With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approac...With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approach the irrational winding number of the KAM torus,are examined.The break-up of quadratic frequency tori is characterized as the exponential growth of the residue means of the convergent periodic orbits.Critical parameters of the break-up of tori with different winding numbers are calculated,which shows that the spiral mean torus is the most robust one in our model.展开更多
We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits...We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits are calculated with their winding numbers approaching the spiral mean torus. The critical values of the parameters when the torus breaks are determined by the criterion that the variance of the distribution on the indices reaches a minimum. Some evidence is revealed about the possible existence of a universal distribution on the stability indices of the periodic orbits at the critical This confirms the picture given by the approximate renormalization theory of the Hamiltonian systems with three degrees of freedom.展开更多
In studying a 2-dimensional symplectic map,the exponential law and algebraic law are observed in the diffusion of orbits in the phase space.The diffusion time in the vicinity of an island is investigated carefully and...In studying a 2-dimensional symplectic map,the exponential law and algebraic law are observed in the diffusion of orbits in the phase space.The diffusion time in the vicinity of an island is investigated carefully and a logarithm law is found for the first time.The distribution of asteroids in the main belt and the diffusion velocities in 3:2 nd 4:3 resonances are discussed using this map.展开更多
目的探讨分化型甲状腺癌(DTC)术后促甲状腺素(TSH)抑制治疗患者心功能、结构及心率改变情况。方法回顾性选取2018年7月至2021年7月安徽省铜陵市人民医院收治的DTC术后行TSH抑制治疗患者40例,其中中高危患者20例(中高危组),低危患者20例...目的探讨分化型甲状腺癌(DTC)术后促甲状腺素(TSH)抑制治疗患者心功能、结构及心率改变情况。方法回顾性选取2018年7月至2021年7月安徽省铜陵市人民医院收治的DTC术后行TSH抑制治疗患者40例,其中中高危患者20例(中高危组),低危患者20例(低危组),中高危组术后TSH抑制到≤0.1 m IU/L,低危组术后TSH>0.1 m IU/L,比较两组治疗前后血清指标游离三碘甲状腺原氨酸(FT3)、游离甲状腺素(FT4)、TSH、总三碘甲状腺原氨酸(TT3)、总甲状腺素(TT4)水平,以及超声心动图指标左心室射血分数(LVEF)、左室舒张末期内径(LVD)、左房内径(LA)、二尖瓣E峰流速/A峰流速(E/A)等的差异。结果中高危组TSH抑制后3、6个月时TSH分别为(0.05±0.01)m IU/L和(0.04±0.01)m IU/L,明显低于低危组[(0.90±0.19)、(0.88±0.16)m IU/L],差异有统计学意义(P<0.05);中高危组和低危组TSH抑制后3、6个月时FT3、FT4、TT3和TT4比较差异无统计学意义(P>0.05)。中高危组TSH抑制后6个月时E/A为0.83±0.10,明显低于低危组(0.96±0.12),差异有统计学意义(P<0.05);中高危组和低危组TSH抑制后3、6个月时LVEF、LVD和LA比较差异无统计学意义(P>0.05)。中高危组和低危组治疗前、TSH抑制后3、6个月时心率、RP间期、QT间期、QRS间期等比较差异无统计学意义(P>0.05)。TSH抑制后6个月时,TSH水平与E/A呈正相关(r=0.300,P<0.05)。结论DTC术后TSH抑制治疗对患者心功能有一定影响,尤其低水平TSH抑制较明显,治疗时应考虑其对患者心血管系统的影响。展开更多
基金Supported by Hong Kong Baptist University Faculty Research Grants,Hong Kong Grant Council Grantsthe National Natural Science Foundation of China under Grant Nos.19903001 and 19633010the Special Funds for Major State Basic Research Projects.
文摘With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approach the irrational winding number of the KAM torus,are examined.The break-up of quadratic frequency tori is characterized as the exponential growth of the residue means of the convergent periodic orbits.Critical parameters of the break-up of tori with different winding numbers are calculated,which shows that the spiral mean torus is the most robust one in our model.
基金Supported by the National Natural Science Foundation of China under Grant No.19903001the Special Funds for Major State Basic Research Projects,and Hong Kong Research Grant Council.
文摘We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits are calculated with their winding numbers approaching the spiral mean torus. The critical values of the parameters when the torus breaks are determined by the criterion that the variance of the distribution on the indices reaches a minimum. Some evidence is revealed about the possible existence of a universal distribution on the stability indices of the periodic orbits at the critical This confirms the picture given by the approximate renormalization theory of the Hamiltonian systems with three degrees of freedom.
基金Supported by the National Natural Science Foundation of China under Grant Nos.19633010 and 19903001the Special Funds for the Major State Basic Research Project.
文摘In studying a 2-dimensional symplectic map,the exponential law and algebraic law are observed in the diffusion of orbits in the phase space.The diffusion time in the vicinity of an island is investigated carefully and a logarithm law is found for the first time.The distribution of asteroids in the main belt and the diffusion velocities in 3:2 nd 4:3 resonances are discussed using this map.
文摘目的探讨分化型甲状腺癌(DTC)术后促甲状腺素(TSH)抑制治疗患者心功能、结构及心率改变情况。方法回顾性选取2018年7月至2021年7月安徽省铜陵市人民医院收治的DTC术后行TSH抑制治疗患者40例,其中中高危患者20例(中高危组),低危患者20例(低危组),中高危组术后TSH抑制到≤0.1 m IU/L,低危组术后TSH>0.1 m IU/L,比较两组治疗前后血清指标游离三碘甲状腺原氨酸(FT3)、游离甲状腺素(FT4)、TSH、总三碘甲状腺原氨酸(TT3)、总甲状腺素(TT4)水平,以及超声心动图指标左心室射血分数(LVEF)、左室舒张末期内径(LVD)、左房内径(LA)、二尖瓣E峰流速/A峰流速(E/A)等的差异。结果中高危组TSH抑制后3、6个月时TSH分别为(0.05±0.01)m IU/L和(0.04±0.01)m IU/L,明显低于低危组[(0.90±0.19)、(0.88±0.16)m IU/L],差异有统计学意义(P<0.05);中高危组和低危组TSH抑制后3、6个月时FT3、FT4、TT3和TT4比较差异无统计学意义(P>0.05)。中高危组TSH抑制后6个月时E/A为0.83±0.10,明显低于低危组(0.96±0.12),差异有统计学意义(P<0.05);中高危组和低危组TSH抑制后3、6个月时LVEF、LVD和LA比较差异无统计学意义(P>0.05)。中高危组和低危组治疗前、TSH抑制后3、6个月时心率、RP间期、QT间期、QRS间期等比较差异无统计学意义(P>0.05)。TSH抑制后6个月时,TSH水平与E/A呈正相关(r=0.300,P<0.05)。结论DTC术后TSH抑制治疗对患者心功能有一定影响,尤其低水平TSH抑制较明显,治疗时应考虑其对患者心血管系统的影响。