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The chapter 3 investigates the constructive method which means that many combinatorial numbers, such as Stirling number, Bell number, harmonic number, Fibonacci number and the number of derangement, are represented to moments of some random variables. This method is used in the computation of combinatorial sums, discovery and proof of combinatorial identities.

第三章研究了构造性概率方法，即一些常见组合变量(以后统称组合数为组合变量)的概率表示，诸如Stirling数、Bell数、调和数、Fibonacci数、错排数都可以表示为一些随机变量的矩，这些概率表示可以用来研究组合和式的计算与恒等式的证明。

Lightfoot sees in this enthusiastic reception proof of Celtic fickleness of character.

lightfoot认为，在这方面的热情接待证明凯尔特变化无常的性格。

I told you figure skating is gay, this video is living proof.

想不到好的标题，不过我相信你会喜欢的！

Although massive filamentary structures have been often observed at relatively small distances from us, solid proof of their existence in the more distant Universe has been lacking until now.

虽然在相对较小的距离内，我们常常观测到这类大质量丝缕结构，但在本报告之前，如此大距离上的确凿证据却一直缺乏。

Let P be a Markov operator in, and Q any ergodic Markov operator possessing finite invariant measure. In this note a simple and direct proof of the equivalence of the mixing property for Q and the ergodicity for Cardesian product PQ is given.

设P是L上的Markov算子，Q是任一具有有限不变测度并且遍历的Markov算子，在这篇注记中我们给出了P的混和性和Cartesian积P×Q的遍历性相互等价这一结果的直接而简单的证明。

"A theorem within such a system is a formula capable of proof through a finite sequence of well-formed formulas, each of which either is an axiom or is validly inferred from earlier formulas."

在这样的系统中，一条定理即是可以通过合式公式的有限序列加以证明的一个公式，这些合式公式中的每一个公式不是公理，就是从前面公式可以推得的公式

Another simple synthetic proof of finiteness of areas of asymptotic triangles in non-Euclidean geometry is given.

给出双曲非欧几何中极限三角形面积有限性的另外一种简单证明。

Produced Flameproof lamp LED light source of roadway safety, energy saving, life of 4 to 5 years, with the same brightness of incandescent energy saving 80% compared to ~ 90%, which is a variety of mines and explosion-proof environment, the ideal lighting tool .

公司生产的隔爆型LED光源巷道灯安全、节能，寿命达4～5年，与同亮度的白炽灯相比节能达80％～90％，是各种矿井和防爆环境中的理想照明工具。

The new marine hazardous area float switch is flameproof and is available for both submersible and hose-proof duties.

新海运危险领域浮动开关为防火型材质，既能应用于潜水领域又能应用于防水领域。

And how perfect a proof of the natural fitness and, I may almost say, the divine origin of the aristocratic constitution of the States in Flatland!

以及如何完善自然健康证明，而且我几乎可以说是对国家宪法，在平地贵族的神源！

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。