Synthesis, Structural Characterization, and Oxidation-Reduction Behavior of the gamma-Isomer of the Dodecatungstosilicate Anion

The reaction of tungstate ions with the gamma-10-tungstosilicate in mixed water-ethanol (v/v) yields the corresponding isomer of the 12-tungstosilicate isolated as its tetrabutylammonium salt. It was characterized by means of (183)W NMR, infrared, Raman, and UV spectroscopies and was identified with the isomer resulting from the Keggin structure (alpha-isomer) by rotation of two tritungstic groups by pi/3. Cyclic voltammetry shows that the reducibility increases in the sequence alpha-beta-gamma as the number of rotated tritungstic groups. Whereas the gamma-12-tungstosilicate anion is unstable in pure aqueous solution whatever the pH value, it is stable in mixed aqueous-organic or pure organic solvents, even at boiling temperatures. In contrast, the two- and four-electron-reduced blue species are stable in aqueous media but not the one-electron-reduced blue. Study of the (183)W NMR spectrum of the two-electron-reduced species showed that the two spin-paired electrons are delocalized on all the W atoms on the NMR time scale but have a larger residency time on one group of four atoms.     

Remote Regiocontrol by a Thioether Group in Diels-Alder Reactions of Naphthazarin: Regioselective Access to Tetracyclic Polyhydroxyquinones

The synthesis of tetracyclic polyhydroxyquinones 5a and 5b was achieved through a sequence involving two Diels-Alder reactions with 1-methoxy-1,3-cyclohexadiene: the first with 2-(p-tolylthio)naphthazarin and the second on the resulting tricyclic derivative previously transformed into a (p-tolylsulfinyl)naphthazarin. The success of this strategy stemmed from the efficient remote regiocontrol exerted by the thioether substituent in the first step.     

On sparse spanners of weighted graphs

Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.The work of G. Das and D. Joseph was supported by NSF PYI Grant DCR-8402375. The work of D. Dobkin was supported by NSF Grant CCR-8700917. The work of J. Soares was supported by CNPq proc 203039/87.4 (Brazil) and NSF Grant CCR-9014562. This research was accomplished while G. Das was a student at the University of Wisconsin-Madison. A preliminary version was presented at the Second Scandinavian Workshop on Algorithm Theory, Bergen, Norway, 1990, under the title Generating Sparse Spanners for Weighted Graphs, and proceedings appear in the series Lecture Notes in Computer Science, Springer-Verlag. The preliminary version also appears as Princeton University Technical Report CS-TR-261-90, and as University of Wisconsin-Madison Computer Sciences Technical Report 882.     

A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W_KP admitting a central extension for generic values of the parameter, reducing naturally to W _n for special values of the parameter, and contracting to the centrally extended W₁₊, W and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic tow _KP. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of which contracts to a new nonlinear algebra of the W-type.Address after October 1993: Queen Mary and Westfield College, UK