分维

Hydrology has obvious characteristics of the upper reaches of the Yangtze, water density, bifurcation ratio, bend coefficient and fractural have close relationship with regional structure, Neotectonics and seismic.

水文具有长江上游的典型特征，河网密度、分歧率、弯曲系数及分维均与区域构造、新构造运动和地震成正相关关系。

Three Gorges area river system fractal dimension value D=1.7239, which indicate that the geomorphy of Three Gorges area is on the mature stage, and river system growth completely.

三峡地区水系分维值D=1.7239，表明三峡地区地貌处于侵蚀发育的壮年期，河网较发育，水系发育的较为完全。

The results show that the compressibility of cohesive soils is closely related to the grain morphology, granulometric distribution, grain packing and pore distribution.

研究表明：粘性土的压缩性与颗粒的形态、分布及排列、孔隙的分布情况密切相关；一般来说，颗粒的分布分维、定向度、圆度越小，土体的压缩性就越低，抗压性能就越好。

For m-modal maps with m turning points C1,C2,…,Cm, by defining equivalent scaling factors α_e as the geometric average of all scaling factors α_Ci (i=1,2,…,m),|α_e|=|α_C1α_C2…α_Cm|1/m, global superuniversal relationship between equivalent scaling factors α_e and fractal dimensions d of Feigenbaum-type attractors on all the infinitely many critical points of transitions to chaos is obtained: dlog_|α_e|=β~, where|W| is the basic period of the m-tuply superstable sequences W, and β~ is not only independent of the concrete sequences W, but also independent of the concrete maps.

对于具有m个转变点C_1，C_2，…，C_m的m峰映射，通过定义等效标度因子α_e为所有标度因子α_(i=1，2，…，m)的几何平均，|α_e|=|α_(C_1)α_(C_2)…α_|~(1/m)，得到了等效标度因子α_e与所有无穷多个转变至混沌的临界点上Feigenbaum型吸引子的分维d之间的一个整体性的超普适关系：dlog_|α_e|=β~(e，其中|W|是m超稳序列W的基本周期，超普适常数β~(e不仅不依赖于具体的序列W，而且也不依赖于具体的映射。

For m-modal maps with m turning points C1,C2,…,Cm, by defining equivalent scalingfactors α_e as the geometric average of all scaling factors α_Ci (i=1,2,…,m),|α_e|=|α_C1α_C2…α_Cm|1/m, global superuniversal relationship between equivalent scaling factors α_e and fractal dimensions d of Feigenbaum-type attractors on all the infinitely many critical points of transitions to chaos is obtained: dlog_|α_e|=β~, where|W| is the basic period of the m-tuply superstablesequences W, and β~ is not only independent of the concrete sequences W, but also independent of the concrete maps.

对于具有m个转变点C_1，C_2，…，C_m的m峰映射，通过定义等效标度因子α_e为所有标度因子α_(i=1，2，…，m)的几何平均，|α_e|=|α_(C_1)α_(C_2)…α_|~(1/m)，得到了等效标度因子α_e与所有无穷多个转变至混沌的临界点上Feigenbaum型吸引子的分维d之间的一个整体性的超普适关系：dlog_|α_e|=β~(e，其中|W|是m超稳序列W的基本周期，超普适常数β~(e不仅不依赖于具体的序列W，而且也不依赖于具体的映射。

The traditional box-counting algorithm is based on the grid document and has some serious shortcomings, such as the distortion of the image being enlarged, the trivialness of the process and the finite of the iterative degree, etc.

实践表明，该算法有3个优点：（1）图像不会随着放大缩小而失真；（2）可完全进行计算机操作，且简单可靠；（3）从某种意义上讲，由于迭代的次数可以是无穷的，所以能非常精确地确定图形的标度空间，并可获得精确的分维值。

Fractal theory quantifies these phenomena mainly by ascertaining their fractal dimensions.Box-counting algorithm is the one most practical and also most frequently adopted method.The traditional box-counting algorithm is based on the grid document and has some serious shortcomings,such as the distortion of the image being enlarged,the trivialness of the process and the finite of the iterative degree,etc.The vector box counting algorithm developed in this paper takes vector document as the carrier and has three advantages.

传统的计盒算法是基于栅格文件的方法，由于其存在图像放大后失真、过程繁琐和迭代次数有限等缺陷，因此为了准确简单方便地进行分维计算，开发了一种以矢量文件为载体的矢量计盒算法，并详细阐述了这种算法的数据结构、处理流程和主要函数，同时以Koch曲线、骨肿瘤边界及水系证明了矢量计盒算法的准确性和优越性。

In this paper, some methods of fuzzy mathematics suah as the direct method of fuzzy pattern recognition, the method of fuzzy clustering analysis the method of fuzzy information retrieval, and the recently advanced method of fuzzy fractal dimension have been applied to earthquake monitoring and prediction in the Surrounding Capital Area based on the seismicity and earthquake precursors. The seismic and unseismic precursors before both the Tangshan M=7.8 great earthquake in July, 1976 and the Datong-yanggao M...

本文把模糊数学中的模糊模式识别的直接方法、模糊聚类分析方法、模糊信息检索方法和新近提出的模糊分维方法应用到以地震活动性和地震前兆为基础的首都圈地震监测预报当中，分析研究了发生在这一地区的两次大地震，即1976年唐山7.8级和1989年大同6.1级地震前用模糊数学方法识别出的地震学前兆和非地震学前兆，并对这一地区大地震的长期和中短期模糊预报方法与途径进行了简要的讨论。

From the perspective of the relationship between crop percent and landscape spatial structure, the fragmentation debases along with the percent enhancing and they are positively correlated.

从农作物百分比与景观空间结构的关系来看，破碎度随农作物百分比的升高而降低，两者呈显著线性相关，而分维数和农作物百分比基本不存在显著关系。

For example, MI behaved most sensitive to heart state when spontaneous respiration inhibited with respiration machine; FD could manifest heart healthy level, which reduced sharply sooner after acute injury but remained almost steady afterwards; the parameters of Poincare dissert-dot plot and HRV could accurately distinguish the state change before and after ligaturing; the HF-ECG excelled in not only revealing injury degree but also locating injury position.

例如，交互信息对自主呼吸被接呼吸机抑制后的状态敏感，分维具有表征心脏健康状况潜力的特性，在急性损伤后明显减少，但不随损伤的时间延续而变化；心率变异性参数和散点图可以灵敏地区分出急性损伤前和损伤后的状态；而高频心电在表征心脏损伤和定位方面独具特色。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐