Near-field subsurface electromagnetic tomography and holography
Methods of multifrequency tomography and holography of subsurface dielectric inhomogeneities in the near-field zone based on the solution of inverse scattering problem are studied from the viewpoint of their applicability for targets with strong dielectric contrasts or with a complicated internal structure. Results based on numerical simulation with input data calculated from Maxwell equations are presented.
Pseudopulse near-field subsurface tomography.
Decisive success has been achieved in developing the subsurface near-field scanning tomography that overcomes the Rayleigh diffraction limit of a resolution. It is related to the transformation of the multifrequency inverse scattering problem to that for a complex-valued synthesized pulse (pseudopulse). It leads to the integral equation that has maxima in the depth dependence of its kernel and, hence, to the much better depth resolution of tomography. Moreover, the noise related to surface scattering is mainly suppressed in such an approach. This idea is realized here in the microwave subsurface tomography of 3D inhomogeneous dielectric structures. For homogeneous dielectric targets, this approach is applied to obtain holography images of their shape.
Wolfe type second-order symmetric duality in nondifferentiable programming
Abstract A pair of Wolfe type second-order symmetric dual programs involving nondifferentiable functions is considered and appropriate duality theorems are established under η 1 -bonvexity/ η 2 -boncavity. Several known results including that of Mond and Gulati et al. are obtained as special cases.