Correction to: Some results on the p(u)-Laplacian problem

Correction to: Mathematische Annalen https://doi.org/10.1007/s00208-019-01803-w In the Original Publication of the article, few errors have been identified in section 5 and acknowledgements section.Agência financiadora Ministry of Education and Science, Russian Federation 117198 Portuguese Foundation for Science and Technology (FCT), Portugal SFRH/BSAB/135242/2017info:eu-repo/semantics/publishedVersio

Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model

We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, $J_A$ and $J_B$, are present, according to the Fibonacci sequence. We calculated the pseudo-critical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents $\beta$, $\delta$, and $\gamma$ and, from the usual scaling relations for anisotropic models at the upper critical dimension (assumed to be 4 for the model we treat), we calculate $\alpha$, $\nu$, $\nu_{//}$, $\eta$, and $\eta_{//}$. Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents which depend on the ratio $r \equiv J_B/J_A$, as expected. But the scaling relation $\gamma = \beta (\delta -1)$ is obeyed for all values of $r$ we studied. We characterize some thermodynamic functions as log-periodic functions of their arguments, as expected for aperiodic-modulated models, and obtain precise values for the exponents from this characterization.Comment: 17 pages, including 9 figures, to appear in Phys. Rev.

GHASP: an H{\alpha} kinematic survey of spiral and irregular galaxies -- IX. The NIR, stellar and baryonic Tully-Fisher relations

We studied, for the first time, the near infrared, stellar and baryonic Tully-Fisher relations for a sample of field galaxies taken from an homogeneous Fabry-Perot sample of galaxies (the GHASP survey). The main advantage of GHASP over other samples is that maximum rotational velocities were estimated from 2D velocity fields, avoiding assumptions about the inclination and position angle of the galaxies. By combining these data with 2MASS photometry, optical colors, HI masses and different mass-to-light ratio estimators, we found a slope of 4.48\pm0.38 and 3.64\pm0.28 for the stellar and baryonic Tully-Fisher relation, respectively. We found that these values do not change significantly when different mass-to-light ratios recipes were used. We also point out, for the first time, that rising rotation curves as well as asymmetric rotation curves show a larger dispersion in the Tully-Fisher relation than flat ones or than symmetric ones. Using the baryonic mass and the optical radius of galaxies, we found that the surface baryonic mass density is almost constant for all the galaxies of this sample. In this study we also emphasize the presence of a break in the NIR Tully-Fisher relation at M(H,K)\sim-20 and we confirm that late-type galaxies present higher total-to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback is actually an important issue in late-type spirals. Due to the well defined sample selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies can be used as a reference for the study of this relation in other environments and at higher redshifts.Comment: 16 pages, 6 figures. Accepted for publication in MNRA