Let n, s1, s2,..., sn be non-negative integers and M(s1, s2,...,sn) ={(a1, a2,..., a.)| ai is an integer and 0≤ai ≤si for each i}. In this paper, the cardinality of maximum trees of finite sequences in M(s1, s2,...,...Let n, s1, s2,..., sn be non-negative integers and M(s1, s2,...,sn) ={(a1, a2,..., a.)| ai is an integer and 0≤ai ≤si for each i}. In this paper, the cardinality of maximum trees of finite sequences in M(s1, s2,..., sn) sn) is obtained, which generalizes some of Frankl's results on families of finite sets with prescribed cardinalities for pairwise intersections.展开更多
The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Se...The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.展开更多
文摘Let n, s1, s2,..., sn be non-negative integers and M(s1, s2,...,sn) ={(a1, a2,..., a.)| ai is an integer and 0≤ai ≤si for each i}. In this paper, the cardinality of maximum trees of finite sequences in M(s1, s2,..., sn) sn) is obtained, which generalizes some of Frankl's results on families of finite sets with prescribed cardinalities for pairwise intersections.
基金This project is supported by National Natural Science Foundation of China(No.50075070).
文摘The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.
