A two-dimensional finite-difference complex wavevector band structure solver for nanophotonics applications is presented, and rigorous computation of modal properties within bandgaps of periodic devices, including mirror strength, is shown. OCIS codes: (000.4430) Numerical approximation and analysis; (050.1755) Computational electromagnetic methods; (130.3120) Integrated optics devices.

Abstract. The asymptotic behaviour for solutions of a difference equation ∆zn = f(n, zn), where the complex-valued function f(n, z) is in some meaning close to a holomorphic function h, and of a Riccati difference equation is studied using a Lyapunov function method. The paper is motivated by papers on the asymptotic behaviour of the solutions of differential equations with complex-valued right...

A class of generalized high order finite compact difference schemes is proposed for shock/vortex, shock/boundary layer interaction problems. The finite compact difference scheme takes the region between two shocks as a compact stencil. The high order WENO fluxes on shock stencils are used as the internal boundary fluxes for the compact scheme. A lemma of the property of smoothness estimators on...

For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...

The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several interesting characteristics of the solutions of this equation, using computations, which does not arise when we consider the same equation with positive real ...

We show that the λ-return target used in the TD(λ) family of algorithms is the maximum likelihood estimator for a specific model of how the variance of an nstep return estimate increases with n. We introduce the γ-return estimator, an alternative target based on a more accurate model of variance, which defines the TDγ family of complex-backup temporal difference learning algorithms. We derive T...

Abstract: Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of comp...

Since there has been a strong demand from industry to have an efficient way of managing color image quality presented in different media, by specifically investigating partly changed complex images, this article proposed a revision to existing CIE color difference model which cannot give a proper color difference assessment on partly changed complex images. The key method applied is to find out...

Possible complex difference system models and their algorithms will be discussed for the analysis of longitudinal asymmetric proximity matrices, whose elements may be intensities of proximity among members of either small formal, or informal groups. Members are naturally assumed to be embedded in a finite-dimensional complex Hilbert space or an indefinite metric space according to the Chino-Shi...