查询词典 Laplacian

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

The Laplacian matrix of G is the difference of degree matrix of G and the adjacent matrix of G, And the Laplacian spectral radius of a graph is the maximum eigenvalue of the Laplacian matrix of G.

图G的拉普拉斯矩阵为图G的度矩阵和它的邻接矩阵之差，而图G的拉普拉斯谱半径为图G的拉普拉斯矩阵绝对值最大的特征值。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

Firstly, we give a new upper bound of a mixed graph′s largest Laplacian eigenvalue, which is more precise. And also we give a lower bound of a mixed connected graph′s largest Laplacian eigenvalue.

首先给出了混合图的最大Laplace特征值的一个新的上界，并且用实例说明我们的结果与以往结果相比更精确，同时也给出了一个连通混合图的最大Laplace特征值的一个新的下界。

Among all the eigenvalues of Laplacian matrix, the most important is thelargest Laplace eigenvalue, which is called the Laplacian spectral radius of a graph.

在图的拉普拉斯特征值中，最重要的一个即是图的最大拉普拉斯特征值，称为图的Laplace谱半径。

The characteristics of the signless Laplacian spectra, the normalized Laplacian spectra, and the clustering coefficients of the measured graphs are also presented.

分析了该实例拓扑图的无符号拉普拉斯谱、规格化拉普拉斯谱以及群集系数等度量特征。

Two edge detection operators of second de ivative model, the discrete Laplacian of Gaussian and Laplacian of binomial distribution operators are introduced in this paper.

摘要本文首先导入了离散的高斯-拉普拉斯及二项分布--拉普拉斯两种二阶导数型边缘检测算子。

Gradient sharpening and Laplacian sharpening are applied to the sharpening. It is obtained from the experimental result that Laplacian sharpening is more valid in image sharpening for infrared image of warship targets in sky-sea background that is smoothened.

采取了梯度锐化和拉普拉斯锐化的方法进行锐化处理，从实验结果得出：对海天背景下平滑后的舰船目标红外图像进行锐化处理时，选用拉普拉斯锐化法比较有效。

The spectral graph theory is one of the main branches in algebraic graph theory, it is mainly concerned with the adjacency spectrum and the Laplacian spectrum.

图的谱理论是代数图论中的一个重要课题，主要涉及图的邻接谱与图的Laplacian谱的研究。

The study of graph spectra is an important direction of research in algebraic graph theory, and its main object of study is the adjacency spectrum and the Laplacian spectrum.

对图谱的研究是代数图论中的一个重要研究方向，其主要研究对象是图的邻接谱与图的Laplacian谱。

Rachel said to Leah, Please give me some of your son's mandrakes.

拉结对利亚说、请你把你儿子的风茄给我些。

This time, it gets more intense, to say the least.

而这一次，争斗变得激烈了很多，这是保守的说法。