This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is...This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.展开更多
By using the involutory transformations, the classical variational principle——Hamiltonian principle of two kinds of variables in general mechanics is advanced and by using undetermined Lagrangian multiplier method, ...By using the involutory transformations, the classical variational principle——Hamiltonian principle of two kinds of variables in general mechanics is advanced and by using undetermined Lagrangian multiplier method, the generalized variational principles and generalized variational principles with subsidiary conditions are established. The stationary conditions of various kinds of variational principles are derived and the relational problems discussed.展开更多
文摘This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19872022)the Doctoral Education Foundation of China (Grant No. 97021710)
文摘By using the involutory transformations, the classical variational principle——Hamiltonian principle of two kinds of variables in general mechanics is advanced and by using undetermined Lagrangian multiplier method, the generalized variational principles and generalized variational principles with subsidiary conditions are established. The stationary conditions of various kinds of variational principles are derived and the relational problems discussed.
