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...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

Structure-preserving discretization of the Rosenbluth–Fokker–Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic scheme introduced. The structure related to energy conservation skew-symmetry in mathematical sense, and action–reaction law physical sense. A thermal relaxation term obtained by using integration-by-pa...

We present the solution of the Boltzmann equation with an applied electric and magnetic field including skew scattering in the collision operator. The observed unusual temperature dependences of the Hall resistance and the magnetoresistance as well as the frequency dependence of the Hall resistance in the normal state of copper oxide metals is shown to arise if the skew scattering rate diverges...

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 ...