Asymptotic stability of the numerical solution for an integrodifferential reaction-diffusion system

This paper presents the study of the numerical solution of a reaction-diffusion system involving a reaction term of integral type arising from biological models. By means of a monotone approach we introduce upper and lower solutions and then we show the existence and the asymptotic behavior of nonnegative numerical solutions. To this end, we require the positivity of the numerical scheme and so we can use some properties of positive and M-matrices. Finally we give some sufficient conditions to verify the asymptotic stability of the numerical solution.     

Spatial regularities in the effect of locking of photon echo signals and associative optical memory

The efficiency of suppression of the generation of a photon echo response depending on the mutual spatial orientation of gradients of external nonumform electric fields acting on a resonant medium is studied. The possibility of creating an associative memory where the mutual orientation of the gradients of external electric fields is an associative key is discussed.     

Reaction of furan compounds with hydrogen peroxide in the presence of vanadium catalysts

The reactions of furan and a number of its derivatives (furfural, furan-2-carboxylic acid, 2-furfuryl alcohol, and others), in systems containing H₂O₂ and vanadium compounds, proceed through a mechanism of radical hydoxylation of the furan ring with the formation of 5-hydroxy-2(5H)-furanone and maleic acid. The total yield and ratio of the synthesized compounds depend on the reaction conditions.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1462–1467, November, 1991.     

The absorptive pion-nucleus optical potential

We calculate s-wave and p-wave absorptive pion-nucleus optical potentials assuming that a pion is absorbed by a pair of nucleons. Employing a model which takes into account both a single nucleon absorption with nucleon-nucleon correlations and rescattering, we obtain simple analytic expressions for Im B₀ sid Im C₀ of the pion-nucleus optical potential. The off-shell effect on the s-wave pion absorption is examined and shown to be strongly modified by short range correlations. The result for the p-wave absorptive part Im C₀ clearly shows the importance of the tensor correlations. The enhanced nn emission after π^? absorption is shown to be related with a large p-wave πN scattering length a₃₃ via the tensor correlations.