定理

And by the 14th century Chinese mathematicians had made significant advances in algebra, in the numerical solution of equations and in the rudiments of the binomial theorem.

到14世纪，中国数学家们在代数、数的方程解答和基础二项式定理方面都取得了重大发展。

Combination of 〓P MAS NMR with the binomial theorem calculation suggests that a restricted random distribution of Mg is present in the molecular sieves.

结合〓P MAS谱和二项式定理计算表明镁在磷酸铝分子筛上的分布是随机的。

Newton to humanity's contribution is huge, just like Engels said:"Newton as a result of invented law of universal gravitation to establish the science astronomy; As a result of has carried on the light decomposition, but established the science optics; As a result of established the binomial theorem and the infinite theory established the science mathematics; As a result of has known the strength essence, but established the science mechanics".

牛顿对人类的贡献是巨大的，正如恩格斯所说："牛顿由于发明了万有引力定律而创立了科学的天文学；由于进行了光的分解，而创立了科学的光学；由于创立了二项式定理和无限理论而创立了科学的数学；由于认识了力的本质，而创立了科学的力学"。

Gauss is a farmer's son, childhood, his math on the show extraordinary talent. Three-year-old father to correct an error in calculation; They found 10-year-old independent series of arithmetic summation of the formula; 11-year-old found the binomial theorem.

高斯是一个农民的儿子，幼年时，他在数学方面就显示出了非凡的才华。3岁能纠正父亲计算中的错误；10岁便独立发现了算术级数的求和公式；11岁发现了二项式定理。

Having discussed Wallis'interpolation in great detail, the paper shows that Wallis mainly relied on incomplete induction and analogical inference to obtain his results, an approach which was key to the creation of many important algorithms during the considered period. A comparison between Wallis'method and previous interpolations is then made and the influence of Wallis' thinking style embodied in his interpolation on Newton's invention of binomial theorem is clearly revealed.

通过考察沃里斯的插值过程，指出沃里斯插值法完全是借助于不完全归纳和类比推理得到的，并与过去的插值法做了比较，最后分析了沃里斯插值法对牛顿发明二项式定理的影响。

The measure transformation law of the binomial tree model and its deduction are obtained, analogous to continuous model.

类似于连续情形的测度变换，获得了二叉树模型的一个测度变换定理和推论。

It was given by the Biot-Savart law that the magnetic fields of single magnetic dipole. For the case of multi-dipole, it can be gotten by vector computation from single dipole.

以一种比较方便的离散的形式描述比奥-沙伐定理（Biot-Savart law），给出磁偶极子周围任意一点的磁感应强度公式，并将其扩展到多个磁偶极子的形式。

If there exist a family of copulas, we could construct any bivariate or multivariate distribution functions of given margins by Sklars theorem and these distributions are always very useful for simulation.

如果我们有一族copula，那么根据Sklar定理，可以构造出任何指定边缘分布的二元或多元联合分布函数，而这些分布函数在建模与模拟方面是非常有用的。

He also proved that the size of the black hole theorem.

他还证明了黑洞的面积定理。

And some results on the isometries and equivalences of quantum codes are presented, one of which generalizes one of results of Bogart et al..

研究了量子纠错码的等价性和保距同构，推广了Bogart等人的一些概念，并给出若干基本引理和定理，这些结论对进一步研究量子码的等价性和保距同构是非常有用的。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。