Some properties of random walk paths

For random walk on the d-dimensional integer lattice we consider again the problem of deciding when a set is recurrent, that is visited infinitely often with probability one by the random walk in question. Some special cases are considered, among them the following: for d = 2, what sequences (n_j) have the property that with probability one the random walk visits the origin for infinitely many n_j. A related problem, which is however not a special case of the recurrence problem, is to decide for what sequences (n_j) the states visited by the random walk at times n_j are all distinct, with only a finite number of exceptions. This problem is dealt with in the final part of the paper.     

Carbocyclization in natural products—II : Brominative cyclization of dihydrocostunolide

Treatment of dihydrocostunolide 1 with NBS in aqueous acetone at room temperature furnished bromolactones 3, 4 and 5. Structural evidence for these bromolactones rests upon spectral data and chemical correlations with santanolide “c” 10. Mass spectral fragmentation patterns for the bromolactones, with special reference to 4, have been also discussed.