Laplacian [lɑ:'plɑ:siən]

Laplacian的基本解释

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[数]拉普拉斯算子, 调和量算子

与Laplacian相关的网络例句 [注：此内容来源于网络，仅供参考]

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。

InSection 2,we give several sufficient conditions for the existence of one solution,multiplesolutions and infinitely many solutions of the Sturm-Liouville bvps via the generalizedpolar coordinates.Then in Section 3,the existence of positive solutions are proved undersuperlinearity,sublinearity and many other conditions by a fixed point theorem in cones.Our results have generalized those in many articles.A detailed discussion of periodic solu-tions of a kind of functional differential equations with high-order Laplacian-like operatorcan be found in Section 4 and this subject has not been studied before.

在第二节，我们定义了一种新的坐标变换-广义极坐标，并利用它讨论了p-Laplacian算子和Laplacian-型算子的Sturm-Liouville边值问题，分别得到了存在一个解、多个解、无穷多个解的多个充分条件；第三节研究p-Laplacian算子的Sturm-Liouville边值问题正解的存在性与多重性，采用的是锥上的不动点定理，全面推广了这一方面已有的结果；对目前研究较少的高维Laplacian-型算子及带有Laplacian-型算子的泛函微分方程的周期解问题，我们在第四节做了一些研究，这也是拓扑方法的一个应用。

According to the distances, the SPWUG algorithm computed the initial partition of the coarsest graph by extending the Laplacian spectral graph theory from the unweighted undirected graph into the weighted undirected graph.

SPWUG算法借助Laplacian矩阵次小特征值对应的特征向量，刻画了节点间相对距离，将基于非赋权无向图的Laplacian谱理论在图的剖分应用方面扩展到无向赋权图上，实现了对最小图的初始剖分。

与Laplacian相关的网络解释 [注：此内容来源于网络，仅供参考]

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