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Abstract: It is well-known that the PRP conjugate gradient method with exact line search is globally and linearly convergent. If a restart strategy is used, the convergence rate of the method can be an -step superlinear/quadratic convergence. Recently, Zhang et al. [L. Zhang, W. Zhou, D.H. Li, A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal. 26 (2006) 629–640] developed a modified PRP (MPRP) method that is globally convergent if an inexact line search is used. In this paper, we investigate the convergence rate of the MPRP method with inexact line search. We first show that the MPRP method with Armijo line search or Wolfe line search is linearly convergent. We then show that the MPRP method with a restart strategy still retains -step superlinear/quadratic convergence if the initial steplength is appropriately chosen. We also do some numerical experiments. The results show that the restart MPRP method does converge quadratically. Moreover, it is more efficient than the non-restart method. [Copyright &y& Elsevier]

Thermo-sensitive nanocomposites based on mesoporous silica SBA-15 and poly(N-isopropylacrylamide) (PNIPAAm) have been synthesized via in situ radical polymerization in mesopores. The resultant materials were used as carriers to construct temperature-responsive controlled drug delivery systems. Loading of model drug ibuprofen (IBU) was ascertained by IR and UV-vis/DRS spectroscopy, and the mesostructure and pore properties of the delivery system were characterized by small-angle XRD and N2 adsorption-desorption experiment. Study on drug uptake indicated that higher polymer content in the composite, higher IBU concentration in loading solution and lower loading temperature below the lower critical solution temperature (LCST) could increase the loading amount of IBU by means of interaction between IBU and polymer and trap effect of the polymer chains in pores. Different from the uptake of IBU, however, the release of drug followed a positive temperature-responsive manner, that is, the release was accelerated upon heating above the LCST, while decelerated and lasted for a longer period of time below the LCST. This feature allows the material to function as a reversible fast/slow transition switch or rate regulator responsive to environmental temperature and to be potentially interesting in controlled delivery and other smart application fields.