A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in al...A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.展开更多
We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are in...We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results.展开更多
We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left...We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results.展开更多
With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical s...With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed展开更多
基金Supported by the National Science Foundation of China.
文摘A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055)
文摘We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results.
基金supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055)
文摘We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results.
文摘With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed
