Experiment 1 investigated whether the activation of the prototypal matters and heuristic information would be facilitated with the increasing of the amount of prototypal matters the subjects solved;Experiment 2 investigated whether the hint of the connection between prototypal matters and quartering problem solvi.

By using Wassermann s idea of(r,s)-stability in singularity theory,(r1,r2,…,rd)-stability of unfolding of Γ-equivariant bifurcation problem is discussed.

The modified gradient path and affine scaling interior method for variational inequality problems with linear inequality constraints;

We introduce a new weak equilibrium principle and transfer the problem to a variational inequality problem.

,58,1993,369-383",we present an affine scaling interior trust region-type modification of Newton method for the strictly monotone variational inequality problem with simple bounds on variables.

Uniqueness and stability of unfoldings of equivariant bifurcation problems with two groups of state variables;

The stability of equivariant bifurcation problems with parameters symmetry and their unfoldings;

Based on the theory of left-right equivalence of smooth map germs in sigularity theory,multiparameter equivariant bifurcation problems of state varibles with symmetry and parameters with symmetry were introduced.

On this base,some properties of ΓΔ-equivariant bifurcation problem under contact equivalence are obtained:the finite modules over the rings of ΓΔ-invariant functons and the property of its tangent space are obtained and an sufficient and necessary conditon that an unfolding of ΓΔ-bifurcation problem is a versal unfolding is given.