By the methods of remote sensing(RS) and geographic information system(GIS),and based on the estimations of degradation degree,risk degree and easy-restoration degree of degraded grasslands,an ecological management index(EMI) model of grassland was established to approach the practical ways of optimizing management of degraded grassland.

The present paper covers the Hopf points bifurcating from double fold points, and gives some computable nondegeneracy conditions and stability conditions of these Hopf points.

A Certain Kind of the Non-degenerate Nilpotent Lie Algebras on C;

The projected gradient of the iterative sequence converges to zero under the certain conditions is proved,and the finite termination under the conditions of weak sharp minima and non-degenerate are obtained respectively.

The non-degenerate of the Markov integrated semigroup is proved according to the definition of transition probability functions.

The relation between the nondegeneracy of their primal-dual optimal solutions and their strictly complementary optimal solutions is characterized, and then the conditions in which the solutions of a pair of primal and dual conic programmings are unique respectively are obtained.