A simple scheme for incompressible, constant density flows is presented, which avoids odd-even decoupling for the Laplacian on a collocated grids. Energy stability is implied by maintaining strict energy conservation. Momentum is conserved. Arbitrary order in space and time can easily be obtained. The conservation properties hold on transformed grids.

Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $A(G)$ the adjacency matrix of $G$. The  signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of  graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

In this article, we establish the existence of minimizers for energy integrals associated with the p-Laplacian in RN with the admissible set being a rearrangement class of a given function. Some representation formulae of the minimizers are also stated.

In order to achieve a multiple resolution with multiple directional feature analysis, a Laplacian pyramid is combined with directional filter bank. This requires the analysis on the design of both the filter in the Laplacian pyramid and the overall directional decomposition structure. Our analysis shows that the energy distribution of the filter in the Laplacian pyramid should match with the an...

The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length. We obtain explicit expressions for this fractional Laplacian matrix and deduce also its periodic continuum limit kernel. The continuum limit kernel gives an exact expression for the fractional Laplacian (Riesz fractional d...

Motion editing requires the preservation of spatial and temporal information of the motion. During editing, this information should be preserved at best. We propose a new representation of the motion based on the Laplacian expression of a 3D+t graph: the set of connected graphs given by the skeleton over time. Through this Laplacian representation of the motion, we propose an application which ...