维数

Through calculating the generalized dimension by covering the signal with n-dimension boxes, three dimension feature vectors including the box dimension, the information dimension and the correlation dimension are got.

首先利用覆盖法求取广义维数得到该语音信号的三维特征向量，包括容量维数、信息维数、关联维数；然后计算信号的维数特征距离；最后根据特征距离对语音信号类别进行决策分类。

The concepts of dimension and dimension distribution of measure are introduced;and the dimensionand dimension distribution of random invariant measure μ* are obtained.

介绍了测度的维数和维数分布的概念，对随机不变测度μ*，获得了μ*的维数及其维数分布

In this paper, the existence of isometric mapping between the manifold in the high-dimensional data space and the parameter space is proved. By distinguishing the intrinsic dimensionality of high-dimensional data space from the manifold dimensionality, and it is proved that the intrinsic dimensionality is the upper bound of the manifold dimensionality in the high-dimensional space in which there is a toroidal manifold.

首先给出了高维数据的连续流形和低维参数空间之间的等距映射存在性证明，然后区分了嵌入空间维数、高维数据空间的固有维数和流形维数，并证明存在环状流形高维数据空间的参数空间维数小于嵌入空间维数。

This thesis mainly discuss following issues, Theory and simple expressions for array covariance matrixes are derived when angular spread functions are symmetric distribution functions, i. e. the Uniform distribution, the Gauss distribution, the Laplace distribution and the Von Mises distribution, and a non-symmetric distribution function, i. e. the Gamma distribution. And the relation between the effective signal subspace and the array number, or and the nominal angle of the distributed source, the angular spread, the distributed functions, and the Signal-to-Noise Ratio is gained. The dimension of the effective signal subspace increases with increment of the array number. And it is more obvious to the non-symmetric distribution. The dimension of the effective signal subspace decreases with increment of the nominal angle. And the distributed source is equal to a point source as θ=π/2. The dimension of the effective signal subspace increases with increment of the angular spread.

本论文针对阵列信号处理中广泛存在的分布源现象，主要讨论了以下问题：推导了角度分布函数分别为对称的均匀分布、高斯分布、拉普拉斯分布、Von Mises分布和非对称的伽马分布时，分布源阵列接收信号协方差阵的严格模型和简化模型，得到了单个分布源的有效信号子空间随阵元数、分布源中心角、分布角、角度分布函数和信噪比的变化规律：随着阵元数的增加，对所有角度分布函数的有效信号子空间维数也随着增加，且非对称分布函数的有效信号子空间充满整个空间的可能性更大；随着分布源中心角逐步增加，有效信号子空间维数逐步减小，当θ=π/2时，等价于点源情形；随着分布源分布角逐渐加大，有效信号子空间维数也随之增加，直到有效信号子空间充满整个空间；随着信噪比的增加，有效信号子空间维数有一定程度的减少。

After it is proved that the fractal dimensions are stable characteristic parameters of images, and there is correlation between them in undeformed and deformed states, the fractal correlation function are found for displacement measurement, which the correlation parameters are Box Dimensions.

在确定了变形前后数字散斑图像的分形维数之间具有相关性，而且其分形维数是稳定的特征参数之后，以图像的盒维数为相关参数进行互相关运算而形成分形相关函数。即利用变形前后数字散斑图像的分形维数序列做为相关参数进行相关运算，实现位移测量。

The results show that the radiative properties of randomly distributed soot aggregates for a given fractal dimension are complex functions of the monomer diameters, the number of monomers in the aggregates,and the refractive index; For a small value of the monomer diameters, the absorption cross section of soot aggregates tends to be relatively constant when the fractal dimension is small but increases rapidly when the fractal dimension exceeds two. However, a monotonical reduction in light absorption with the increase of the fractal dimension is observed for soot aggregates with sufficiently large monomer diameters, number of monomers,and refractive index. The scattering cross section , extinction cross section and single-scattering albedo increase monotonically with the increase of the fractal dimension. Overall, the results for soot aggregates differ profoundly from those calculated for the equivalent spherical particles, and the discrepancies between them will change small with the increase of the fractal dimension.

研究表明，在给定分形维数的情况下，烟尘団簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率；原始微粒较小的団簇粒子，当分形维数较小时，吸收截面变化不明显，但当分形维数大于二时，吸收截面骤然增大，然而，对于具有比较大的原始微粒粒径、数量及复折射率的烟尘団簇粒子，吸收截面随着分形维数的增大而单调递减；随着分形维数的增大，団簇粒子的散射截面、消光截面及单次散射反照率均单调递增；从整体上来讲，団簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别，并且这种差别随着分形维数的增大而减小。

But, such a vectorization will bring three potential problems at least:① Some implicit structural or contextual information may be corrupted;②the higher the dimension of input pattern, the more space are needed for storing weight vector;③When the dimension of pattern is very high and the sample size is small, linear classifier tends to be overstrained.

但如此至少会带来3个不足：①原有矩阵模式的空间或结构信息可能会遭到破坏；②由于权向量的维数等于输入模式的维数，当输入模式维数很大时，权值的存储空间相应地会很大；③对于大维数的模式，当样本数不多时，利用线性分类器易导致过拟合。

Result shown: value of fractal dimension is a comprehensive index, which reflect the changes of landscape, patch areas, patch numbers, area per patch, and their interaction. And the index can reflect the irregular degree and the complex degree of landscape patch in dumping place. The fractal dimension of mixed vegetation of arbors – shrubs and mixed vegetation of shrubs maintain the high level, while fractal dimension of new reclamation land and grass land are low. The difference of other type landscape fractal dimension is not significant. Vegetation landscape is influenced by many kinds of factors. It is primarily influenced by surface material composition and terrain in south and west dumping place, which diversity index is high. It is primarily influenced by vegetation type in inner dumping place and expanded west dumping place. The landscape multiplicity index of the mixed vegetation of grass and shrubs is higher than other landscape type, but landscape dominance index of this area maintains on the lower level.

结果表明：分维数的大小反映了景观斑块面积、斑块数量和平均斑块面积等因素的相互作用，反映了排土场内景观斑块的不规则程度和复杂程度；乔灌混交地和灌木混交地保持着较高的分维数，新造复垦地和草地的分维数较低，其它景观类型的分维数则差别不大；植被景观受多种因子的影响，在南排土场、西排土场受地表物质组成和地形的影响为主，其多样性指数较高，在内排土场、西排扩大区受植被类型的影响为主；草灌混交地的景观多样性远高于其它现有的复垦植被区，但其景观优势度则保持在较低水平上。

After analyzingthe short-term memory capacity and its relation with the flactional dimension property of40Hz ERPs, we find out the that the d￣ion value will change gmetiy is the nUmber ofword chads is around 7, i.e., the relative value of dimension of the two hemisphere willrreverse, and the abeolute value of the same helnjsphere wb dlop diamatically.

通过短时记忆容量与40HzERPs分维特性的相关分析，发现在测试组块数在7附近时，40HzERPs分维数分形维数特性发生了突变，表现为左右半球分维数值相对大小的反转和同一半球内分维数的突降。

Compared with the two dimension FD, the methos are fast and simple,the experiment result shows it is feasible to classify manmade targets and natural objects by the FD of the rough profile of contour.

实验表明，水杯及车辆轮廓的分形维数较低，岩石则具有较高的分形维数，通过同二维结果的对比，从计算量和分形维数两方面证明用所提出的算法计算轮廓分形维数区别人工目标和自然物体是可行的。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。