We consider a second order differential operator A( ) = − ∑d i,j=1 ∂iaij( )∂j + ∑d j=1 ∂j ( bj( )· ) +c( ) on R, on a bounded domain D with Dirichlet boundary conditions on ∂D, under mild assumptions on the coefficients of the diffusion tensor aij . The object is to construct monotone numerical schemes to approximate the solution of the problem A( )u( ) = μ( ), ∈ D, where μ is a positive Radon ...

A necessary and sufficient condition for a class of matrix operators acting from l1 into l2 to be continuous and compact is given in this paper, which answers I. J. Maddox’s open problem. Suppose A = (aij) be an infinite real matrix. It determines a linear operator A from l1 into l2 (1 6 p1, p2 6∞) according to the following raw:

The general problem of representing the Greens function G(k,z) in terms of self-energy in field theories lacking Wick’s theorem is considered. A simple construction shows that a Dyson-like representation with a self-energy !(k,z) is always possible, provided we start with a spectral representation for G(k,z) for finite-sized systems and take the thermodynamic limit. The self-energy itself can t...

we describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. we present a new method for computing, electronic transport wave function and greens function of the disordered graphene. in this method, based on the small rectangular approximation, break up the potential barriers in to small parts. then using the f...

We describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. We present a new method for computing, electronic transport wave function and Greens function of the disordered Graphene. In this method, based on the small rectangular approximation, break up the potential barriers in to small parts. Then using the f...

The main feature of this paper concerns extensions of the Liouville theorem to the following class of elliptic equations in non-divergence form: aij(x)∂iju + bi(x)∂iu + c(x)u = 0 in R N , with c ≤ 0. We show that the Liouville property holds (that is, the space of bounded solutions has at most dimension one) if the coefficients aij , bi and c are periodic, with the same period, and it does not ...

A vast amount of indices has been proposed in the literature [1] to quantify the deviation of a pairwise comparison matrix A = (aij)n×n from the consistency property aik = aijajk ∀i, j, k. In this paper we propose a unifying approach by expressing an inconsistency index as a function of the matrix entries aij satisfying a set of suitable properties. More precisely, we first consider the ‘local’...

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...