度量

To get the low dimensional data with regular structure,the measure of the regularity is constructed and then the dimension reduction is brought forward.

为了寻求具有规则拓扑结构的低维数据集，构造了数据结构规则性的度量，提出了保持数据集拓扑结构不变的降维方法。

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。

Each kind of theory and technology about health safeguard can be integrated into a grading describable system. The 5 kinds basic space, which is derived sequentially from topological space, regular space, metric space, measured space and continuous space, are the mathematical base to structure the method of health safeguard.

从泛函分析的角度全面总结了各种健康保障理论与技术，将其统一到一个递级的描述系统中，由拓扑空间、规则空间、度量空间、测度空间和连续空间逐步继承而来的5类基本空间是构造健康保障方法的数学基础。

These results also show that the relatedness measurements can make up the defects of ontology while expressing knowledge relevancy.

同时，结果表明此类度量方法能够弥补本体在表示相关性时的缺陷。

The basic data type for adequacy measurement is analyzed,and the data relevancy model is established.

分析了充分性度量的基本数据类型，建立了数据关联模型。

In this paper, we proposed a novel text representation model named Graph Space Model and introduced a novel way to measure the representation ability of a text representation model.

本文总结了文本表示过程，提出了一种新颖的用于度量文本表示模型表示能力的方法，同时也提出了一系列与文本图表示相关的值得探讨的问题。

A drawdown is measured from the time a retrenchment begins to when a new high is reached.

资金回撤的度量是从资金开始下滑的时间开始，直到出现一个新的高点。

2The new cloud physical model is put forward the metric geometry.(3)The generalized cloud equations of cloud is derived on the generalized function and the Sobolev space on the Riemannian manifold.

提出了 大气模式中新一代云方案的动力学：(1)基于拓扑的云分类；(2)基于度量几何的云模型(3)利用黎曼流型上的广义函数和索伯列夫空间，系统建立了云之动力学方程组。

Endowed with a Riemannian metric derived from the gray scale information of a given image, the image space became a Riemannian manifold. On this Riemannian manifold, we evolved a curve by the mean curvature flow using the level set methods.

在图像空间上直接赋予一种由图像灰度信息导出的黎曼度量，使之成为黎曼流形，然后在此黎曼流形上利用水平集方法对曲线以平均曲率流进行演化。

In order to prove the existence of the periodic boucing solutions, firstly we will introduce a new coordinate transformation, transform the system from right half plane to the whole plane. And give the relation of the eigenvalues of Hill's equation and the rotation numbers, using this approach and Pioncar -Birkhoff twist theorem, we proved the existence of the periodic bouncing solutions for asymptotical linear oscillator.

对于周期解的存在性证明，我们引进新的坐标变换把右半平面上的碰撞问题转化到整个平面上，给出旋转数与Hill方程的特征值的关系，并以此来度量渐近线性振子，再应用Pioncaré-Birkhoff扭转定理得到周期碰撞解的存在性。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。