Synthesis of pyrrolo[1,2-a]pyrimidine derivatives

8-Cyanopyrrolo[1,2-a]pyrimidines, the cyano group of which is eliminated when they are heated with phosphoric acid, were obtained by reaction of 2-amino-3-cyanopyrroles with acetylacetone.Compounds Ia, c-g were described earlier in [3], while Ib, h are described in the present work.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1677–1681, December, 1976.     

Temperature dependence of size of disperse-system inclusions in metal alloy

Thermodynamic considerations of a disperse system (DS) cannot lead to a formula describing the dependence of the radius of inclusions (R) of ordered phase on the annealing temperature (T), but a suitable dependence R (T) may be obtained by taking into account the kinetics of DS formation. This problem is investigated quantitatively, and the analytic expression obtained for the dependence R (T) is in qualitative agreement with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 13–16, October, 1977.     

Exactly solvable quantum mechanical models with Stückelberg divergences

We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue of the model of N scalar fields (λ/N)(ϕ^{a a})² in the leading order in 1/N. The model involves vacuum and S-matrix divergences and also the Stückelberg divergences, which are absent in other known renormalizable quantum mechanical models with, divergences (such as the particle in a δ-shape potential or the Lee model). To eliminate divergences, we renormalize the vacuum energy and charge and transform the Hamiltonian by a unitary transformation with a singular dependence on the regularization parameter. We construct the Hilbert space with a positive-definite metric, a self-adjoint Hamiltonian operator, and a representation for the operators of physical quantities. Neglecting the terms that lead to the vacuum divergences fails to improve and, on the contrary, worsens the renormalizability properties of the model. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 91–106, October, 2000.     

On Epsilon-Cores of Cooperative Games with Fuzzy Payoffs

Mathematical Notes - It is well known that, for cooperative games with transferable utility (and with crisp payoffs), the set of reasonable imputations is nonempty. It is also known for what values...     

Synthesis of heterocycles on the basis of iminotetrahydrocarbazoles. 1. 3-Benzyl-8-methyl-2-oxo-2,3,3a,4,5,6-hexahydro-1H-pyrazino[3,2,1-j,k]-carbazole

The reaction of 6-methyl-1-oxo-1,2,3,4-tetrahydrocarbazole and benzylamine gave 1-benzylimino-6-methyl-1,2,3,4-tetrahydrocarbazole, which was converted by two methods to a pyrazinocarbazole derivative. The promising character of the use of iminotetrahydrocarbazoles for the synthesis of more complex heterocyclic systems was thereby demonstrated.Translated from Khimiya Geterosiklicheskikh Soedinenii, No. 12, pp. 1632–1635, December, 1987.The authors thank L. M. Alekseeva for investigating the PMR spectra and N. M. Rubtsov and V. V. Chistyakov for investigating the IR and mass spectra.