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A weak form equation containing boundary parameters was given for elastic problems in three-dimension.

本文从弹性力学平衡方程更为一般的弱形式出发，给出了含边界参数的弱形式方程。

These compression waves reflect from the plume boundary in the form of a series of expansion waves that eventually intersect the nozzle wall downstream of the compression zone.

这些压缩波反映，从羽流边界的形式了一系列的膨胀波，最终相交喷嘴墙下游压缩区。

The cross and the empty tomb form an immovable boundary between who we were and who we have become, between our former realm of sin and guilt and death and our new realm of righteousness and life.

十字架与空坟墓形成一道不可移动的界限，把过去的我与现在的我，及先前受罪恶、过犯、死亡辖制的生命与如今公义的新生命，截然划分开来。

Except Yuanqi , all things had form, boundary, sideand beginning and end.

他认为天地万物都是有形有象的，而作为宇宙本原的元气，则是无形无象的；宇宙间的具体事物都是有固定的属性，也要受到其他物的限制，而元气则是"混全之称"；一切具体事物都是有生有灭的，而元气则是无始无终、无生无灭的；元气的运动变化，聚散化生并不影响元气的总量，正如能量守恒定律一样；性也为元气所固有。

The method used the principle of superposition, where the annual mean boundary temperatures form a basic steady-state temperature distribution and the amplitude of the external and internal temperatures contribute periodic seasonal alterations.

这个方法采用迭加原理，在一年一度的平均气温是一项基础边界的稳态温度分布和幅度的外部与内部温度贡献定期季节改动。

Based on image statistical characteristic, the algorithm can search automatically the boundary start-point using Sobel operator and special template operation, then according to the connection status of every boundary point in its 8-connection neighbor field, seek automatically the search direction, form the whole data collection of a target boundary outline.

该算法依据目标图象特征，在二值图象中利用Sobel算子和特定的模板操作，自适应搜索边界起点；然后，按照每个边界点在其8邻域内的连通情况，自动寻找搜索方向，形成了完整目标边界轮廓数据集。

R~n(n≥0) is a bounded domain with smooth boundaryΩ;ΔisLaplace operator; u and v, respectively, denote populaton densities of prey andpredator species, inhabit the domainΩ; a_i, b_i, c_i, D_i(i=1,2) are positive constants.the form of boundary parameter B is?

R~n(n≥0)是边界Ω充分光滑的有界区域；△为Laplace算子；u，v分别表示区域Ω中食饵和捕食者的密度，参数a_i，b_i，c_i，D_i(i=1，2)均为正常数，而边值参数B形式为这里的？

We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.

接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

It is proved that when all the ratios of the generic term of a subaddtive sequence to its ordinal number form a lower bounded sequence,the ratio sequence must have limitation .

从这一结果出发证明了，当定义在(0，+∞)上的次可加函数与其自变量之比为有界函数时，次可加函数必存在上下确界函数，并证明了其上下确界函数均为齐次线性函数。

He paid $5,000 for this cupcake.

他我这个纸杯蛋糕花了5000美元。

I mean, if you want to, that is

我的意思是，如果你们想吃的话。