In this paper we study in detail some spectral properties of the magnetic discrete Laplacian. We identify its form-domain, characterize the absence of essential spectrum and provide the asymptotic eigenvalue distribution.

Abstract. We study a general transition operator, generated by a random walk on a graph X ; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from l(X) into itself. Moreover we characterize compact operators and we relate this property to the behaviour of the associated random walk. We give a necessary ...

It is well known that, under certain circumstances, discrete plane waves can propagate through lattices. Waves can also be generated by oscillating one point in the lattice: the corresponding solution of the governing partial difference equations is the discrete Green’s function, gmn. The far-field behaviour of gmn is obtained using three methods: textbook derivations are corrected and a formul...

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory po...

The present study attempts to unravel the determinants of public acceptance Treated Wastewater (TWW) reuse in United Arab Emirates. A representative sample (1426) Al-Ain city residents, were interviewed, using a structured questionnaire, on their knowledge and attitudes towards TWW reuse, other demographic characteristics. Descriptive analysis shows high for applications with low contact lower ...