Génesis, clasificación y problemas agronómicos de los barros. Tierra de Barros, Extremadura.

Sin resume

Classical solutions to integral equations with zero order kernels

We show global and interior higher-order log-H\"older regularity estimates for solutions of Dirichlet integral equations where the operator has a nonintegrable kernel with a singularity at the origin that is weaker than that of any fractional Laplacian. As a consequence, under mild regularity assumptions on the right hand side, we show the existence of classical solutions of Dirichlet problems involving the logarithmic Laplacian and the logarithmic Schr\"odinger operator.Comment: We added a lower-order regularity estimate for the logarithmic Laplacian (Corollary 5.8

When tanß meets all the mixing angles

Models with two-Higgs-doublets and natural flavour conservation contain $\tan \beta = v_2 / v_1$ as a physical parameter. We offer here a generalization of a recently proposed idea where only the Cabibbo angle, $\theta_\text{c} \simeq 0.22$, was related to $\tan \beta$ by virtue of the $\mathbb{D}_{4}$ dihedral symmetry group. The original proposal consisted of a massless first generation of quarks and no mixing with the third generation. In our case, through the addition of a third Higgs doublet with a small vacuum-expectation-value but very large masses, thus later decoupling, all quarks become massive and quark mixing is fully reproduced. In fact, all quark mixing angles are expressed in terms of $\tan \beta$ and one recovers trivial mixing in the limit $\beta \rightarrow 0$. We also explore the consequences in lepton mixing by adopting a type I seesaw mechanism with three heavy right-handed neutrinos