The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finite number N of identical particles is introduced. We suggest a ”fractional elastic harmonic potential”, and obtain the N -periodic fractional Laplacian operator in the form of a power law matrix function for the finite chain (N arbitrary not necessarily large) in explicit form. In the limiting ...

The purpose of multi-focus image fusion is gathering the essential information and the focused parts from the input multi-focus images into a single image. These multifocused images are captured with different depths of focus of cameras. Multi-focus image fusion is very time-saving and appropriate in discrete cosine transform (DCT) domain, especially when JPEG images are used in visual sensor n...

The problem of recovering the asymptotics of a short range perturbation of the Euclidean Laplacian on R n from xed energy scattering data is studied. It is shown that for n 3 that a magnetic potential is determined, modulo Gauge invariance, by its scattering matrix at a xed non-zero energy. This result also holds for a wide class of scattering manifolds.

let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the p...