荷兰阿姆斯特丹国际剧团的《战争之王》(Kings of War)改编自莎士比亚的《亨利五世》《亨利六世》和《理查三世》,是比利时导演一凡·范霍夫(Ivo van Hove)继《罗马悲剧》后的又一巨作。本剧首演于2015年6月,之后进行了多个国家和...荷兰阿姆斯特丹国际剧团的《战争之王》(Kings of War)改编自莎士比亚的《亨利五世》《亨利六世》和《理查三世》,是比利时导演一凡·范霍夫(Ivo van Hove)继《罗马悲剧》后的又一巨作。本剧首演于2015年6月,之后进行了多个国家和城市的巡回演出,并于今年一月进行了全球线上放映。根据导演本人在线上放映前的致辞,这是一部关于领导者和领导力.展开更多
The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling an...The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling and an inner product were introduced in the space of homogeneous polynomials. Theorems were established for the explicit expression of the simplest normal forms in terms of the coefficients of both the conventional normal forms of Hopf and generalized Hopf bifurcation systems. A symbolic manipulation was designed to perform the calculation of the coefficients of the simplest normal forms using Mathematica. The original ordinary differential equation was required in the input and the simplest normal form could be obtained as the output. Finally, the simplest normal forms of 6-dimensional generalized Hopf singularity of type 2 and 5-dimensional Hopf bifurcation system were discussed by executing the program. The output showed that the 5th- and 9th-order terms remained in 6-dimensional generalized Hopf singularity of type 2 and the 3rd- and 5th-order terms remained in 5-dimensional Hopf bifurcation system.展开更多
文摘荷兰阿姆斯特丹国际剧团的《战争之王》(Kings of War)改编自莎士比亚的《亨利五世》《亨利六世》和《理查三世》,是比利时导演一凡·范霍夫(Ivo van Hove)继《罗马悲剧》后的又一巨作。本剧首演于2015年6月,之后进行了多个国家和城市的巡回演出,并于今年一月进行了全球线上放映。根据导演本人在线上放映前的致辞,这是一部关于领导者和领导力.
基金National Natural Science Foundation of China (No 10372068)
文摘The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling and an inner product were introduced in the space of homogeneous polynomials. Theorems were established for the explicit expression of the simplest normal forms in terms of the coefficients of both the conventional normal forms of Hopf and generalized Hopf bifurcation systems. A symbolic manipulation was designed to perform the calculation of the coefficients of the simplest normal forms using Mathematica. The original ordinary differential equation was required in the input and the simplest normal form could be obtained as the output. Finally, the simplest normal forms of 6-dimensional generalized Hopf singularity of type 2 and 5-dimensional Hopf bifurcation system were discussed by executing the program. The output showed that the 5th- and 9th-order terms remained in 6-dimensional generalized Hopf singularity of type 2 and the 3rd- and 5th-order terms remained in 5-dimensional Hopf bifurcation system.
