维数

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。

The surface fractal dimensions have distinct different change trend from specific surface area and pore volume.

石油焦表面分形维数与比表面积和孔容积在变化趋势上存在明显差异。

This paper summarizes the research job of predecessors, full text is divided in four part:The first part introduces the develop history and present conditions of MCRE;In the second part, the concept of average Markov process is introduced. Moreover we investigate the relations for Markov processes, martingales, stationary processes and average Markov process systematically.The third part summarizes the model that constructs the MCRE by p-m chains and skew product Markov chains by p-m chains, also we discuss the relations among the basic gunctions of the probability character for MCREIn the fourth part, we discuss the dimension of GW-tree and the canonical branching chain in random environment, furthermore we summarize the exact formulas of mathematical expectation and variance of branching chain in random environment.

本文主要是综述这方面前人工作，全文分成四个部分：第一部分介绍了MCRE的发展历史和研究现状；第二部分研究了马氏过程、鞅和平稳过程这三类经典的随机过程的相互关系，包括他们之间的包含和排斥关系，引入了&均马氏过程&的概念，研究了它与三类经典过程—马氏过程、鞅及平稳过程的关系；第三部分综述了用p-m链构造的构造的随机环境中的马氏链和绕积马氏链，讨论了与之相关的概率特性函数的性质；第四部分讨论了GW树的维数，并综述了随机环境中的典范的分枝链，讨论了随机环境中的分枝链的数学期望和方差的计算公式。

The second shortcoming taken into account, such nomenclatures as the real critical contact area, minimum effective fractal dimension, dimensionless maximum effective fractal roughness parameter and minimum effective material property were presented.

针对第2个缺陷，提出了实际临界接触面积、最小有效分形维数、量纲一的最大有效分形粗糙度参数、最小有效材料特性等术语。

Fractal image coding, based on the fractal dimension of the image segmentation block, a mixed-encoding method, the intr...

分形图像编码，基于分形维数对图像进行块分割，提出了一种混合编码方法，引入不变矩限制匹配块的搜索范围。

The fault pattern recognitions of rolling bearings are thus to be effective and accurate.

因此，可以利用分形维数效地诊断出流动轴承的故障。

In this paper, the dimension of the double periodic cubic C1 spline space over non-uniform type-2 triangulations is determined and a local support basis is given.

本文确立了非均匀Ⅱ型三角剖分上双周期三次样条函数空间的维数，并给出了一组具有局部支集的基底。

Taking ground-state helium for example,toget the ground-state energy as well as -2.90328 a.u.,withthe full-set scheme,we have to use 361 HH and 4 GLF;whilewith PHGL,only 51 PH and 4 GLF is needed,the eigenenergyis -

所需超球径耦合微分方程的个数或广义本征矩阵的维数较完备展开法显著降低。如对He原子的基态，完备展开为了得到-

This thesis is devoted to various topics of physics of CP violation.

通过两个例子本文演示了带有额外维数的物理模型能够产生新的CP破。。。

Probably due to fertilizer ,clay content and other basic property or constitute of clay mineral changed, which resulted in variety of fractal dimension.

这可能是由于施肥使粘粒含量等土壤的基本理化性状或者粘土矿物组成发生了变化，才导致了分形维数的变化。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新