The original van Laar's theory has been modified. The internal pressures of components and mixture are expressed by Frank's relation and the excess entropy for mixing of components is also considered. A new ac...The original van Laar's theory has been modified. The internal pressures of components and mixture are expressed by Frank's relation and the excess entropy for mixing of components is also considered. A new activity coefficient equation, which can be satisfactorily applied to polymer solutions, is obtained. The calculated results for the VLE of 179 polymer solutions show that the accuracy of fit is evidently superior to UNIQUAC equation.展开更多
The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identi...The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identities,it can be shown that the constraint multipliers connected with the first-class constraints may not be independent, so a query to a conjecture of Dirac is presented. Based on the symmetry properties of the constrained Hamiltonian system in phase space, a counterexample to a conjecture of Dirac is given to show that Dirac's conjecture fails in such a system.We present here a different way rather than Cawley's examples and other's ones in that there is no linearization of constraints in the problem. This example has a feature that neither the primary first-class constraints nor secondary first-class constraints are generators of the gauge transformation.展开更多
基金Supported by the National Natural Science Foundation of China(No.29376236).
文摘The original van Laar's theory has been modified. The internal pressures of components and mixture are expressed by Frank's relation and the excess entropy for mixing of components is also considered. A new activity coefficient equation, which can be satisfactorily applied to polymer solutions, is obtained. The calculated results for the VLE of 179 polymer solutions show that the accuracy of fit is evidently superior to UNIQUAC equation.
文摘The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identities,it can be shown that the constraint multipliers connected with the first-class constraints may not be independent, so a query to a conjecture of Dirac is presented. Based on the symmetry properties of the constrained Hamiltonian system in phase space, a counterexample to a conjecture of Dirac is given to show that Dirac's conjecture fails in such a system.We present here a different way rather than Cawley's examples and other's ones in that there is no linearization of constraints in the problem. This example has a feature that neither the primary first-class constraints nor secondary first-class constraints are generators of the gauge transformation.
