证明是...

By the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proof is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity.

恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Moreover, by the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proofs is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity. Because of the 1-1 property of bijection, the identity is proved.

此外，恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proofs on the subspace-lattice. Especially, one remarkable result is that a new q-analogue of the cube-sums identity is obtained with its combinatorial proof over the vector space.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从向量空间角度给出了一些恒等式的q-模拟及组合证明，其中突出的成果是给出了立方和恒等式的一个新的q-模拟及组合证明。

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

On the basis of thorough introspectionof the popular viewpoints of "The claimer should give evidenceand"the shifting of burden of proof"among Chinese scholars,Iput forward my humble view of the standard of the share of burden ofproof,among which that"the civilcode enactment should consider theshare of burden of proof is alegislative proposal.

第十章是关于我国证明责任分配标准理论的反思与完善。在对我国学术界流行的"谁主张、谁举证"和"举证责任倒置"的观点进行全面反省的基础上，提出了建立与完善我国证明责任分配标准理论的拙见，其中"民法典的制定应考虑证明责任分配"属于立法建议。

In order to study the popular curve shortening flow in the plane, Gage[3] has shown in 1983 the following inequality, if k is the signed curvature of a closed convex plane curve γ with length L and enclosing area A, then one gets Gage calls it an isoperimetric inequality in [3], but he does not show that the equality holds if and only if the curve γ is a circle, while as an isoperimetric-type inequality, one should prove this kind of result.

Gage称之为等周不等式，但他没有证明其中等号成立当且仅当，γ为圆周，而作为等周型的不等式是应该证明这种结果的，本文我们利用单位速率外法向量流，通过努力证明了这种结果，从而把Gage不等式加强成更加等周的形式。

LIU Hui's Cyclotomic Method is one of the greatest achievements in the history of mathematics in China,even in the world,in which the special approach to understand the infinity and the method to solve it are presented.

有的著作认为在极限公式limx→0sinxx=1的证明中，要用到圆的面积公式S=21Lr，而对后者的证明中必须要用到重要极限limx→0sinxx=1，从而犯了循环论证的错误。魏晋刘徽的&割圆术&是对无限问题的独特认识和致用的处理方式，是为证明圆面积公式而设计出来的一种方法。

The defender must be allowed to affirm the pasties on the count.

共同危险行为人如果认为自己不应承担责任，可在以下几个方面提供证据：1、指明谁是实际致害者，或者证明其不可能具有侵害原告的危险行为或状态。2、证明原告的损害完全是由其本身的责任造成的或是由共同危险行为以外的行为造成的，即由第三方行为造成的。3、证明其具有法定的免责条件(不可抗力、正当防卫、紧急避险等)。

Your second question proves that you are totally fooled by the Priest who organised the Church and created some stories and take advantages on all human beings by the name of God that is monopolised by their exclusive rights to interpert the natures and characteristics of so called God.

但相信我的出生、就证明了我对母亲的信任、事实上，有必要在这里大费周章的解释吗？提出「上帝」的是发帖人 passbyhk。若不是他先提出这、我也不会回应。我虽然有将圣经内容写出来、但我有说过我有去过教会教堂吗？别说你不能证明、面对一个教徒、我自己也不能证明我有去过。因此、你「怀疑」的这些、可以免去了。我可没有兴趣讨论神是否存在。

Thomas Aquinas argues that the beginning of the world can not be demonstrated but is a truth knowable only through revelation. Bonaventura not only holds that we know by faith and revelation that the world has a beginning; he also asserts that reason can demonstrate it.

托玛斯阿奎那认为，世界有开端乃信仰的对象，属於教理神学的信条，理性对之无能为力，自然理性既不能证明世界的永恒性，也不能证明世界不是永恒而有开端的；波纳文图拉则坚持&世界有开端&是理性可以证明的。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。