查询词典 fractal

On the basis of the fractal theory, general form and calculation method of the fractal characteristic are given, that is the calculation model of non-close fractal curve length and closed area, and box counting dimension algorithm.

基于分形理论，给出了分形特征的一般形式及其计算方法———非闭合分形曲线长度与围成面积的估算模型和盒维数的算法。

The experimental results have shown that the common logarithm values of transverse rupture strength lgσ〓 increase with the increase of fractal dimension D〓, and has a linear equation relationship. The microfracture fractal model of cermets has been founded and the estimated fractal dimension formula of fracture surfaces proposed.

建立了颗粒型复合材料金属陶瓷断裂的微观fractal模型，提出了计算断口表面分形维数的公式，指出断口分形维数依赖于测量码尺的选择，对金属陶瓷来说其临界测量码尺为0.07μm。

A tensile facture fractal model of grain filled polymer composites on the base of the fractal theory was established,and an equitation of the tensile fracture fractal dimension was proposed.

梁基照，吴成宝，颗粒填充高分子复合材料拉伸断口的分形模型基于分形理论构建了颗粒填充高分子复合材料拉伸断口的分形模型，进而提出了分形维数计算公式。

Based on the methods of Hausdorff fractal dimension and space relation fractal dimension ,the paper advances calculation models on the fractal dimension and the arriving degree of network of Liaoning s highway network.

分析了辽宁省公路交通网络的基本现状，根据分形理论，利用Hausdorff维数简化算法和空间关联维数的计算方法，测算了以省内国道干线为基础的辽宁省公路交通网络的分维数和网络直通度。

Secondly, it is not the same fractal diagram by the same codes of IFS to produce fractal diagram. The two graphs are extraordinary similar, but they are different in detail. The problem is researched and the algorithm which calculates the intersection points of two graphs created by the same coefficient of the IFS is proposed. The curve described changing of the intersection points number is drawn. The conclusion is that the curve fluctuates in the tiny range and is smooth when it is seen as a whole. In fact, the curve is a fractal curve.

其次，针对同一IFS迭代码两次迭代绘制得到的分形图并非完全相同这一问题展开研究，提出了IFS分形覆盖相交交点变化曲线的概念，给出了覆盖相交交点变化曲线的绘制算法，在此基础上进一步研究了分形覆盖相交交点变化曲线的变化率情况，得到了分形覆盖相交交点变化曲线宏观上比较光滑，但实际上小范围内异常波动的实验结果。

C for the fractal dimension, we present a classification method that is based on the fractal dimension with the help of multiresolution fractal dimension and lacunarity data.

对于分形维方法，我们提出应以一级分辨率分维为基本依据，辅之以多分辨率分维值和空隙数据进行纹理分类的方法。

The Hausdorff measure for the level sets of multi-parameter symmetric stable processes has been obtained and the inner connection of the measures and local times for it has been demonstrated, which describes the fractal nature for the level sets of this kind of processes. As we know, it is always one of the focuses in the field of random fractal. The reasult of the existence and continuity of the local time for multi-parameter stochastic processes with stable components has been got in the project. Then we gained the measure for the random fractal sets such as the range and graph of this kind of processes. Furthermore, a progress besides the mentioned above in the project is that we have resolved the multifractal analysis of the sample paths for Brownian sheet, that is the multifractal decomposition of white noise in high dimension.

解决了多指标对称稳定过程水平集的Hausdorff测度问题，同时给出N指标d维稳定过程水平集的Hausdorff测度下界的最佳估计，它们揭示了其水平集的测度与局部时之间的内在关系，刻划了多指标对称稳定过程水平集的分形特征，表明了研究此类问题的积极意义，该问题是随机分形研究领域的国内外学者所关注的热点问题之一；解决了多指标稳定分量过程的局部时存在性与连续性问题，进而解决了由多指标稳定分量过程产生的随机分形集--象集、图集的测度问题；此外，本研究项目还解决了布朗单样本轨道的重分形分析，即高维白噪音的重分形分析问题。

Based on investigating the short and intermittent structural plane, surrounding rockmass of the huge underground powerhouse in Three Gorge has been divided into five statistical similar areas according to its characteristic of rockmass structure by applying structure plane network simulation. Distributed characteristic of structural plane has been studied and based on it mechanics macrocharacteristic has been studied:(1) It is the first time that based on the result of structural plane network simulation rockmass quality of every structure area has been studied with applying blurred information optimum seeking technique and be compared with and RQD method. The result indicated that it has better effect to evaluate rock quality with blurred information optimum seeking technique.(2) It is the first time that the interrelated relationship of the result of in-suit rockmass deformation test and fractal characteristic of structure on test point has been applied to determine rockmass deformation parameter. The question of evaluating deformation parameters of engineering rockmass has been solved.(3) Anisotropy strength parameters have been determined by applying shear zones simulating method. The result indicated that there are different strength parameters in every structural area, after comparing the result of Fast Lagranian Analysis in continua number simulation method with that of method of weighted mean according to continuity. The result indicated that when a suitable reduction coefficient is been considered rockmass strength parameters can be simply and fast determined with method of weighted mean according to continuity where there is not enough test result.(4) Damage characteristic has been studied based on analysis fractal characteristic of structural plane network by applying fractal-damage coupling method. It is the first time that the concept of damage degree has been set up to evaluate rockmass quality according to the biggest principal damage.

通过对短小、断续性结构面统计特征的研究，将地下厂房区划分为五个岩体结构统计均质区，应用结构面网络模拟技术研究了各个岩体结构均质区结构面的发育分布特征，并以此为基础对岩体宏观力学特性进行了深入研究：(1)首次通过在结构面网络模拟计算结果的基础上，应用模糊信息优化技术研究了厂房区各个岩体结构分区的岩体质量并与岩体基本质量指标研究法、岩体质量指标RQD值研究法作了对比，结果表明以结构面网络模拟结果为基础，应用模糊信息优化技术进行岩体质量评价能够取得很好的效果，解决了工程岩体质量的定量评价问题；(2)首次通过对已有的现场大型岩体变形试验结果的分析及相应试验点岩体结构分形特征的研究，建立了结构面分布的分形维数和岩体变形指标间的相关关系，并首次应用这种相关关系根据结构面网络模拟及分形维数计算结果确定了缺少试验结果的地下厂房各工程部位的岩体变形指标而且应用于围岩稳定性计算，解决了工程岩体宏观变形参数的评价问题；(3)应用在结构面模拟网络图上模拟岩体剪切破坏带的方法，得出了岩体在不同方向上的强度参数，结果表明岩体的强度特性与结构面的发育方向和程度有着明显的关系，各个岩体结构均质区具有不同的强度参数；同时还通过应用拉格朗日差分法对岩体强度指标的数值分析并与按连通率加权平均计算法对比表明，按连通率加权平均计算法在考虑合理的折减系数情况下，可以简单快速地对缺少现场大型试验结果的具体工程部位实现岩体强度指标的估计，通过以上研究解决了工程岩体抗剪强度参数的评价问题；(4)通过结构面网络分形维数的研究，应用分形损伤耦合分析方法，研究了厂房区岩体的损伤特征，并首次引入"损伤度"的概念，建立了应用最大主损伤评价岩体质量的指标体系。

Using fractal method, the fractal dimensions of these images are calculated to compare their fractal characteristics.

利用分形学方法，计算图像的分维数，然后比较其分形特征。

The third one is that fracture fractal of wood cells is analyzed by SEM. It is found that the fracture of some cells has fractal characteristics, and latter research can focus on studying quantitatively the micromechanics behaviors by fractal theory.

第三部分，对扫描电镜下拍摄的木材细胞断口进行了分形分析，发现某些细胞的断口具有分形特征，今后可以进一步尝试应用分形理论定量研究木材的微观力学行为。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。