A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending ...A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending some results on block-transitive Steiner 2-designs to block-transitive 3-designs,and then based on these results,investigate the G-point-primitive block-transitive 3-(v,k,λ)designs for alternating or symmetric groups G.We prove that when n≥min{λ^(2),30}the point stabilizer in G must be of intransitive type,and specifically,when n≥30 there exists no nontrivial G-point-primitive block-transitive 3-(v,k,2)design.展开更多
In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to ob...In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.展开更多
基金supported by the National Natural Science Foundation of China(No.12471022)。
文摘A t-(v,k,λ)design is said to be G-point-primitive or G-block-transitive,if its automorphism group G acts primitively on the point set or transitively on the block set,respectively.In this paper we begin by extending some results on block-transitive Steiner 2-designs to block-transitive 3-designs,and then based on these results,investigate the G-point-primitive block-transitive 3-(v,k,λ)designs for alternating or symmetric groups G.We prove that when n≥min{λ^(2),30}the point stabilizer in G must be of intransitive type,and specifically,when n≥30 there exists no nontrivial G-point-primitive block-transitive 3-(v,k,2)design.
基金Supported by the Natural Science Foundation of Ningxia(2023AAC03114)National Natural Science Foundation of China(72464026).
文摘In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.
