Let G = (V,E) be an undirected graph, LG ∈ R ×V be the associated Laplacian matrix, and b ∈ R V be a vector. Solving the Laplacian system LGx = b has numerous applications in theoretical computer science, machine learning, and network analysis. Recently, the notion of the Laplacian operator LF : R V → 2 V for a submodular transformation F : 2 → RE+ was introduced, which can handle undirected gr...

The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and the structure of ‘local’ subgraphs of the network. We call a subgraph local when it is induced by the set of nodes obtained from a breath-first search (BFS)...

The spin-polarized calculations in generalized gradient approximation density–functional theory (GGA–DFT) have been used to show how the existence of second metals can modify the atomic hydrogen adsorption on Au (100), Cu (100), and Pt (100) surfaces. The computed adsorption energies for the atomic hydrogen adsorbed at the surface coverage of 0.125 ML (monolayer) for the monometallic Au (100), ...

the electrocatalysis of the oxygen reduction reaction (orr) on carbon supportedpt-v (1:1) catalyst in polymer electrolyte fuel cells (pefc) was investigated. atan oxygen pressure of one atm an enhanced electrocatalytic property of pt-v/ccompared with pt/c is revealed. these results indicate the occurrence of adifferent electrocatalytic mechanism for the orr on pt/c and pt-v/c. anincrease of mas...

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

Nickel base superalloy alloys are used in the manufacture of gas turbine engine components, which in use are exposed to high temperatures and corrosive environments. The platinum aluminide coatings described here have been developed to protect nickel base superalloy alloys from oxidation. In this study, the effect of cyclic oxidation, platinum layer thickness and aluminizing process on beha...

In this paper, we consider the Lévy Laplacian acting on multiple Wiener integrals by the Lévy process, and give a necessary and sufficient condition for eigenfunctions of the Lévy Laplacian. Moreover we give a decomposition by eigenspaces consisting of multiple Wiener integrals by the Lévy process in terms of the Lévy Laplacian.

Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ(G), obtained from the Smith normal form of M , and whose order is the number of spanning trees of G. We provide some general results on the relationship between the eigenvalues of M and the structure of Φ(G), and address the question of how often the group Φ(G) is cyclic.