In extended equal area criterion(EEAC),dynamic saddle points(DSP)encountered in disturbed trajectories can be regarded as not only the criterion of power system instability,but also the observation point for the quantitative analysis of stability degree.

It is revealed that unstable machine possesses the feature of dynamic individual saddle point (DISP) based on th.

We calculate the positions and the widths of 21 2P 0 resonances in BeⅡ between 1 1S 0 and 2 1P thresholds with a saddle point complex rotation method.

The center-weak focus of a general system of degree “n” was transformed into a problem of generalized center-weak saddle.

A problem of center-weak focus system of degree n(n denotes odd numbers) in qualitative theory of differential equation is transformed into the problem of generalized center-weak saddle system by a generalized transformation of generalized polar coordinates,which offers the calculation formula of eleven-order weak saddle values.

We discuss the types of the equilibrium points,Hopf bifurcation,saddle separate relation place.

Incomplete Lagrange function and saddle point optimality criteria fora class of nondifferentiable generalized fractional programming;

Existence of the saddle points under the weak continuity;

It will present consistency of saddle point with Nash equilibrium,and prove the corresponding theorems.

During the definition of new saddle point,x0∈V is not needed,so the new saddle-point optimality condition is obtained in this paper.

The saddle-point type optimality criteria are also proven by using the existing necessary conditions under the assumption of the class of(F,α,ρ,d)-convexity.

For a class of generalized fractional programming whose objective function is composed of infinite fractions,the saddle-point type optimality criteria are proven by using the existing necessary conditions,under the assumption of the class of B-(p,r)-invexity.