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For TSFEM, the formulas of the mean value and the variance of water head at each node are derived directly with Taylor series expansions.

由此可计算出每个节点水头的均值、方差和协方差，这样就获得模型结果的不确定性。

Use the summoned Shadow Teams to destroy any possible expansions and use the third to stop possible Disintegrator Rushes.

使用召唤得影队去摧毁任何可能得扩张点，同时用第三队影子去阻止可能得粉碎者快攻。

Then after the author researches the interaction problem of the partial derivative operators with respect to the two points P and Q, analytical expressions as well as series expansions of the kernel function within disturbing gravity field elements are determined, and their explicit expressions which can be applied practically are given for the first time.

深入研究了关于 P 和 Q 两点局部导数算子的相互作用问题，得到了扰动场元之间核函数和协方差函数的解析与级数展开式，首次给出了较为实用的明晰表达式。

Many authors have studied the properties of the Edgeworth expansions for the distributions of Ustatistics since the invention.

关于标准化和学生化U统计量的分布，二阶展开的收敛速度问题成为了研究的核心内容，相关的研究成果已经非常丰富。

Neighbor-Joining analyses of teleost hepcidins showed that the eelpout 4cys variant arose independently from the notothenioid version, which lends support to adaptive evolution of reduced cysteine hepcidin variants on cold selection. The NJ tree also showed taxonomic-specific expansions of hepcidin variants, indicating that duplication and diversification of hepcidin genes play important roles in evolutionary response to diverse ecological conditions.

另外我们在另一种生活于南极水域的eelpout中也发现了一种含有4个半胱氨酸残基的hepcidin，而eelpout和南极鱼notothenioid在分类学上分属于不同亚目，是一类相差较远的物种，利用Neighbor-Joining方法建树分析发现eelpout的hepcidin虽然同样仅含有4个半胱氨酸残基，但和notothenioid的4cys_hepcidin有着不同的起源，这也进一步说明了hepcidin中半胱氨酸残基数目的减少确实是对寒冷环境的一种适应性进化。

Through the polynomial approximation to function, resulting in more than a Peano-type and Lagrange remainder of the Taylor formula, using elementary functions Maclaurin expansions to address the limits and the approximate evaluation of the problem.

通过多项式来逼近函数，从而得到带有佩亚诺型余项和拉格朗日余项的泰勒公式，利用初等函数的麦克劳林展开式来解决极限及近似求值的问题。

Advanced course covering topics selected from: semimartingale theory, stochastic integrals, homogeneous chaos expansions, stochastic differential equations, Malliavin calculus, infinite dimensional processes, functional central limit theorems, Feynman-Kac formula, Feynman integral.

随机分析：高级课程，包括：半鞅理论，随机积分，齐次混沌展开，随机差分方程， Malliavin 微积分，，有限维过程，泛函中心极限理论， Feynman-Kac公式， Feynman积分，过滤理论的应用，无限粒子系统，量子力学，神经学中的随机模型。

China has already pulled off one of the most remarkable expansions of education in modern times, increasing the number of undergraduates and people who hold doctoral degrees fivefold in 10 years.

中国教育已经实现了现代最为引人注目的发展，10年间大学本科生和拥有博士学位的人数增加了5倍。

In a wide-ranging fusillade against Obama, Cheney also criticised his choice of ambassador in Iraq, Christopher Hill, calling him inexperienced, and said the president was using the recession to try to justify "one of the biggest expansions of federal authority … in the history of the republic".

在一连串针对奥巴马的抨击中，切尼还提到奥巴马的驻伊拉克大使人选克里斯托弗·希尔，批评此人经验不足；他还说这位总统正以经济衰退作为理由，试图推行"共和国历史上最大规模的一次联邦权力扩张"。

But the great bulk of the glosses resemble the Greek additions in the Book of Proverbs; they are expansions of the thought, or hellenizing interpretations, or additions from current collections of gnomic sayings.

但绝大部分的粉饰类似於希腊补充在这本书中的谚语，它们是扩张的思想，或hellenizing解释，或补充从目前收集的gnomic谚语。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。