Results 61 to 70 of about 302,460 (378)

Hypergraph $p$-Laplacian: A Differential Geometry View

, 2017
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph ...
Mandic, Danilo P, Saito, Shota, Suzuki, Hideyuki   +2 more
core   +1 more source

On the Laplacian and fractional Laplacian in an exterior domain

Advances in Differential Equations, 2012
We see that the generalized Fourier transform due to A.G. Ramm for the case of $n=3$ space dimensions remains valid, with some modifications, for all space dimensions $n\ge 2$. We use the resulting spectral representation of the exterior Laplacian to study exterior problems. In particular the Fourier splitting method developed by M.E.
Kosloff, Leonardo, Schonbek, Tomas
openaire   +2 more sources

Spectrum of the Laplacian with weights [PDF]

Annals of Global Analysis and Geometry, 2018
Given a compact Riemannian manifold (M, g) and two positive functions $ $ and $ $, we are interested in the eigenvalues of the Dirichlet energy functional weighted by $ $, with respect to the L 2 inner product weighted by $ $. Under some regularity conditions on $ $ and $ $, these eigenvalues are those of the operator $ $^{-1} div($ $$\nabla$u)
Bruno Colbois, Ahmad El Soufi
openaire   +4 more sources

Interlacing Properties of Eigenvalues of Laplacian and Net-Laplacian Matrix of Signed Graphs [PDF]

arXiv, 2023
This paper explores interlacing inequalities in the Laplacian spectrum of signed cycles and investigates interlacing relationship between the spectrum of the net-Laplacian of a signed graph and its subgraph formed by removing a vertex together with its incident edges.
arxiv  

Fractional Laplacian pyramids [PDF]

2009 16th IEEE International Conference on Image Processing (ICIP), 2009
We provide an extension of the L 2 -spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyharmonic splines to derive an efficient, non-separable filterbank implementation.
Delgado-Gonzalo, Ricard, Tafti, Pouya Dehghani, Unser, Michael   +2 more
openaire   +3 more sources

On the $ A_{\alpha^-} $-spectra of graphs and the relation between $ A_{\alpha} $- and $ A_{\alpha^-} $-spectra

AIMS Mathematics
Let $ G $ be a graph with adjacency matrix $ A(G) $, and let $ D(G) $ be the diagonal matrix of the degrees of $ G $. For any real number $ \alpha\in [0, 1] $, Nikiforov defined the $ A_{\alpha} $-matrix of $ G $ as $ A_{\alpha}(G) = \alpha D (G) +
Wafaa Fakieh, Zakeiah Alkhamisi, Hanaa Alashwali   +2 more
doaj   +1 more source

The second immanant of some combinatorial matrices [PDF]

Transactions on Combinatorics, 2015
Let $A = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrix where $n geq 2$. Let $dt(A)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$.
R. B. Bapat, Sivaramakrishnan Sivasubramanian   +1 more
doaj  

On singularity and properties of eigenvectors of complex Laplacian matrix of multidigraphs

AKCE International Journal of Graphs and Combinatorics, 2023
In this article, we associate a Hermitian matrix to a multidigraph G. We call it the complex Laplacian matrix of G and denote it by [Formula: see text]. It is shown that the complex Laplacian matrix is a generalization of the Laplacian matrix of a graph.
Sasmita Barik, Sane Umesh Reddy, Gopinath Sahoo   +2 more
doaj   +1 more source

Eigenvectors of Laplacian or signless Laplacian of Hypergraphs Associated with Zero Eigenvalue [PDF]

Linear Algebra and its Applications, Volume 579, 2019, Pages 244-261, 2018
Let $G$ be a connected $m$-uniform hypergraph. In this paper we mainly consider the eigenvectors of the Laplacian or signless Laplacian tensor of $G$ associated with zero eigenvalue, called the first Laplacian or signless Laplacian eigenvectors of $G$. By means of the incidence matrix of $G$, the number of first Laplacian or signless Laplaican (H- or N-
arxiv   +1 more source

Overdetermined boundary value problems for the $\infty$-Laplacian

, 2009
We consider overdetermined boundary value problems for the $\infty$-Laplacian in a domain $\Omega$ of $\R^n$ and discuss what kind of implications on the geometry of $\Omega$ the existence of a solution may have.
Buttazzo, G., Kawohl, B.
core   +2 more sources