In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

Shadow detection and removal is an important task when dealing with color outdoor images. Shadows are generated by a local and relative absence of light. Shadows are, first of all, a local decrease in the amount of light that reaches a surface. Secondly, they are a local change in the amount of light rejected by a surface toward the observer. Most shadow detection and segmentation methods are based on image analysis. However, some factors will affect the detection result due to the complexity of the circumstances. In this paper a method of segmentation test present to detect shadows from an image and a function concept is used to remove the shadow from an image.

The present work aimed to study the efficiency of nanofiltration (NF) and reverse osmosis (RO) process for treatment of heavy metals wastewater contains zinc. In this research, the salt of heavy metals were zinc chloride (ZnCl2) used as feed solution.Nanofiltration and reverse osmosis membranes are made from polyamide as spiral wound module. The parameters studied were: operating time (0 – 70 min), feed concentrations for zinc ions (10 – 300 mg/l), operating pressure (1 – 4 bar).The theoretical results showed, flux of water through membrane decline from 19 to 10.85 LMH with time. Flux decrease from 25.84 to 10.88 LMH with the increment of feed concentration. The raise of pressure, the flux increase for NF and RO membranes.The maximum

All-optical canonical logic units at 40 Gb/s using bidirectional four-wave mixing (FWM) in highly nonlinear fiber are proposed and experimentally demonstrated. Clear temporal waveforms and correct pattern streams are successfully observed in the experiment. This scheme can reduce the amount of nonlinear devices and enlarge the computing capacity compared with general ones. The numerical simulations are made to analyze the relationship between the FWM efficiency and the position of two interactional signals. © 2015 Chinese Laser Press

In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.

Second harmonic generation (SHG) is a phenomenon observed in nonlinear optics that leads to frequency duplication for a high intensity laser incident on nonlinear crystal using BBO crystal. The SHG yield is achieved when the photons interact with a nonlinear optical material and effectively combine to form new photons with double frequency, and therefore double energy and half wavelength. This paper is concerned with the establishment of an SHG experiment to govern the process of producing half-wavelength laser beam from the input one. The theoretical effort was extended to compute the efficiency by using MATLAB software based on mathematical relationships. The values of the conversion maximum efficiencies, which were computed as a funct

  Problem solving methods and mechanisms contribute to facilitating human life by providing tools to solve simple and complex daily problems. These mechanisms have been essential tools for professional designers and design students in solving design problems.
This research dealt with one of those mechanisms, which is the (the substance-field model model), as it has been mentioning that this mechanism is characterized by the difficulty of its application, which formed the main research problem. In home gardens (the sub-problem of research), an analysis of this problem was applied and then a solution was found to address it. The researcher used the 3dsmax program to implement the proposed design.
The most important research res

Magnetohydrodynamic (MHD) effects of unsteady blood flow on Casson fluid through an artery with overlapping stenosis were investigated. The nonlinear governing equations accompanied by the appropriate boundary conditions were discretized and solved based on a finite difference technique, using the pressure correction method with MAC algorithm. Moreover, blood flow characteristics, such as the velocity profile, pressure drop, wall shear stress, and patterns of streamlines, are presented graphically and inspected thoroughly for understanding the blood flow phenomena in the stenosed artery.

The approximate solution of a nonlinear parabolic boundary value problem with variable coefficients (NLPBVPVC) is found by using mixed Galekin finite element method (GFEM) in space variable with Crank Nicolson (C-N) scheme in time variable. The problem is reduced to solve a Galerkin nonlinear algebraic system (NLAS), which is solved by applying the predictor and the corrector method (PCM), which transforms the NLAS into a Galerkin linear algebraic system (LAS). This LAS is solved once using the Cholesky technique (CHT) as it appears in the MATLAB package and once again using the General Cholesky Reduction Order Technique (GCHROT), the GCHROT is employed here at first time to play an important role for saving a massive time. Illustrative

     By taking into account various food components in the ecosystem, the research intends to develop a set of difference equations to simulate a plant-herbivore interaction of Holling Type II. We determine the local stability of the equilibrium points for the scenarios of extinction, semi-extinction (extinction for one species), and coexistence using the Linearized Stability Theorem. For a suitable Lyapunov function, we investigate theoretical findings to determine the global stability of the coexisting equilibrium point. It is clear that the system exhibits both Flip and Neimark-Sacker bifurcation under particular circumstances using the central manifold theorem and the bifurcation theory. Numerical simulations are