developing a time domain finite element method for modeling of electromagnetic cylindrical cloaks in this paper we propose a time domain finite element method for modeling of electromagnetic cloaks the permittivity and permeability of the cloak model are described by the drude dispersion model the model to be solved is quite challenging in that we have to solve a coupled problem with different partial differential equations given in different regions our method is based on a mixed finite element method using edge elements with different types of meshes in different regions numerical results demonstrate that our algorithm is quite effective for simulating cloaks in time domain to our knowledge this is the first cloak simulation carried out by the time domain finite element method

approximate cloaking for the helmholtz equation via transformation optics and consequences for perfect cloaking in this paper we study approximate cloaking of active devices for the helmholtz equation in the whole space of dimension 2 or 3 using the scheme introduced by kohn shen vogelius and weinstein more precisely we assess the degree of invisibility determine the limit of the field inside the cloaked and cloaking regions and show that the scheme is unstable with respect to the material parameters as a consequence we obtain some feasible properties of perfect cloaking 2011 wiley periodicals inc

well posedness study for a time domain spherical cloaking model in this paper we study a time domain spherical cloaking model recently introduced by zhao and hao 2009 this model is quite complicated and is composed of four coupled differential equations here we first prove the existence and uniqueness of a solution for this model then we obtain a stability result which analysis is quite involved due to the coupling between the four variables to our best knowledge this is the first well posedness study carried out for the time domain cloaking model with metamaterials

the persistence of nonoscillatory solutions of delay differential equations under impulsive perturbations abstract we obtain a sufficient condition for the persistence of nonoscillatory solutions of the delay differential equation under impulsive perturbations

periodic boundary value problems for first order impulsive dynamic equations on time scales this paper deals with the periodic boundary value problem for a class of first order impulsive dynamic equations on time scales we introduce a new notion of lower and upper solutions which extends the classical lower and upper solutions the existence of extremal solutions is presented by virtue of the method of lower and upper solutions coupled with monotone iterative technique an example is also included to illustrate the main results

oscillation for difference equations with continuous variable consider the delay difference equation y t y t p t h y t t t 0 where 0 0 and p c r r f c r r h c r r some oscillation criteria for this equation are obtained

oscillation and comparison results for delay difference equations abstract we establish a necessary and sufficient condition for the existence of positive solutions and obtain sturm type comparison theorem for the difference equation x n 1 x n i 1 m pi n x n ki o n 0 we also obtain the following comparison result equation oscillates if and only if x n 1 x n i 1 m qi n x n ki o n 0 oscillates provided n lim pi n qi i 1 2 m

the persistence of nonoscillatory solutions of difference equations under impulsive perturbations we obtain a sufficient condition for the persistence of nonoscillatory solutions of the difference equation with continuous variable x t t x t i 1mp i t x t c i t 0 under the impulsive perturbations x t k t x t k i k x t k k n 1

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

on near cloak in acoustic scattering abstract invisibility cloaking in acoustic scattering via the approach of transformation optics is considered the near cloaks of both passive medium and active radiating object are investigated from a practical viewpoint we are especially interested in the cloaking of an arbitrary but regular content it is shown that one cannot achieve the near cloak unless some special mechanism is introduced into the construction a general lossy layer is incorporated into the construction of our near cloaking devices we derive very accurate estimates of the scattering amplitude in terms of the regularization parameter and the material parameters of the lossy layer in different settings

oscillation criteria for difference equations with unbounded delay consider the delay difference equation n 1 n pn n 0 n 0 1 2 where n z is nondecreasing n n for n n and limn n pn is a nonnegative sequence some oscillation criteria for this equation are obtained

cloaking via change of variables for the helmholtz equation in the whole space this paper is devoted to the study of a cloaking device that is composed of a standard near cloak based on a regularization of the transformation optics i e a change of variables that blows up a small ball to the cloaked region and a fixed lossy layer for the helmholtz equation in the whole space of dimension 2 or 3 with the outgoing condition at infinity we establish a degree of near invisibility which is independent of the content inside the cloaked region for this device we also show that the lossy layer is necessary to ensure the validity of the degree of near invisibility when no constraint on physical properties inside the cloaked region is imposed 2010 wiley periodicals inc

an application of topological transversality to non positive higher order difference equations in this paper we shall provide sufficient conditions on the non positive function i u 1 u n 1 so that the boundary value problem bvp given by e d nu i m i u i du i d n 2 i 0 and bc d mu 0 0 0 m n 3 a d n 2 0 b d n 1u 0 0 c d n 2u t 1 d d n 1u t 1 0 has at least one positive solution

oscillations of delay difference equations consider the delay difference equation n 1 n pn n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer new oscillation criteria for this equation are established an extension of the results to difference equations with several delays is also presented

an adaptive edge finite element method for electromagnetic cloaking simulation in this paper we develop an adaptive edge finite element method based on a reliable and efficient recovery type a posteriori error estimator for time harmonic maxwell equations the asymptotically exact a posteriori error estimator is based on the superconvergence result proved for the lowest order edge element on triangular grids where most pairs of triangles sharing a common edge form approximate parallelograms the efficiency and robustness of the proposed method is demonstrated by extensive numerical experiments for electromagnetic cloaking problems with highly anisotropic permittivity and permeability

mathematical analysis and finite element time domain simulation of arbitrary star shaped electromagnetic cloaks in this paper we establish the explicit expression for two dimensional 2d electromagnetic cloaks of arbitrary star shapes without explicit contour expressions of the objects furthermore 2d arbi

oscillations of delay difference equations with oscillating coefficients abstract in this paper we establish sufficient conditions for the oscillation of all solutions of the delay difference equation y n 1 y n p n y n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer an open problem in ladas in international conference on differential equations stability and control dekker new york 1990 is solved

convergence rate of the fuzzy generalized nearest neighbor rule tizzy k nearest neighbor rule k nnr has been applied in a variety of substantive areas yang and chen l described a fuzzy generalized k nn algorithm which is a unified approach to a variety of fuzzy k nnr s they created the strong consistency of posterior risk of the fuzzy generalized nnr in this paper we give their convergence rate that is the convergence rate of posterior risk of the fuzzy generalized nnr is exponentially fast