A scheme is proposed to explain the hierarchy of fermion masses. In the model presented, which has no horizontal symmetry, generations pick up masses one by one through radiative corrections as we go to higher orders in perturbation theory. An extra generation of isosinglet heavy fermions plays an important role in implementing the scheme.PACS numbers: 12.15.Ff

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The putative classical soliton in the minimal nonlinear u model (no Skyrme term) is known to be unstable to collapse. We note that the imposition of a short-distance cutoff (which is anyway physically reasonable for a nonrenormalizable model) yields a stable classical soliton. We further suggest that this cutoff, carrying as it does some implicit dynamical information, be treated as a quantized dynamical variable. The resulting one-(experimentally fixed) parameter model agrees with experiment roughly as well as the simple a model with the Skyrme term. We interpret this feature as an indication of the robustness of the description of the nucleon as being dominated by a hedgehog-type meson cloud. It is suggested that the same approach might be useful in some other situations where the long-distance description of the physics is more precisely known than is the short-distance description.

A semi-analytical parametric approach to modeling default dependency is presented. It is a multi-factor model based on instantaneous default correlation that also takes into account higher order default correlations. It is capable of accommodating a term structure of default correlations and has a dynamic formulation in the form of a continuous time Markov chain. With two factors and a constant hazard rate, it provides perfect fits to four tranches of CDX.NA.IG and iTraxx Europe CDOs of 5, 7 and 10 year maturities. With time dependent hazard rates, it provides perfect fits to all the five tranches for all three maturities.