Given far field data of a time-harmonic wave radiated by an ensemble of well separated acoustic or electromagnetic sources as well as a priori information on the locations of these sources, we discuss an algorithm to approximate the far field data radiated by each of these sources separately. The method is based on a Galerkin procedure considering subspaces spanned by the singular vectors of “r...

where λ, δ > 0 and Ω ⊂ Rn is a smooth and bounded domain. We show that when the fringing field exists (i.e. δ > 0), given any μ > 0, we have uniform upper bound of classical solutions u away from the rupture level 1 for all λ ≥ μ. Moreover, there exists λδ > 0 such that there are at least two solutions when λ ∈ (0, λ ∗ δ); a unique solution exists when λ = λδ ; and there is no solution when λ >...

The multi-field generalisation of the Bateman equation arises from considerations of the continuation of String and Brane equations to the case where the base space is of higher dimension than the target space. The complex extension of this equation possesses a remarkably large invariance group, and admits a very simple implicit form for its general solution, in addition to the special case of ...

We develop a spinor equation of the electromagnetic field, which is equivalent to the Maxwell equation and has a similar form as the Dirac equation. The spinor is the very conjugate momentum of the vector potential in the Lagrangian mechanics. In this framework the electromagnetic field described by the spinor exhibits the SU(2) internal symmetry. The quantization and the problem of longinal an...