Renormalization towers and their forcing

Mass Matrices and Their Renormalization

Abstract: We obtain explicitly the renormalization group equations for the quark mass matrices in terms of a set of rephasing invariant parameters. For a range of assumed high energy values for the mass ratios and mixing parameters, they are found to evolve rapidly and develop hierarchies as the energy scale decreases. To achieve the experimentally observed high degree of hierarchy, however, th...

Forcing Protection on Children and Their Parents

The Attractor of Renormalization and Rigidity of Towers of Critical Circle Maps

We demonstrate the existence of a global attractor A with a Cantor set structure for the renormalization of critical circle mappings. The set A is invariant under a generalized renormalization transformation, whose action on A is conjugate to the twosided shift.

Changing the heights of automorphism towers by forcing with Souslin trees over L

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.

Corridors and towers.

Editorial Corridors and Towers When C P Snow wrote "The Corridors of Power" he sought to demonstrate the inner workings of the political process in Whitehall. Now that we are coming towards the end of the useful life of the building known as the "RVH corridor" it is time to consider some of the inner workings of our own profession. Wards 1-20 in the Royal Victoria Hospital represent only a smal...