维数

There are two problems,the first is the fact that its natural covering under the self-affine transformation is not a efficient covering, the second is the fact that the limiting frequency of some digits or fibers may not exit.

其困难在于由于其仿射背景，导致它们的自然覆盖不是一个有效的覆盖，以及某些点或纤维的频率可能不存在导致维数估计的困难。

Cowper G R%Symonds P S Strain Hardening and Strain-rate Effects in the Impact Loading of Cantilever Beams Brown Univ Division of Applied Mathematics Report No.28 , 1957,null

封加波 对薄层柱壳爆炸膨胀断裂过程的研究高压物理学报， 1988，(2)章冠人韧性和脆性断裂的分形维数爆炸与冲击， 1996，2

The precision of criticality analysis is improved, and can be a support for characteristic parameters extraction in condition evaluation.

对于具有较多状态特征参数的系统，提出了基于主成分分析的神经网络状态预测模型，通过降低神经网络的输入维数，提高了预测的速度和精度。

We will call the construction a crossed product. The results about the sufficient and necessary conditions for A#H, the smash product, to have finite global homological dimension have been discussed in ~WYZ. which will be extended to crossed prodcut A#a.

关于smash积有有限整体同调维数的充分必要条件这一结果在中已有了一定的讨论，本文主要是将关于smash积的这一结果推广到crossed积。

The Pinching problems are discussed on the sectional curvature of compact space-like pseudo-umbilical submanifolds M~n with parallel mean curvature vector in De Sitter space S~_p, and the theory of reduction of the codimension is obtained in De Sitter space through evaluating the Laplacian of square of the length.

讨论了De Sitter空间Snp+p中，具有平行平均曲率向量的紧致类空伪脐子流形Mn的截面曲率的拼挤问题，通过估计第二基本形式模长平方的Laplacian，得到了De Sitter空间中的余维数压缩定理。

Inspired by it, we give a condition that allows the iterated function system having the overlapping property, and obtain the multifractal decomposition formula of M-W fractal through the code space.

正是在这样的背景下，我们研究了一类允许弱重叠条件下的图有向自相似集的重分形分解，并通过码空间的局部维数的方法，得到了它的的重分形分解公式。

Studying the positive definitiveness of the covariance matrix from discrete data is important to design the sampling plan and provides the base for the data analysis.However, there have been few outcomes about the positive definitiveness of covariance matrix, most of which have been restricted to the Covariance-matrix of continuous sample.

研究离散型样本协方差矩阵的正定性有助于判断是否可以降低样本的维数，有利于优化抽样个数，为抽样调查的优化设计方案提供一定的理论基础；为基于特征根的多元统计分析提供理论指导。

The vibration signals measured from diesel engine in the stage of deflagrate are analyzed with slide Wigner higher order moment spectrum.

对现场测试的柴油机爆燃阶段振动信号波形图像和切片Wigner高阶矩谱图像进行了分形维数计算。

Fractal dimension can be used to describe the morphology of tertiary dendrite.

可以用分形维数来描述三次枝晶的形态。

For any dimension vector , there exist the generic decomposition, and a dense and closed subset V of system space R〓 corresponding to this decomposition such that, for each dynamical system M∈V, every indecomposable summand of M thus M is clear.

对任意的维数向量，存在一般分解，以及系统空间Rm，n，p中稠密的开子集V，并且我们对V中每个系统的不可分解直和项知道得很清楚，进而对V中每个系统也非常清楚。

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。