特征函数

The fact that the naural projection is smooth and proper Fredholm map of index zero has been proven which enables us to show that the Brouwer degree of the natural projection is equal to unity.

第六章用经管系统解释和描述了经济与经营管理的最优化行为，建立了经管系统的特征方程，给出了生产函数与特征方程间的关系，以及经管变换的确定方法。

Firstly, we collected and sorted out the GPS data, established the uniform velocity field for the Chinese mainland and the surrounding regions, and the horizontal deformation field relative to the Eurasia plate; Secondly, we established a motion model for the entire rotation and homogeneous strain of the first and second level blocks in Chinese mainland, analyzed the motion pattern and strain behavior of active blocks in Chinese mainland, as well as the motion pattern of principal fault zones in Chinese mainland; Thirdly, considering the heterogeneity of strain distribution inside a block and supposing that the strain tensor inside the block is the linear function of location, we derived and established an equation for the entire rotation and linear strain of block and a motion model for the entire rotation and linear strain of principal blocks in Chinese mainland; We also calculated the principal strain field and the maximum shear strain field in Chinese mainland and the surrounding regions, analyzed the basic characteristics of strain field in Chinese mainland, as well as the relationship between the spatial distribution of strain field and large tectonic zones; Finally, we established the 2-D geotectonic model and digital model for Chinese mainland and the surrounding regions, calculated the stress field in Chinese mainland and the surrounding regions, and analyzed the basic features of stress field in Chinese mainland and the principal driving force for the motion and deformation in Chinese mainland.

收集整理了已有GPS资料，建立了中国大陆及周边地区统一的速度场以及相对欧亚板块的水平形变场；建立了中国大陆一、二级地块整体旋转与均匀应变的运动模型；分析了中国大陆活动地块的运动状态，应变状态，以及中国大陆主要断裂带的运动状态；考虑到一个块体内部应变张量空间分布的非均匀性，假设块体内部的应变张量是位置的线性函数，推导建立了块体整体旋转与线性应变方程，建立了中国大陆主要地块整体旋转与线性应变的运动模型；计算了中国大陆及周边地区的主应变场与最大剪应变场，分析了中国大陆应变场的基本特征，以及应变场的空间分布与大型构造带的关系；建立了中国大陆及周边地区二维的地质构造模型和数值模型，计算了中国大陆及周边地区的应力场，分析了中国大陆应力场的基本特征以及中国大陆运动、形变的主要驱动力。

Fractal is a subdiscipline of nonlinear area, researches on fractal characteristics of the deoxyribonucleic acid sequence may reveal some secret hidden in the DNA sequence during the process of biological evolution. Chaos Game Representation was proposed as a scale-independent representation for genomic sequences by Jeffrey in 1990. This technique, based on iteration function system, represents the word distribution statistics in DNA sequence as the fractal graphic. Therefore, we can get the distribution of sequence through analysis of fractal theory.

分形是非线性领域的一门分支学科，关于脱氧核糖核酸序列分形特征的研究，可以揭示生物在进化过程中隐藏在DNA序列中的某些秘密。1990年Jeffrey提出了基因组序列的与尺度无关的混沌游戏表示法，这是基于迭代函数系统的一种方法，它将DNA序列中一定长度字的分布规律表现为图形的分形特征，进而通过分形分析就可获取序列的分布规律，从而也成为DNA序列分析的一种统计方法。

An adaptation method based on the classification of a trigram's style feature computes weights dynamically according to the trigram's language style tendency with several ...

基于trigram语体特征分类的自适应算法根据trigram单元的语体特征倾向动态分配权值，并选取了几种不同的权值生成函数。

The height of bulliform cell groups reached 0.18 of leaves thickness, which was another important quantitative characteristic to achieve function of bulliform cells.

泡状细胞的周长面积比仅占普通表皮细胞的0.723，是泡状细胞功能实现的重要数量特征；(2)以细胞面积、周长、等效圆直径、每平方公厘细胞数、周长面积比，可以建立小麦叶片泡状细胞Fisher's线形判别函数，判别正确率达99%；(3)泡状细胞组高占叶厚的比例达到了0.18，是泡状细胞功能实现的又一重要数量特征；(4)相关分析表明，泡状细胞组长、泡状细胞组高、泡状细胞组面积均与泡状细胞距离叶缘的位置呈极显著负相关。

By using the kernel function, the input space is mapped to a high dimension feature space where the data are expected to be more separable, the initial centroids in the feature space are selected by applying the KRA algorithm, and the large and small clusters are partitioned and the outliers can be split from the large clusters iteratively after the kk-means clustering. As a result, the audit data can be clustered better. Secondly, the closed sequential patterns mining algorithm CloSpan is improved according to the restrictions that is composed of the axis properties and reference properties.

该方法通过核函数把数据样本空间映射到一个高维的特征空间，使数据在新的空间中具有更好的可分离性；在特征空间采用KRA算法选取初始聚类中心，然后在核k-means聚类的基础上，划分出大簇小簇并在大簇中分离出异类再次进行核聚类，从而不断地优化聚类结果。

The SVM method is based on the theory of structural risk minoration. It can map the sample space to a higher feature space by selecting an optimal Kernel function, and get a linear regression in this higher feature space.

中文摘要：支持向量机方法是基于结构风险最小化原理提出的，通过采用合适的核函数将样本空间映射到一个高维特征空间，再在高维特征空间进行线性回归。

The numerical results show that our method is effective. For the noncharacteristic Cauchy problem for 2-D and 3-D heat equation, we give the explicit H\"{o}lder type stability estimates by using weighted energy method. Especially,H\"{o}lder type stability estimate for discrete solutions of the heat equation is obtained through a fully discrete method. The numerical results are presented.

对于二维和三维的热传导方程的非特征Cauchy 问题，我们利用权函数方法，给出了一个显式的H\&{o}lder 型的稳定性估计，特别的，对于二维的非特征Cauchy问题，我们利用充分离散的方法，对二维问题的离散形式同样给出了H\&{o}lder 型的稳定性估计，同时，我们也给出了数值例子来说明我们的估计。

The system categorizes and recognizes the visible urine sediment components based on the technology of image processing and support vector machine.

在应用SVM分类方法的过程中，首先建立已知分类的图像，进而提取图像的特征，再对这些特征进行训练，同时交叉验证确定最优的SVM核函数和参数。

Therefore, due to the fact that the (111) pole density in the subsurface of decarburized bands still have a higher intensity, adding Mo into Hi-B steels could lower the slab reheating temperature.

本文采用X射线极密度和取向分布函数方法，证明含Mo Hi-B钢采用1310℃低温铸坯加热时，其热轧板表层织构特征与不含Mo并在1380℃高温铸坯加热时相似，为典型的剪切形变织构，两者的热轧板与脱碳板表层织构特征也极为相似，而含Mo Hi-B钢在1380℃铸坯加热时却没有以上这些相似性。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。