Narrow Results

The temperature dependence of the NMR spin-lattice relaxation time is analyzed for preliminary evaluation of the correlation time of the local dynamics of the polymeric chain, for the molten polyisoprene and some polyisoprene-CCl₄ solutions. Complementary information concerning this dynamics were obtained from the analyze of the ESR spectra recorded from the nitroxide molecules (2, 2, 6, 6, tetramethyl piperidin-1-yloxyl) dissolved in the polyisoprene-CCl₄ solutions.

The activation energy of the local dynamics of the polymeric segments is calculated from the spin–lattice relaxation time, measured by NMR method. A new algorithm of analysis of the experimental data is proposed in order to increase the accuracy of the evaluation of this parameter. This method was applied for some polyisoprene-C₇D₈ solutions and for the molten polyisoprene.

In this paper, the local dynamics of differential equations is studied with two asymptotically large proportional delays. Depending on the parameters, critical cases in the problem of the stability of the equilibrium state are identified. In all critical cases, special evolutionary equations (quasinormal forms) are built. Their nonlocal dynamics determine the local behavior of solutions of the original equations.

A two-parameter family of discrete models, consisting of two coupled nonlinear difference equations, describing a host–parasite interaction is considered. In particular, we prove that the model has at most one nontrivial interior fixed point which is stable for a certain range of parameter values and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter.