证明是

Combining NA samples the EB estimation with convergence rates is also obtained; Thirdly, for one-parameter exponential distribution family, we give the parameters' EB estimator that is admissible and asymptotically optimal with convergence rates. Finally, Bayesian and hierarchical Bayesian approaches are applied to analyze the reliability performances for series system with cold standby units and the numerical simulation results show that multiple Bayes estimator is superior to Bayes estimator.

其次，针对一类双边截断分布族，在非对称linex损失下构造了经验Bayes决策函数，建立了它的收敛速度，给出了渐近最优的证明；并结合NA样本研究了参数的经验Bayes估计及其收敛速度；接着给出了指数族参数的经验Bayes估计，证明了它是渐近最优的，也是可容许的，同时也获得了该EB估计的收敛速度；最后，运用Bayes与多层Bayes方法研究了具有冷贮备部件串联系统的可靠性指标的估计，并给出了数值模拟结果，结果表明多层Bayes估计优于Bayes估计。

In chapter 3, we give a unifying proof for some known difference sets by using Gauss sums, and we construct a new family of divisible difference sets.

在第三章中，我们用Gauss和给出了几个已知差集的统一的代数证明，它们原有的证明要么是用组合设计的方法，要么是用很技巧性的计数方法得到的。同时我们构造了一族新的可分差集。

In 1892, D.Ivanowsky of Russia had first shown that the causal agent of tobacco mosaic disease was filterable, but Beijerinck went much further and provided strong evidence that although the causal agent was filterable, it had amny of the properties of a living organism.

在 1892年，俄国的 D.Ivanowsky 首先证明了烟草花叶病的病原体是具有可滤过性。但是荷兰的Beijerinck研究得更深入，不仅提供了充分的证据证明尽管病原体是可滤过的，但是它却具有了生命体的所有特征。

Taking the evidence both scriptural and traditional as it actually stands, one may fairly maintain that it proves papal infallibility in a simpler, more direct, and more cogent way than it proves the general doctrine independently; and there can be no doubt but that this is so if we accept as the alternative to papal infallibility the vague and unworkable theory of ecumenical infallibility which most High-Church Anglicans would substitute for Catholic teaching.

以证据都圣经和传统，因为它其实是主张，有人可能会保持相当，这证明教皇infallibility在一个更简单，更直接，更有力的方式证明它比一般学说独立；有可以，但毫无疑问，这是因此，如果我们接受作为替代教皇infallibility含糊不清的和不可行的理论合一infallibility ，其中最高教会圣公会将取代天主教教学。

It was proof, once again, that in times of trouble the people of China open their hearts to each other.

这是在证明，再次证明，在遇到麻烦的时候，中国人民的心扉是对外敞开的。

Mathematics proved to be direct and two indirect method, the reduction to absurdity is a kind of indirect proof, it is mathematical proof of Dafa.

帮我翻译：数学证明有直接法和间接法两，反证法是间接证法的一种，它是数学证明的大法。

Mathematical induction is an important method in mathematics.

数学归纳法是数学中一种重要的证明方法，也是中学数学一个非常重要的内容，用于证明与无穷的自然数集相关的命题。

We only prove an inequation rather than the standard dataflow equation (8) because we are interested only in the correctness of the solution, not in its optimality.

我们只证明这个不等式方程，而没有证明标准数据流方程(8)，原因是我们所感兴趣的只是解的正确性而不是解的最优性。

In Europe, the Christian community, to prove that Christianity is right, it is necessary to prove that Judaism is wrong.

在欧洲基督教社会，要证明基督教是对的，就必须证明犹太教是错的。

Taking advantage of a rDNA mutant,rdna-A3,which is of paromomycin resistance marker and has replication predominance over wild type r dna+,we demonstrated that among 10 000 copies of rDNA in the old macronucleus no ne could "leak" into the developing new macromucleus during conjugation.

本文以1种具有强大复制优势而且是抗药性的rDNA分子，rdna-A3，为指标，证明在接合过程中旧大核内上万个rDNA分子没有1个能进入新大核，从而在基因分子水平上证明旧大核的退化是极为彻底的。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。