尺度

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。

In this thesis, we mainly study the multi-scale asymptotic expansion and high accuracy algorithm for the periodic structure of composite materials.

本文主要研究复合材料周期结构的多尺度渐近展开与高精度算法，特别对多孔复合材料的多尺度渐进展开与高精度算法作了比较详细的研究。

Subline matching method based on binary system small wave transform is proposed, which expliots the character that the model maximum point of spline binary small wave transform coefficient at different scales can provide position information of signal's fast changing point. The matching scheme from thick to thin for point matching is adapted. Then, the point to point matching is calculated with the sequence consistent principle in each subline.

设计基于二进小波变换的子线段匹配方法，通过求解样条二进小波变换系数在不同尺度下的模极大点确定不同尺度下信号急速变化点位置，采用由粗到细的匹配策略匹配端点，再对端点之间的每一个子线段采用顺序一致的原则，进行点对点匹配。

Quantum theory generalizes classical mechanics to provide accurate descriptions for many previously unexplained phenomena such as black body radiation and stable electron orbits .

有人引用量子力学中的随机性支持自由意志说，但是第一，这种微观尺度上的随机性和通常意义下的宏观的自由意志之间仍然有着难以逾越的距离；第二，这种随机性是否不可约简还难以证明，因为人们在微观尺度上的观察能力仍然有限。

With the use of karst water deposit (calc-sinter) analysis system, historical document analysis system, and modern observation data statistic analysis system, we study the evolutive regularity in three temporal scales and the evolutive process in geologic temporal scale in Niangziguan karst water spring, and divide this karst water evolution into five stages.

同时运用岩溶沉积物分析法、历史文献分析法、现代观测资料的统计分析法研究了娘子关泉岩溶水系统在三个时间尺度上的演化规律及在地质时间尺度上的演化过程，并将该岩溶水系统演化分为五个阶段。

Whatsoever cannot but be acknowledged to be of advantage to the society, and people in general, upon just and lasting measures, will always, when done, justify itself; and whenever the people shall chuse their representatives upon just and undeniably equal measures, suitable to the original frame of the government, it cannot be doubted to be the will and act of the society, whoever permitted or caused them so to do.

无论做什么，只要基于公正和持久的尺度，总是能够自己证明自己为正当，并最终为普通的人和社会的利益所承认；并且无论什么时候人们基于公正和无可争辩的的平等尺度挑选他们的代表，只要与最初的政府框架相符合，就无可置疑的行使着社会的意志和行动，无论是谁允许或驱使他们这样做。

Multi-scale CODON and Natural scales are presented to solve the problem of noise in differential operator.

同时提出了自然尺度和多尺度CODON特征的概念，以克服基于曲率运算的CODON编码对噪声的敏感性。

As we know, with the exception of the Haar function, uni-real-valued orthogonal wavelet filter banks with compact support lack symmetry and do not possess linear phase.

我们知道，紧支撑正交的单一小波除Hair小波外不具有任何对称性，它用作滤波器不可能有线性相位，而由实单一紧支撑正交的尺度函数构造出的二重尺度函数却是对称的，对应的二重小波可以是对称或反对称的，从而使得这种小波在信号处理的过程中具有线性相位。

ABSTRACT: There is a significant contrast in scale between Chang'an of Tang Dynasty and ancient western cities , based on a comparative study on the city scale , city contexture and the scale of streets in two different cultures. This paper provides a unique interpretation of Chang'an from the perspective of urban form.

从城市形态的角度出发，从城市规模、城市肌理、街道尺度三个方面对唐长安和西方古代城市进行对比，对唐长安进行了新的解读，认为唐长安与西方古代城市存在着巨大的尺度差异。

The rate of fall is dependent on the continuity of the scale function in time domain. Furthermore, it relates with the multiplicity of zero point at ω=π of the amplitude spectrum of the low pass filter. The distribution of zero points was investigated thoroughly. From the above statement, the dominant interval is deduced to be [0, 2π].

衰减性取决于尺度函数的连续性，进一步它与低通滤波器在ω＝π处零点重数有关；详细讨论了零点的分布及其重数；由零点的分布和衰减性推出尺度函数的幅值谱主导区间为[0，2π]；ω＝0处极大值性态与低通滤波器在该处性态相同。

We will see more and more activist government policies that distinguish economic activities according to the nationality of the actors.

我们将看到越来越多激进的政府政策，这些政策根据企业的国籍来区分经济活动。

If we can prove the independence of an axiomatic system, then we can guarantee the conciseness of this system, ie.

如果能够证明某个一阶谓词系统的独立性，那么就能够保证该系统的建立是精炼的，即没有任何一条公理或推理规则是多余的。