Existence of solutions for generalized variational inequality problems in Banach spaces

In this paper, we prove the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over compact convex subsets in a reflexive Banach space with a Fréchet differentiable norm. Moreover, we give some conditions that guarantee the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over unbounded closed convex subsets. The result obtained in this paper improves and extends the recent ones announced by Yu and Yang [J. Yu, H. Yang, Existence of solutions for generalized variational inequality problems, Nonlinear Anal., 71 (2009) e2327-e2330] and many others.     

Transformation of an irregularly bridged epidithiodiketopiperazine to trichodermamide A

[reaction: see text] An unusually bridged epidithiodiketopiperazine, pretrichodermamide A (3), was isolated from the fungus Trichoderma sp. BCC 5926. During the extensive effort to crystallize 3 for X-ray crystallographic analysis, conversion of this compound to trichodermamide A with coproduction of S(8) occurred.