Spiropyrans based on nitrogen heterocycles

The corresponding merocyanins (II and III), which are not capable of intramolecular cyclization to form spiropyrans, were obtained by the condensation of quaternary salts of 2- and 4-methylquinoline with o-hydroxyaryl aldehydes. In contrast to II and III, the products of the condensation of 5, 6-dimethylphenanthridinium salts with o-hydroxyaryl aldehydes (IV and V) exist, under the usual conditions, in the spiropyran form, while the derivative of 5-nitrosali-cylaldehyde can be isolated in both the cyclic and merocyanin forms. These differences are associated with the magnitude of the positive charge on the carbon atom which participates in closing the pyran ring.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 167–170, February, 1971.     

Boltzmann equation in the α, u representation

It is proposed, as in [1, 2], to regard the distribution function as a set of all possible Maxwellian distributions with arbitrary temperatures and mean velocities, with each Maxwelian distribution taken with its own weight (, u). An equation equivalent to the Boltzmann equation is constructed for this weight function. The cases of one-dimensional, twodimensional, operator in the arbitrary case in the , u representation it suffices to know the corresponding kernel for the one-dimensional problem.Leningrad. Traslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–123, July–August, 1972.