Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is the multiset of eigenvalues of Laplacian matrix. The Laplacian energy of a graph is the sum of the...

A Laplacian matrix, L = (lij) ∈ R , has nonpositive off-diagonal entries and zero row sums. As a matrix associated with a weighted directed graph, it generalizes the Laplacian matrix of an ordinary graph. A standardized Laplacian matrix is a Laplacian matrix with − 1 n ≤ lij ≤ 0 at j 6= i. We study the spectra of Laplacian matrices and relations between Laplacian matrices and stochastic matrice...

A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, some necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless Laplacian eigenvalues are given. And the trees and unicyclic graphs with exactly two main signless L...

Cooperative behaviour of an array of microelectrodes: The interplay of bistable reaction kinetics with global coupling results in a spontaneous sequential activation of electrodes when the applied current is increased.

The catalytic dehydrogenation of LiBH(4) doped with exceptionally low quantities of carbon-supported Pt nanoparticles can be improved significantly, and smaller Pt nanoparticles result in greater enhanced catalytic dehydrogenation of LiBH(4) than do larger Pt nanoparticles.

Extensive efforts have been devoted to the study of spin-orbit torque in ferromagnetic metal/heavy metal bilayers and exploitation of it for magnetization switching using an in-plane current. As the spin-orbit torque is inversely proportional to the thickness of the ferromagnetic layer, sizable effect has only been realized in bilayers with an ultrathin ferromagnetic layer. Here we demonstrate ...

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎. 

In this work, Pt, Fe and Co nanoparticles were prepared by chemical reduction of the metal salts in chitosan as the support. NaBH4 was used as the reducing agent Pt-Fe, Pt-Co and Pt-Fe-Co-chitosan nanocomposites were synthesized and characterized by UV–Vis spectra and Transmission electron microscopy images. GC/Pt-chitosan, GC/Pt-Co-chitosan, GC/Pt-Fe-chitosan and GC/Pt-Co-Fe-chitosan electrode...

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.