系数域

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

The two methods are presented for non-stationary leakage signals based on original feature gradate. One is a combination of the peak-peak and grads, the other is mean energy method, with the methods eliminate influence of noise and the stress concentration identification is improved. Based on the relativity for wavelet coefficient square, the signal singularity detection theory of wavelet transform was employed to determine metal magnetic memory. Experiment shows that the method is valid for leakage signal.

针对含有噪声非平稳性的漏磁信号，在原有信号特征量梯度的基础上，给出了新的时域空间梯度和峰-峰值组合特征量，以及能量峰值处理方法，有效消除了随机噪声对磁记忆信号的影响，提高了应力集中区的识别率；从磁记忆信号的奇异性检测角度出发，通过多尺度小波系数的平方相关一致性来确定真正的应力集中区；实验验证了所提方法的有效性。

The watermark data are embedded into some proper hypercomplex frequency components and their corresponding HFT coefficients are modified to fulfill the symmetry constraint. The prerequisite, the watermarked host image in spatial domain should also be transferred in red, green, and blue channels, of embedding watermark data into the hypercomplex frequency domain is obtained.

它通过对彩色载体图像进行快速超复数傅氏变换，在超复数频域选择合适频段嵌入水印，并且修改其对称系数的值，保证了嵌入水印图像仍然可以用彩色图像的红、绿、蓝三色进行传输。

In order to refine a method for defence against at least one attack made by means of differential power analysis on at least one hyperelliptic cryptosystem, in particular at least one hyperelliptic public key cryptosystem, which is given by at least one hyperelliptic curve of any genus over a finite field in a first group, where the hyperelliptic curve is given by at least one co-efficient, so that an essential contribution can be made towards an efficient and secure implementation of the hyperelliptic cryptosystem, it is proposed that the hyperelliptic curve and/or at least one element of the first group, in particular at least one in particular reduced divisor and/or at least one intermediate result of a scalar multiplication, is randomised.

为了改进用于防御在至少一个超椭圆密码系统中、特别是在至少一个超椭圆公共密钥密码系统中通过微分功率分析作出的至少一个攻击的方法，该超椭圆公共密钥密码系统是通过在第一组中有限域中任何种类的至少一个超椭圆曲线给出的，其中超椭圆曲线由至少一个系数给出，以使得可以对于超椭圆密码系统的有效而安全的实施方案作出重要的贡献，提出将超椭圆曲线和/或第一组的至少一个元素、特别是至少一个特定的减小的除数和/或标量乘法的至少一个中间结果进行随机化。

Then, it introduces an adaptive blind watermark algorithm based on odd-even judgement. This algorithm uses the neighboring symbols mean value and the odd-even judgement to embed the watermark into the 2-level subband of the carrier image. The results of the test demonstrate that this algorithm has a good imperceptivity and robustness.

然后，在此基础上介绍了一种基于奇偶判决的图像自适应盲水印算法，该算法利用图像小波系数的相邻特征平均值和奇偶判决法在图像小波域的二阶子带上嵌入水印，试验结果表明该方法具有不错的不可见性和鲁棒性。

The transient free-surface Green function was used to formulate the integral equation on the body surface.

采用时域自由面 Green 函数将定解问题转化为物面上的积分方程，进而求解水动力系数和船舶运动方程。

Owing to the approximate and detail coefficients at each level after decomposition using undecimated wavelet transform have the same length as the original signal, the transform can possess time invariant property and retain more characteristics in time domain, and therefore improve the effect of denoising.

由于非降采样小波分解后的各层系数和原始信号的长度均相同，因此在具备平移不变性的同时还能保留更多的时域信息，从而可以提高信号的降噪效果。

The inverse polynomial and the invertible affine transformation exist by the finite field, linear algebra and matrix theory. The invertible affine transformation and the inversion in are easily realized by using lookup table. An algorithm can be used to get the inverse element of modulo .

本文运用有限域、线性代数和矩阵理论，论证了逆多项式和逆仿射的存在性，并且应用查表法简捷地实现了中元素的求逆和逆仿射变换；设计了一个易于在在计算机上实现的算法，来求形如的多项式模时的逆元，该多项式的系数在上。

Deterministic irreducible polynomial and primitive polynomial over finite rings, i. e. polynomial rings with coefficients in finite fields, are obtained.

在系数属于有限域的多项式环即有限环上，给出确定型的不可约多项式和本原多项式。

At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled.

首先，采用Fourier积分变换解析求解了Biot方程，得到了该动力控制方程在Fourier变换域上的一组通解，然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程，并应用Jacobi正交多项式将其转化为一组线性代数方程组，通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv，编制了相应的计算程序。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。