Strong convergence of a regularization method for Rockafellar’s proximal point algorithm

In this paper, for a monotone operator T, we shall show strong convergence of the regularization method for Rockafellar’s proximal point algorithm under more relaxed conditions on the sequences {r _k } and {t _k }, $$\lim\limits_{k\to\infty}t_k = 0;\quad \sum\limits_{k=0}^{+\infty}t_k = \infty;\quad\ \liminf\limits_{k\to\infty}r_k > 0.$$ Our results unify and improve some existing results.     

Preparation and characterization of polymer-clay nanocomposite films

Polymer/clay nanocomposite films were prepared by means of electrodeposition of aqueous suspension including cathodic electrophoretic acrylic resin (CEAR) and Na⁺-montmorillonite (NMMT). Studies of XRD, SEM and TEM indicated well-dispersed NMMT platelets in the films prepared. The ideal dispersity achieved was thought to be the result of aqueous compatibility between CEAR molecules and NMMT platelets and the result of the water-involved process as well. The modulus and strength of the polymer/clay nanocomposite coatings tested by tensile testing and nano-indentation were effectively improved compared to those of the virgin CEAR film. In addition, the adhesion strength, flexibility and water-resistance represented by Chinese national standard (GB) kept the best grades.