Two simple protocols for the synthesis of tetrahydrobenzo[a]xanthenes-11-ones using nano silica phosphoric acid are reported. Short reaction times, high yields, reusability of catalyst and easy workup are some advantages of these protocols.

In the course of our synthetic studies on biologically active compounds using dimedone, tetronic acids, and tetramic acids,1) we reported that some 10-substituted 3,3-dimethyl3, 4, 9, 10tetrahydro1Hfuroand -pyrrolo [4, 3-b] [1, 5] benzodiazepin1-ones (1 and 2) showed analgesic activity as strong as that of aminopyrine in the phenylquinone writhing test in mice.2) Namely, the extents of inhibiti...

In this paper bearing the same title as our earlier survey-paper [11] we pursue the goal of characterizing the global solutions of an optimization problem, i.e. getting at necessary and sufficient conditions for a feasible point to be a global minimizer (or maximizer) of the objective function. We emphasize nonconvex optimization problems presenting some specific structures like ‘convexanticonv...

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A lower time bound Ω(min(ν(x), n − ν(x)) for counting the number of ones in a binary input word x of length n corresponding to the word length of a processor architecture is presented, where ν(x) is the number of ones. The operations available are increment, decrement, bit-wise logical operations, and assignment. The only constant available is zero. An almost matching upper bound is also obtained.