A Carleman estimate for the two dimensional heat equation with mixed boundary conditions

It is well known that in a regular domain, the solutions of the Laplace equation with mixed boundary conditions can present a singular part. In this work, we prove a Carleman estimate for the two dimensional domain heat equation in presence of these singularities.     

Selective Separation of Uranium(VI), Thorium(IV), and Lanthanum(III) from Their Aqueous Solutions using a Chelating Resin Containing Amine Functionality

A glycidyl methacrylate/divinylbenzene resin containing triethylenetetramine functional group was synthesized. The adsorption behavior of the obtained resin toward U(VI), Th(IV), and La(III) in aqueous solutions was investigated by batch and column techniques at different experimental conditions. Kinetic and thermodynamic characteristics of the adsorption process have been investigated. The regeneration of the loaded resin was also studied.     

Molding versus dispersion: effect of the preparation procedure on the capacitive and cycle life of carbon nanotubes aerogel composites

Binderless carbon nanotubes aerogel (CNAG) composites represent a new class of high-performing electrodes for energy storage applications such as electrochemical double layer capacitors. The composites developed here differ significantly from these previously prepared with dispersion processes. The CNAG material was prepared by a molding procedure that is the synthesis by a chemical vapor deposition method to grow carbon nanotubes directly onto a microfibrous carbon paper substrate. Then the carbon aerogel is synthesized on the carbon nanotubes. The key feature of the method is eliminating the need of controlling the carbon nanotube concentration, which permits optimized dispersion processes to reinforce the aerogel's networks. The CNAG electrode delivered very high specific capacitances of 524 F g⁻¹ in KOH electrolyte and 280 F g⁻¹ in H₂SO₄ electrolyte. Furthermore, this better integration of carbon nanotubes in the matrix of carbon aerogel improved its resistance to the attack by the electrolyte and conferred an excellent cycle life over 5,000 cycles of charge–discharge in both electrolytes.