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.

Growth of boehmite nanofibers by assembling nanoparticles with surfactant micelles

It is known that boehmite (AlOOH) nanofibers formed in the presence of nonionic poly(ethylene oxide) (PEO) surfactant at 373 K. A novel approach is proposed in this study for the growth of the boehmite nanofibers: when fresh aluminum hydrate precipitate was added at regular interval to initial mixture of boehmite and PEO surfactant at 373 K, the nanofibers grow from 40 to 50 nm long to over 100 nm. It is believed that the surfactant micelles play an important role in the nanofiber growth: directing the assembly of aluminum hydrate particles through hydrogen bonding with the hydroxyls on the surface of aluminum hydrate particles. Meanwhile a gradual improvement in the crystallinity of the fibers during growth is observed and attributed to the Ostwald ripening process. This approach allows us to precisely control the size and morphology of boehmite nanofibers using soft chemical methods and could be useful for low temperature, aqueous syntheses of other oxide nanomaterials with tailorable structural specificity such as size, dimension and morphology.

Experimental Infection of Culex Annulirostris, Culex Gelidus, and Aedes Vigilax With a Yellow Fever/Japanese Encephalitis Virus Vaccine Chimera (Chimerivax TM-JE)

Australian mosquitoes from which Japanese encephalitis virus (JEV) has been recovered (Culex annulirostris, Culex gelidus, and Aedes vigilax) were assessed for their ability to be infected with the ChimeriVax-JE vaccine, with yellow fever vaccine virus 17D (YF 17D) from which the backbone of ChimeriVax-JE vaccine is derived and with JEV-Nakayama. None of the mosquitoes became infected after being fed orally with 6.1 log(10) plaque-forming units (PFU)/mL of ChimeriVax-JE vaccine, which is greater than the peak viremia in vaccinees (mean peak viremia = 4.8 PFU/mL, range = 0-30 PFU/mL of 0.9 days mean duration, range = 0-11 days). Some members of all three species of mosquito became infected when fed on JEV-Nakayama, but only Ae. vigilax was infected when fed on YF 17D. The results suggest that none of these three species of mosquito are likely to set up secondary cycles of transmission of ChimeriVax-JE in Australia after feeding on a viremic vaccinee.