维数

Fault diagnosis; chaos theory; correlation dimension; wavelet analysis; virtual instrument; hydraulic pump

故障诊断；混沌理论；关联维数；小波分析；虚拟仪器；液压泵

It contains a 2 dimensional array of fields.

它包含的领域2维数组。

But what if the dimensionality is 1000?

但是，如果维数是1000？

Data set size, dimensionality and sparsity have been identified as aspects that make cluster more difficult.

数据集合的大小，数据的维数和数据的稀疏性都是制约聚类的不同方面。

Chaos optimization algorithm is global search method and it need not to consider SVM dimensionality and complexity.

混沌优化算法是一种全局搜索方法，在选取SVM参数时，不必考虑模型的复杂度和变量维数。

This method can overcome the curse of dimensionality.

此方法能解决"维数灾难"问题。

Fractal dimension is the simple and effective dimensionless index to reveal the complexity of object.

故障的出现增加了信号的复杂性，而分形维数是描述事物复杂性的简单而有效的无量纲指标。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

The second motivation is the replacement of a Boolean algebra of sets by the distributive lattice of filters of a finite partially ordered set.

一个自然的问题是：能否给出射影空间中放置不同维数的线性族类似的公理体系？

Results showed that fractal dimensions of different disfigurement categories have better distributivity aiming at the mean values and mean square values of nine characteristic quantities,and it was feasible to use feature parameter to describe wood surface disfigurement.

针对这九个特征量的均值和均方差值做了分析，结果表明不同缺陷类别的分形维数有较好的分布性，用这些特征参数描述木材表面缺陷是可行的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。