In this paper, we report the modification of polyamide sample (PA) with different contents of chitosan (CS) using citric acid (CA) as a cross-linker [PA-CA-CS]. New materials were confirmed to be formed in PA using FT-IR spectrum. It is also checked in terms of the change in thermal stability event and decomposition behavior in thermogravimetry through TG-DTA instruments. Then, the ability of unmodified and modified supports was tested for the adsorption of two reactive dyes i.e. Cibacron Brilliant Yellow 3G-P and Cibacron Blue P-3R. Sorption experiments were performed under varying several experimental conditions such as pH, contact time, initial dye concentration, and temperature. The isotherm and kinetic models were undertaken to assess the dye removal mechanism. The applicability of Langmuir, Freundlich, DubininRadushkevich, and Temkin equations was checked and data were fitted using Langmuir model. The second-order equation was shown to fit the adsorption kinetics. Data gleaned from both thermodynamic results and modeling data indicate that the adsorption follows a chemical and exothermic process.

In this paper, we are interested in a boundary damped wave problem with a singular potential. Using a careful spectral analysis, asymptotic expressions of the eigenvalues and eigenvectors of the system operator are derived in terms of the dissipative coefficient and the potential. The Riesz basis property of eigenfunctions and generalized eigenfunctions is also studied. As a consequence, we obtained the exponential stability.