以下为句子列表：
英文: At the same time the new algorithm is applied to find necessary conditions for such isochronous center, then proofs of isochronicity of these systems by using some effective methods are given.
中文: 同时通过一种最新算法求出无穷远点为中心时的周期常数，得到了拟等时中心的必要条件，并利用一些有效途径一一证明了条件的充分性。
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英文: In this article, the center conditions, isochronous center conditions and bifurcation of limit cycles at infinity for a class of fifth system are investigated.
中文: 摘要研究一类五次系统无穷远点的中心、拟等时中心条件与极限环分支问题。
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