证明

In Chapter 2, we show that Xi 3 for all planar graphs of girth not less than 4 which contains no 5- and 6-circuits or contains no 7- and 8-circuits or contains no 8- and 9-circuits, we also show that Xi 3 for each planar graph of girth not less than 4 which contains no 6-, 7- and 9-circuits.

在第二章，论文证明了每个围长至少为4且不含5-圈和6-圈或7-圈和8-圈或8-圈和9-圈的平面图是3-可选色的。同时还证明了每个围长至少为4且不含6-圈，7-圈和9-圈的平面图是3-可选色的。

A sex offender is a person who has been criminally charged and convicted of a sexual offense, or has plead guilty but not convicted.

性犯罪者：是那些在刑法上被指控或证明犯有性侵害罪的人，或者是虽未证明有性侵害罪但已服罪的人。

If the accused does not willingly plead guilty, all the essential elements of guilt must be proven to a jury, and they must be proven "beyond a reasonable doubt."

如果被告人并非自愿地认罪，那么，便必须向一个陪审团证明有罪的所有基本要素，而且，其必须被得到排除合理怀疑'的证明。

Targeted enterprises should provide a chart of all their branches and the stock-right relationships of all their shareholders, documents of securities possessed by the enterprises, documents of the securities and stocks pledged.

应要求目标企业提供公司所有分公司或分支机构的设立和参股的所有公司的股权关系架构图文件、公司拥有证券的相关证明文件、设置质押的股权、有价证券等的相关证明文件等。

In US, there is a trend towards pluralization of proof of causation of insider trading and the standard of proof is different in proceedings initiated under different laws, but generally speaking, this standard is relatively low.

在美国，内幕交易因果关系的证明呈现多元化，根据不同的法律提起的诉讼对因果关系的证明要求也不同，总体而言要求较低。

Afterward Waldhausen ([7]) showed that this topological hypothesis was true. Besides, Stallings ([11]) gave another conjecture that was equivalent to Poincare"s Conjecture. Thus we know both conjectures made respec- tively by Traub and Stallings are equivalent to Poincare"s Conjecture.

另外Stallings([11])又提出了另一个代数的猜想并同时证明也证明了这个猜想与庞加莱猜想是等价的，由此可知Traub所给的猜想与Stallings的猜想都与庞加莱猜想是等价的，从而这两个代数的猜想也是等价的。

We prove that the solution of a nonlinear complementarity problem is exactly the equilibrium point of differential equation system, and prove the asymptotical stability and global convergence.

在一定的条件下我们证明了非线性互补问题的解是该微分方程系统的平衡点，并且证明了该微分方程系统的稳定性和全局收敛性。

This paper summarizes several decidabilities for predicate logic inference and several points for attention, which may help people in proof of such subjects.

本文总结了几种谓词逻辑推理的判定方法和注意事项，以帮助掌握证明题的证明。

Experiment has confirmed the prediction of theory.

实验确认了理论的预测，50年前赫兹第一次证明了电磁波的存在，而且用实验证明了它的速度等于光速。

The applicable scope of the high probable standard of proof include the standind of preponderant evidence.

高度的盖然性的证明标准的适用范围含盖了优势证据的证明标准。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。