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The Borel sum of a series is the Laplace transform of the sum of the term-by-term inverse Laplace transform of the original series.

系列的 Borel 总和是原始系列的逐条款倒转的 Laplace 转换的总和的 Laplace 转换。

The constitutive equation between current density vector and electric field strength vector is tranformed into s-domain by the principle of Laplace transform,and the inverse Laplace transform is adopted for the explicit equations between them in time-domain. Finally through exponential time stepping,the FDTD iteration equations are obtained,which can be easily solved in discrete-time-domain.

该方法是将电流密度矢量与电场强度矢量之间的本构方程基于拉普拉斯变换原理转到复频域，然后再逆变换到时域得到它们之间显式的方程，最后再结合指数差分，得到离散时域的显式的FDTD迭代方程，解决了本构方程中电流密度矢量的分量相互耦合而不易直接离散的困难。

The harmonic field of electric dipole source on the uniform earth surface is converted into transient field by inverse Laplace transform,and the Bz/ t transient curve is calculated.The Hz transient curves on the stratified earth surface are obtained from cosine transform calculated by broken line approximation.

由逆拉普拉斯变换将均匀大地面上的电偶极子源谐变电磁场转换为瞬变电磁场，并计算出Bzt瞬态曲线；对分层大地面上的瞬变电磁场，采用折线逼近法计算余弦变换得出Hz瞬态曲线。

The main results of the study are obtained as follows:1 In order to analyze and study the physical and mechanical characteristics of Lianyungang marine soft clay deeply, large numbers of basic mechanical characteristics tests and tri-axial shear tests are completed.2 In order to investigate the loaded and failure characteristics of the cement-soil, the cement-soils for the different ratio and different cure time are studied in the laboratory, and their unconfined compression tests and tri-axial shear tests are performed.3 Based on the solution of one-dimension consolidation, the one-dimension consolidation of the double-layered foundation is solved for two-grade loading in virtue of transcendental equation; Simultaneously, the one-dimension consolidation of the double-layered foundation is solved by means of Laplace transform for two-grade loading, and Stehfest numerical transform is applied in Laplace's inverse transformation; Furthermore, according to the practical foundation shapes, the consolidation models of the soil between piles and the substratum are built and solved respectively.4 The effect of each parameters on the consolidation of the double-layered foundation is discussed, and the solution of load transfer method for double-layered foundation is applied in A1-A4 section of Lian-Xu expressway. The results of calculating settlement of the double-layered consolidation theory are basic agreement with the measuring settlement results.

取得了以下几方面的研究成果：1针对连云港海相软土进行一维固结和三轴剪切试验，深入分析连云港海相软土的物理力学特性。2模拟水泥土搅拌桩施工，在室内制备不同配比、不同龄期的水泥土试样，并进行无侧限抗压试验和三轴剪切试验，揭示水泥土的受力特性及破坏特性。3运用超越方程，以双层地基一维固结解析解为基础，推导出二级加荷条件下双层地基的固结解析解；同时，通过荷载传递法并借助Laplace变换对双层地基的固结问题进行了数值求解；此外，根据实际的地基结构，建立了桩间土和下卧层的固结模型并分别进行求解分析。4分析探讨了双层地基中各参数对双层地基固结的影响程度，并运用荷载传递法的解答计算了连-徐高速公路A1-A4标水泥土搅拌桩处理段的六个断面，计算结果与实测数据有较好的一致性。

Fourier transform and inverse Fourier transform build up mapping for signal between time domain and frequency domain.

傅立叶变换及其反变换建立了信号时域与频域的映射关系。

The modulation function can be calculated by Fourier transform, filtering and inverse Fourier transform. The value of modulation function in areas of local shadow and abrupt discontinuities is lower than that in other parts. So modulation is a useful threshold to determine the quality of carrier stripe.

针对这种情况，本论文提出了通过傅立叶变换得到变形条纹图像的调制度函数，设置调制度函数阈值判断条纹质量的优劣，低于阈值的部分认为是不连续、阴影或陡峭区域，使用模板覆盖。

According to the algorithm of inverse transform in AVS audio video coding standard, this paper proposes a highly efficient hardware architecture for implementing the inverse transform function on FPGA.

根据AVS音视频编码标准中提出的反变换算法设计了一个基于FPGA的高效的反变换实现框架和方案。

We can obtain the n-dimensional inversion reconstruction formula of the image convolution-back projection by one-dimensional wavelet transform on Radon transform.

在医学上，问题的一种重要方式是从多个X射线投影值获得人体内部的密度分布，这个过程被称为计算机断层扫描。

Integrating the advantage of shorttime window Fourier transform and wavelet transform, Stransform has many characteristics such as linearity, lossless invertibility, high timefrequency resolution and so on.

之后发展起来的S变换时频分析方法综合了短时窗傅里叶变换和小波变换的优点，具有线性化，无损可逆性以及高时频分辨率等特性。

The diffusion structure has important impact on the rate of the diffusion and safety intensity for block cipher.Using the linear transform which has branch numbers as large as possible as the diffusion structure is a main method to devise block cipher.The linear transform is usually achieved by constructing the invertible matrix.

扩散结构的好坏直接影响了分组密码的扩散速度和安全强度，以分支数尽可能大的线性变换为分组密码算法的扩散结构是设计分组密码的一种重要方法，线性变换的构造可通过可逆矩阵的构造完成。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。