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The stress intensity factors and the size of saturation strips were derived analytically and their dependencies on the ratio of the periodicity to half-length of the crack h/l were analyzed in detail.

对应力强度因子和饱和条带尺寸进行了理论推导，详细分析了它们与周期长和半裂纹长的比值h/l之间的关系。

The DFP method is proved a officient one in processing unconstrainted optimization problem, so in this thesis, used the idea of mechanical structural optimization for reference analytically and extended modified formula of DFP—matrix to shape optimiation the DFP—Hamilton function method is put forward.

由于变尺度方法是有效的无约束优化方法，本文在分析的基础上借鉴了机械结构参数优化的思想，并将变尺度矩阵的修正公式扩展至形状优化中去，进而提出了变尺度—H函数极值法，并用其解决了梁、柱和复杂曲面的形状优化设计问题，取得了较好的效果。

From the start [50] I can apprehend the concept of body analytically through the characters of extension, impenetrability, figure, etc.

从一开始，我就可以分析性的理解物体的概念(空间性，密性，形状等等)，这些都是包含在物体概念之内的。

The error of quadratic interpolation method on sine wave signal was analytically studied and numerical evaluated in this paper.

该文从理论分析和数值仿真两个方面，对二次插值算法在正弦信号分析中存在的误差进行了详细的研究，得到了误差范围的解析表达式。

For example, a floor joist may be subjected to loads that cause bending moment and shear as well as torsion.in these situations ,measurement of the inherent strength becomes analytically and experimentally complex,and in many situations cannot be done .

例如，地板龙骨可能受到荷载引起的弯矩和剪力以及torsion.in这种情况下，测量的固有实力和实验解析变得复杂，在许多情况下不能做。

Basing on the law of conservation and conversion of energy, we can obtain analytically Newton\\\\\\\s three laws of motion and the law of conservation of momentum.

文章深入讨论了能量与力之间的内在联系，根据能量守恒和转换定律，直接获得牛顿三大运动定律和动量守恒定律。

Recurrent formulas for calculating the coefficients of the Legendre polynomial and the expressions for calculating the sedimentation coefficient are deduced analytically.

为了研究多分散低Péclet数沉降问题，我们先以Legendre多项式展开法得到了计算对分布函数的普遍递推式，以及由Legendre多项式的系数表示的沉降积分。

Finally, the contribution of the boundary fields to both the magnetic susceptibility and specific heat are obtained, and their exact expressions are analytically derived.

最后，得到了边界场对于磁化率和比热的贡献，并给出了确切的表达式。

In my paper I shall argue in favor of this approach, while at the same time emphasizing the need for improvements - briefly stated: less emphasis on their notion of "idealization" and more of an emphasis on a "gradualist" and "meliorist" approach, operating more analytically, by cautious analysis of a variety of situated thought-experiments, preferably in terms of "arguments from absurdity" in a pragmatic sense.

在本文中，我将支持这种进路，同时强调改进的必要性。简要地讲，就是较少强调他们的"理想化"的观念，而更多地强调一种逐级主义的和淑世主义的进路，通过对处于不同境遇下的思想实验的谨慎分析，特别倚重语用学意义上的"归谬论证"，更具分析精神地来进行这种探讨。

Selecting proper single valued variable separation functions in the 2+1 variable separation solutions,we construct many types of single valued coherent soliton structures such as dromion,dromion lattice,solitoff,2-solitoff,static and kinetic breather,instanton,compacton, peakon,and so on.The interactions among these coherent localized excitations including the collisions of compaction and compacton,peakon and peakon,line soliton and y-periodic soliton,dromion and dromion,dromion and solitoff,et al,are investigated analytically and graphically,and found that can be elastic and nonelastic respectively,which reveal various exotic and important nonlinear characters and interaction properties.

在2+1维分离变量解中选择适当的的单值分离变量函数，构造了2+1维非线性波动模型多种单值相干孤子结构如Dromion，Dromion格子，Solitoff，2-Solitoff，静止和运动呼吸子、瞬子、Compacton、Peakon等；考察了一些典型的非线性激发模式间如Compacton和Compacton，Peakon和Peakon，线孤子和y-周期孤子，Dromion和Dromion，Dromion和Solitoff之间等相互作用行为，发现其相互作用可以弹性的也可以是非弹性的，揭示了多样奇异而重要的非线性特性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失