ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...     

New mechanism of energy release in astrophysical objects

Conclusions The above qualitative analysis of the evolution of astrophysical objects shows that in the field theory of gravitation with minimal coupling objects in the regionM/a<1/3 of values of the mean gravitational potential are stable to small perturbations of their radius with unchanged rest mass.However, the mean gravitational potential of these objects increases when they capture matter surrounding them. When the mean potential reaches the valueM/a=1/3, the object passes abruptly from an infinitely stable state to an infinitely unstable state (with respect to small perturbations of its radius). Therefore, even small perturbations in the radius of the object once the critical value of the mean gravitational potential has been reached necessarily lead to expansion of the matter, which may be accompanied by the ejection of mass of this object and the release of energy.Therefore, instead of gravitational collapse, the outcome of the instability of astrophysical objects in general relativity, in the present theory there is a new mechanism of energy release.Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 48, No. 3, pp. 275–283, September, 1981.     

Photochemical reactions of 7-aminocoumarins

The photochemical reactions of 4-methyl-7-diethylaminocoumarin with the dimethyl ester of acetylenedicarboxylic acid, diethyl ester of maleic acid, and N-phenylmaleimide in the presence of oxygen and acetophenone give products of the heterocyclization at C(₆) and C(₈) of coumarin fragment with participation of the diethylamino group. The stereochemical structure of the compounds synthesized was demonstrated using PMR spectroscopy. A mechanism was proposed for this reaction involving the formation of an -amino radical and its addition to the acetylene or olefin, accompanied by attack on the aromatic ring with subsequent aromatization.See [1] for Communication 2.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 30–36, January, 1989.     

On the n = 1 exciton line of the green series in Cu2O

The weak isotropic line λ = 5830 Å observed on the wing of the yellow 2p-exciton line in Cu₂O is usually ascribed to the 1s(Γ⁺₄)-exciton of the green series. It is shown that if this is correct, then the stronger anisotropic line associated with the 1s(Γ⁺₅)-exciton of the green series should be nearly observed.