相似函数

Asymmetrical dynamic propagation problems under the action of variable loads and (P^3t/x^2) located at the origin of the coordinates respectively, are resolved by the measures of self-similar functions, and the universal expressions of analytical solutions to stresses, displacements and stress intensity factors are gained.

采用自相似函数的方法对坐标原点分别受到变载荷Px/t、Pt^3/x^2作用下的非对称动态扩展问题进行求解，获得了应力、位移和动态应力强度因子解析解的一般表达式。

In terms of relevant relationship to equation of motion of the elastodynamics plane problem for an orthotropic anisotropic body, the universal representations of analytical solutions are obtained with the method of self-similar functions.

根据正交异性体弹性动力学平面问题运动方程的相应关系，采用自相似函数的方法可以获得解析解的一般表达式。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

At first, the examples are given to explain a new method in signal processing, in which functions are defined from the viewpoint of multi-scale analysis. Then the authors present "coordinate heft separate" method, discover self-similar structure of points set on plain area; based on this self-similar structure, construct orthogonal complete 2-value function system of high-dimension simplicity; enrich and extend the theory and application of Rademacher function and Walsh function.

首先，举例说明在多尺度分析观点下，信号处理中某些函数定义的新方法；进而提出"坐标分量分离方法"，并由此发现了平面区域上点集坐标数值的自相似结构；在揭示了如此自相似结构的基础上，构造了高维单纯形上的正交完备的二值函数系统；丰富与推广了Rademacher函数及Walsh函数的理论及应用。

By the theory of complex functions, dynamic propagahon problem on Dugdale model of mode Ⅲ interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of serf-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simple by this approach.

通过复变函数论的方法，对材料的非线性特性下的Ⅲ型界面裂纹Dugdale模型的动态扩展问题进行了研究，采用自相似函数的方法可以获得解析解的一般表达式，应用该法还可以很容易将所讨论的问题转化为Riemann-Hilbert问题，并可以相当简单地得到问题的闭合解，利用这些解并采用叠加原理，就可以求得任意复杂问题的解。

Quantifying similarity/difference between two objects plays an important role in many contexts The quality of the similarity/difference scores can be improved by considering the semantic information related to the features of objects A flexible semantic distance function called X Dist is proposed, which can utilize the semantic information to measure the difference between two objects based on a solution to the transportation problem from linear optimization With a ground distance function for single features being a metric, X Dist is also a metric This property is very useful for making searching efficient, but is not investigated in the previous research Moreover, the experimental results show X Dist can be as good as the previously studied similarity measures in nearest neighbor searching, discriminative power and computing speed

量化对象间相似性/差别的方法具有广泛的用途，利用相关的语义信息能够得到更好的量化结果提出了一个量化对象间语义差别的距离函数XDist，它基于线性优化中的运输问题模型和相关的语义信息量化两个对象之间的差别在量化特征的差别函数是度量的情况下，XDist是一个度量，在提高搜索的效率方面具有优势，弥补了以往研究的不足，而且实验初步表明，此函数在最近邻查询效果、差别分辨力和计算速度方面能与已有函数相媲美1 引言量化对象间相似性/差别的方法具有广泛的用途，例如数据挖掘中的聚类；信息检索中的相似文档查询；协同过滤中的相似用户查询；CBR中的相似案例查询集合是对象特征表示的常用结构，集合的元素是与对象特征相关的项，它们可以

As a solution, a new gray-level value natural logarithm ratio range filter kernel is pointed out for the Bilateral filtering, a representative method of Neighborhood filters.

在此基础上针对具有代表性的双边滤波模型进行修改，提出新的灰度值自然对数比率相似函数模型。

It can be translated into a Riemann-Hilbert problem by means of self-similar functions, and the universal representations of analytical solution were obtained when there is $Pt / x$ or $Px^3 / t^2$ load at the origin of the crack coordinates.

采用自相似函数的方法可以轻易地将所论问题转化为Riemann-Hilbert问题，并求得了裂纹坐标原点分别受到变载荷$Pt/ x$，$Px^3 /t^2$作用下的解析解的一般表达式。

Based on fractal coding the index file have two characters: First, similar images have similar iterative function so as to produce similar index file, and the similar index file can retrieval the similar image; Second, unsimilar images have unsimilar iterative function, vice versa.

这个分形编码方法建立的索引文件具有三个性质：(1)相似图像有相似分形函数能产生相似索引文件，相似索引文件能检索到相似图像；(2)不相似图像有不相似分形函数，反之亦然。

The analytical solutions can be attained by the approaches of self-similar functions.

采用自相似函数的方法可以获得解析解。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失