.Based on the similarity model,we develop a typical scenario selector by clustering and a scenario matcher by nearest neighbor algorithm.The proposed method is pragmatic because it does not change the existing procedure.Moreover,it is much more reasonable than the traditional method.Test results verify the validity of the method.展开更多
The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method f...The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.展开更多
A hierarchy of multidimensional Hénon-Heiles(M-H-H)systems are constructed via the x-and t_n-higher-order-constrained flows of KdV hierarchy.The Lax representation for the M-H-H hierarchy is determined from the a...A hierarchy of multidimensional Hénon-Heiles(M-H-H)systems are constructed via the x-and t_n-higher-order-constrained flows of KdV hierarchy.The Lax representation for the M-H-H hierarchy is determined from the adjoint representation of the auxiliary linear problem for the KdV hierarchy.By using the Lax representation the classical Poisson structure and r-matrix for the hierarchy are found and the Jacobi inversion problem for the hierarchy is constructed.展开更多
基金Supported by the National Science Foundation of China under Grant No.10971031the Natural Science Foundation of Shandong Province under Grant No.ZR2009AL021
文摘Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup （BK） hierarchy and the dispersive long wave （DLW） hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especiaily, the coupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variationai identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-eonstrained flows whose adjoint representations and the Lax pairs are given.
文摘By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A method to construct the Lax representations for both x- and t(n)- constrained flows via reduction of the adjoint representations of the auxiliary linear problems is developed.
基金Supported by the Chinese National Basic Research Project"Nonlinear Science"
文摘By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is presented.The Darboux transformation for these FDIHSs is derived.
基金Project supported by the National Basic Reseach Project "Nonlinear Scijence
文摘Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.
文摘Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has also increased as more devices are being connected to the network. To understand the physical laws governing the operation of the network, techniques such as optimal power flow (OPF), Economic dispatch (ED) and Security constrained optimal power flow (SCOPF) were developed. These techniques have been used extensively in network operation, planning and so on. However, an in-depth presentation showcasing the merits and demerits of these techniques is still lacking in the literature. Hence, this paper intends to fill this gap. In this paper, Economic dispatch, optimal power flow and security-constrained optimal power flow are applied to a 3-bus test system using a linear programming approach. The results of the ED, OPF and SC-OPF are compared and presented.
文摘This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progress payment （PP） and the payment at an equal time interval （ETI）. The objective of each model is to maximize the net present value （NPV） for all cash flows in the project, subject to the related operational constraints. The models are characterized as NP-hard. A heuristic algorithm, coupled with two upper bound solutions, is proposed to efficiently solve the models and evaluate the heuristic algorithm performance which was not performed in past studies. The results show that the performance of proposed models and heuristic algorithm is good.
基金Supported by the National High Technology Research and Development Program of China("863"Program)(20060AA12A105)the Chinese Airspace Management Commission Researching Program(GKG200802006)~~
文摘The airspace congestion is becoming more and more severe.Although there are traffic flow management（TFM）initiatives based on CDM widely applied,how to reschedule these disrupted flights of different airlines integrating TFM initiatives and allocate the limited airspace resources to these airlines equitably and efficiently is still a problem.The air traffic management（ATM）authority aims to minimizing the systemic costs of congested airspaces.And the airlines are self-interested and profit-oriented.Being incorporated into the collaborative decision making（CDM）process,the airlines can influence the rescheduling decisions to profit themselves.The airlines maybe hide the flight information that is disadvantageous to them,but is necessary to the optimal system decision.To realize the coincidence goal between the ATM authority and airlines for the efficient,and equitable allocation of airspace resources,this paper provides an auction-based market method to solve the congestion airspace problem under the pre-tactic and tactic stage of air traffic flow management.Through a simulation experiment,the rationing results show that the auction method can decrease the total delay costs of flights in the congested airspace compared with both the first schedule first service（FSFS）tactic and the ration by schedule（RBS）tactic.Finally,the analysis results indicate that if reallocate the charges from the auction to the airlines according to the proportion of their disrupted flights,the auction mechanism can allocate the airspace resource in economy equitably and decrease the delay losses of the airlines compared with the results of the FSFS tactic.
基金Supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10801083
文摘Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy withself-consistent sources,of the TD hierarchy with self-consistent sources,and of the Jaulent Miodek hierarchy with self-consistentsources,together with their Lax representations are presented.
基金Supported by National Basic Research Program of China(973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant Nos.10901090,10801083,11171175+1 种基金Chinese Universities Scientific Fund under Grant No.2011JS041China Postdoctoral Science Foundation Funded Project under Grant No.20110490408
文摘A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The zero-curvature representation for the （γn, σk ）-CKPH is derived. The reduction and constrained flows of （γn, σk ）-CKPH are studied.
基金This work was supported by National Key R&D Program of China(2018YFB0904500)and State Grid Corporation of China。
文摘In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many methods of computing TS-IRPFL have been proposed.However,in practice,the method widely used to determine TS-IRPFL is based on selection and analysis of typical scenarios as well as scenario matching.First,typical scenarios are selected and analyzed to obtain accurate limits,then the scenario to be analyzed is matched with a certain typical scenario,whose limit is adopted as the forecast limit.In this paper,following the steps described above,a pragmatic method to determine TS-IRPFL is proposed.The proposed method utilizes data-driven tools to improve the steps of scenario selection and matching.First of all,we formulate a clear model of power system scenario similarity.Based on the similarity model,we develop a typical scenario selector by clustering and a scenario matcher by nearest neighbor algorithm.The proposed method is pragmatic because it does not change the existing procedure.Moreover,it is much more reasonable than the traditional method.Test results verify the validity of the method.
基金Supported by the National Basic Research Project forNonlinear Sciences and the Doctorate DissertationFoundation of Tsinghua University
文摘The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.
基金Supported by National Research Project "Nonlinear Sciences"
文摘A hierarchy of multidimensional Hénon-Heiles(M-H-H)systems are constructed via the x-and t_n-higher-order-constrained flows of KdV hierarchy.The Lax representation for the M-H-H hierarchy is determined from the adjoint representation of the auxiliary linear problem for the KdV hierarchy.By using the Lax representation the classical Poisson structure and r-matrix for the hierarchy are found and the Jacobi inversion problem for the hierarchy is constructed.
