Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a loc...Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral,which then defines a local center manifold of the system. Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them.展开更多
The momentum behind China’s economic rebound remains strong. But underpinned by recently announced economic indicators of the third quarter, the quality of the economic growth has been somewhat worrying. Driven mainl...The momentum behind China’s economic rebound remains strong. But underpinned by recently announced economic indicators of the third quarter, the quality of the economic growth has been somewhat worrying. Driven mainly by credit, the economic upturn has fueled inflationary risks. Hu Yuyue, Director of the Securities and Futures Institute of the Beijing Technology and Business University, shared his opinions on these issues in an article recently published in the Shanghai Evening Post. Edited excerpts follow:展开更多
基金VR acknowledges the support of this work by the Slovenian Research Agency and by a Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme,FP7-PEOPLE-2012-IRSES-316338
文摘Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral,which then defines a local center manifold of the system. Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them.
文摘The momentum behind China’s economic rebound remains strong. But underpinned by recently announced economic indicators of the third quarter, the quality of the economic growth has been somewhat worrying. Driven mainly by credit, the economic upturn has fueled inflationary risks. Hu Yuyue, Director of the Securities and Futures Institute of the Beijing Technology and Business University, shared his opinions on these issues in an article recently published in the Shanghai Evening Post. Edited excerpts follow:
