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This paper is devoted to study the topological normal forms of families of maps on R which, under nondegeneracy conditions of high degree, also present the simplest bifurcations.

This paper generalizes the nondegenerated conditions that imply the most common bifurcations in uniparametric families of maps defined on ‫.ޒ‬ It also presents a new very simple proof of the Hopf bifurcation theorem of maps on ‫ޒ‬ 2 Ž Ž . . see G. Iooss, ''Mathematical Studies, '' Vol. 36, 1979 , based on one of the results obtained in one dimension and generalizes one of the nondegenerated conditions Ž . the Hopf condition of the theorem. ᮊ

In this paper, the kinetics of the tail end selective hydrogenation of a C, cut over palladized alumina catalyst have been studied. In the absence of finite transport limitations, experiments have been carried out to analyse the influence of methylacetylene (MA) and propadiene (PD) content in the feed, hydrogen/MAPD molar ratio, temperature and space time on the corresponding conversion and selectivity. The main aim of this process is to improve propylene yield by removing MAPD in the propylene rich cut.The experiments were performed in an integral plug flow and the integral method was used for the kinetic analysis. The minimization of the objective function was made by the Marquardt algorithm for multiple response and the continuity equation set integrated by fourth order Runge-Kutta technique.The most adequate models were the power law type for the experimental range. The comparison between experimental and observed values of the MAPD, propylene and propane molar fraction in the hydrocarbon mixture, which were used for the minimization, confirm the suitability of the fit.

This article describes DSamala toolbox, a computational tool for simulating and analysing discrete, continuous, stochastic dynamic systems; It is presented as a MATLAB toolbox. DSamala toolbox makes a significant contribution to studying dynamic systems through the use of information and communication technology (ICT), especially when equations modelling these systems are difficult or impossible to solve analytically.