介绍了分形和分形维数在催化剂研究中的应用。
Fractal and fractal dimension theories applied on catalysts were introduced in this paper.
分析了一阶分形模糊控制滤波器的频率-幅度特性，白噪声和有色噪声分形盒维数的变化；
The frequency-magnitude response of the fractal filter and the change of fractal box dimension of white noise and color noise are analyzed.
基于分形理论和计算机图像处理技术，编制计算材料断口形貌计盒分形维数的MATLAB程序。
Based on the fractal theory and computer images analysis technique, a MATLAB program which computes box fractal dimension of material fracture was designed.
石油焦的燃烧具有分形动力学的行为特征，且表面分形维数的变化趋势和比表面积和孔容积不同。
The fractal characteristics of petroleum coke combustion are validated, which proves that the change of surface fractal dimension differs from that of specific surface area and pore volume.
计算了岩溶元的分形生长维数和岩溶发育的分形评价指数，据此对岩溶发育程度进行判别。
Fractal dimension and fractal assessment index of karst were calculated, and they were used to evaluate karst development degree.
首先通过计算原始图像和特征灰度图像的分形维数实现第一次的粗分类提取，然后采用多重分形奇异谱方法进一步完成了细分。
At first, the fractal dimension is extracted from the original image and special gray image for the rough classification, and then the multi-fractal dimension is used for further classification.
基于小角X射线散射理论，利用逐级切线法和材料分形理论中的散射强度法，分别计算PAN基炭纤维内微孔大小、体积分数及微孔表面分形维数。
Based on SAXS theory and fractal theory, we obtain the calculating method and calculating formulas of the pore size, pore volume percentage and the fractal of pore surface in PAN - based carbon fiber.
从四个方面分析了近年来催化剂分形研究的方向和进展分形维数与催化剂评定和筛选，催化剂分形孔结构，分形与反应动力学，模型建立。
The development of fractal catalysts study in recent years was analyzed from four aspects: selection and assessment of catalysts, fractal pore structure, reaction dynamics and mathematics model.
分形维数是描述自然界和非线性系统中不光滑和不规则几何体的有效工具，是所有分形对象的主要特征之一。
Fractal dimension is usually an effective way that used to describe the non-smooth and non-regular geometry objects in the nature and non-liner systems.
应用计盒维数法的基本原理考察了大豆酸奶和酸牛奶是否具有以自相似性为特征的分形结构，并最终确定豆浆酸奶和酸牛奶的分形维数分别为1.9105、1.9268。
Box counting method was applied to investigate the fractal structure and the fractal dimension for soy based and dairy yoghurt was determined to be 1.9105 and 1.9268 respectively.
本文将分形布朗模型和分形维数引入火焰图像分析中，可以预报早期火灾，减少火灾的损失。
This paper introduces fractal brown model and fractal dimension into the texture analysis of flame images, which can forecast early fire and reduce the losses of property when fire happened.
储层岩石的孔隙空间具有良好的分形特征，孔隙结构的分形维数可以定量描述孔隙结构的复杂程度和非均质性。
There is fractal property in reservoir rocks, the fractal dimension can describe quantitatively the complexity and the heterogeneity of pore structure.
样本计算和统计结果表明，证券交易数据的时域波形信号具有分形标度不变性，分形维数能够反映交易数据的时域波形信号的复杂性和不规则性。
The specimen calculation outcome indicates that transaction data waveform of time domain assume fractal scale invariant property, which fractal dimensionality can reflect complexity and irregularity.
实验表明，将纹理图像的分形尺度与分形维数结合，既反映了物理表面分形的尺度范围又反映了该尺度范围内的纹理粗糙程度，从而更有效地描述和区分纹理特征。
Experiments indicate that the fractal scale, together with the fractal dimension can effectively reflect the fractal scale range of natural textures and the texture roughness within the scale range.
基于分形理论和现场岩体结构面调查，对岩体结构面进行了统计分析、网络模拟和分形维数计算。
Based on the fractal geometry theory and the survey of the on-site rock mass, the statistical analysis, the network simulation and the fractal dimension calculation of the structural planes were made.
建立管网分形模型，并给出了合适的分形算法和计算程序，能够方便的计算出管网分形维数。
Network fractal model is built and proper algorithm is put forward too, so is the program. With them, we can calculate fractal dimensions conveniently.
从产品性能公差设计的角度探讨分形公差理论的建模、分析、设计等有关方法，着重研究分形维数的计算理论和工程方法。
Some methods about fractal based tolerancing are discussed in this paper. The engineering calculation on profile fractal dimension is presented in detail.
在了解分形理论的基本知识和分形几何的维数的基础上，对分形图形的算法作了总结。
It sums up some fractal algorithm on the basis of mastering the base knowledge of the fractal theory and dimension of the fractal geometry.
测量了多相材料复合涂层的断裂挠度和断口表面的分形维数，分析了复合涂层的断裂特征结果表明：随着硬质相增加，复合涂层的断裂挠度和断口表面的分形维数降。
The test results showed that the fracture deflections of the composite coatings and the fractal dimensions of the fractured surfaces decreased with increasing the contents of hard phases.
介绍了分形理论及其在岩石爆破破碎过程中的应用，指出岩石分形维数与岩石所受的压力和作用时间相关联。
The fractal theory is applied to describe the process of the rock blasting. The fractal dimension of rock fracturing is considered to associate with the blasting stress and the impact time.
阐述了分形与分形维数的定义，给出了铁谱磨粒分形维数和无标度区间的计算原理。
The definition of the fractal and fractal dimension were expatiated, the calculation principle of fractal dimension was set forth.
利用分形几何学理论对煤孔隙结构进行了定量的描述和研究，推导了煤孔隙分形维数的表达式；
The paper quantitatively stated and researched the coal borehole fissure structure with the sharp geometry theory. The paper derived the expression of the coal borehole fissure sharp dimension.
引用岩体力学方法和分形几何学，用强度因子和分形维数对煤体变形进行定量评价。
Quoted rock mechanics and fractal geometry, used strength coefficient and fractal dimension quantitatively evaluated the deformation of coal.
因此，分形丛集维数和分形密集维数可以作为矿床分布、矿化强度和聚集的定量指标。
Therefore, the fractal cluster dimension and fractal density dimension can be used as the quantitative indicators of deposits distribution, intensity of mineralization and accumulation.
尝试应用分形理论表征多孔材料的微结构，介绍了曲线和孔隙面积分形维数的定义，并采用盒维法对2个分形维数进行计算。
Fractal theory is applied to do it. The definition of curve and pore area fractal dimension is introduced. Two fractal dimensions are determined by box-counting method.
尝试应用分形理论表征多孔材料的微结构，介绍了曲线和孔隙面积分形维数的定义，并采用盒维法对2个分形维数进行计算。
Fractal theory is applied to do it. The definition of curve and pore area fractal dimension is introduced. Two fractal dimensions are determined by box-counting method.
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