查询词典 topological dimension

Why a higher spatial dimension is ingressing at an ever-accelerating rate into space-time we shall perhaps not understand until we achieve, through a concrescence of time, a return to the higher topological dimension.

为什么一个更高维度是永远-加速度进入时空的入口，直到我们达到了我们才能理解，通过一个时间的愈合，返回到更高拓扑维度。

The method includes the following steps: firstly, a spherical neighborhood of present sample points is established by using the geometric spherical-modelling theory and all the sample points contained in the spherical neighborhood are adopted as candidate neighbor points, thus not only preserving the effectivity of the dimension reduction capability when data sets are sparse but also getting the advantages of low-sensitivity to isolated points and good stability of the preserved topological structure; then a data relevance matrix more matching semantics can be obtained by relevance measurement based on route clusters to update the candidate neighbor points in the spherical neighborhood and optimize the regular neighborhood space of the present sample points, thus improving the phenomenon that the dimension reduction of sample sets provided with folded curved faces is apt to suffer the integrated-structure distortion in case of heterogeneous data distribution.

首先利用几何开球原理建立当前样本点的球状邻域，将包含在球状邻域内的所有样本点作为候选近邻点，不但能够保持在数据集稀疏情况下的降维性能的有效性，而且具有对孤立点敏感性不高、保留拓扑结构稳定性好的优点。然后利用基于路径聚类的相关性度量得到更符合语义的数据相关性矩阵，用来对球状邻域内的候选近邻点进行更新，优化当前样本点的规则邻域空间，改善了当数据不均匀分布时在带有折叠弯曲面的样本集上降维容易出现整体结构扭曲的现象。

Usually the fractal dimension of F is greater than its topological dimension.

以某种方式定义的分形集合的分形维数通常是大于它的拓扑维数。

Although its topological dimension is 2, its Hausdorff-Besicovitch dimension is log(3)/log(2)~1.58, a fractional value (that's why it is called a fractal).

虽然它的拓扑维数是2 ，其的Hausdorff - besicovitch层面是日志（ 3 ）/日志（ 2 ）？ 1.58 ，分数的价值（这就是为什么它被称为分形）。

A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.

这个定义说明分形是Hausdorff-Besicovitch维数严格大于拓扑维数的集合。

It includes: The high frequency components and the low frequency components of EEG data are filtered by FFT, The correlation dimension is calculated primarily to replace the original topological dimension.

在第五章，我们把第三章所提的方法具体运用到脑电分析中去，我们认为应依据EEG数据的特点作一些预处理。

As a result, the features can be of 2-dimension, 1-dimension or 0-dimension, such as auxiliary face and center line axes.

这样，基本特征用一个体表示，模型中可以定义不同维数的特征，如辅助面、中心线等特征。

Regular Fractal Dimension Calculation is discussed by using Koch Curve and Cantor Ternary Set.Additivity of regular fractal dimension is discussed by continuation of Koch Curve with line and Cantor Ternary Set in vertical direction.CircumferenceArea,Variation,Grid and Radius methods of calculation statistical fractal dimension are introduced.

本文以科赫曲线与康托尔三分点集为例，讨论了有规分形维数的计算；以科赫曲线在垂直方向的两种拓展为例，讨论了有规分形维数的加和性；以周长—面积法、变量法、网络法与半径法为例，介绍了无规分形维数的计算方法。

In this design, the dimension M of the memory vector field may be not necessarily equal to the dimension N of the network vector field. This may be the usually case in applications. Designing a network with either static or oscillating behavior, after analysing the dynamical. behavior of its four-dimension subspace, we get 2-torus in the subspace. If we vary the ratio of the imagine parts of the complex conjugate eigenvalues, the periodic motion of all kinds of period ratio on 2-torus are obtained.

设计一个既具有静态平衡点又具有动态振荡的网络，其静态平衡点由多余维叉形分叉得到，动态振荡形式由多余维Hopf分叉得到，通过对其中一个具有振荡行为的四维子空间的进一步分析，可以得到网络在四维子空间中的二环面运动，适当调整约当形中共轭复特征根虚部的比值，可以得到各种周期比的二环面上的周期运动。

Part 2, particularizes the ecological dimension, the social dimension and the economics dimension of the sustainable development theory.

第二部分，具体分析了可持续发展理论的生态环境维度、经济维度和社会维度。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。