分维

In this research a new mathematical model - cubic polynom with two given derivatives at end points - was proposed which can good match the S-shpae curve.This model has a number of analytical features:describing the geographic phinomena prosesses in three hierarchies (textural fractal,structural fractal and state fractal); the boundary values of the structural fractal can be considered as the boundary values of interval of scaleless.

在研究中提出了扩展分维表达函数：带导数三次多项式，它能很好地表达反S形分布曲线，具有一系列解析特征：可从三个层次（纹理分形、结构分形和态势分形）上描述地理现象或过程；其中结构分形的边界可近似地看作是非扩展分维无标度区的上下界。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

Some basic theories on fractal and fractal dimension are introduced in this paper.

文章介绍了分形和分维的基本理论，并且利用分形理论对675钢断裂面的分维进行了分析，在此基础上探讨了分维对塑性金属材料断裂的影响。

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 geological explanation of different fractal dimensions was presented via mathematical analyses.Two methods of estimation for fractal dimension,linear and n...

同时，通过模型及其分维值的数理分析，得出不同分维值的地学解释，讨论了分维的线性与非线性最小二乘回归估计法。

Through utilization of box counting method, the fractal dimensions of spatial distribution of oil-gas fields are calculated.

应用盒维数方法计算了油气田空间分布的分维值，对不同区块的分维特征进行了比较，探讨了分维值的物理意义。

Fractal dimension structure of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, of fractal dimension calculus and fractal measure are given.

摘 要：探讨了宇宙分维构造的形式，给出了分维微积分及分形测度的数学基础，包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。

The experimental method of mercury porosimetry was applied to determine the porous properties of typical mixed bio\|briquettes in two typical pore systems to overcome the limitations of past researches on the characteristics of their sulfur retention were compared to those of classical sulphuration reaction.

根据生物质型煤的孔径分布特征，建立孔隙分形结构模型，模拟相同分维的生物质型煤的孔隙率和比表面积；从孔隙分形结构的形核、生长的角度，探究生物质型煤的脱硫机理；进而得出生物质型煤分形结构存在的孔径范围，以及分维、均孔等分形几何参数与生物质质量分数的规律。

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。

After analyzingthe short-term memory capacity and its relation with the flactional dimension property of40Hz ERPs, we find out the that the d￣ion value will change gmetiy is the nUmber ofword chads is around 7, i.e., the relative value of dimension of the two hemisphere willrreverse, and the abeolute value of the same helnjsphere wb dlop diamatically.

通过短时记忆容量与40HzERPs分维特性的相关分析，发现在测试组块数在7附近时，40HzERPs分维数分形维数特性发生了突变，表现为左右半球分维数值相对大小的反转和同一半球内分维数的突降。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。