On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

SAP-Related Education - Status-Quo and Experience

Integrating Enterprise Systems solutions in the curriculum of not only universities but all types of institutes of higher learning has been a major challenge for nearly ten years. Enterprise Systems education is surprisingly well documented in a number of papers on Information Systems education. However, most publications in this area report on the individual experiences of an institution or an academic. This paper focuses on the most popular Enterprise System - SAP - and summarizes the outcomes of a global survey on the status quo of SAP-related education. Based on feedback of 305 lecturers and more than 700 students, it reports on the main factors of Enterprise Systems education including, critical success factors, alternative hosting models, and students’ perceptions. The results show among others an overall increasing interest in advanced SAP solutions and international collaboration, and a high satisfaction with the concept of using Application Hosting Centers.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.