维数

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。

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。

The results indicate that as the value of fractal dimension is increased, the interfacial static friction coefficient first increases and then decreases; the interfacial static friction coefficient decreases as the fractal roughness parameter increases; while the inter-facial static friction coefficient increases as the material property or total normal load increases; the curve of static friction coefficient versus dimensionless total normal load is convex when the fractal dimension becomes smaller or fractal roughness parameter is larger or material property becomes smaller.

研究结果表明：界面的静摩擦因数首先随分形维数的增加而增加，然后随分形维数的增加而减小；界面的静摩擦因数随分形粗糙度参数的增加而减小，但随材料特性的增加而增加，也随总法向载荷的增加而增加；当分形维数较小或分形粗糙度参数较大或材料特性较小时，静摩擦因数－量纲一的总法向载荷曲线为凸弧。

The variation in surface elements of fog has high complementariness with that of sensing images.

在卫星遥感图像上，雾与积云的纹理结构特征差别非常明显，与层云也有着一定的差别，其关系为：雾的分形维数≤层状云的分形维数＜非层状云的分形维数。

Finally, the calculation process of CGR graphic's multi-fractal analysis was studied. the scope of choice of the weight factor and the scale invariance range were discussed, the weight factor can be chosen as ? 15≤q≤50; multi-fractal spectrum and generalized dimension of different sequence were calculated, multi-fractal spectrum and generalized dimension in different scales of different sequences were compared, it was found that multi-fractal spectrum and generalized dimension can show different levels of fractal characteristics of CGR graphics of DNA sequence, which can distinguish more complex structure of sequences.

最后，研究了DNA序列CGR图形的多重分形的计算过程，讨论了权重因子及满足标度不变性的范围选择等问题，得到结论：对CGR图形进行多重分形时权重因子可以选择为-15≤q≤50；计算了不同序列的多重分形谱和广义维数，比较了不同序列不同尺度的多重分形谱和广义维数，发现多重分形谱和广义维数能够表现DNA序列CGR图形的不同层次的分形特征，能够区分更复杂的序列结构。

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。

One is a independent subsystem of the dimension equal to the difference of the dimensions between the total system and the symmetry Lie group.

这种标准形由一个维数等于系统维数与对称性Lie群维数之差的独立子系统和一个不含控制量的子系统串联而成。

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。

The three dimension reticular cell counting method is adopted to calculate the fractal dimension characterizing skew degree of gray level surface. With the two-dimension reticular cell counting method, the fractal dimension characterizing wrinkle shadow block distribution is obtained. By means of distribution function, the fractal dimension for the size distribution of wrinkle shadow block can be achieved.

提出以尺度变化的立体网格计算灰度曲面的分维数，表示灰度曲面的起伏程度；以尺度变化的平面网格计算织物折皱阴影块分布的分维数，表示阴影块的离散程度；以当量直径为尺度，计算分布函数的分维数，表示织物折皱阴影块尺寸的分布。

In this paper,a two dimension variation method is applied to compute tensile fracture surface fractal dimensions of a grain composite material LDPE/CaCO 3,and set the relationship of tensile fracture surface fractal dimensions and tensile ultimate stress and material filler weight content percent .

应用计算断口表面分形维数的二维变差法，计算了颗粒复合材料LDPE／CaCO3拉伸断口的分形维数，并且建立了断口分形维数与强度极限和填料颗粒含量之间的关系。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。