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We show that smooth maps are$C$^{1}-dense among$C$^{1}volume-preserving maps.

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It is well known that complementarity functions play an important role in dealing with complementarity problems. In this paper, we propose a few new classes of complementarity functions for nonlinear complementarity problems and second-order cone complementarity problems. The constructions of such new complementarity functions are based on discrete generalization which is a novel idea in contrast to the continuous generalization of FischerBurmeister function. Surprisingly, these new families of complementarity functions possess continuous differentiability even though they are discrete-oriented extensions. This feature enables that some methods like derivative-free algorithm can be employed directly for solving nonlinear complementarity problems and second-order cone complementarity problems. This is a new discovery to the literature and we believe that such new complementarity functions

It has been reported that the plasma levels of VEGF in tumor patients decreased during dendritic cell (DC)-based immunotherapy, but the underlying mechanism remains unclear. Our current report demonstrates that VEGF levels were significantly decreased in the supernatants of DCs incubated with rhVEGF or tumor conditioned medium (TCM) while the intracellular VEGF in DCs was increased. The increased intracellular VEGF was not due to the <i>de novo</i> VEGF synthesis by DCs because exogenous VEGF inhibited the mRNA expression of VEGF in DCs. More direct evidence was provided to demonstrate that Cy3-labeled VEGF could be internalized by DCs specifically and efficiently. In addition, the activity of DCs to internalize VEGF was abolished by neutralizing antibody against VEGF receptor-1 (Flt-1) and inhibitors of endocytosis such as carbonyl cyanide m-chlorophenyl hydrazone (CCCP) and genistein. This