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. ‎

Development of improved methods for the synthesis of metal oxide nanoparticles are of high priority for the advancement of material science and technology. Herein, the biosynthesis of ZnO using hydrahelix of beta vulgaris and the seed of abrus precatorius as an aqueaus extracts adduced respectivily as stablizer and reductant reagent. The support are characterized by spectroscopic methods ( Ft-IR, Uv-vis ).The FTIR confirmed the presence of ZnO band. The Uv-visible showed absorption peak at corresponds to the ZnO nanostructures. X-ray diffraction, scaning electron microscopy (SEM), dispersive X-ray spectroscopy (EDX) techniques are taken to investigation the size, structure and composition of synthesised ZnO nanocrystals. The XRD pattern mat

Sawdust has the ability to adsorb the dyestuff from aqueous solution. It may be useful low cost adsorbent for the treatment of effluents, discharged from textile industries. The effectiveness of sawdust has been tested for the removal of color from the wastewater samples containing two dyes namely Direct Blue (DB) and Vat Yellow (VY). Effect of various parameters such as agitation time, adsorbent dose and initial concentration of each dye has been investigated in the present study. The adsorption of dyes has been tested with various adsorption isotherm models. The Langmuir isotherms model is found to be the most suitable one for the dye adsorption using sawdust and the maximum adsorption capacity is 8.706 mg/g and 6.975 mg/g for DB and V

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.

The present study addresses the behavior of gases in cultivation media as an essential factor to develop the relationship between the microorganisms that are present in the same environment. This relationship was explained via mass transfer of those gases to be a reasonable driving force in changing biological trends. Stripping and dissolution of oxygen and carbon dioxide in water and dairy wastewater were investigated in this study. Bubble column bioreactor under thermal control system was constructed and used for these processes. The experimental results showed that the removal of gases from the culture media requires more time than the dissolution. For example, the volumetric mass transfer coefficient for the removal

The ability of using aluminum filings which is locally solid waste was tested as a mono media in gravity rapid filter. The present study was conducted to evaluate the effect of variation of influent water turbidity (10, 20and 30 NTU); flow rate(30, 40, and 60 l/hr) and bed height (30and60)cm on the performance of aluminum filings filter media for 5 hours run time and compare it with the conventional sand filter. The results indicated that aluminum filings filter showed better performance than sand filter in the removal of turbidity and in the reduction of head loss. Results showed that the statistical model developed by the multiple linear regression was proved to be
valid, and it could be used to predict head loss in aluminum filings

The study involved the effectiveness of Iraqi attapulgite (IQATP) clay as an environmentally friendly material that easily adsorbs brilliant green (BG) dye from water systems and is identified by various complementary methods (e.g., FTIR, SEM‐EDS, XRD, ICP‐OES, pH_pzc, and BET), where the result reported that the IQATP specific surface area is 29.15 m²/g. A systematic analysis was selected to evaluate the impact of different effective adsorption performance variables on BG dye decontamination. These variables included IQATP dosage (0.02–0.8 g/L), solution pH (3.05–8.15), contact time (ranging from 2 to 25 min), and initial BG dye concentration from 20 to 80 mg/L. The parameter

In this paper the process of metal ions extraction (Zn(II) and Cu(II)) was studied in PEG-KCl aqueous two phase system was investigated without using an extracting agent. The experimental runs were performance at constant temperature (25 ^oC), constant mixing time (30 min), and constant PH of the solution (about 3). The effect of KCl salt concentration (from 10% to 25%), volumetric phase ratio of PEG solution to KCl solution (from 0.5 to 2), and the initial metal ion concentration (from 0.25 ml to 2 ml of 1 gm/L solution) were investigated on the percent extraction of Zn(II) and Cu(II). The results indicated that the percent extraction of metal ions increase with increasing of salt concentration and phase ratio, and slightly de