In this paper the centers and limit cycles for a class of three-dimensional cubic Kukles systems are investigated.First,by calculating and analyzing the common zeros of the first ten singular point quantities,the nece...In this paper the centers and limit cycles for a class of three-dimensional cubic Kukles systems are investigated.First,by calculating and analyzing the common zeros of the first ten singular point quantities,the necessary conditions for the origin being a center on the center manifold are derived,and furthermore,the sufficiency of those conditions is proved using the Darboux integrating method.Then,by calculating and analyzing the common zeros of the first three period constants,the necessary and sufficient conditions for the origin being an isochronous center on the center manifold are given.Finally,by proving the linear independence of the first ten singular point quantities,it is demonstrated that the system can bifurcate ten small-amplitude limit cycles near the origin under a suitable perturbation,which is a new lower bound for the number of limit cycles around a weak focus in a three-dimensional cubic system.展开更多
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
Both the long-life and multi-mode versions of LIPS-200 ion thruster are under investigation in LIP(Lanzhou Institute of Physics).To confirm the feasible ranges of the beam current and accel(abbreviation for accelarati...Both the long-life and multi-mode versions of LIPS-200 ion thruster are under investigation in LIP(Lanzhou Institute of Physics).To confirm the feasible ranges of the beam current and accel(abbreviation for accelaration)grid potential to apply to the thruster,the wide-range beam perveance(the state of beam focus)and saddle point potential(the lowest potential along beamlet centerline)characteristics of LIPS-200 are studied with a test-verified PIC-MCC(Particle in Cell-Monte Carlo Collisions)model.These characteristics are investigated with both the initial and the eroded states of the accel grid aperture diameter.The results show that the feasible ranges of these parameters with respect to perveance/crossover(overfocused)limit extend as the operating time accumulates,while the feasible range of accel grid potential narrows due to a reduced EBSF(electron backstreaming failure)margin.The feasible ranges determined by the initial condition are:(i)the beam current up to 0.981 A,and(ii)the accel grid potential up to−85 V.A 23%enlargement of the aperture diameter would bring up to 48 V of EBSF margin loss.展开更多
基金supported by the National Natural Science Foundation of China(No.12061016)the Project for Enhancing Young and Middle-aged Teacher’s Research Basis Ability in Colleges of Guangxi(No.2024KY0814)。
文摘In this paper the centers and limit cycles for a class of three-dimensional cubic Kukles systems are investigated.First,by calculating and analyzing the common zeros of the first ten singular point quantities,the necessary conditions for the origin being a center on the center manifold are derived,and furthermore,the sufficiency of those conditions is proved using the Darboux integrating method.Then,by calculating and analyzing the common zeros of the first three period constants,the necessary and sufficient conditions for the origin being an isochronous center on the center manifold are given.Finally,by proving the linear independence of the first ten singular point quantities,it is demonstrated that the system can bifurcate ten small-amplitude limit cycles near the origin under a suitable perturbation,which is a new lower bound for the number of limit cycles around a weak focus in a three-dimensional cubic system.
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.
基金Group independent research and development projects(No.YF-ZZYF-2021-132).
文摘Both the long-life and multi-mode versions of LIPS-200 ion thruster are under investigation in LIP(Lanzhou Institute of Physics).To confirm the feasible ranges of the beam current and accel(abbreviation for accelaration)grid potential to apply to the thruster,the wide-range beam perveance(the state of beam focus)and saddle point potential(the lowest potential along beamlet centerline)characteristics of LIPS-200 are studied with a test-verified PIC-MCC(Particle in Cell-Monte Carlo Collisions)model.These characteristics are investigated with both the initial and the eroded states of the accel grid aperture diameter.The results show that the feasible ranges of these parameters with respect to perveance/crossover(overfocused)limit extend as the operating time accumulates,while the feasible range of accel grid potential narrows due to a reduced EBSF(electron backstreaming failure)margin.The feasible ranges determined by the initial condition are:(i)the beam current up to 0.981 A,and(ii)the accel grid potential up to−85 V.A 23%enlargement of the aperture diameter would bring up to 48 V of EBSF margin loss.
