A Numerical solution to the linear and nonlinear Fredholm integral equations using Legendre wavelet functions

Two methods for solving the Fredholm integral equation of the second kind in linear case, i.e. f (x) – λ ∫_a^b K (x,y)f (y)dy = g (x), and nonlinear case, i.e., f (x) = g (x) + λ ∫_a^b K (x,y)F (f (y))dy, are proposed. In order to solve the linear equation, the kernel K (x,y) as well as the functions f and g are initially approximated through Legendre wavelet functions. This leads to a system of linear equations its solution culminates in a solution to the Fredholm integral equation. In nonlinear case only K (x,y) is approximated by Legendre wavelet base functions. This leads to a separable kernel and makes it possible to employ a number of earlier methods in solving nonlinear Fredholm integral equation with separable kernels. Another feature of the proposed method is that it finds the solution as a function instead of specific solution points, what is done by the majority of the existing methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parasupersymmetry of Non-Linear and Isotropic Oscillator on Constant Curvature

In this paper we discuss the one-dimensional non-linear harmonic oscillator and isotropic oscillator in positive curvature. We will see that in the special case two different oscillator have a same behavior. Finally, by using the parasupersymmetry algebra we obtain the partner potential and superpotential. These superpotential lead us to obtain the corresponding superchares.     

CVD Growth of Carbon Nanotubes and Nanofibers: Big Length and Constant Diameter

Summary: We report mass production of carbon nanotubes (CNTs) and carbon nanofibers (CNFs) with relatively high length and aspect ratio. We synthesized carbon nanomaterials by chemical vapor deposition (CVD) of methane as the feeding gas on Fe/Mo nanoparticles that use alumina-aerogel support. Alumina-aerogel-supported Fe/Mo catalyst was prepared using sol-gel. Drying step performed using rotary evaporation and freeze-drying. CVD was performed using a quartz tube furnace. Samples were analyzed using scanning electron microscopy (SEM), Transmission electron microscopy (TEM) and Raman spectroscopy.     

Accelerating role of clay in photo-oxidation of polypropylene/clay multifilament yarns

Photo-oxidative degradation of polypropylene/clay multifilament yarns containing different amounts of clay was investigated. These samples and pure polypropylene(PP) multifilametns were exposed to long wavelength radiations(λ 300 nm) under atmospheric condition of constant temperature and relative humidity. The photo-oxidative stability was studied using FTIR spectroscopy, tensile testing and microscopy. The results indicate that the addition of clay particles decreases the stability of PP/clay composites to photo-oxidative degradation according to comparison with pure PP. From FTIR study and tensile properties, it was also found that the multifilaments with higher clay loading reveals a faster loss of mechanical properties, higher photo-oxidative product formation and more reduction in the induction time of photooxidation. Moreover, the crack formation on surface of irradiated filaments corresponds well to the conclusions in tensile properties and FTIR characterization.     

Cost-effective combination of contention resolution/avoidance schemes in bufferless slotted OPS networks

Contention is a major problem for Optical Packed Switched (OPS) networks. Many studies have shown that to obtain a very small optical packet loss rate, a large number of specific contention resolution or contention avoidance hardware must be used. However, this may not be so cost-effective. Instead of using the same technique to achieve a very low packet loss rate, the idea of this paper is to use the combination of different contention avoidance and contention resolution schemes, but using a lower amount of each scheme, to reduce packet loss rate in slotted bufferless OPS networks. A number of cost-effective contention resolution and avoidance schemes are studied in order to decrease traffic loss and increase TCP throughput as a result. Designing a multi-fiber architecture that uses inexpensive shared-per-node wavelength converters and additional drop-ports can significantly reduce network-wide traffic loss. The lost traffic can also be retransmitted in the optical domain in order to have a loss-free OPS network. A cost model is also provided to obtain cost-effective combinations of fibers, wavelength converters and drop ports under a desirable TCP throughput and investment on network hardware. The effectiveness of the combined contention avoidance and resolution schemes are demonstrated under Internet traffic.