In this paper the unbounded increasing solution of the scalar nonlinear partial equation of the parabolic type for the finite time is investigated. The sufficient condition for nonlinearity is established under this condition every solution of the investigated problem is exploded by absence restriction to smallness on the initial function. The existence of the solution is proved by smallness of...

We compute the conversion factors needed to obtain theMS and renormalization-group-invariant (RGI) up, down, and strange quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI=SMOM renormalization schemes. This is important for obtaining the MS masses with the best possible precision from numerical lattice QCD simulat...

The smallness of the baryon asymmetry in our universe is one of the greatest mysteries and may originate from some profound physics beyond the standard model. We investigate the Affleck-Dine baryogenesis in split supersymmetry, and find that the smallness of the baryon asymmetry is directly related to the hierarchy between the supersymmetry breaking squark/slepton masses and the weak scale. Put...

We consider the neural ODE and optimal control perspective of supervised learning, with ℓ1-control penalties, where rather than only minimizing a final cost (the empirical risk) for state, we integrate this over entire time horizon. prove that any (for cost) vanishes beyond some positive stopping time. When seen in discrete-time context, result entails an ordered sparsity pattern parameters ass...

Properties of categories enriched over the category metric spaces are investigated and applied to a study well-known constructions Banach spaces. We prove e.g. that weighted limits colimits exist in metric-enriched iff ordinary ε-(co)equalizers given by ε-(co)isometries for all ε. An object is called approximately injective w.r.t. morphism h:A→A′ morphisms from A into it arbitrarily close those...