原尺度

In chapter 5, heat mechanism and heat radiating forms of the hydraulic system faults are studied. Based on relationship between degree of the hydraulic system faults and thermal image shapes, multi-scale entropy of temperature field is taken to express the fault degree. Entropy of low frequency means its absolute temperature, and entropy of high-frequency means distribution of temperature field.

同时针对系统故障程度的不同，提出了用温度场的熵进行表征的思路，通过多尺度小波对原热场图像进行小波变换，提取其中低频分量的熵用来衡量其绝对温度大小，提取高频分量的熵来衡量其温度场的分布，给出了实验结果，通过实验结果分析，证明这种分析方法是可行的。

Then the digital audio signal is set into segments and DWT is performed. Finally the modulated signal is embedded in the coefficients with relatively large absolute value on middle frequency range detail signal adaptively. The original digital audio signal is necessary when detecting the watermark.

在应用扩频技术的算法中，首先将视觉上可辨的二值水印图像降维为一维序列，再将一维水印序列伪随机排序并与m序列作扩频调制，最后对数字音频信号进行分段离散小波变换，把经过调制的水印信息自适应地嵌入到原音频信号小波分解中等尺度绝对值较大的分量上。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

By means of the qualitative and quantitative analyses on the characteristic of energy spectrum of the scaling functions, the stuitable region of this numerical method of inversion in the image by inversion is given.

通过对小波尺度函数的低带通谱特性的定性与定量讨论，给出了这一反演方法所得原像函数的适用域。

Under this situation, sparse signal expansion theories, a kind of new multiscale analysis theory that has been developed in recent years, possess a better performance in detecting the singularities of the signal with straight line or curve in high dimensional space and can be used to express signals with sparse coefficients.

而稀疏信号表示理论是近几年发展起来的一类新的多尺度分析方法，它们对高维空间中具有直线或曲线奇异性信号具有良好的检测性能，可以用稀疏的系数来表示原信号。

Provided there is adequate resolution, we can find that line of thought is, in fact, a lot more small-scale linked to the dogleg.

只要有足够的分辨率，就可以发现原以为是直线段的部分，其实由大量更小尺度的折线连成。

Also, the additional micropore was generated by thermal dehydration in glycerine compared to that in air.

采用原子力显微镜研究了纳米结构TiO〓基晶须在500nm尺度以下的形貌和表面结构。

It is found that if the ratio of the number stored in the model P to the size of the network N is less than 0.1, the following results exist. The overlap between the stable state of networks and the pattern is independent of the size of networks. And the relation between the overlap and the ratio of links of new nodes to the number of patterns abides by the sigmoidal curve.

发现在模型的储存模式的数目P与网络尺度N的比值P/N＜1／10的条件下，网络对受污模式做出响应达到稳态后，这个模式与原模式的重叠随网络平均度变化的规律与网络尺度无关，并且模式重叠与每个新增节点的连接度m和储存模式的数目的比值m／P满足S型曲线。

The characterization of modified surfaces were explored by contact angle measuring meter and atomic force microscopy,the tribological properties of samples in nanometer and millinewton scale were measured by friction force microscopy and CETR UMT-2 tribometer. The effects of ultraviolet radiation,sliding velocity and load on tribological properties of samples were analyzed.

在铝、钛金属薄膜和铝、镁、钛及钛合金上制备自组装分子膜，使用接触角测量仪、原子力显微镜对改性的表面进行表征，使用摩擦力显微镜和微摩擦磨损试验机对试样在纳米尺度和毫牛尺度下的摩擦学特性进行测试，分析了紫外照射、滑动速度、载荷对试样的摩擦学特性的影响。

The TST was applied to multi-scaling vector to increase it's approximation order, and with PR condition, the dual of transformed multi-scaling vector was obtained. Then the special TST was taken for this dual, the dual of original multi-scaling vector with higher approximation order obtained, finally the multi-wavelet function with higher vanishing moment maybe constructed.

我们先对已知的尺度向量进行双尺度相似变换，以提高其逼近阶，再求出变换后的尺度向量的对偶，对这个对偶再进行特定的双尺度相似变换，就可得到原尺度向量的有高逼近阶的对偶，从而可能得到具有高阶消失矩的多小波函数。

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。