Let （E,ξ）=ind（En,ξn） be an inductive limit of a sequence （En,ξn）n∈N of locally convex spaces and let every step （En,ξn） be endowed with a partial order by a pointed convex （solid） cone Sn. In the framew...Let （E,ξ）=ind（En,ξn） be an inductive limit of a sequence （En,ξn）n∈N of locally convex spaces and let every step （En,ξn） be endowed with a partial order by a pointed convex （solid） cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence （Sn）n∈N of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.展开更多
A class of polynomial system was structured, which depends on a parameter delta. When delta monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand ...A class of polynomial system was structured, which depends on a parameter delta. When delta monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with thee. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an 'analogue rotated vector field' with delta. They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.展开更多
基金supported by the National Natural Science Foundation of China(10871141)
文摘Let （E,ξ）=ind（En,ξn） be an inductive limit of a sequence （En,ξn）n∈N of locally convex spaces and let every step （En,ξn） be endowed with a partial order by a pointed convex （solid） cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence （Sn）n∈N of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.
文摘A class of polynomial system was structured, which depends on a parameter delta. When delta monotonous changes, more than one neighbouring limit cycles located in the vector field of this polynomial system can expand (or reduce) together with thee. But the expansion (or reduction) of these limit cycles is not surely monotonous. This vector field is like the rotated vector field. So these limit cycles of the polynomial system are called to constitute an 'analogue rotated vector field' with delta. They may become an effective tool to study the bifurcation of multiple limit cycle or fine separatrix cycle.
