LIMIT CYCLE PROBLEM OF QUADRATIC SYSTEM OF TYPE （ Ⅲ ）m=0, （ Ⅲ ）

To continue the discussion in （Ⅰ ） and （ Ⅱ ）,and finish the study of the limit cycle problem for quadratic system （ Ⅲ ）m=0 in this paper. Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation,the number of limit cycles depends on the different situations of separatrix cycle to be formed around O. If it is a homoclinic cycle passing through saddle S1 on 1 ＋ax-y = 0,which has the same stability with the limit cycle created by Hopf bifurcation,then the uniqueness of limit cycles in such cases can be proved. If it is a homoclinic cycle passing through saddle N on x= 0,which has the different stability from the limit cycle created by Hopf bifurcation,then it will be a case of two limit cycles. For the case when the separatrix cycle is a heteroclinic cycle passing through two saddles at infinity,the discussion of the paper shows that the number of limit cycles will change from one to two depending on the different values of parameters of system.     

Comparative analysis of long-haul system based on SSB modulation utilising dual parallel Mach–Zehnder modulators

In this paper, we have proposed a long-haul optical transmission system, based on a single sideband (SSB) modulation scheme. Analytical and simulation models have been developed, optimised and demonstrated for the proposed SSB system configurations. The SSB modulation scheme was proposed to overcome dispersion in the fibre. We have shown that the related link losses can be minimized by increasing the quality of the optical signal at the modulation. We have optimised the radio over fibre configuration scheme based on dual parallel dual drive Mach–Zehnder Modulator, thereby increasing transmission length of the fibre. With the proposed SSB, by suppressing some of the harmonics and cancelling one of the sidebands, we have halved the RF power fading and interference. The developed analytical (theoretical/mathematical) model agrees very well with the simulation results using two (both) different commercial simulation tools. The optical signal is boosted while minimizing the number of repeaters. We report a SSB configuration, compensation and amplification with individual spans of 150 km, by extending the length of the link up to 3250 km. The proposed system configuration exhibits high performance with less complexity and lower cost.     

Mechanical behaviour of MWCNTs reinforced electrospun nanofibres

Abstract

The nanoscale dimension of electrospun polymeric nanofibres produced by electrospinning are highly captivating, yet facing limitation of resisting external forces due to the weak tensile properties. Carbon nanotubes providing tremendous toughness due to extraordinary strong sp² bonding network of carbon atoms in honeycomb lattice structure, augmented the physical resistant strength and is easily recover to its original state after load is removed. This study reports the performance of multi-walled carbon nanotubes (MWCNTs) as filler in the electrospinning of poly (_L-lactide)-co-ε-caprolactone) (PLCL) composite nanofibres. Voltage of 10?kV is applied to the spinning solution mixture of 11?wt% (w/v) PLCL and MWCNTs, yielded nanofibres having diameters less than 400?nm. Results obtained showed the formation of composite nanofibres with tailored tensile behavior by modifying the content of MWCNTs. The addition of MWCNTs improved the tensile properties of resultant composite nanofibres, signified by tensile strength of 5.82 to 15.95?MPa, which were obtained using 0.1 to 1.0?wt% of MWCNTs. The structural integrity of nanofibres mats were retained in phosphate buffer saline (PBS) medium. Scanning Electron Microscopy (SEM) micrographs revealed the minimal of fiber deformation over 30?days of incubation and are closely identical to the initial diameter of as-spun fiber.     

Synthesis and characterization of magnesium doped lead titanate

Magnesium (Mg) doped lead titanate powders (PT: Mg) ceramics, with various Mg contents (0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, and 30 mole %), are prepared by the sol‐gel method and characterized by X‐Ray diffraction (XRD), scanning electron microscopy (SEM) and Raman spectroscopy. XRD results show that the magnesium diminishes the lattice tetragonality of PT:Mg. The average particle size and morphology were studied by SEM. The investigations done by Raman spectroscopy allow the analyzis of the substitution mechanism behavior related to the Mg incorporation into PT structure. A concentration threshold appears around 10% of Mg corresponding in a change of the compensation process with Mg²⁺ ions replacing Pb²⁺ ions below and both Pb²⁺ and Ti⁴⁺ above. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)