Dual Forms on Supermanifolds and Cartan Calculus

We introduce and study the complex of “stable forms” on supermanifolds. Stable forms on a supermanifold M are represented by Lagrangians of “copaths” (formal systems of equations, which may or may not specify actual surfaces) on M×ℝ ^D . Changes of D give rise to stability isomorphisms. The resulting (direct limit) {Cartan-de Rham} complex made of stable forms extends both in positive and negative degree. Its positive half is isomorphic to the complex of forms defined as Lagrangians of paths, studied earlier. Including the negative half is crucial, in particular, for homotopy invariance. For stable forms we introduce (non-obvious) analogs of exterior multiplication by covectors and contraction with vectors and find the anticommutation relations that they obey. Remarkably, the version of the Clifford algebra so obtained is based on the super anticommutators rather than the commutators and (before stabilization) it includes some central element σ. An analog of Cartan's homotopy identity is proved, which also contains this “stability operator”σ. Received: 3 January 2000 / Accepted: 15 September 2001     

Hydrohalogenation of 1- and 2-vinylindazoles

The electronic absorption spectra of 1-vinyl- and 2-vinylindazoles and their protonated forms were analyzed. The spectra were subjected to quantum-chemical calculation within the Pariser-Parr-Pople (PPP) -electron approximation, and the thermodynamic parameters of the reaction of indazoles with phenol (K_as and H) were calculated. It is shown that 1-vinylindazole adds hydrogen halides to the nitrogen atom or the double bond of the vinyl group, depending on the reaction temperature. The formation of hydrohalides is characteristic for 2-vinylindazole.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 952–956, July, 1982.     

Reaction of 3-mercaptoindole and its ethyl derivatives with acetylene

1-Vinyl-3-vinylthioindole, 1-vinyl-3-ethylthioindole, and 1-ethyl-3-vinylthioindole, respectively, were obtained by the reaction of 3-mercaptoindole, 3-ethylthioindole, and 1-ethyl-3-mercaptoindole with acetylene. 3-Mercaptoindole reacts with acetylene in aqueous media to give 3-vinylthioindole. The structures of the vinyl derivatives of 3-mercaptoindole obtained were proved by means of IR and PMR spectroscopy and the results of elementary analysis.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 352–354, March, 1979.     

Synthesis and properties of vinyl derivatives of 4,5-diphenyl-2-mercaptoimidazole

S-Vinyl-, N,S-divinyl-, and S-ethyl-N-vinyl-4,5-diphenyl-2-mercaptoimidazoles were synthesized by reaction of 4,5-diphenyl-2-mercaptoimidazole with acetylene under pressure. The reactivities of these monomers were investigated. It is shown that they have lower reactivities than S-and N,S-vinyl-2-mercaptobenzimidazoles in radical polimerization reactions and do not form complexes with transition metal salts.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 516–520, April, 1976.     

A new phenol fromPinus sylvestris

Conclusions From the extractive substances of Scotch pine a phenolic compound has been isolated for which the structure of 3-hydroxy-5-methoxybenzyl alcohol has been established; it has been given the name sylvopinol.