The large-scale periodic orbits of a nonlinear mechanics system can represent the homology classes, which are generally non-trivial, of the energy level surface and the topology properties of an energy level surface a...The large-scale periodic orbits of a nonlinear mechanics system can represent the homology classes, which are generally non-trivial, of the energy level surface and the topology properties of an energy level surface are determined by the that of the phase space and the large-scale properties of the Hamiltonian. These properties are used for estimate of the rank of the first homology group of energy level surfaces in the paper.展开更多
This paper studies the judgement problem of full-period maps on Z(p^n) and proposes a novel congruential map with double modulus on Z(p^n). The full-period properties of the sequences generated by the novel map are st...This paper studies the judgement problem of full-period maps on Z(p^n) and proposes a novel congruential map with double modulus on Z(p^n). The full-period properties of the sequences generated by the novel map are studied completely. We prove some theorems including full-period judgement theorem on Z(p^n) and validate them by some numerical experiments. In the experiments, full-period sequences are generated by a full-period map on Z(p^n). By the binarization, full-period sequences are transformed into binary sequences. Then, we test the binary sequences with the NIST SP 800-22 software package and make the poker test. The passing rates of the statistical tests are high in NIST test and the sequences pass the poker test. So the randomness and statistic characteristics of the binary sequences are good. The analysis and experiments show that these full-period maps can be applied in the pseudo-random number generation(PRNG), cryptography, spread spectrum communications and so on.展开更多
During the late Qing Dynasty and the early period of the Republic of China(1870-1930),the social classes in Yangzhou were basically dominated by officials,businessmen,and scholars.In the building number,scale,and func...During the late Qing Dynasty and the early period of the Republic of China(1870-1930),the social classes in Yangzhou were basically dominated by officials,businessmen,and scholars.In the building number,scale,and functional evolution of their home gardens,these three classes were different,reflecting abundant connotation of characteristic of the time and regional culture,revealing the inheritance path of Yangzhou culture,as well as the richness and diversity of home gardens in Yangzhou during the late Qing Dynasty and the early period of the Republic of China.展开更多
文摘The large-scale periodic orbits of a nonlinear mechanics system can represent the homology classes, which are generally non-trivial, of the energy level surface and the topology properties of an energy level surface are determined by the that of the phase space and the large-scale properties of the Hamiltonian. These properties are used for estimate of the rank of the first homology group of energy level surfaces in the paper.
基金supported in part by the National Natural Science Foundation of China(NSFC)(Grant Nos.11365023)the Science and Technology Program of Shaanxi Province(Grant Nos.2018GY-050)+1 种基金the Key Scientific Research Program of Department of Education of Shaanxi Province(Grant No.16JS008)the Key Projects of Baoji University of Arts and Sciences(Grant Nos.ZK2017037)
文摘This paper studies the judgement problem of full-period maps on Z(p^n) and proposes a novel congruential map with double modulus on Z(p^n). The full-period properties of the sequences generated by the novel map are studied completely. We prove some theorems including full-period judgement theorem on Z(p^n) and validate them by some numerical experiments. In the experiments, full-period sequences are generated by a full-period map on Z(p^n). By the binarization, full-period sequences are transformed into binary sequences. Then, we test the binary sequences with the NIST SP 800-22 software package and make the poker test. The passing rates of the statistical tests are high in NIST test and the sequences pass the poker test. So the randomness and statistic characteristics of the binary sequences are good. The analysis and experiments show that these full-period maps can be applied in the pseudo-random number generation(PRNG), cryptography, spread spectrum communications and so on.
基金Sponsored by Philosophical and Social Science Research Project in Colleges and Universities of Jiangsu Province in 2015(2015sjd751)
文摘During the late Qing Dynasty and the early period of the Republic of China(1870-1930),the social classes in Yangzhou were basically dominated by officials,businessmen,and scholars.In the building number,scale,and functional evolution of their home gardens,these three classes were different,reflecting abundant connotation of characteristic of the time and regional culture,revealing the inheritance path of Yangzhou culture,as well as the richness and diversity of home gardens in Yangzhou during the late Qing Dynasty and the early period of the Republic of China.
