查询词典 fractal

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。

Land use type is the outcome of duple influence of nature and human activity, which possessing scrambling, relative instability and complexity, and it can be discussed by fractal theory. Application of fractal theory in land use structure involve in the calculation of fractal dimension of land use type, research method and fractal description of change of land use structure, fractal model of region landscape and so on, but fractal mechanism of spatial diversity of land use type is rarely reported.

土地利用类型是一种在自然和人类活动双重作用下的产物，具有不规则、相对不稳定性和复杂性特征，可以利用分形方法进行探讨；分形理论在土地结构研究中的应用涉及土地利用类型分数维的计算、土地利用结构分形研究方法、土地利用结构及其动态变化的分形描述、区域景观结构的分形模型等方面；但土地利用类型的分形机制的空间差异研究少见报道。

The results show that the radiative properties of randomly distributed soot aggregates for a given fractal dimension are complex functions of the monomer diameters, the number of monomers in the aggregates,and the refractive index; For a small value of the monomer diameters, the absorption cross section of soot aggregates tends to be relatively constant when the fractal dimension is small but increases rapidly when the fractal dimension exceeds two. However, a monotonical reduction in light absorption with the increase of the fractal dimension is observed for soot aggregates with sufficiently large monomer diameters, number of monomers,and refractive index. The scattering cross section , extinction cross section and single-scattering albedo increase monotonically with the increase of the fractal dimension. Overall, the results for soot aggregates differ profoundly from those calculated for the equivalent spherical particles, and the discrepancies between them will change small with the increase of the fractal dimension.

研究表明，在给定分形维数的情况下，烟尘団簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率；原始微粒较小的団簇粒子，当分形维数较小时，吸收截面变化不明显，但当分形维数大于二时，吸收截面骤然增大，然而，对于具有比较大的原始微粒粒径、数量及复折射率的烟尘団簇粒子，吸收截面随着分形维数的增大而单调递减；随着分形维数的增大，団簇粒子的散射截面、消光截面及单次散射反照率均单调递增；从整体上来讲，団簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别，并且这种差别随着分形维数的增大而减小。

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。

The main work and innovation1 In general , a image compression method has different effect to different image . Some are fit for image which has much high frequency . Some are fit for image which has much low frequency .This paper analysis the applicability of fractal algorithm . In this dissertation , an improved algorithum is given . The basic algorithum without eight change and the joint use of quantitative coding , The compression ratio and PSNR can be adjusted , and it can get more quickly speed of coding .2 To a group of exact fractal code , the decoding image can be any resolution .With this characteristic ,choose the proper domain block and range block,this paper get an algorithum which can get higher decoding PSNR and speed than the basic fractal algorithum.3 Give a new method to calculate the scale factor . The calculation of basic algorithum is complex and enormous . The factor of scale is an important variable of the basic algorithm. Now there are two methods to calculate the factor of scale .A new method was given to calculate the factor of scale. The calculation load and complexity are reduced by the new method. Compared with the basic algorithm , the method can reduce coding time.4 The basic fractal algorithum is based on the Collage theorem and contraction mapping theorem . A mathematic model based on basic fractal algorithum is given .

本文的主要工作及创新点主要包括以下几点：1一般情况下，一种图像压缩的方法对不同特点的图像，压缩效果会有所不同，本文利用分形压缩编码对不同特点的图像进行编码，分析了分形编码对不同图像的编码适用性，利用去掉8种变换的分形编码算法与简单的均匀量化编码方案相结合，得到了一种可以调节压缩比与解码质量的分形编码方案，该提高编码速度6倍以上。2分形编码的特点之一是分形解码的分辨率无关性，即对于一组分形编码可以将其解码到任意分辨率下，本文利用分形编码的这一特点，结合不同的量化编码方案，选择合适的定义域块与值域块及适当的编解码分辨率，得到了一种提高解码质量，编码速度提高12倍以上的加速算法。3比例因子是基本分形算法中的一个重要变量，目前有两种计算比例因子的方法，文中给出了一种新的求比例因子的方法，该方法简化了求比例因子的计算，从整体上减小了基本分形算法的计算量，简化了算法4分形压缩的数学基础是不动点定理与拼贴定理，本文根据基本的自动分形编码方法，建立数学模型对其进行推导，得到了用普通数学的极限理论解释分形编码的数学表达式，从而对由基本分形编码得到的解码图像中的像素点的值给出了确定的表达式。

The desulfurization experiments of CaO samples with various fractal dimensionswere carried out in the TGA to investigate the influences of fractality on the sulfationreaction, and the evolution of pore structures during the reaction. Under certainsulfation conditions, the calcium conversions of the CaO samples increase with theincrease in fractal dimension when fractal dimension is less than 2.68, and decreaseswhen it is more than 2.68. In the range of the experiment temperatures, the calciumconversion for a sample with a lower fractal dimension increases with the increase inthe temperature, and for a sample with a higher fractal dimension there exist anoptimum temperature at which the sample can reach the highest calcium conversion.

选用具有不同分形结构的CaO试样进行了硫化实验，研究孔结构的分形特性对硫化反应的影响以及硫化过程中分形孔结构的变化特性，实验结果表明，在一定的分形维数范围内，随着分形维数的增加，钙利用率增大，但分形维数超过一定值时(约为2.680)，钙利用率反而降低。

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。

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 principle of the fractal-interpolated surface was discussed. The formula and the theorem of fractal dimension of the fractal-interpolated surface were analyzed. The numerical analysis of height anomaly fit by the fractal interpolated surface and the result comparison with the quadric polynomial surface model with practical data were given.

本文论述了分形插值曲面的原理，分析了分形插值曲面的计算公式，讨论了分形插值曲面的维数估计方法和公式，用实际数据进行了分形插值曲面拟合高程异常的数值分析以及与二次多项式曲面拟合模型结果的比较。

Experiments show that rhomb partitioning is more powerful in suppressing block artifacts than square partitioning, results in much higher reconstructed image quality, but takes longer encoding time; 2 For solving exhausting encoding problem of fractal image coding, we present a fast rhomb-partitioning fractal image coding based on neighbor-searching; we present a fast rhomb-partitioning fractal image coding based on block classification; we present a fast square-partitioning fractal image coding based on neighbor-searching, block classification and wavelet transform.

2针对分形图象压缩编码过程非常耗时的致命弱点，提出了基于邻域搜索的菱形块分割的快速分形图象压缩编码方法，提出了基于块分类的菱形块分割的快速分形图象压缩编码方法，提出了基于邻域搜索·块分类和小波变换的方块分割的快速分形图象压缩编码方法，实验结果表明，我们提出的快速分形图象压缩编码与传统的分形图象压缩编码相比，编码速度提高了近40倍。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。