For inspecting topological and geometrical unanimity of a solid model, principle of closed path topology and Euler′s formula are important tools.

闭路拓扑原理和欧拉公式是检验实体模型边界表示的拓扑与几何一致性的重要工具。

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We have given the critical formula of the closed orbits and have got conclusion of unclosed orbits in the above-mentioned conditions.

我们证明了轨道闭合的判别公式，并得到在上述情形下轨道非闭合的结论。

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Theoretically, a new closed-form parameter re-estimation formula is suggested for training LPHMM.

理论上，本文还给出了LPHMM的一组闭式参数重估公式。

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