An extended algorithm of flexibility analysis with a local adjusting method for flexibility region of chemical processes, which is based on the active constraint strategy, is proposed, which fully exploits the flexibi...An extended algorithm of flexibility analysis with a local adjusting method for flexibility region of chemical processes, which is based on the active constraint strategy, is proposed, which fully exploits the flexibility region of the process system operation. The hyperrectangular flexibility region determined by the extended algorithm is larger than that calculated by the previous algorithms. The limitation of the proposed algorithm due to imperfect convexity and its corresponding verification measure are also discussed. Both numerical and actual chemical process examples are presented to demonstrate the effectiveness of the new algorithm.展开更多
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
文摘An extended algorithm of flexibility analysis with a local adjusting method for flexibility region of chemical processes, which is based on the active constraint strategy, is proposed, which fully exploits the flexibility region of the process system operation. The hyperrectangular flexibility region determined by the extended algorithm is larger than that calculated by the previous algorithms. The limitation of the proposed algorithm due to imperfect convexity and its corresponding verification measure are also discussed. Both numerical and actual chemical process examples are presented to demonstrate the effectiveness of the new algorithm.
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.
