The renormalized ϕ44\phi^4_4-trajectory by perturbation theory in the running coupling

We compute the renormalized trajectory of $\phi^4_4$-theory by perturbation theory in a running coupling. We introduce an iterative scheme without reference to a bare action. The expansion is proved to be finite to every order of perturbation theory.Comment: 23 pages LaTeX, Large momentum bound correcte

An Iterative Procedure for Combining the Advantages of a Multi-Frequency and Multi-Resolution Inversion Algorithm

Starting from the iterative multi�]scaling approach previously studied for monochromatic illuminations, two multi�]resolution strategies for dealing with multi�]frequency inverse scattering experiments have been developed. The first procedure is based on the integration of the iterative multi�]scaling algorithm into a frequency�]hopping reconstruction scheme, while in the second one the multi�]frequency data are simultaneously processed exploiting a multi�]resolution expansion of the problem unknowns. The numerical and the experimental analysis presented in this contribution concern with a preliminary assessment of the reconstruction effectiveness of the proposed approaches in comparison with a monochromatic multi�]step process. This is the author's version of the final version available at IEEE