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Homotopy perturbation method; MOL method; nonlinear partial differential equation; approximate solution

基础科学，数学，数学分析同伦摄动法；直线法；非线性偏微分方程；近似解

For composite foundation with compressible piles, based on displacement harmony condition, and combining with load transfer method and approximate solution of differential equation, analysis methods of linear and nonlinear interaction between piles and surrounding soil were suggested. A lot of significative results, for example availability pile length, load distribution between piles and surrounding soil, load distribution among all piles under rigidity pile-cap, load-settlement relation etc, were obtained.

对柔性桩复合地基，是基于位移协调条件，并结合荷载传递法与微分方程的近似解法—子域法，提出了变截面自由单桩与地基土、刚性承台下柔性单桩和变截面柔性单桩与地基土、刚性承台下柔性群桩与地基土线性及非线性相互作用的分析方法，并得到有效桩长、桩与基土的荷载分配及刚性承台下各桩桩顶荷载分配、荷载一沉降关系、荷载传递规律等有意义的结果。

With the advancement of science and technology, some new theories and new ways emerged gradually, some of them merged with specific theoretical tools, this specific theoretical tools include mathematical morphology, fuzzy techniques, neural networks, wavelet and so on. Secondly, in this paper, it described and analyzed the segmentation method based on the edge in the domain of image segmentation in detail. It did experiments on several edge detection operators using MATLAB, it summarized the advantage and the shortcoming of traditional edge detection operators, and the operating environment. On the basis of the experimental analysis, it implemented an edge location more precise, more efficient operating speed edge extraction method——Template Vector. In this method, it optimized differential approximate calculation of first differential operators the paper mentioned. After experimented on this edge extraction method, contracted with the traditional methods, the edge outline is extracted more accurately and more exquisitely, furthermore, it retained the object outline furthest, and achieved more satisfied edge extraction result.

其次，对图像分割领域中常用的基于边缘的分割方法进行了详细的研究与分析，对各种边缘检测算子进行了MATLAB环境下的实验，分析总结了各种传统边缘检测算子的优缺点和适应环境，并针对传统边缘检测算子在处理显微图像时的缺陷，在实验分析的基础上研究并实现了一种边缘定位更加精确、运算速度更加快捷的边缘提取方法——模板向量算法，在该算法中，对文章提到的一阶微分算子中微分的近似计算作进一步优化，经过对该边缘提取方法进行实验，其结果与传统方法相比，轮廓提取更为精确细腻，且最大程度的保留了图像中物体(目标个体或者明显噪声点)的轮廓，得到了比较理想的边缘提取效果。

An approximate formula of the signal-to-noise ratio is obtained based on the expression of the average error power.

在给出误差平均功率表达式的基础上，推导出信噪比的近似计算公式。

To give a load capacitance value,in fact,the two frequencies are equal.The approximate formula see above.

对某一个给定的负载电容值，实际上这两个频率是相等的，可近似表述为

An approximate formula based on single mode work condition of semiconductor laser is put forward.

从半导体激光器的单模工作条件出发，提出一个远场发散角的近似公式。

Through analyzing the mechanism of FFT, an approximate formula for image transformation is proposed at first.

本文主要围绕着局部支撑的基函数展开，建立了一系列视觉信息处理模型和快速算法。

By using experimental method, approximate formula of bulletproof velocity was found for high stength GFRP in this paper.

本文采用试验的方法，建立了高强玻璃纤维复合材料防弹性能近似公式。

The contribution of the light gain to engineering detection is discussed, then the approximate formula of the detection is given.

分析了象增强高速电影摄影的光增益与及其影响的主要因素，同时讨论了光增益对工程探测的贡献，给出了其近似的数学表达式。

The validity of the analysis by transmission line theory and the approximate formula is confirmed by comparison with some experimental results.

进而在传输线理论分析PIFA输入特性的基础上，为工程设计导出了谐振频率的近似公式。

Methods: Five patients with parkinsonism or dystonia were assigned to general anesthesia using an modified endotracheal tube.

本实验依照人体实验之相关规定进行，五位患有帕金森氏症或肌张力异常的病人接受神经立体定位手术。

If you can benefit from this book, it is our honour.

如果您能从本书获益，这将是我们的荣幸。