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.

Experimental studies on comparison of microwave curing and thermal curing of epoxy resins used for alternative mould materials

In this present work attempts have been made to study the glass transition temperature of alternative mould materials by using both microwave heating and conventional oven heating. In this present work three epoxy resins, namely R2512, R2515 and R2516, which are commonly used for making injection moulds have been used in combination with two hardeners H2403 and H2409. The magnetron microwave generator used in this research is operating at a frequency of 2.45 GHz with a hollow rectangular waveguide. In order to distinguish the effects between the microwave and conventional heating, a number of experiments were performed to test their mechanical properties such as tensile and flexural strengths. Additionally, differential scanning calorimeter technique was implemented to measure the glass transition temperature on both microwave and conventional heating. This study provided necessary evidences to establish that microwave heated mould materials resulted with higher glass transition temperature than the conventional heating. Finally, attempts were also made to study the microstructure of microwave-cured materials by using a scanning electron microscope in order to analyze the morphology of cured specimens.