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 tungsten inert gas (TIG) welding is one of the most popular kinds of welding used to join metals mainly for aluminum alloys.  However, many challenges may be met with this kind of joining process; these challenges arise from decay of mechanical properties of welded materials. In the present study, an attempt was made to enhancing the mechanical properties of TIG weld joint of 6061-T6 aluminum alloy by hardening the surfaces using shoot peening technique. To optimize the shoot peening process three times of exposure (5, 10, and 15) min. was used. All peened and unpeened, and welded and unwelded samples were  characterized by metallographic test to indicate the phase transformation and modification in microstructure occurring d

Abstract 

The Phenomenon of Extremism of Values ​​(Maximum or Rare Value) an important phenomenon is the use of two techniques of sampling techniques to deal with this Extremism: the technique of the peak sample and the maximum annual sampling technique (AM) (Extreme values, Gumbel) for sample (AM) and (general Pareto, exponential) distribution of the POT sample. The cross-entropy algorithm was applied in two of its methods to the first estimate using the statistical order and the second using the statistical order and likelihood ratio. The third method is proposed by the researcher. The MSE comparison coefficient of the estimated parameters and the probability density function for each of the distributions were

This paper was aimed to study the efficiency of forward osmosis (FO) process as a new application for the treatment of wastewater from textile effluent and the factors affecting the performance of forward osmosis process.
The draw solutions used were magnesium chloride (MgCl2), and aluminum sulphate (Al2 ( SO4)3 .18 H2O), and the feed solutions used were reactive red, and disperse blue dyes.
Experimental work were includes operating the forward osmosis process using thin film composite (TFC) membrane as flat sheet for different draw solutions and feed solutions. The operating parameters studied were : draw solutions concentration (10 – 90 g/l), feed solutions concentration (5 – 30 mg/l), draw solutions flow rate (10 – 50 l/hr

This experimental study focuses on scouring in box culvert inlets under steady-state conditions and at different percentages of blockage ranging from 0% to 65%, and also looks at the hydraulics of water in the culvert. The investigation shows that the blockage of the culverts has influenced the scouring pattern at the blocked culverts' entrances. Ten experiments were carried out at the laboratory to see how blockage impacts the scouring pattern upstream of a box culvert during steady flow. Both partially blocked and unblocked cases were implemented in this study. The experimental tests were done until the equilibrium scour occurred, which took about 3.5 hours of water flow to reach equilibrium conditions.  The results r

Polymer electrolytes systems compose of (PEO+KI+I₂) and (PEO+RbI+I₂) with different concentration, and a fixed amount of ethylene carbonate (EC) and propylene carbonate (PC) over temperatures range 293-343 K prepared by solution cast me

To determine the relationship between celiac disease and reproductive disorder, twenty two women with recurrent spontaneous abortion (18-35) years have been investigated from the period 2017/11/1 – 2018/2/1 and compared wih twenty two parentally healthy women. All studied groups were carried out to measure antitissue transglutaminase IgA and IgG antibodies by Enzyme linked immunosorbent assay (ELISA) technique, There were a highly significant differences (P < 0.01) in the concentration of anti TtG IgA and IgG Ab compared to control group, while there was non-significant differences (P > 0.05) in the concentration of anti TtG IgA according to the age group and there was a significant difference (P < 0.05) in the concentration of anti TtG I