We demonstrate that radiative breaking of conformal symmetry (and simultaneously electroweak symmetry) in the Standard Model with right-chiral neutrinos and a minimally enlarged scalar sector induces spontaneous breaking of lepton number symmetry, which naturally gives rise to an axion-like particle with some unusual features. The couplings of this ‘axion’ to Standard Model particles, in partic...

We consider a family of practical stopping criteria for linear solvers for adaptive finite element methods for symmetric elliptic problems. A contraction property between two consecutive levels of refinement of the adaptive algorithm is shown when the a family of smallness criteria for the corresponding linear solver residuals are assumed on each level or refinement. More importantly, based on ...

Much of the debate over the allocation of education resources focuses on the alleged benefits of smallness—of classroom or school—and is based on evidence from smallscale studies. This paper reframes the question in terms of cohort size. Using national data, we find that a 10-percent increase in kindergarten enrollment yields a 0.5 percent increase in cohort shrinkage across early grade transit...

We show VC-minimality is Π4-complete. In particular, we give a local characterization of VC-minimality. We also show dp-smallness is Π1complete.