局部

The data in LLE are optimized using the small world algorithm, and the shortest path and the local neighbor set clustering coefficients are used as the local parameters. As a result, the problem of the embedding distortion using only local linear patch of the manifold to define neighborhood in Euclidean space is effectively solved. Three groups of standard data sets are selected to test and to compare the efficiency and robustness of SLLE and LLE.

将复杂网络算法引入到流形学习中，利用小世界算法对LLE算法进行数据优化，并以最短路径和局部集群系数作为局部优化参数，解决了数据点不规则时以欧氏空间作为邻域判别标准在构建局部超平面造成嵌入结果扭曲的难题。

In scale space,the local extremum ofwavelet transform modulo of image not only describes the local characteristics of ir-regular structure of image but also displays distribution of local singular point s.

在尺度空间，图像的小波变换模局部极值能在刻画图像不规则结构的局部特征的同时，给出它们的局部奇性点的分布。

Yu introduced in 1997 the localization Roe algebras , and shown that, to attack the Coarse Baum-Connes Conjecture, it suffices to prove that the local index map is an isomorphism from the coarse K-homology to the K-theory of the localization Roe algebras.

Yu受热方程方法的启发，引入局部化Roe代数，把粗Baum-Connes猜测的证明归结为证明从粗化K-同调群到局部化Roe代数的K-理论群的局部指标映射为同构。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

It's main feature is that we can obtain many types of edges simultaneously by detecting the maximum value of local energy.After that,we get the initial edge.

对于边缘的检测，近年来，人们的研究兴趣更多的转向了局部能量的方法，这是一种基于局部相位的方法，它的特点是通过局部能量的最大值可以同时得到不同类型的边缘。

The LMD algorithm uses extrema to define the local mean and envelope, then to smooth the mean and envelope. To decrease errors in the smoothing process by using moving averaging, a new local mean and envelope definition method (the spline-based LMD) is proposed. The upper envelope and the lower envelope are obtained by connecting the local maxima and the local minima using a cubic spline line. The local mean is defined as a mean of the upper envelope and the lower envelope. A nonlinear simulation signal and a practical vibration signal are decomposed by the LMD and the spline-based LMD.

LMD算法用极值点来定义局部均值函数和局域包络函数，然后用滑动平均来平滑均值和包络函数，针对用滑动平均平滑均值和包络函数误差较大的缺点，提出了采用三次样条对上、下极值点分别插值求得上下包络线，然后由上下包络线的平均获得局部平均函数，由上下包络线相减的绝对值获得局部包络的方法。

However, for hill-climbing strategies to be guaranteed to find the global optimum the optimality landscape must be unimodal. Moreover, research has demonstrated that multiple maxima exist under the maximum likelihood principle. Therefore, hill climbing based evolutionary tree reconstruction methods often return local optima.

但是由于进化树的似然函数通常含有多个局部极优解，而爬山算法没有逃离局部极优的能力，因此基于爬山算法的进化树构建算法很容易陷入局部极优。

In chapter 4 , with S-KKM mapping , a new Ky Fan\'s minimax inequality is proved , the locally convex H-space with uniform structure is introduced , s-HKKM mapping is defined as the generalization of KKM mapping, with the H-convexity of Hausdorff locally convex H-space , a new fixed point theorem for the compact andclosed mapping belonging to the class s-HKKM is established ;with local intersection property of muti-function ,K-H-quasi-convexity of mapping , connectedness of set and condensing correspondences, some new vector quasi-variational inequalities are established , respectively .

第四章利用S-KKM映射，建立了新的Ky Fan极小极大不等式；定义了带有一致结构的局部凸H-空间，利用Hausdorff局部凸H-空间的H-凸性，对于属于s-HKKM中紧的闭映射建立了新的不动点定理，利用对应的局部交性质、映射的K-拟-凸性、集合的连通性以及φ-condensing对应分别建立了相应的拟向量变分不等式。

Furthermore, we will discuss the corresponding decay rates problem when the viscous term tends to zero.The first part is about the local existence. We will regularize the equations by the standard mollifier to get the approximate solutions . Then by making uniform estimates to the approximate solutions and by passing to the limit, we obtain the local existence for the above problem.

我们主要研究了此方程组古典解的局部存在性，爆破准则以及通过粘性消失方法来研究如上方程组的局部存在性和收敛率问题，主要结论有：(1)解的局部存在性利用光滑子对方程组进行正则化，从而得到原方程组的逼近解。

On the basis of the study on the petrology, Trace element, and isotopic geochemistry, the primary magma of volcanic rocks can be divided into two series according to their originated rocks and degree of partial melting. One is the basanite-alkaline basalt-Olivine tholeiite magma series, which are generated by partial melting from spinel Iherzolite; the other is nephelinite magma-alkaline picritic basalt magma, which are generated by partial melting of the garnet Iherzolite.

岩石化学、微量元素、同位素地球化学证据都表明，华北、华南地区的火山岩根据源岩和局部熔融程度的不同，可以分为两个原生岩浆系列：一个是源岩为尖晶石二辉橄榄岩，随着局部熔融程度的增加，形成的碧玄岩岩浆-碱性玄武岩岩浆-橄榄拉斑玄武岩岩浆；另一个是源岩为石榴石二辉橄榄岩，随着局部熔融程度的增加形成的霞石岩岩浆-碱性苦橄玄武岩系列。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。