A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

The in vitro antioxidant properties of the Al-quercetin/beta CD and Al-catechin/beta CD inclusion compounds, rationalized in terms of their electrochemical behaviour

Inclusion compounds of Al-quercetin and Al-catechin complexes with beta-cyclodextrin (beta CD) were investigated. The complex and the inclusion compound of quercetin are more effective DPPHaEuro cent scavengers than the corresponding catechin compounds and the inclusion does not compromise their scavenging abilities, with only a slight decrease in the EC50 values. This is in accordance with the electrochemical data, which revealed that the inclusion compounds have lower diffusion coefficients in aqueous solution than the non-included compounds. For the quercetin compounds, some spectroscopic properties were also addressed by means of UV-visible and NMR measurements in aqueous media.

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

Renal function evaluation in patients with American Cutaneous Leishmaniasis after specific treatment with pentavalent antimonial

Background Renal evaluation studies are rare in American Cutaneous Leishmaniasis (ACL). The aim of this study is to investigate whether specific treatment reverts ACL-associated renal dysfunction. Methods A prospective study was conducted with 37 patients with ACL. Urinary concentrating and acidification ability was assessed before and after treatment with pentavalent antimonial. Results The patients mean age was 35.6 ± 12 years and 19 were male. Before treatment, urinary concentrating defect (U/Posm <2.8) was identified in 27 patients (77%) and urinary acidification defect in 17 patients (46%). No significant glomerular dysfunction was observed before and after specific ACL treatment. There was no reversion of urinary concentrating defects, being observed in 77% of the patients before and in 88% after treatment (p = 0.344). Urinary acidification defect was corrected in 9 patients after treatment, reducing its prevalence from 40% before to only 16% after treament, (p = 0.012). Microalbuminuria higher than 30 mg/g was found in 35% of patients before treatment and in only 8% after treatment. Regarding fractional excretion of sodium, potassium, calcium, phosphorus and magnesium, there was no significant difference between pre and post-treatment period. Conclusion As previously described, urinary concentrating and acidification defects were found in an important number of patients with ACL. Present results demonstrate that only some patients recover urinary acidification capacity, while no one returned to normal urinary concentration capacity.

Induced tooth movement: standardization of terms to describe the effects of forces on the periodontal ligament: compression/Traction instead of Pressure/Tension

There is no reason for Dentistry to use different terms for phenomena defined in Physics, the specific field in which concepts associated with forces are established and adapted. In place of pressure/tension, the compression/traction pair should be used. This study defines each one of these terms and justifies their use. Our contemporary world demands standardized criteria, methods, measures, concepts and terms to ensure that study protocols, results and applications are used in the same way in any country or area of human action.