A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Comparison between clinical results of two diffractive multifocal lenses with the same platform but different additions

PURPOSE: To evaluate visual results with two multifocal diffractive lenses designed with the same platform but with different additions. SETTING: Grupo Innova Ocular clinics. METHODS: A total of 50 eyes from 50 patients were included. Group 1 (n = 25) was implanted with the TECNIS® 1 ZLB +3.25 and group 2 (n = 25) with the TECNIS® 1 ZKB +2.75. Patients were assessed at 24 hours, 1 week and 1 month postoperatively. At surgical discharge, corrected (CDVA) and uncorrected distance visual acuity (UCDVA), near visual acuity (VA) at 25, 40 and 80 cm, visual quality and the defocus curve were measured. RESULTS: Changes in sphere and spherical equivalent were statistically significant (p<0.01) in both groups at 1 week and 1 month compared to preoperative values. In group 1, UCDVA logMAR at 1 month was 0.06 ± 0.02. In group 2, UCDVA at 1 month was 0.03 ± 0.03. In near vision, the TECNIS® 1 ZLB group obtained a VA logMAR of 0.35 ± 0.02 at 25 cm, 0.13 ± 0.02 at 40 cm and 0.27 ± 0.02 at 80 cm, while in the TECNIS® 1 ZKB group, the values were 0.38  ± 0.03, 0.14 ± 0.03 and 0.23 ± 0.06, respectively. No statistically significant differences were found either when results for visual quality were compared. CONCLUSION: Both the TECNIS® 1 ZLB and TECNIS® 1 ZKB are excellent options for obtaining good distance and near vision, in addition to providing good intermediate vision, especially at distances such as those required for working with computers.

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.