A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

A new application of a combined solvent extraction and two-phase biodegradation processes using two-liquid phase partitioning bioreactor (TLPPB) technique was proposed and developed to enhance the cleanup of high concentration of crude oil from aqueous phase using acclimated mixed culture in an anaerobic environment. Silicone oil was used as the organic extractive phase for being a water-immiscible, biocompatible and non-biodegradable. Acclimation, cell growth of mixed cultures, and biodegradation of crude oil in aqueous samples were experimentally studied at 30±2ºC. Anaerobic biodegradation of crude oil was examined at four different initial concentrations of crude oil including 500, 1000, 2000, and 5000 mg/L. Complete removal of crud

Partial shading is one of the problems that affects the power production and the efficiency of photovoltaic module. A series of experimental work have been done of partial shading of   monocrystalline PV module; 50W, I_sc: 3.1A, V_oc: 22V with 36 cells in series is achieved. Non-linear power output responses of the module are observed by applying various cases of partial shading (vertical and horizontal shading of solar cells in the module). Shading a single cell (corner cell) has the greatest impact on output energy. Horizontal shading or vertical shading reduced the power from 41W to 18W at constant solar radiation 1000W/m² and steady state condition. Vertical blocking a column

Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n₂), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ³) were e

A mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc

The possibility of using activated carbon developed from date palm seeds wastes as a permeable reactive barrier (PRB) to remove copper from polluted shallow groundwater was investigated. The activated carbon has been developed from date palm seeds by dehydrating methods using concentrated sulfuric acid. Batch tests were performed to characterize the equilibrium sorption properties of new activated carbon in copper-containing aqueous solutions, while the sandy soil (aquifer) was assumed to be inert. Under the studied conditions, the Langmuir isotherm model gives a better fit for the sorption data of copper by activated carbon than other models. At a pilot scale, One-dimensional column experiments were performed, and an integrated model ba