查询词典 fractal

Fractal is a subdiscipline of nonlinear area, researches on fractal characteristics of the deoxyribonucleic acid sequence may reveal some secret hidden in the DNA sequence during the process of biological evolution. Chaos Game Representation was proposed as a scale-independent representation for genomic sequences by Jeffrey in 1990. This technique, based on iteration function system, represents the word distribution statistics in DNA sequence as the fractal graphic. Therefore, we can get the distribution of sequence through analysis of fractal theory.

分形是非线性领域的一门分支学科，关于脱氧核糖核酸序列分形特征的研究，可以揭示生物在进化过程中隐藏在DNA序列中的某些秘密。1990年Jeffrey提出了基因组序列的与尺度无关的混沌游戏表示法，这是基于迭代函数系统的一种方法，它将DNA序列中一定长度字的分布规律表现为图形的分形特征，进而通过分形分析就可获取序列的分布规律，从而也成为DNA序列分析的一种统计方法。

The features of the fractured medium and the rock matrix in the fractal composite reservoirs are describes with the fractal dimension (which describes the geometric features) and the fractal index (which depicts the connectivity of the fractal fluid flow network); An analysis mathematical model of well testing is proposed for inconstant flow rate with the closed outer boundary and the wellborn storage and the skin effects.

分形是研究自然和社会中广泛存在的零碎而复杂、无序、不规则、非线性、不光滑，具有自相似、自仿射和标度不变性的复杂系统、图形、构造、功能、性质和复杂现象，及隐藏在这些复杂现象背后的，具有精细结构、内在随机性，局部与整体本质联系的，被传统线性科学排斥在外的不规则"病态"，不可微的事体，形体。

The 3D topography of fractured surfaces was reconstructed and quantified by the means of SEM stereo pairs, image processing and analysis, and computer vision. It was shown that measured 3D roughness indexes Rs, Rq and Rmax have good positive relations to the crack propagation part of absorbed impact energy. Although fractal behavior had been checked out on the fractured surfaces, the fractal dimension was found nonsensitive to the fracture mode and mechanical properties. The geometric characteristics of fractal fractured surfaces should be quantified in fractal dimension together with absolute parameters.

利用扫描电镜立体对技术、图像处理与分析和计算机视觉方法对示波冲击断口形貌进行了三维重建和定量分析结果表明，断口三维粗糙度指数Rs，Rq和Rmax与示波冲击裂纹扩展功有很好的对应关系，显示了它们良好的应用前景断面虽然表现出分形行为，但分形维数是一个对断裂模式和性能不敏感参量对分形断口的几何特征描述应将分维和绝对尺度结合起来

Result shown: value of fractal dimension is a comprehensive index, which reflect the changes of landscape, patch areas, patch numbers, area per patch, and their interaction. And the index can reflect the irregular degree and the complex degree of landscape patch in dumping place. The fractal dimension of mixed vegetation of arbors – shrubs and mixed vegetation of shrubs maintain the high level, while fractal dimension of new reclamation land and grass land are low. The difference of other type landscape fractal dimension is not significant. Vegetation landscape is influenced by many kinds of factors. It is primarily influenced by surface material composition and terrain in south and west dumping place, which diversity index is high. It is primarily influenced by vegetation type in inner dumping place and expanded west dumping place. The landscape multiplicity index of the mixed vegetation of grass and shrubs is higher than other landscape type, but landscape dominance index of this area maintains on the lower level.

结果表明：分维数的大小反映了景观斑块面积、斑块数量和平均斑块面积等因素的相互作用，反映了排土场内景观斑块的不规则程度和复杂程度；乔灌混交地和灌木混交地保持着较高的分维数，新造复垦地和草地的分维数较低，其它景观类型的分维数则差别不大；植被景观受多种因子的影响，在南排土场、西排土场受地表物质组成和地形的影响为主，其多样性指数较高，在内排土场、西排扩大区受植被类型的影响为主；草灌混交地的景观多样性远高于其它现有的复垦植被区，但其景观优势度则保持在较低水平上。

The fractal theory was used to build fractal microfibril in wood cell wall,and fractal dimension of fractal microfibril layer S1 and layer S2 were calculates,then wood fiber frame with nanometer scale was pointed out.

利用分形理论构建了木材细胞壁中的分形木质纤维，并计算了分形木质纤维 S1层和S2层的扭曲分形维数，指出木材中具有纳米尺度的纤维结构；同时，以木材液化和纳米纺丝技术为基础，提出了木材苯酚液化产物制备碳素纤维材料的构思和技术路线，为解决木材纳米、微米材料的制备提出了新思路。

Finally, fractal characteristic is researched in the thesis. Fractional Brownian motion characteristic of sea clutter is validated and fractal dimention of sea clutter without taget and sea clutter with target are calculated by box-dimention method.Target detection based on fractal dimention is analyzed in brief and sea clutter multi-fractal characteristic is analyzed by MF-DFA.

最后，本文对海杂波分形特性进行了研究，验证了海杂波符合分数布朗运动的特性，通过盒维数法计算纯海杂波和目标海杂波的分形维数，简要分析了基于单重分形维数的目标检测，并采用MF-DFA对海杂波多重分形特性进行了研究分析。

Taking landscape pattern fractal model and Landsat TM/ETM images in 1995 and 2000 as the basic data,the spatialtemporal database of land use in Chongqing City was established; and using fractal model of landscape pattern,fractal dimension and stability index of landscape pattern,landscape diversity index,landscape apartness index,landscape fragmentation index,landscape evenness index and landscape dominance index were obtained.

采用1995和2000年Landsat TM/ETM影像为基础数据，提取并建立土地利用空间数据库，应用景观空间格局分形模型，获取景观类型的分形维数和稳定性指数以及景观多样性指数、分离度指数、破碎度指数、均匀度指数和优势度等指标。

The results showed that during the research period,the fractal dimensions of paddy fields,dry land and wet areas increased obviously,whereas for forest land,shrubbery land and grass land,the fractal dimensions decreased.For all types of land,the values of landscape diversity index and landscape apartness index have increased but landscape dominance index value has rather decreased.Meanwhile it was found that the relation between fractal dimension and landscape fragmentation index showed significant positive correlation.

结果表明：水田、旱地、水域等土地类型的分形维数在研究时间段内有明显上升，有林地、灌木林地和草地等景观要素类型的分形维数降低；景观多样性和破碎度指数以及均匀度略有增加，而优势度指数下降；分形维数和破碎度指数呈极显著正相关。

The paper according to fractal autoregressive integrated moving average process models network self-similar traffic, estimates fractal dimension through fractal analysis methods directly and indirectly, and emphasizes on rescaled range analysis.

本文由分形自回归整合滑动平均流量模型产生自相似性数据。针对流量分形维数的求解，本文分别从直接估计和间接估计两个方面进行研究，采用分形分析方法对产生的业务流进行统计分析，其中重点讨论了变标度极差分析法。

Regular Fractal Dimension Calculation is discussed by using Koch Curve and Cantor Ternary Set.Additivity of regular fractal dimension is discussed by continuation of Koch Curve with line and Cantor Ternary Set in vertical direction.CircumferenceArea,Variation,Grid and Radius methods of calculation statistical fractal dimension are introduced.

本文以科赫曲线与康托尔三分点集为例，讨论了有规分形维数的计算；以科赫曲线在垂直方向的两种拓展为例，讨论了有规分形维数的加和性；以周长—面积法、变量法、网络法与半径法为例，介绍了无规分形维数的计算方法。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。