Mild and practical cycloaddition reactions of furans with phenyl vinyl sulfonate

Phenyl vinyl sulfonate reacts with various alkyl furan derivatives under mild conditions to produce excellent yields of the corresponding cycloadducts.     

Benzodiazepine analogues. Part 21. 13C NMR analysis of benzoxathiepine derivatives

The influence of substituents and structure on the 13C NMR spectra of four series of benzoxathiepine derivatives has been investigated. Signal assignments in the 13C NMR spectra have been facilitated by the use of several predictive methods, permitting comparison of their relative efficacy.     

Synthesis of pyrrolo[1,2-b]cinnolines

The synthesis of the pyrrolo[1,2-b]cinnoline analogs 2 and 4–13 is described. The key step of this synthesis involves an intramolecular aromatic halide displacement on [2-(2-halobenzoyl)pyrrol-1-yl]carbamic acid esters. Several reactions of these cinnoline analogs with electrophilic reagents have been investigated.     

An approximate max-flow min-cut relation for undirected multicommodity flow,with applications

In this paper, we prove the first approximate max-flow min-cut theorem for undirected multicommodity flow. We show that for a feasible flow to exist in a multicommodity problem, it is sufficient that every cut's capacity exceeds its demand by a factor ofO(logClogD), whereC is the sum of all finite capacities andD is the sum of demands. Moreover, our theorem yields an algorithm for finding a cut that is approximately minimumrelative to the flow that must cross it. We use this result to obtain an approximation algorithm for T. C. Hu's generalization of the multiway-cut problem. This algorithm can in turn be applied to obtain approximation algorithms for minimum deletion of clauses of a 2-CNF formula, via minimization, and other problems. We also generalize the theorem to hypergraph networks; using this generalization, we can handle CNF clauses with an arbitrary number of literals per clause.Most of the results in this paper were presented in preliminary form in Approximation through multicommodity flow,Proceedings, 31th Annual Symposium on Foundations of Computer Science (1990), pp. 726–737.Research supported by the National Science Foundation under NSF grant CDA 8722809, by the Office of Naval and the Defense Advanced Research Projects Agency under contract N00014-83-K-0146, and ARPA Order No. 6320, Amendament 1.Research supported by NSF grant CCR-9012357 and by an NSF Presidential Young Investigator Award.     

Two new bounds on the size of binary codes with a minimum distance of three

We prove two new upper bounds on the size of binary codes with a minimum distance of three, namelyA(10, 3)76 andA(11, 3)152.