We establish inequalities for the eigenvalues of Schrödinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related to inequalities for the Laplacian on Euclidean domains due to Payne, Pólya, and Weinberger and to Yang, but which depend in an explicit way on the mean curvatur...

The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the graph Laplacian for given a degree sequence, the Laplacian coefficients, the algebraic connectivity and the graph doubly stochastic matrix, and the spectra of ra...

Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define corona graphs. Given a small simple connected graph which we call basic graph, corona graphs are defined by taking corona product of the basic ...

We study the spectrum of Robin Laplacian with a complex parameter $$\alpha $$ on bounded Lipschitz domain $$\Omega . start by establishing number properties corresponding operator, such as generation properties, analytic dependence eigenvalues and eigenspaces \in {\mathbb {C}}$$ , basis eigenfunctions. Our focus, however, is bounds asymptotics for functions : we providing estimates numerical ra...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

Bayesian compressive sensing (BCS) is an important sub-class of sparse signal reconstruction algorithms. In this paper, a modified complex multitask (MCMBCS) algorithm using the Laplacian scale mixture (LSM) prior proposed. The LSM first introduced into BCS framework by exploiting its better characteristic and flexibility than traditional prior. Furthermore, integrating out noise variance analy...