R-matrices for elliptic Calogero-Moser models

The classicalR-matrix structure for then-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independentR-matrix (without spectral parameter) whenn 4. The assumption of momentum independence is sufficient to reproduce the dynamicalR-matrices of Avan and Talon for the type I, II, III degenerations of the elliptic potential. The inclusion of a spectral parameter enables us to findR-matrices for the general elliptic potential.     

Generation of 6-(Trifluoromethyl)-4,5-dihydro-2(3H)-pyridone and the Application to Synthesis of Some Fused Nitrogen Heterocycles Carrying a Trifluoromethyl Group on the Bridgehead Position via Radical Cyclization of Dihydropyridones

Staudinger/aza-Wittig reaction of 6,6,6-trifluoro-5-oxohexanoyl azide with PPh(3) or PBu(3) was examined. A reactive intermediate acyl imine 1 was trapped by methanol. Without nucleophile, isomerized enamide form 3 was obtained. N-Iodobenzoylation and N-haloalkylation of 3 and following radical cyclization via the 5-exo or 6-exo mode gave benzoindolizidinone, indolizidinone, and quinolizidinone derivatives 10-14, which have a trifluoromethyl group at the bridgehead position adjacent to nitrogen. Although LiAlH(4) reduction of 10 and 11 gave a mixture of saturated benzoindolizidine 15 and amino alcohol 16, reduction with BH(3)/THF selectively gave the desired 15 and indolizidine 17 from 13.     

Isolation and Stereostructures of Dolastatin G and Nordolastatin G, Cytotoxic 35-Membered Cyclodepsipeptides from the Japanese Sea Hare Dolabella auricularia

A bioassay-directed fractionation of the cytotoxic constituents of the Japanese sea hare Dolabella auricularia resulted in the isolation of two 35-membered depsipeptides dolastatin G (1) and nordolastatin G (2), which showed cytotoxicity against HeLa S(3) cells with IC(50) values of 1.0 and 5.3 &mgr;g/mL, respectively. The gross structures of these substances were established by spectroscopic analysis including 2D NMR techniques. The absolute stereostructure of 1 was determined by chiral HPLC analysis of amino acid components obtained from acid hydrolysis of 1 and by the enantioselective syntheses of two degradation products arising from polyketide portions. Nordolastatin G (2) is a congener that has the same absolute stereochemistry as that of 1.     

Quasi-classical limit of Toda hierarchy andW-infinity symmetries

Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W _{1 +} symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow _{1 +} symmetries of the dispersionless hierarchy through their action on the tau function.