Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that [Formula: see text], [Formula: see text] and [Formula: see...

We spell out a formal equivalence between the naive Laplacian editing and semi-supervised learning by bi-Laplacian Regularized Least Squares. This allows us to write the solution to Laplacian mesh editing in a closed form, based on which we introduce the Generalized Linear Editing (GLE). GLE has both naive Laplacian editing and gradient based editing as special cases. GLE allows using diffusion...

Let η(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper, bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimize...

Calculation of watermarking capacities of private Laplacian watermarking systems with the magnitude-error distortion measure under fixed attacks is addressed. First, in the case of an additive Laplacian attack, a nice closed-form formula for the watermarking capacities is derived, which involves only the distortion level and the parameter of the Laplacian attack. Second, in the case of an arbit...

in the present work, the electrooxidation of formic acid and formaldehyde; potentially important fuels for future fuel cells, was investigated on the fe3o4@pt core-shell nanoparticles/carbon-ceramic electrode (fe3o4@pt/cce). the fe3o4@pt nanoparticles were prepared via a simple and fast chemical method and their surface morphology, nanostructure properties, chemical composition, crystal phase, ...

1 Laplacian Methods: An Overview 2 1.1 De…nition: The Laplacian operator of a Graph . . . . . . . . . . 2 1.2 Properties of the Laplacian and its Spectrum . . . . . . . . . . . 4 1.2.1 Spectrum of L and e L: Graph eigenvalues and eigenvectors: 4 1.2.2 Other interesting / useful properties of the normalized Laplacian (Chung): . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 Laplacians of Weight...

In this paper we provide‎ ‎existence results for positive solution to‎ ‎Dirichlet p(t)-Laplacian boundary value problems‎. ‎The sublinear and‎ ‎superlinear cases are considerd‎.

According to recent advances in digital image processing techniques, interest in high-quality images has been increased. This paper presents a resolution enhancement (RE) algorithm based on the pyramid structure, in which Laplacian histogrammatching is utilized for high-frequency image prediction. The conventional RE algorithms yield blurring near-edge boundaries, degrading image details. In or...