In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

Background: Large amounts of oily wastewater and its derivatives are discharged annually from several industries to the environment. Objective: The present study aims to investigate the ability to remove oil content and turbidity from real oily wastewater discharged from the wet oil's unit (West Qurna 1-Crude Oil Location/ Basra-Iraq) by using an innovated electrocoagulation reactor containing concentric aluminum tubes in a monopolar mode. Methods: The influences of the operational variables (current density (1.77-7.07 mA/cm2) and electrolysis time (10-40 min)) were studied using response surface methodology (RSM) and Minitab-17 statistical program. The agitation speed was taken as 200 rpm. Energy and electrodes consumption had been studi

      Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

Since the beginning of mankind, the view of the sky was present through observations with the naked eye, then it developed with time, and the sciences and tools of astronomical observations developed, including photometric measurements, which reached a high degree of accuracy in describing various cosmic phenomena, including the study of galaxies, their composition, and the differences between them, and from here the importance of this study emerged, to determine the differences between two distinct types of classification of galaxies, which are normal and barred spiral galaxies, where two galaxies NGC 4662 and NGC 2649 were chosen that represented certain types of galaxies to study the morphological structure of the two galaxies, a

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Objective: Econazole nitrate (ECZ) is one of the triazole antifungal drugs with poor aqueous solubility and dissolution rate; there is a need for enhancement of solubility. Therefore; inclusion complexation with β cyclodextrin (βCD) was performed. Methods: In this study kneading method and co-evaporation method of preparation of inclusion complex between βCD and ECZ using two molar ratios of βCD. The solubility of these complexes in isotonic saline solution and distilled water was studied. Complexes prepared by kneading method were used for the preparation of different ophthalmic gel formulas using carbomer (CB) and sodium carboxymethylcellulose (sod CMC) as a gelling agent. The release profile and the rheological behaviour of the gel w