On the Stability of a Degenerate Wave Equation Under Fractional Feedbacks Acting on the Degenerate Boundary

Journal of Dynamical and Control Systems - In this work, we are concerned with the study of stabilization of one-dimensional weakly degenerate wave equation utt ? (xγux)x = 0 with x...     

Exponential inequalities for Mann’s stochastic algorithm

Abstract

In this article, we investigate the problem of approximating the fixed point for some function using a Mann iterative process with random errors. After establishing some exponential inequalities, we prove the complete convergence of Mann’s algorithm toward the fixed point and deduce a confidence interval for this one. In addition, we establish the convergence rate of Mann’s algorithm. Several numerical examples are sketched to illustrate the performance of the proposed algorithm.     

Influence of grafting with acrylic acid on the dyeing properties of polyamide 6.6 fibres

Polyamide 6.6 fibres were modified for the improvement of dyeing affinity using a graft copolymerisation method. These fibres were grafted with acrylic acid as monomer. The influence of the chemical modification of polyamide 6.6 fibres on the dyeing properties was investigated using a cationic dye (Red Astrazon 5BL). It was shown that the dye uptake of the modified fibres was greater than that of the unmodified fibres. The kinetic study of the cationic dye used at various grafting percentages showed an improvement of the dye build‐up rate, such as its exhaustion. In addition, an increase in the adsorption of the dye quantity fixed on the surface layer of the fibre made up of the grafted molecules was announced. Colour fastness to washing was improved with the grafting percentage. The modelling of the adsorption isotherms using Langmuir, Freundlich and Jossen relations allows the determination of isotherm constants. The results obtained from this modelling study show the existence of several models corresponding to various percentages of grafting.     

Robust feature points extraction for image registration based on the nonsubsampled contourlet transform

In this letter, a new feature points extraction method based on the nonsubsampled contourlet transform (NSCT) is proposed for image registration. The primary motivation of this work is to determine the effectiveness of the NSCT transform in extracting feature points for image registration. Preliminary experimental results show that the registration accuracy and robustness of the proposed algorithm is acceptable and very promising, and confirm the success of the proposed NSCT-based feature points extraction approach.     

The effect of hot water setting treatment on the dyeing properties of grafted polyamide 6.6 microfibres

Polymeric fibres are semicrystalline structures in which macromolecules are rarely oriented in their equilibrium state. Further instabilities are imparted when the fibres are converted into yarns and the yarns into fabrics. Heat setting is an important industrial process, as it reduces the fibre strain to an acceptable limit. Although this process provides dimensional stability to polyamide 6.6, yet it affects its dyeability. This paper investigates the effects of hot water setting treatment on the dyeing properties of grafted polyamide 6.6 microfibres dyed with a cationic dye. It reveals that the dye uptake of the hot water-set samples is inferior to those unset. A kinetic study showed a change in the build-up rate. In addition, an increase in the percentage of grafting improved the quantity of the dye fixed on both unset and hot water-set samples. Comparing the wash fastness of the unset samples, the hot water ones are found to be lower. The modelling of the adsorption isotherms using Langmuir, Freundlich and Jossen relations allows the determination of isotherm constants. The results obtained have been modelled using standard adsorption isotherms.