The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

In this work, the possibility of a multiwavelength mode-locked fiber laser generation based on Four-Wave Mixing (FWM) induced by Fe2O3-SiO2 nanocomposite material is investigated for the first time. A multiwavelength mode-locked pulses fiber laser are generated from Ytterbium–doped fiber laser (YDFL) due to the combined action of high nonlinear absorption and high refractive coefficients of Fe2O3-SiO2 nanocomposite incorporated inside YDFL ring cavity. Up to more than 20 lasing lines in the 1040–1070 nm band with an equally lines separation of ~0.6 nm have been observed by just simple variation of passive modulation of the state of the polarization and the pump power altogether. Moreover, a passively mode-locked operation of YDFL laser

Ab – initio density function theory (DFT) calculations coupled with Large Unit Cell (LUC) method were carried out to evaluate the electronic structure properties of III-V zinc blend (GaAs). The nano – scale that have dimension (1.56-2.04)nm. The Gaussian 03 computational packages has been employed through out this study to compute the electronic properties include lattice constant, energy gap, valence and conduction band width, total energy, cohesive energy and density of state etc. Results show that the total energy and energy gap are decreasing with increase the size of nano crystal . Results revealed that electronic properties converge to some limit as the size of LUC increase .

A thin film of (SnSe) and SnSe:Cu with various Cu ratio (0,3,5 and 7)% have been prepared by thermal evaporation technique with thickness 400±20 nm on glass substrate at (R.T). The effect of Cu dopants concentration on the structural, morphological, optical and electrical properties of (SnSe) Nano crystalline thin films was explored by using X-ray diffraction (XRD), scanning electron microscopy (SEM), atomic force microscopy (AFM), energy dispersive spectroscopy (EDS), UV–Vis absorption spectroscopy and Hall Effect measurement respectively. X-ray diffraction analysis reveal the polycrystalline nature of the all films deposited with orthorhombic structure which possess a preferred orientation along the (111) plane. The crystalline sizes o

Nanomaterials enhance the performance of both asphalt binders and asphalt mixtures. They also improve asphalt durability, which reduces resource consumption and environmental impact in the long term associated with the production and transportation of asphalt materials. Thus, this paper studies the effectiveness of Nano Calcium Carbonate (Nano CaCO3) and Nano Hydrated Lime (NHL) as modifiers and examines their impact on ranges from 0% to 10% through comprehensive laboratory tests. Softening point, penetration, storage stability, viscosity, and mass loss due to short-term aging using the Rolling Thin Film Oven Test (RTFO) were performed on asphalt binders. Results indicated a significant improvement in binder stiffness, particularly

In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system ar