In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

A liquid membrane process of Alkaloids extraction from Datura Innoxia solution was studied applying pertraction process in rotating discs contactor (RDC). Decane as a liquid membrane and dilute sulphuric acid as stripping solution were used. The effect of the fundamental parameters influencing the transport process, e.g. type of solvent used, effect of disks speed, amount of liquid membrane and effect of pH for feed and strip solution. The transport of alkaloids was analysed on the basis of kinetic laws of two consecutive irreversible first order reactions. Thus, the kinetic parameters (k1, k1, , tmax, and ) for the transport of alkaloids were determined. The effect of organic membrane type on percentage of Alkaloids transport was found

This study investigates the treatment of used lubricating oils from AL-Mussaib Gas Power Station Company-Iraq, which was treated with different extractive solvents (heptane and 2-propanol). The performance activity of these solvents in the extraction process was examined and evaluated experimentally. Operating parameters were solvent to oil ratios of (1:2, 1:4, 1:6, and 1:8), mixing time (20, 35, 50, and 65 min), temperatures (30, 40, 50, and 60 ºC), and mixing speed (500 rpm). These parameters were studied and analyzed. The quality is determined by the measuring and assessment of important characteristics specially viscosity, viscosity index, specific gravity, pour point, flash point, and ash content. The results confirm that the

This research investigates manganese (Mn) extraction from Electric Arc Furnace Steel Slag (EAFS) by using the Liquid-liquid extraction (LLE) method. The chemical analysis was done on the slag using X-ray fluorescence, X-ray diffraction, and atomic absorption spectroscopy. This work consisted of two parts: the first was an extensive study of the effect of variables that can affect the leaching process rate for Mn element from slag (reaction time, nitric acid concentration, solid to liquid ratio, and stirring speed), and the second part evaluates the extraction of Mn element from leached solution. The results showed the possibility of leaching  83.5 % of  Mn element from the slag at a temperature of 25°C, nitric acid co

A liquid membrane process of Alkaloids extraction from Datura Innoxia solution was studied applying pertraction process in rotating discs contactor (RDC). Decane as a liquid membrane and dilute sulphuric acid as stripping solution were used. The effect of the fundamental parameters influencing the transport process, eg type of solvent used, effect of disks speed, amount of liquid membrane and effect of pH for feed and strip solution. The transport of alkaloids was analysed on the basis of kinetic laws of two consecutive irreversible first order reactions. Thus, the kinetic parameters (k1, k1,, tmax, and) for the transport of alkaloids were determined. The effect of organic membrane type on percentage of Alkaloids transport was found to be i

The extraction of Cupressus sempervirens L. or cypress essential oil was studied in this paper. This cypress oil was extracted by using the hydro-distillation method, using a clevenger apparatus. Cupressus sempervirens L. leaves were collected from Hit city in Al-Anbar province – Iraq. The influences of three important parameters on the process of oil extraction; water which used as a solvent to the solid ratio (5:1 and 14:1 (ml solvent/g plant), temperature (30 to 100 °C) and processing time, were examined to obtain the best processing conditions to achieve the maximum yield of the essential oil. Also, the mathematical model was described to calculate the mass transfer coefficient. Therefore, the best conditions, that were obtained in

In this research, a group of gray texture images of the Brodatz database was studied by building the features database of the images using the gray level co-occurrence matrix (GLCM), where the distance between the pixels was one unit and for four angles (0, 45, 90, 135). The k-means classifier was used to classify the images into a group of classes, starting from two to eight classes, and for all angles used in the co-occurrence matrix. The distribution of the images on the classes was compared by comparing every two methods (projection of one class onto another where the distribution of images was uneven, with one category being the dominant one. The classification results were studied for all cases using the confusion matrix between every

Two simple, rapid, and useful spectrophotometric methods were suggest or the determination of sulphadimidine sodium (SDMS) with and without using cloud point extraction technique in pure form and pharmaceutical preparation. The first  method was based on  diazotization of the Sulphdimidine Sodium drug by sodium nitrite at 5 ºC, followed by coupling with α –Naphthol in basic medium to form an orange colored product . The product was stabilized and its absorption was measured at 473 nm. Beer’s law was obeyed in the concentration range of (1-12) μg∙ml^-1. Sandell’s sensitivity was 0.03012 μg∙cm^-1, the detection limit was 0.0277 μg∙ml^-1, and the limit of Quantitation was 0.03605μg