We study the Robin Laplacian in a domain with two corners of the same opening, and we calculate the asymptotics of the two lowest eigenvalues as the distance between the corners increases to infinity.

Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. 131 (2003) 631-636), we report a new and sharp estimate for the dimension of the global attractor associated to the complex Ginzburg-Landau equation supplemented with Dirichlet boundary conditions.

one of the main goals of interpretation of gravity data is to detect location and edges of the anomalies. edge detection of gravity anomalies is carried out by different methods. terracing of the data is one of the approaches that help the interpreter to achieve appropriate results of edge detection. this goal becomes a complex task when the gravity anomalies have smooth borders due to gradual ...

We provide an efficient method to calculate the pseudo-inverse of the Laplacian of a bipartite graph, which is based on the pseudo-inverse of the normalized Laplacian.

In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special ...

Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we show that the Peres-Horodecki positive partial transpose separability condition is necessary and sufficient for separability in C2 ⊗ C. In addition, we pres...

The purpose of this paper is to prove the L∞ gradient estimates and L∞ gradient estimates for the unit spectral projection operators of the Dirichlet Laplacian and Neumann (or more general, Ψ1-Robin) Laplacian on compact Riemannian manifolds (M, g) of dimension n ≥ 2 with C2 boundary . And we also get an upper bounds for normal derivatives of the unit spectral projection operators of the Dirich...