对中学数学教学中数形结合思想方法的反思与展望。
For middle school mathematics teaching method combining the number of reflection and prospect.
利用数形结合的思想为不等式构造解析几何模型，并加以推广。
This article structures and extends an analytic geometry model for a inequation based on combining Numbers and shapes.
本文结合几个实例，探讨数形转换问题，使问题得到十分简捷的解决。
In this paper, several examples of the mathematical conversion, the problem is a very simple solution.
利用数形结合结合，介绍了金字塔、杨辉三角形与一些特殊数列之间的关系。
Taking advantage of the combination of the Numbers and their shapes, this article introduces the relationship of some special arrays with the pyramid Numbers and the Yanghui Triangle.
对如何利用数形结合中的“以形辅数”方法，直观形象地解决数学问题加以阐述。
Ways of solving mathematic problems objectively and vividly by using the method of "Assisting Number with Graphics", combining number and graphics, are expounded.
数形结合不应仅仅作为一种解题方法，而应作为一种基本的、重要的数学思想来学习，研究和掌握运用。
Number shape union should not merely be as a problem solving method, but should serve be as a basic and important mathematical idea to learn, study and master.
下一步也还是泛化。这次就是不光要画正方形了，要画一个多边形，可以指定边数的。下面是样例。
The next step is also a generalization. Instead of drawing squares, polygondraws regular polygons with any number of sides. Here is a solution.
本文提出了分形维数估计的子波函数方法。理论和计算机模拟实验表明，新方法不仅实现简单，而且具有较强的噪声抑制能力。
Wavelet - based method is proposed to estimate fractal dimension. It is shown in theory and in experiment that the new method is simple to implement and robust to noises.
分形维数是描述图像粗糙程度的主要参数。
Fractal dimension is an important parameter to characterize roughness in an image.
本文提出了一种新的计算分形维数的方法。
In this dissertation, a new computation method of fractal dimension has been presented.
文摘：以土壤颗粒组成数据为基础，分析了我国土壤颗粒组成的分形维数。
Abstract: This paper analyzed the fractal features of particle size distribution (PSD) of soils in China.
在实数域分形盒维数计算方法的基础上，提出了双金字塔数据形式的盒维数快速计算方法。
In this paper, a fast approach for box dimension estimation based on a dual pyramid data structure is developed.
然后，通过分形维数计算车辆的纹理特征，排除非车辆区域。
Second, the no-vehicle regions are filtered by texture feature of AOI based on DBC.
实验结果表明，分形维数能很好地表征表面轮廓，可为进一步的接触分析提供更合理的几何模型。
Taking rigid disk surface as an example, fractal parameters are obtained by means of power spectrum and structure function, providing a proper geometric model for further contact analysis.
用裂隙密度分形维数定量描述了巷道围岩裂隙的分布和演化。
The crack distribution and evolution of the surrounding rocks of roadway can be quantitatively depicted by the fractal dimension of crack density.
分析的结果表明，单一分形维数并不能完整地描述万州区滑坡的空间分布结构；
The result indicates that a fractal dimension could not integrally describe the spatial distribution structure of landslides in the region.
分形维数随外加电压的改变呈现不规则的变动。
The change of fractal dimension was irregular with the change of voltage.
结果表明：木材内部孔隙度的分形维数是定量反映干燥过程中木材内部孔隙复杂程度新的有效指标。
The results showed that the fractal dimension is an effective index to quantitatively characterize the complexity of wood interior porosity during the drying process.
林隙冠空隙的斑块分形维数小于扩展林隙的斑块分形维数。
The patch fractal dimension of canopy gaps is smaller than that of the expended gap.
人们所熟知的常用以代替分形维数的各种度量将在分维谱意义下加以统一，最后讨论多重分形及其分维谱的应用。
The usual fractal dimensions familiar to all us will be united by the multifractal dimension spectrum. Finally, the applications of the multifractal and its dimension spectrum will be discussed.
由于故障发生时系统表现异常，这些异常可导致测量信号分形维数的变化，根据这些变化可进行故障检测。
When the fault appears, there will be some variation in the fractal dimension of measurement signal, and the fault detection can be carried out according to this change.
在此基础上，讨论了断裂尺度分形维数与地壳活动性的关系。
Based on this, the relation between fracture fractal dimension and the Earth crust activity was discussed.
目的：探索肺癌图像的纹理分形维数特征。
Objective: To probe the fractional dimension feature of lung cancers texture.
考察了晶粒度与分形维数之间的关系。
The relation between grain size and fractal dimension is investigated.
将该模型用于销盘磨合磨损试验，对最佳分形维数进行了准确预测。
When it is used in the running-in process, the model can predict optimum fractal dimension precisely.
将该模型用于销盘磨合磨损试验，对最佳分形维数进行了准确预测。
When it is used in the running-in process, the model can predict optimum fractal dimension precisely.
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