For the

Maxwell equations, i.e., step (iii) of Algorithm 4.2, we choose the special pair of test functions ([[psi].sub.h], [[zeta].sub.h]) = ([E.sup.i+1.sub.h], [H.sup.i+1.sub.h]) and get from (4.2b)-(4.2c)

If we want to obtain the unique solution to

Maxwell equation within V, we must initialize the electromagnetic fields E and H within V at time t = 0.

Inserting the

Maxwell equations [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in (5) and rearranging the terms we easily obtain

At the centre, the

Maxwell equations at the wave equations of the second order with respect to, for example, the electrical field.

The related Euler-Lagrange (E-L) equations provide the

Maxwell equations in the Lagrangian form, the balance equation of momentum and additional constitutive-like equations for P and M.

In this letter, by introducing a new method to reduce the error caused by splitting of equations [15] (other methods of reducing perturbation error caused by splitting of differential equations can be seen in [18]), we propose two modified splitting FDTD methods (called MS-FDTDI and MS-FDTDII) for the 2D

Maxwell equations. It is proved by the energy method that MS-FDTDI with the perfectly electric conducting boundary conditions is second-order convergent in both time and space.

We investigate the scenario of the modified

Maxwell equations resulting from this CPT-even scenario of Lorentz violation.

Mathematicians and physicists from Europe discuss motifs stability in hierarchical modular networks, asymptotic techniques in the solution of the

Maxwell equations in plasmas, simple exact and asymptotic solutions of the one-dimensional run-up problem over a slowly varying (quasiplanar) bottom, universality for couplings correlation in mean field spin glasses, poker cash games in terms of thermodynamics systems, accretion processes in astrophysics, density functional theory and its time-dependent extension, the nonlinear Schr|dinger equation on a torus, portfolio optimization using a mean field theory approach, and fluctuation of the eigenvalue number.

In this review, we start with the

Maxwell equations in curved space-time, which when applied to the isotropic metric of the Schwarzschild black hole, gives the refractive index of equivalent medium.

(1) it can be seen that for [alpha] = 0, ([E.sub.fd], [eta][H.sub.fd]) reduces to the original solutions whereas ([E.sub.fd], [eta][H.sub.fd]) gives dual to the original solution to the

Maxwell equations for [alpha] = 1.

Writing for graduate students researchers, and technologists he discusses such aspects as the Hamiltonian formulation of

Maxwell equations for the modes of anisotropic waveguides, circular fibers made of isotopic materials, modes at the interface between two materials, planar metal/dielectric metamaterials, and semi-analytical methods of solving nonlinear equations of two variables.

Villone, "Interpolating wavelets for the solution of

Maxwell equations in the time domain," IEEE Trans.