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MDCT (Modified Discrete Cosine Transform) and IMDCT (Inverse Modified Discrete Cosine Transform) are two of the most complex computation modules.

改进离散余弦变换与其反变换是当今主流音频压缩标准中普遍采用的时频变换单元，也是计算量最密集的模块之一。

In the method the discrete cosine transform DCT is first applied to noisy facial images to remove its high frequency component noise, the removed noisy face images can be obtain through performing inverse discrete cosine transform. Then the two dimensional principal component analysis (2DPCA) is exploited to the removed noisy face images to obtain a set of eigenvectors that have larger correspondent eigenvalues, and the features of images with lower information dimensions are extracted to get fast recognition speed.

这方法首先对具杂讯脸部影像进行离散余弦转换去除高频杂讯，取得低频影像以降低高频杂讯干扰，然后再对低频影像以二维主分量分析(2DPCA)撷取前几个较高特徵值所对应的一组特徵向量，以降维与资讯集中达到快速辨识的目的。

This algorithm decomposed each source image by wavelet transform, and constructed multi-level tolerance granularity in wavelet coefficients. Finally, selected the appropriate level to fusion image by granularity and through the inverse wavelet transform to form the final fused image.

该算法通过将待融合源图像进行小波变换，然后对小波系数构造多层次的相容粒度，最后选择合适的层次进行粒度融合并进行小波逆变换形成最终的融合图像。

This paper puts forward an image super-resolution enhancement algorithm based on wavelet transform. This algorithm makes full use of the wavelet multi-resolution transform, and embodies the natural process of decrease of image resolution; it estimates the high resolution wavelet coefficient and gets the reconstructed high resolution image by interpolation inverse transformation.

文章在研究和分析小波变换理论的基础上提出了一种基于小波变换的图像超分辨率增强算法，该算法充分利用小波多分辨率分解思想，体现图像分辨率降低的自然过程；通过估计高分辨率小波系数，经插值逆变换可得到重构的高分辨率图像。

This is achieved using Matlab on Laplace transform and inverse transform of the few examples.

这是用Matlab实现的关于Laplace变换及反变换的几个实例。

In the numerical calculation of electromagnetic transient response, the G-S transform method is used frequently for inverse Laplace transform.

在电磁场瞬变响应的数值计算中，常采用G-S变换法作逆拉氏变换。

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 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。

The statistical analysis of this large set of mutations has led us to propose a diagnostic strategy that should help with the molecular work-up of optic neuropathies.

这一大系列基因突变的统计学分析引导我们提出一个诊断策略，可以帮助我们对视神经病变进行分子学的诊断检查。

The results show that the pipe grouting changes the mechanical parameters of surrounding rocks to achieve the security of engineering objectives by reinforcing surrounding rocks and bolcking the water.

研究表明：小导管注浆一方面改变了围岩的力学参数，另一方面利用浆液的固结特性可以实现堵水和加固围岩的工程目标，使隧道在开挖过程中的安全得到保障。