Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action o...Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action of a group G,then G contains a free subsemigroup and the action has positive geometric entropy.As a corollary,X admits no sensitive nilpotent group action.展开更多
The regular small-world network, which contains the properties of small-world network and regular network, has recently received substantial attention and has been applied in researches on 2-person games. However, it ...The regular small-world network, which contains the properties of small-world network and regular network, has recently received substantial attention and has been applied in researches on 2-person games. However, it is a common phenomenon that cooperation always appears as a group behavior. In order to investigate the mechanism of group cooperation, we propose an evolutionary multi-person game model on a regular small-world network based on public goods game theory. Then, to make a comparison of frequency of cooperation among different networks, we carry out simulations on three kinds of networks with the same configuration of average degree： the square lattice, regular small-world network and random regular network. The results of simulation show that the group cooperation will emerge among these three networks when the enhancement factor r exceeds a threshold. Furthermore, time required for full cooperation on regular small-world network is slightly longer than the other networks, which indicates that the compact interactions and random interactions will promote cooperation, while the longer-range links are the obstacles in the emergence of cooperation. In addition, the cooperation would be promoted further by enhancing the random interactions on regular small-world network.展开更多
基金Supported by NSFC(Grant Nos.11771318 and 11790274)。
文摘Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action of a group G,then G contains a free subsemigroup and the action has positive geometric entropy.As a corollary,X admits no sensitive nilpotent group action.
基金Supported by the National Natural Science Foundation of China(71601148)the National Social Science Foundation of China(14ZDA062)Humanities and Social Science Research Foundation of Ministry of Education(14JDGC012)
文摘The regular small-world network, which contains the properties of small-world network and regular network, has recently received substantial attention and has been applied in researches on 2-person games. However, it is a common phenomenon that cooperation always appears as a group behavior. In order to investigate the mechanism of group cooperation, we propose an evolutionary multi-person game model on a regular small-world network based on public goods game theory. Then, to make a comparison of frequency of cooperation among different networks, we carry out simulations on three kinds of networks with the same configuration of average degree： the square lattice, regular small-world network and random regular network. The results of simulation show that the group cooperation will emerge among these three networks when the enhancement factor r exceeds a threshold. Furthermore, time required for full cooperation on regular small-world network is slightly longer than the other networks, which indicates that the compact interactions and random interactions will promote cooperation, while the longer-range links are the obstacles in the emergence of cooperation. In addition, the cooperation would be promoted further by enhancing the random interactions on regular small-world network.
