We prove that assuming the Colmez conjecture and “no Siegel zeros” conjecture, stable Faltings height of a CM abelian variety over number field is less than or equal to logarithm root discriminant definition times an effective constant depending only on dimension variety. In view fact for fields, averaged fields with no complex quadratic subfields are already proved, we unconditional analogues ...

The Jarlskog Invariant Jν−map of the neutrino mapping matrix is calculated based on a phenomenological model which relates the smallness of light lepton masses me and m1 (of ν1) with the smallness of T violation. For small T violating phase χl in the lepton sector, Jν−map is proportional to χl, but me and m1 are proportional to χ2l . This leads to Jν−map ∼= 1 6 √ me mμ +O ( √ memμ m2τ )

In [8] a class of initial data to the three dimensional, periodic, incompressible Navier-Stokes equations was presented, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The aim of this article is twofold. First, we adapt the construction of [8] to the case of the whole space: we prove that if a certain nonlinear function of the initial ...

If the observed light neutrino masses are induced by their Yukawa couplings to singlet right-handed neutrinos, natural smallness of those renders direct collider tests of the electroweak scale neutrino mass mechanisms almost impossible both in the case of Dirac and Majorana (seesaw of type I) neutrinos. However, in the triplet Higgs seesaw scenario the smallness of light neutrino masses may com...

In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.

In [8] a class of initial data to the three dimensional, periodic, incompressible Navier-Stokes equations was presented, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The aim of this article is twofold. First, we adapt the construction of [8] to the case of the whole space: we prove that if a certain nonlinear function of the initial ...

In this note we investigate propagation of smallness properties for solutions to heat equations. We consider spectral projector estimates the Laplace operator with Dirichlet or Neumann boundary conditions on a Riemanian manifold without boundary. show that using new approach Logunov and Malinnikova (2018) allows one extend type Jerison Lebeau (1999) from localisation open sets localization arbi...

Abstract We present a new proof of the turnpike property for nonlinear optimal control problems, when running target is steady control-state pair underlying system. Our strategy combines construction quasi-turnpike controls via controllability, and bootstrap argument, does not rely on analyzing optimality system or linearization techniques. This in turn allows us to address several problems fin...